lightweight design optimizaton of an urban eco car prototype using topology optimization based on...

Reglerentwurf zur Synchronisation einer hybridenAktuatorkonfiguration

Diplomarbeit

Diplomarbeit

Störungsmanagement in Unternehmen mit einer

kundenindividuellen Produktgestaltung

Bearbeiter: Max Muster

Matrikelnummer: 0815

Studiengang: Produktentwicklung

Erstprüfer: Prof. Dr.-Ing. D. Krause

Zweitprüfer: Zweitprüfer (nur bei Diplomarbeit)

Betreuer: Betreuender Assistent

Hamburg, 01. Juli 2009

Diplomarbeit

Lightweight design op miza on of an urban eco carprototype using topology op miza on based onfinite element analysis

Bearbeiter: Ralf Seemann

Matrikelnummer: 20522605

Studiengang: Produktentwicklung

Erstprüfer: Prof. Dr.-Ing. D. Krause

Zweitprüfer: Prof. Dr.-Ing. T. Schüppstuhl

Betreuer: Dipl.-Ing. Benedikt PlaumannAssoc. Prof. Dr. Ian Gibson

Hamburg, 15.06.2011

Aufgabenstellung der Diplomarbeit von

Herrn Ralf Seemann, Matr.-Nr. 20522605

Thema:

Lightweight design optimization of an urban eco car prototype using

topology optimization based on finite element analysis

Steigende Rohstoffpreise sowie ein wachsendes Umweltbewusstsein in der Bevölkerung im Zuge der

weltweit zunehmenden Umweltbelastung haben dazu geführt, dass die Autoindustrie mehr denn je

versucht elektrisch angetriebene Fahrzeuge in großen Stückzahlen zu vermarkten. Der große

Nachteil von Elektroautos ist die eingeschränkte Reichweite bedingt durch die limitierte

Energiespeicherkapazität von herkömmlichen Batterien sowie der hohe Preis für diese

Energiespeicher. Für die praxistaugliche Umsetzung eines elektrischen Antriebkonzeptes eignen sich

daher vor allem kleine Stadtautos, welche ausschließlich auf kurzen Distanzen in einer urbanen

Umgebung mit guter Infrastruktur genutzt werden. Aufgrund des stark limitierten sowie kostspieligen

Energiespeichers ist es von entscheidender Bedeutung den Energieverbrauch zu minimieren.

Zur Untersuchung verschiedener elektrischer Antriebskonzepte wird an der National University of

Singapore ein Prototyp eines elektrischen Stadtautos entwickelt. Ziel dieser Diplomarbeit ist es

zunächst den Einfluss des Gewichts auf den Energieverbrauch sowie die Reichweite

anwendungsspezifisch für diesen Prototypen zu untersuchen. Darauf aufbauend wird eine geeignete

Komponente zur Gewichtsoptimierung ausgewählt. Für diese Komponente ist eine

Topologieoptimierungsberechnung durchzuführen. Die Ergebnisse der Topologieoptimierung sollen

dann in einem optimierten Designvorschlag umgesetzt werden. Der entwickelte Designvorschlag ist

daraufhin entsprechend der ermittelten Lastfälle mittels einer FEM-Rechnung auf Lastfähigkeit zu

untersuchen. Diese Diplomarbeit wird im Rahmen eines studentischen Austauschprogrammes an der

National University of Singapore als Beitrag zum NUS City Car Projekt angefertigt.

Die Arbeit gliedert sich in folgende Abschnitte:

1. Erfassung des Stands der Technik und Einarbeitung

• Literaturrecherche im Bereich elektrische Fahrzeuge, Modellierung des Energieverbauchs

von Fahrzeugen

• Einarbeitung in rechnergestütze FEM-Berechnung und Topologieoptimierung

2. Entwicklung eines Parametermodells für den Energieverbauch des Prototypen

Institut für Produktentwicklung und Konstruktionstechnik

Prof. Dr.-Ing. D. Krause

• Modellierung der verschiedenen Einflussfaktoren

• Durchführung einer parametrischen Sensisitvitätsanalyse

3. Ermittlung einer geeigneten Komponente für eine Topologieoptimierung

4. Durchführung einer Topologieoptimierung für ausgewählte Komponente

• Topologieoptimierungsrechnung entsprechend ermittelter Lastfälle

• Berechnung der Lastfähigkeit des optimierten Designs

Hinweise zur Durchführung der Arbeit:

Nach Einführung durch den Betreuer legt der Bearbeiter nach einer Einarbeitungsphase von maximal

einem Monat einen Arbeitsplan vor, der mit dem Betreuer abgestimmt wird; die Bearbeitungszeit

beträgt maximal 4 Monate nach Ausgabe der Aufgabenstellung.

Nach der Einführungsphase kann die Aufgabenstellung entsprechend dem Stand der Erkenntnisse

modifiziert werden. Die Modifikation ist vom Betreuer zu bestätigen.

Der Bearbeiter berichtet regelmäßig, mindestens im Abstand von einem Monat, über den Fortgang

der Arbeit; zu Beginn des Zusammenschreibens ist mit dem Betreuer ein Inhaltsverzeichnis abzu-

stimmen. Das Ergebnis der Arbeit ist in Form einer schriftlichen Fassung in drei Exemplaren zu doku-

mentieren und im Rahmen des Assistentenseminars im Institut für Produktentwicklung und

Konstruktionstechnik vorzustellen. Die verwendeten Hilfsmittel (z.B. Literatur) sind vollständig

anzugeben.

Alle im Rahmen der Arbeit gewonnenen Erkenntnisse und Ergebnisse sowie zugänglich gemachte

Informationen sind vertraulich zu behandeln und gelten im Rahmen der studentischen Arbeit als

hochschulöffentlich; sie bleiben Eigentum des Instituts für Produktentwicklung und

Konstruktionstechnik (PKT) und dürfen ohne dessen Erlaubnis weder Dritten zugänglich gemacht

noch in irgendeiner Form gewerblich genutzt werden.

Ausgabe der Aufgabenstellung am: 15. Februar 2011

Abgabe der Arbeit bis: 15. Juni 2011

Betreuer der Arbeit: Prof. Dr.-Ing. D. Krause

Assoc. Prof. Dr. Ian Gibson

Dipl.-Ing. Benedikt Plaumann

Prof. Dr.-Ing. D. Krause Ralf Seemann

-

Eidessta liche Erklärung

Ich erkläre hiermit, dass die vorliegende Diplomarbeit ohne fremde Hilfe selbstständigverfasst wurde und nur die angegebenen Quellen und Hilfsmi el benutzt worden sind.

Wörtlich oder sinngemäß aus anderen Werken entnommene Stellen sind unter Angabe derQuelle kenntlich gemacht.

DieseDiplomarbeitwurdebisher keinemanderenPrüfungsamt in gleicher oder vergleichbarerForm vorgelegt oder veröffentlicht.

Hamburg, ________________________- Ralf Seemann

Contents

List of Abbrevia ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI1 Introduc on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Thesis Objec ves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Theore cal Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1 Electric Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Electric Propulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.2 Electric Energy Storage . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Three Wheeled Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.1 Til ng Three Wheeled Vehicles . . . . . . . . . . . . . . . . . . . . . 82.2.2 Non-Til ng Three Wheeled Vehicles . . . . . . . . . . . . . . . . . . . 9

2.3 Vehicle Energy Consump on . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.1 Energy Losses and Trac ve Effort . . . . . . . . . . . . . . . . . . . . 102.3.2 Energy Demand in Actual Driving Condi ons . . . . . . . . . . . . . . 13

2.4 Lightweight Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.5 Structural Op miza on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.5.1 Basic Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5.2 Topology Op miza on . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5.3 Topology Op miza on Using Altair Hyperworks . . . . . . . . . . . . 26

3 Parameter Study for the Vehicle Range . . . . . . . . . . . . . . . . . . . . . . . 273.1 Parameter Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.1.1 Modeling of Electric Components . . . . . . . . . . . . . . . . . . . . 283.1.2 Model Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.1.3 GUI Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2 Sensi vity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.3 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Contents III

4 Determina on of a Component for a Topology Op miza on . . . . . . . . . . . 454.1 Implementa on of the Selec on Approach . . . . . . . . . . . . . . . . . . . 454.2 Visualiza on of Collected Data. . . . . . . . . . . . . . . . . . . . . . . . . . 474.3 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5 Structural Op miza on of the Chassis Frame. . . . . . . . . . . . . . . . . . . . 535.1 Iden fica on of Load Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.1.1 Sta c and Dynamic Loads . . . . . . . . . . . . . . . . . . . . . . . . 555.1.2 Crash Situa ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2 Modeling Considera ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.2.1 Unconstrained Structures . . . . . . . . . . . . . . . . . . . . . . . . . 645.2.2 Suspension Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.2.3 Design Space Defini on. . . . . . . . . . . . . . . . . . . . . . . . . . 675.2.4 Op miza on Problem Formula on . . . . . . . . . . . . . . . . . . . 72

5.3 Final Topology Op miza on Setup and Results. . . . . . . . . . . . . . . . . 765.3.1 Final Design Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.3.2 Load Case Implementa on . . . . . . . . . . . . . . . . . . . . . . . . 785.3.3 Op mized Topologies . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.4 Size Op miza on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825.4.1 Foregoing Considera ons . . . . . . . . . . . . . . . . . . . . . . . . . 825.4.2 Final Size Op miza on Setup and Results. . . . . . . . . . . . . . . . 87

5.5 New Design Sugges on. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 896 Structural Analysis of the New Design . . . . . . . . . . . . . . . . . . . . . . . 92

6.1 Strength Analysis Based on the Developed Beam Model . . . . . . . . . . . 926.2 Recalcula on of Cri cal Frame Members . . . . . . . . . . . . . . . . . . . . 956.3 Torsional S ffness Comparison. . . . . . . . . . . . . . . . . . . . . . . . . . 97

7 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Appendix 109A Dynamic behvaiour of Three Wheeled Vehicles . . . . . . . . . . . . . . . . . . 109B Valida on of the Parameter Model through PSAT . . . . . . . . . . . . . . . . . 113C Component Weight and Op miza on Ap tude Database . . . . . . . . . . . . . 117D Center of Mass and Dynamic Stability. . . . . . . . . . . . . . . . . . . . . . . . 118

D.1 Determina on of preliminary CM . . . . . . . . . . . . . . . . . . . . . . . . 118

Contents IV

D.2 Check of Dynamic Stability Criteria . . . . . . . . . . . . . . . . . . . . . . . 120E Summary of the Applied Forces in the Preprocessor Model . . . . . . . . . . . 122F Complementary HyperWorks Illustra ons . . . . . . . . . . . . . . . . . . . . . . 123

F.1 Compara ve Study - Iner a Relief . . . . . . . . . . . . . . . . . . . . . . . . 123F.2 Considered Load Cases in the Topology Op miza on Setup . . . . . . . . . 124F.3 Comparison of Topologies from Examined Op miza on Formula ons . . . . 125F.4 Comparison of Different Approaches to Modeling Frame Nodes in FEA . . . 126F.5 Stress Contours of Non-Cri cal Load Cases . . . . . . . . . . . . . . . . . . . 127

F.5.1 Steel Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127F.5.2 Aluminum Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

List of Abbrevia ons

AC . . . . . . . . . . . . . . . . . Alterna ng currentBESO . . . . . . . . . . . . . . . Bi-direc onal evolu onary structural op miza onCAE . . . . . . . . . . . . . . . . Computer aided engineeringCFD . . . . . . . . . . . . . . . . Computa onal fluid dynamicsCFRP . . . . . . . . . . . . . . . Carbon fibre reinforced plas csCM . . . . . . . . . . . . . . . . Center of massDC . . . . . . . . . . . . . . . . . Direct currentDOD . . . . . . . . . . . . . . . Depth of dischargeDSP . . . . . . . . . . . . . . . . Design spaceESO . . . . . . . . . . . . . . . . Evolu onary structural op miza onGUI . . . . . . . . . . . . . . . . Graphical user interfaceICE . . . . . . . . . . . . . . . . . Internal combus on engineIR . . . . . . . . . . . . . . . . . . Iner a ReliefLC . . . . . . . . . . . . . . . . . Load caseLWD . . . . . . . . . . . . . . . Lightweight designMBS . . . . . . . . . . . . . . . Mul body systemNiMH . . . . . . . . . . . . . . Nickel metal hybride ba eryNSP . . . . . . . . . . . . . . . . Neutral steer pointNUS . . . . . . . . . . . . . . . . Na onal University of SingaporeNYCC . . . . . . . . . . . . . . . New York City cyclePKT . . . . . . . . . . . . . . . . Ins tut für Produktentwicklung und Konstruk onstechnikPSAT . . . . . . . . . . . . . . . Powertrain Systems Analysis ToolkitSM . . . . . . . . . . . . . . . . . Sta c marginSoC . . . . . . . . . . . . . . . . State of chargeTUHH . . . . . . . . . . . . . . Technische Universität Hamburg-HarburgTWV . . . . . . . . . . . . . . . Three wheeled vehicleUDDS . . . . . . . . . . . . . . Urban dynamometer driving schedule

List of Symbols

Symbol Unit Descrip on

C − Compliance

C0 Ah Rated ba ery capacity

Cp Ah Nominal ba ery capacity (Peukert corrected)

Cr Ah Charge removed from ba ery

Fad N Aerodynamic resistance force

Fhc N Hill climb resistance force

Fla N Accelera on resistance force

Frr N Rolling resistance force

Ftrac N Total trac on force of the vehicle

Fr N Wheel load (front, right)

Fl N Wheel load (front, le )

K − Dynamic factor for sta c loads

KTNmdeg

Torsional s ffness of vehicle body

I0 A Rated ba ery discharge current

Idis A Actual ba ery discharge current

I2 A Ba ery current in equivalent circuit

Lv N Ver cal bump load

Lh N Horizontal bump load

M kg Vehicle sprung mass

Pb W Ba ery power (input or output)

Ptrac W Total trac on power needed

Pmot, in W Motor input power

Pac W Constant accessory power

R N Wheel load (rear)

Ri Ω Internal resistance of ba ery

Q Ah Charge

Contents VII

T Nm Motor torque

Uoc V Open circuit voltage of ba ery

U2 V Terminal voltage of ba ery

a ms2

Vehicle accelera on

atoms2

Tip over accelera on

h mm Height of CM above road surface

hb mm Maximum bump height

k − Peukert Coefficient

kc,ki,kw − Electric motor efficiency constants

lf mm Distance from front axle to CM

lh mm Distance from rear axle to CM

nCells − Number of ba ery cells

p − Penalty factor

r mm Wheel radius

t0 h Ba ery hour ra ng

tr mm Track width of the vehicle

v ms

Vehicle velocity

wb mm Wheel base

α deg Hill climb angle

β deg Road bump angle

µx,y − Tire fric on coefficients

ηmot − Motor efficiency

ηgear − Gear efficiency (belt drive)

ηrecup − Efficiency of recupera on system

ρ − Finite element density

σvN

mm2 Equivalent tensile stress

ω 1s

Angular velocity of the motor

Θ deg Deforma on angle resul ng from pure torsion

1 Introduc on

The first decade of the 21st century has seen a tremendous increase in the interest inelectric vehicle technology by both the industry and poli cs. By now, almost all majorautomobile manufacturers made large investments in electric vehicle programmes whileseveral governments around the world subsidize the purchase of electric cars or imposeother measures to promote the ownership of electric vehicles. The reasoning behindthis development is o en related to the limited fossil fuel reserves of our planet as wellas the increasing environmental impact, along with the resul ng rising environmentalconsciousness of our society. In the general public opinion, electric vehicles are o enseen as the future of automobile transporta on. However, there are numerous seriouschallenges that come with electric vehicle technology. Most notably, there is the lack ofsuitable energy storage systems. Available ba eries are very costly and heavy, have alow energy density and require a considerable recharging me, with no comprehensivecharging infrastructure implemented yet. The sum of these facts results in a low range,limited flexibility yet high price of electric vehicles, which s ll makes them an excep on ontoday’s roads. Due to the omnipresent disadvantage of limited range, electric propulsionis especially suited for small city cars that are mostly operated on short distances in urbanenvironments. However, further research is required to keep improving the performanceand reducing the cost of electric vehicles, in order to make them more compe ve. Onecrucial aspect in this context is the consequent applica on of affordable lightweight design.

The Department of Mechanical Engineering of the Na onal University of Singapore (NUS)ini ated the NUS City Car, a research project intended to study electric vehicle technologywith the objec ve of building and refining a small urban electric car prototype. During thework on this thesis, the NUS City Car was in the manufacturing stage of the first designitera on. Hence, the main objec ve was to build the first func oning prototype. Thecurrent design of the City Car is illustrated in Figure 1.1. The car is implemented as anopen three wheeled pla orm based on a welded tubular steel space frame with enclosingCFRP body shell. The alignment of the drivetrain is derived from motorcycle technologyand consists of a single rear wheel which is mounted onto a suspension swingarm anddriven by a belt drive. Conven onal deep cycle lead acid ba eries serve as energy storagewhile the electric propulsion is generated by a brushed series wound DC motor.

The present work originates from an university exchange programme between the NUSand the Technische Universität Hamburg-Harburg (TUHH) . While this thesis was supervisedby researchers from both NUS and TUHH, the work on the thesis took place primarily in

1.1 Thesis Objec ves 2

Singapore where the City Car project is based. In the following sec ons, the objec vesand the workscope of the present work is briefly summarized.

Belt Drive

Brushed

DC Motor

Rack &

Pinion

Steering

Lead Acid

Battery Pack

Doublewishbone

Suspension

Swingarm

Suspension

+ -

Figure 1.1: NUS City Car project, current design itera on

1.1 Thesis Objec vesThe objec ve of this thesis was to merge the automo ve exper se of the NUS Departmentof Mechanical Engineering resul ng from several successful par cipa ons in the ShellEco-Marathon, with the lightweight design exper se of the Ins tut für ProduktentwicklungundKonstruk onstechnik (PKT)origina ng fromthe long me involvement in thedevelopmentof lightweight aircra cabin systems. Reducing the weight of a vehicle translates directlyinto a reduc on of the vehicle’s energy consump on and thus range. Due to the limitedenergy storage capabili es and the high weight of the ba eries, lightweight design ispar cularly important for electric vehicles. However, lightweight design concepts haveplayed a minor role in the development of the current design. This thesis is intended tocontribute to the NUS City Car project by inves ga ng lightweight possibili es based onstructural op miza on.

Therefore, in the first stage, the aim is to perform a parametric sensi vity analysis that showsthe influence of basic vehicle parameters such as mass, rolling resistance, aerodynamicsand ba ery size on the energy consump on and range of the current vehicle configura on.Here, it is especially of interest to get an idea of the range extension poten al resul ngfrom op mizing the vehicle’s mass. In the second stage, it is intended to select onecomponent that is suitable for structural op miza on. And in the final stage, a structuralop miza on process is to be performed with the selected component and the resul ngnew design sugges on is to be subjected to a structural strength analysis.

1.2 Thesis Structure 3

1.2 Thesis StructureThe present document reports the processing of the set objec ves in five chapters, whichalso reflects the sequence of the processing.

3. Parameter

Study on the

Vehicle’s Range

4. Component

Analysis and

Selection

5. Structural

Optimization of

Selected Component

6. Structural

Analysis of

New Design

2.

Theoretical

Background

Development of a

Parametric Range

Estimation Model

Supportive Side Studies on the

implemented FE-Modeling and

Optimization Setup

Figure 1.2: Thesis structure scheme

• In Chapter 2, fundamentals and basic informa on are established as theore calbackground for the subsequent chapters. This includes an introduc on to electricvehicle technology and an overview about existent three-wheeled vehicles. In addi on,basic concepts of modeling the energy consump on of vehicles are discussed inprepara on of the proposed parameter model. Lastly, lightweight design is generallyintroduced and categorized, before the concept of finite element based structuralop miza on is extensively described.

• In Chapter 3, the development of a parametric model that es mates the range ofthe NUS City Car depending on basic vehicle parameters is described. This model isthe basis for the following sensi vity analysis, where it is shown to what extent thedifferent vehicle parameters influence the energy consump on and the range of thevehicle in an urban driving environment.

• Chapter 4 depicts, the analysis of the current vehicle configura on with the objec veof selec ng a par cularly promising vehicle component for a subsequent structuralop miza on process.

• The structural op miza on process for the selected component is reported in Chapter5, while topology and size op miza on are performed in cascade. In addi on, severalside studies, which support the made FE-modeling and op miza on setup decisions,are documented. Overall, most of the a en on in this thesis was spent on thestructural op miza on process.

• In Chapter 6, the resul ng new design sugges on is analyzed for its structuralperformance in terms of strength and s ffness.

2 Theore cal Background

Before going into the following chapters, that specifically address the steps taken to fulfillthe set objec ves, this chapter is intended to create a general theore cal background forthe coming parts of this thesis. Firstly, electric vehicle technology is briefly introduced.Subsequently, an overview on recent three-wheeled vehicle concepts is given as referenceto the increasing interest in three-wheelers during the past decade. This is followed byan introduc on into modeling the energy demand of road vehicles depending on thedriving pa ern. Lastly, different lightweight design concepts are established and structuralop miza on as one lightweight design tool is is explained into more detail, as this is thefounda on of the later performed op miza on process.

2.1 Electric VehiclesElectric vehicles came into existence together with their internal combus on engine (ICE)counterparts in the mid-19th century. In the beginning of the 20th century they were eventhe preferred choice of commercially produced automobiles, since the ICEs of that mewere unreliable and inconvenient to start [Lar03]. However, with the advent of widelyavailable oil and the self starter for internal combus on engines, the ICE proved to bethe be er source of propulsion and replaced the electric vehicles almost completely. Thereason for this lies mainly in the extremely limited range capabili es of electric vehiclesif compared to gasoline cars. This results from the low specific energy of the availableba ery technology. For instance, 4.5 litres of gasoline will give a typical ICE car a range of50km. In order to store the same amount of useful electric energy, the vehicle requires alead acid ba ery of about 270kg. If one would want to double the range of a gasoline car,it requires only 4kg addi onal weight, but it would need an addi onal ba ery mass of wellover 270kg to compensate the considerably increased energy demand due to the addedba ery. Another major problem that arises with electric vehicles is that it takes severalhours to recharge the ba ery, while refueling a gasoline car is done in about two minutes.When also considering the high price for adequate electric ba eries, it becomes clear whyICE powered cars have been the predominant vehicle concept for most of the 20th century.Despite these omnipresent disadvantages, electric vehicles have always been used in certainniche applica ons, due to some advantages over IC engines. Mainly because they do notproduce direct exhaust emissions and they are inherently quiet. [Lar03]. As a result,electric vehicles are ideal for environments where noise and pollu ons are not tolerated.This includes warehouses, the inside of buildings or on golf courses.

2.1 Electric Vehicles 5

However, during the late 20th and early 21st century, this situa on began to change. Thisresults firstly from the increasing environmental concerns in terms of both the local emissionof exhaust and the overall emissions of carbon dioxide and secondly, from technologicalimprovements to electric vehicle components. This also includes the development ofadvanced fuel cells, which opened the possibility of using hydrogen as alterna ve energystorage for electric vehicles. In addi on, the concept of hybrid propulsion has been refinedto such an extent that several hybrid vehicles are currently on the market, with their shareexpected to grow rapidly in the years to come. One such example, it is the Toyota Prius,which is by far the most successful hybrid vehicle. The Prius uses a 1.5 litre IC engineand a 33kW electric motor in combina on or separately to enable the most fuel-efficientperformance depending on the driving situa on. With the help of regenera ve braking,the overall fuel economy of the Prius is about 24km per litre [Lar03]. Another milestone isthe launch of the Nissan Leaf in 2010. It is the first purpose built mass-produced all-electriccar and marked the beginning of several similar cars being introduced in the coming years.

Figure 2.1: 3rd genera on Toyota Prius[Toy11] Figure 2.2: Nissan Leaf [Nis11]

In the following sec ons, different aspects of ba eries and electric motors, as the twomajor specific components of electric vehicles are discussed into more detail.

2.1.1 Electric Propulsion

Electric machines can be found in any conven onal vehicle as starters or generators thatproduce electricity to charge the ba ery and to supply electric auxiliary devices. However,in electric vehicles, electric machines are also the sole provider of trac ve force, whichmakes them one of the key components. Electric machines/motors can usually work intwo ways: (1) transform electrical energy from the ba ery into mechanical energy to drivethe vehicle, (2) recuperate mechanical energy available at the powertrain to recharge theba ery (regenera ve braking). Electric motors can be organized in two main catergories:direct-current (DC) and alterna ng-current (AC) motors. Within these two categories thereare several subtypes which are currently used in electric vehicles, including brushed DC,permanent-magnet brushless DC, induc on motors and switched reluctance motors. Anyof these machines could enable any imaginable vehicle applica on. However, the ques onfor the designer is, what is the most cost effec ve-motor? [Hod01]. A rough comparisonamong these types reveals that DC motors are generally simpler and less cost intensive,

2.2 Three Wheeled Vehicles 6

since they do not require complicated control electronics. Their main disadvantage is thehigh maintenance effort as the brushes wear over me. AC motors on the other handneed more sophis cated control electronics, which raises their overall cost. At the sameme, they are characterized by higher power density and higher efficiency if compared

to DC motors [Guz08]. However, at this point it is not intended to discuss the differentmotor types into more detail. The interested reader is referred to publica ons on electricvehicle design [Lar03, Lei09, WH10].

2.1.2 Electric Energy Storage

The ba ery is undoubtedly one of the key components of every electric vehicle as it is usuallythe only energy source and the component with the highest cost, weight and volume [Lar03].Thus, a basic understanding of ba ery technology is essen al when dealing with electricvehicles. An electric ba ery generally comprises two or more electric cells joined together,where each cell consists of posi ve and nega ve electrodes connected by an electrolyte.A chemical reac on between the electrodes converts chemical energy into DC electricityand also vice versa in the case of rechargeable ba eries. There are several different typesof rechargeable ba eries, including sealed lead acid, nickel metal hybride (NiMH) , nickelcadmium, lithium polymer and lithium ion as well as more recent developments such asaluminum-air and zinc-air ba eries, which can be mechanically recharged. However, upun l today there s ll is no suitable ba ery that allows the unrestricted use of electricvehicles in terms of range and recharge me [Lar03], which further supports the statusof the ba ery as crucial component. The performance of an electric vehicle is closelylinked to the equipped ba ery. From the men oned ba ery types, deep cycle lead acidba eries are most widely used and known ba eries for electric vehicles. This is a resultof their comparably low cost and well established infrastructure for charging, service andrecyclable disposal [Hod01]. It is these reasons that it was also the preferred choice forthe NUS City Car. However, they are characterized by a low specific energy (20-35Wh/kg),which significantly limits their long range capabili es. Another well introduced ba erytype is the NiMH, which is used in the very successful Toyota Prius. NiMH are the be erchoice where range and performance are needed as their specific energy is roughly doubledcompared to lead acid (up to 65Wh/kg). Nevertheless, in the framework of this thesis,lead acid ba eries are assumed as design constraint, which is why this work does notprovide a more detailed discussion on the various ba ery types and their performancecharacteris cs. As for the different electric motor types, interested readers are referredto publica ons on electric vehicle design to get more informa on on the different ba erytechnologies [Lar03, Lei09, WH10].

2.2 Three Wheeled VehiclesApplying the three wheel concept as pla orm for an automobile is not a new approachconsidering the fact that the early automobile pioneers started to experiment with three


wheeled pla orms [Pay01]. However, this concept never really made its way as dominantvehicle design considering their numbers on todays roads. Except for parts of South andSouth East Asia where they are tradi onally widely used in public transport, three wheeledvehicles (TWV) play a minor role in the global volume of traffic. Nevertheless, there hasbeen an increasing interest in three wheel design concepts during the last decade. This is aresult of the rising environmental awareness of our society together with the increasinglycongested roads in themetropolitan areas due to growing individual transporta on demands.The three wheeled vehicle design has the poten al to achieve a reasonable compromisebetween the safety and comfort of a standard four wheel passenger car and the fueleconomy, size and cost of a motorcycle. Therefore, considerable effort has been put intothe development of new three wheel concepts in the recent past. This chapter reviewsseveral concepts of modern three wheeled vehicles pu ng them into two main categories.

As a result of the literature review on three wheeled vehicles two layout concepts havebeen iden fied depending on the alignment of the three wheels. Naturally, the threewheels are aligned in triangular shape with the single wheel placed on the center axisoffset to the two wheel axle. Having the two wheel axle in the front is o en referred toas tadpole configura on, while the reverse configura on with the two wheel axle in therear can be called delta.

v

Delta Tadpole

Figure 2.3: Dominant three wheeled vehicle layouts

Irregardless of the configura on, recent three wheel concepts o en feature a l ngmechanism. This mechanism allows the vehicle to lean into turns similar to motorcyclesoffering an improved resistance to roll over [Ril09]. Thus, they strongly resemble conven onalmotorcycles in their general appearance as they usually also accommodate driver andpassenger in tandem. Another approach are non- l ng vehicles that accommodate driverand passenger side by side. Therefore, these vehicles generally feature larger dimensionsthan their l ng counterparts, making them appear more like a car than a motorcycle.This differen a on between l ng and non- l ng three wheelers reflects the view of theauthor as a result of the literature review in the frame work of this thesis. In the following,both types are briefly described accompanied by a few examples.


2.2.1 Til ng Three Wheeled Vehicles

In order to implement the l ng mechanism, a comparably narrow track width and vehiclebody is favored. A wide body may contact the ground already at small lean angles, while alarger distance between the side-by-side wheels requires a greater overall wheel movementat equivalent lean angles. The l ng mechanism furthermore generally complicates theaccommoda on of the steering and suspension systems [Ril09]. The l ng of the vehicle canbe controlled by the driver (free leaning) as with ordinary motorcycles or it is controlled byan ac ve lt control system. The ac ve lt control is accomplished by actuators opera ngaccording to signals from several sensors. These sensors monitor relevant factors such asthe lateral accelera on, vehicle yaw and lean angle or the steering angle [Ril09].

The Mercedes F 300 Life Jet is an example for an ac ve lt control three wheeler. Thisconcept car from 1997 features a tadpole configura on with a Mercedes A-Class combus onengine driving the single rear wheel [MB11].

Figure 2.4: Mercedes Benz F 300 Life Jet Concept Car [MB11]

Another approach to l ng three wheelers has been implemented in the CLEVER project.CLEVER stands for “Compact Low Emission Vehicle for Urban Transport“ and refers toa research project performed in coopera on by several European universi es as well asindustry partners under the technological management of the BMW Group [BMW09]. Thisthree wheel concept features the delta configura on while only the single front wheel isleaning through an ac ve lt control system. Due to the strong university involvement inthis project, several research papers regarding the design of the vehicle systems are openlyavailable (e.g. [Hol07] [Ber08]).

Figure 2.5: CLEVER Concept Vehicle [Hol07]


2.2.2 Non-Til ng Three Wheeled Vehicles

The second established category of modern three wheelers comprises non- l ng vehicleswith passenger and driver situated side by side. The NUS City Car which is being consideredin this work falls into this category. As with the l ng three wheelers reviewed above,non l ng vehicles can be implemented on both, the tadpole and the delta configura on.However, the performed literature review indicates that recent developments are o enbased on the tadpole layout. This may be explained by the beneficial aerodynamiccharacteris cs of this configura on. The tadpole layout conveniently enables a body shellmodeled in streamlined droplet shape. Furthermore, it enables a single rear wheel drive,which significantly simplifies the drive train, making it more efficient and less costly. As aresult of this, it is also the preferred configura on for par cipants of the various solar carchallenges [Sta06].

A commercial example for this category is the Campagna T-Rex 14R. As a deriva ve fromformula racing technology, this high performance vehicle powered by a 1400cc four-cylindercombus on engine opposes the general trend of energy efficient urban transporta on.However, it is a good demonstra on of the performance capabili es of the three wheeldesign.

Figure 2.6: Campagna T-Rex 14R [Cam10]

A fuel-efficient representa ve of non- l ng TWVs is the currently developed Aptera 2e.The objec ve of this project is to market a super fuel-efficient electric vehicle based onextensive light weight design and superb aerodynamics, while making no compromisesregarding the safety of the passengers.

Figure 2.7: Aptera 2e, super fuel-efficient vehicle. [Apt09]

2.3 Vehicle Energy Consump on 10

Since the NUS City Car is also based on a non- l ng TWV pla orm, it shares many basicdesign features with these two examples.

2.3 Vehicle Energy Consump onStudying the mechanical energy demand of a vehicle is a crucial step in the vehicle designprocess. Dynamic performance characteris cs such as top speed, maximum grade andmaximum accelera on are o en used as design specifica ons. In addi on, the over allenergy consump on and for electric vehicles also the vehicle range have become increasinglyimportant design specifica ons. Dimensioning the powertrain so that it meets the settargets requires accurate knowledge of the present driving resistances and the resul ngenergy losses. In this context, the present work focuses on studying the impact of basicvehicle parameters such as weight and aerodynamics on the range of the NUS City Car.Therefore, this sec on serves as background for the later in this work developed rangees ma on model as basis for the proposed parameter study. The following paragraphsreview the various driving resistances ac ng on a vehicle in mo on as well as the influenceof the driving pa ern on the over all energy consump on and thus on the range of avehicle.

2.3.1 Energy Losses and Trac ve Effort

The total trac ve effort needed to keep a vehicle in a par cular driving condi on is equalto the sum of all present driving resistances [Hei08]. Figure 2.8 illustrates the main energylosses of a vehicle in mo on in form of longitudinal forces ac ng on the vehicle body.

v

Frr

α

Fhc

Fad

Ftrac

Fla

Mg

Figure 2.8: Longitudinal forces ac ng on vehicle in mo on

The illustrated driving resistances are respec vely:

• Rolling resistance Frr

• Aerodynamic resistance Fad

• Hill climb resistance Fhc

• Accelera on resistance Fla


while Ftrac represents the total trac ve effort supplied at the driving axle. The followingparagraphs are concerned with the four considered driving resistances.

2.3.1.1 Rolling Resistance

Rolling resistance is a result of the con nuous elas c deforma on and return of material inthe contact zone between road surface and re. The energy used to deform the re andsurface cannot be completely recovered due to the internal damping of the material. Thisenergy loss causes rolling resistance [Gen09a]. Therefore, it becomes apparent that therolling resistance increases as the elas c deforma ons increase. In the case of pneuma cres rolling on concrete, the deforma ons are almost en rely localized on wheel side,

while the deforma on of the surface are neglected. In addi on, other effects such asaerodynamic drag on the disc or fric on in the wheel bearings contribute to the overallrolling resistance. However, these effects are only in the order of a few percent [Gen09a].The rolling fric on force is o en modeled as

Frr(v,r,...) = cr(v,r,...) ·M · g, v > 0 (2.1)

where M is the vehicle mass and g the gravita onal accelera on [Guz08]. The rollingfric on coefficient cr is a func on of many variables, while the most important factors arethe vehicle speed v, the re pressure and the road surface condi ons. For approxima ngpurposes it is o en assumed that most of these factors are constant, with the vehiclespeed being the only value that considerably changes during normal driving condi ons.Therefore, the rolling fric on force is o en modeled as func on of the velocity only[Gen09a]. The vehicle speed generally influences the rolling resistance to a smaller extendat lower values. However, its influence significantly increases when it reaches a cri calvalue, where vibra on phenomena start to take place in the re [Jaz09]. This rela onshipalong with the influence of the re pressure is shown in Figure 2.9.16 2 Vehicle Energy and Fuel Consumption – Basic Concepts

v20 40 60

0.01

0.02

00

m/s

cr -

p = 0. 4 p0

p = 1. 6 p0

p0[20 C]

[25 C]

[28 C]

minimum

average

Fig. 2.2. Tire friction coefficient as a function of the vehicle speed v and variations

of the tire pressure p.

Uphill Driving Force

The force induced by gravity when driving on a non-horizontal road is conser-vative and considerably influences the vehicle behavior. In this text this forcewill be modeled by the relationship

Fg(α) = mv · g · sin(α) , (2.4)

which, for small inclinations α, may be approximated by

Fg(α) ≈ mv · g · α (2.5)

when α is expressed in radians.

Inertial Forces

The inertia of the vehicle and of all rotating parts inside the vehicle causesfictitious (d’Alembert) forces. The inertia force induced by the vehicle mass isincluded in (2.1) by the term on the left side. The inertia of the rotating massesof the powertrain can be taken into account in the respective submodels.Nevertheless, sometimes for rapid calculation, it may be convenient to add theinertia of the rotating masses to the vehicle mass. Such an analysis usuallyconsiders a prime mover and a transmission with a total transmission ratio γ.

The total3 inertia torque of the wheels is given by

3 The inertia Θw includes all wheels and all rotating parts that are present on the

wheel side of the gear box. The speed of all wheels ωw is assumed to be the same.

Figure 2.9: Tire fric on coefficient depending on the vehicle speed v and varia ons of there pressure p0. [Guz08]

For many applica ons, especially when the vehicle operates at moderate veloci es, the


considera on of cr is even further simplified by assuming it is constant [Guz08, Lar03].This approach is also adopted throughout this work, as the examined car is intended tobe operated solely in an urban environment with rather low maximum veloci es.

2.3.1.2 Aerodynamic Resistance

The aerodynamic resistance ac ng on a vehicle body in mo on originates from threesources [PK10]:

• shape resistance due to turbulences of the air flow at the vehicle rear (85%)• viscous fric on of the surrounding air flow on the vehicle surface itself (10%)• internal resistance due to the air flow through the engine and passenger compartmentneeded for cooling and ven la on (5%)

The aerodynamic resistance force is usually approximated by assuming the car to be aprisma c body with a certain frontal area Af . The force caused by the turbulent flow isthen modeled as func on of the stagna on pressure pL mul plied with the aerodynamicdrag coefficient cw and the frontal area Af .

Fad = pL · cw · Af =1

2ρav

2L · cw · Af (2.2)

Here, vL is the velocity of the air flow rela ve to the car and ρa the density of the ambientair. The drag coefficient models the actual flow condi ons and heavily depends on the bodydesign and the direc on of the air flow. It is found either experimentally in wind tunnelsor evaluated numerically with the help of computa onal fluid dynamics (CFD) so ware.For the es ma on of the mechanical energy demand of vehicles it is usually assumed thatthe aerodynamic resistance only depends on the vehicle speed, while neglec ng externaleffects such as ambient wind veloci es and direc ons [Guz08].

2.3.1.3 Hill Climb Resistance

The hill climb resistance simply represents the force induced by gravity when driving on anon-horizontal road (see Figure 2.8). This force is conserva ve, meaning that it is storedas poten al energy, which makes it possible to recover a part of the energy used toovercome the hill climb resistance. Therefore, there is addi onal energy available whengoing downhill. The hill climb force considerably influences the vehicle behaviour alreadyat moderate grade levels [Gen09b]. Based on simple geometry it can be modeled as

Fhc = M · g · sin(α) (2.3)

where α denotes the grade level in arc degrees.


2.3.1.4 Accelera on Resistance

In transient driving condi ons, the powertrain has to overcome not only the rolling,aerodynamic and hill climb resistances, but also the iner a forces resul ng from accelera ngthe vehicle mass from velocity v1 to v2 with the accelera on ax = dv/dt. Along with thistranslatory accelera on of the vehicle mass, one has to consider the iner a of all rota ngmasses in the powertrain. This includes amongst others the wheels, drive sha s, the clutchand the motor, while the present gear ra o has to be taken into account for the motor andclutch iner a moments. These rota onal iner a forces are o en regarded as addi onalweight added to the total vehicle mass Mv based on the rota onal mass iner a momentsof the considered components.

M = Mv +Mrot (2.4)

The impact of the rota ng parts on the vehicle behaviour can be considerable, which iswhy it is usually not neglected. However, the problem is that the actual mass iner amoments of the rota ng masses are o en unknown, which makes it difficult to determinethe addi onal weight Mrot. In such a case, Larminie and Lowry (2003) [Lar03] suggest toassume 5% of the total vehicle mass as addi onal weight to account for the rota ng masseswhen es ma ng the energy consump on of electric vehicles. With this approxima on, theaccelera on resistance yields

Fla = (Mv + 0.05Mv) · ax (2.5)

2.3.2 Energy Demand in Actual Driving Condi ons

In the previous paragraphs, it was derived what components make up the total trac veeffort necessary to maintain the present driving condi on of a vehicle. Therefore, the totaltrac ve effort adds up to:

Ftrac = Frr + Fad + Fhc + Fla (2.6)

The magnitude of these components heavily depends on the present driving condi on,namely the current velocity, accelera on and grade. In order to es mate the total energyused to cover a certain distance it is thus necessary to assume a realis c driving pa ern,which indicates the speed, accelera on and grade throughout the driving. For this purpose,standardized test driving cycles that describe the actual use of the vehicle through ame history of the vehicle speed, have been introduced. Depending on the examined

applica on, various test cycles exist ranging from city to highway cycles, while one has tokeep in mind that real driving pa erns are o en much more complex due to unpredictabledriver behaviour and traffic condi ons [Gen09b]. Commonly used test cycles include theurban dynamometer driving schedule (UDDS) , the federal highway cycle (FHDS) and theNew York City cycle (NYCC) , all USA, as well as the European urban driving cycle (ECE).These cycles are some mes combined or adjusted to form a test procedure suited for a


certain examined applica on. The homepage of the U.S. Environmental Protec on Agency[U.S10] provides a wide range of driving cycles downloadable as text files, while Figure2.10 exemplarily illustrates the velocity profile of the UDDS cycle.

0 200 400 600 800 1000 1200 14000

10

20

30

time [s]

velo

city

[m/s

]

UDDS Test Cycle

Figure 2.10: Urban dynamometer driving schedule (UDDS), length: 12.07 km, maximumspeed: 91.2 km/h, average speed: 31.5 km/h

For the computa on of the energy consumed in a driving cycle, the reference cycleis discre zed into small parts, while the sum of the par al consump ons in each partapproximates the total energy consump on. In other words, the test cycle is subdividedinto a series of short me intervals ∆t, where for each me interval the present trac veforce is computed with eq. (2.6) using the present velocity, accelera on and grade extractedfrom the test cycle data. The present trac ve force is then mul plied with the distance∆si covered during the me interval in order to obtain the par al energy consump on.

Ecycle =n∑

i=1

Ftrac, i ·∆si (2.7)

This quasista c approach assumes that the vehicle runs at constant speed v, accelera ona and grade α for short period of me ∆t, while its accuracy correlates to the length ofthe chosen me interval. Experience shows, that a dura on of about ∆t = 1 s representsan acceptable interval length [Gen09b]. Considering each me interval is represented by∆ti = ti+1 − ti, the respec ve quasitsta c veloci es vi and accelera ons ai are extractedfrom the test cycle profile as follows:

vi =vi+1 + vi

2ai =

vi+1 + viti+1 − ti

(2.8)

The respec ve power to be provided by the drive train during each me interval is thencalculated by mul plying the presently needed Ftrac, i with the current velocity vi

Ptrac, i = Ftrac, i · vi (2.9)

The quasista c method is well suited to model the energy consump on of complexpowertrain structures. It enables the incorpora on of the driving pa ern and can be


implemented with rela vely low numerical effort. However, one has to keep in mind thatthis method is based on a “backward” formula on, which means the driving profile to befollowed has to be known beforehand making it incapable of handling feedback controlproblems [Guz08].

It is worth no ng that depending on the value of Ftrac the vehicle operates in threedifferent driving modes [Guz08]:

• Ftrac > 0, trac on mode, the engine has to provide propulsion force to the wheelsto enable the current driving condi on

• Ftrac < 0, braking mode, the vehicle does not require any mechanical energy sincethe aerodynamic and rolling resistance losses are compensated by the kine c energyof the vehicle, while the brakes dissipate the surplus in kine c energy

• Ftrac = 0, coas ng mode, the motor is disengaged and the fric on losses of thevehicle exactly match the decrease of its kine c energy

In electric vehicles it is comparably easy to disengage or “switch off” the motor in caseof coas ng, braking or stopping (vi = 0) so that the vehicle truly only uses up energyin trac on mode. In case the vehicle is equipped with an energy recupera on device,the addi onal kine c energy during braking is converted back into electric energy andstored in the ba ery, making it available for future propulsive effort. The efficiency ofthe recupera on system however, has its upper limit linked to the powertrain efficiency[Guz08]. The driving pa ern considerably influences the energy consump on as well asthe extent to which the different driving resistances contribute to the over all energyconsump on. An urban driving cycle with low average velocity and many braking andaccelera on phases is naturally characterized by a large share of accelera on resistance,while an autobahn driving cycle mostly demands energy due to aerodynamic resistance asthe aerodynamic drag increases with the square of the vehicle speed. Figure 2.11 comparesthe composi on of the energy consump on in two different driving environments.

Aerodynamics

Rolling Resistance

Transmission

Acceleration

Highway City Average

72%

20%

8%5%

18%

12%

65%

32%

39%

19%

10%

Figure 2.11: Compos on of the over all energy demand for a medium sized saloon car,comparison of city and highway driving cycle [Gen09b]

2.4 Lightweight Design 16

2.4 Lightweight DesignWiedemann describes lightweight design (LWD) as the inten on to reduce or minimizethe weight of a design without reducing its load capacity, s ffness or other func ons.This inten on may originate from economic or func onal reasons [Wie07]. The involvedlightweight design concepts have seen a tremendous growth in applica ons across differentdisciplines. Most notably, the avia on industry is to be named as the major driver inthe development of lightweight design concepts. However, lightweight design increasinglypromises economic benefits in other fields. This especially includes the automobile industry.Like in aeronau cs, the energy consump on of road vehicles is directly linked to the massthat is being moved. This rela onship is further inves gated based on the NUS City Carin Chapter 3. Due to the rising cost of fossil fuels, weight minimiza on has become oneof the dominant design criteria also for automobile manufacturers. Electric vehicles arepar cularly dependent on efficient lightweight design in order to compensate the highweight and limited energy storage capacity of current ba eries.There are numerous researchers and publica ons, which define and categorize the subjectof lightweight design. However, the boundaries between the different ways of classifyinglightweight design principles remain blurry. One categoriza on that appears to be consistentwith the lightweight design approach of this thesis is described by Sobek [Sob07] (seeFigure 2.12).

Lightweight

Design

Lightweight

Design

MaterialMaterial

SystemSystem

StructuralStructural

Manufacturing

Figure 2.12: Categoriza on of lightweight design principles by Sobek [Sob07]

• Material LWD Describes the applica on of materials with a favorable ra o betweenweight and available strength, s ffness or other features.

• Structural LWD Describes the principle of minimizing the weight by finding the

2.5 Structural Op miza on 17

op mal topology, shape and size of a structure with regards to the present constraints.• System LWD Describes the principle of making components mul -func onal, forinstance by alloca ng addi onal func ons to purely load bearing components.

The focus of the present thesis clearly lies in the applica on of structural lightweight designconcepts, which is why the following sec on discusses this subcategory into more detail.However, as the illustra on in Figure 2.12 tries to indicate with the chain of arrows, thedifferent lightweight design concepts are interrelated and should not be understood asisolated concepts. For instance, the used material has a direct impact on the op malstructural lightweight design. This is demonstrated in the later course of this work, usingthe example of the selected component.

2.5 Structural Op miza onAlong with the increasing importance of lightweight design, structural op miza on hasemerged as a comprehensive tool for the development of lightweight, low cost andhigh performance structures (structural lightweight design). The availability of high-speedcomputers as well as the improvement in op miza on algorithms further aided thisdevelopment. The subsequent sec ons review the concept of structural op miza on neededas background for the topology op miza on performed later in this work. Therefore, thefocus lies in describing the principles and general issues of topology op miza on.

2.5.1 Basic Principle

Structural op miza on describes the subject of making an assemblage of materials best interms of sustaining loads [Chr09]. To illustrate this, one can think of a situa on where acertain load has to be transmi ed from a point in space to a fixed support. Such a situa onis shown in Figure 2.13, where the area enclosed by the do ed line is o en referred toas design domain. However, the objec ve of making a structure best has to be specifiedin order to make any sense. Possible specifica ons that quickly come into mind includeminimizing a structure’s weight or maximizing its s ffness. Performing such minimiza ons ormaximiza ons clearly requires further constraints in order to get a well defined op miza onproblem. For instance, to make a structure as s ff as possible, one has to define a limit ofmaterial to be used. Without such a constraint, the op miza on process will suggest toendlessly add material, as this generally leads to an increase in s ffness. Other commonconstrained quan es include, stresses, displacements or geometry. In addi on to thesestructural performance measures, one also has to consider other crucial factors such asfunc onality, economy and esthe cs. Structural op miza on as it is considered in thiswork is a subset of numerical design op miza on. That means, the op miza on problemof making something as good as possible with respect to set of constraints is given anexact mathema cal form. This requires that each considered factor is measurable as amathema cal figure.


2 1 Introduction

Fig. 1.1 Structural

optimization problem. Find

the structure which best

transmits the load F to the

support

position of structural optimization in relation to such, usually not mathematically

defined, factors, we give a short indication of the main steps in the process of de-

signing a product in general, as described by Kirsch [22]. At least in an ideal world

these steps are as follows:

1. Function: What is the use of the product? Think of the design of a bridge: how

long and broad should it be, how many driving lanes, what loads can be expected,

etc.?

2. Conceptual design: What type of construction concept should we use? When we

are to construct a bridge we need to decide if we are to build a truss bridge, a

suspension bridge or perhaps an arch bridge.

3. Optimization: Within the chosen concept, and within the constraints on function,

make the product as good as possible. For a bridge it would be natural to mini-

mize cost; perhaps indirectly by using the least possible amount of material.

4. Details: This step is usually controlled by market, social or esthetic factors. In

the bridge case, perhaps we need to choose an interesting color.

The traditional, and still dominant, way of realizing step 3 is the iterative-intuitive

one, which can be described as follows. (a) A specific design is suggested. (b) Re-

quirements based on the function are investigated. (c) If they are not satisfied, say

the stress is too large, a new design must be suggested, and even if such require-

ments are satisfied the design may not be optimal (the bridge may be overly heavy)

so we still may want to suggest a new design. (d) The suggested new design is

brought back to step (b). In this way an iterative process is formed where, on mainly

intuitive grounds, a series of designs are created which hopefully converges to an

acceptable final design.

For mechanical structures, step (b) of the iterative-intuitive realization of step 3,

is today almost exclusively performed by means of computer based methods like

the Finite Element Method (FEM) or Multi Body Dynamics (MBD). These meth-

ods imply that every design iteration can be analyzed with greater confidence, and

probably every step can be made more effective. However, they do not lead to a

basic change of the strategy.

The mathematical design optimization method is conceptually different from the

iterative-intuitive one. In this method a mathematical optimization problem is for-

mulated, where requirements due to the function act as constraints and the concept

“as good as possible” is given precise mathematical form. Thus, step 3 in the de-

Figure 2.13: Structural op miza on problem [Chr09]

Structural op miza on problems can be generally expressed by the following func onsand variables [Chr09]:

• Objec ve func on f(x, y) A func on that classifies the design by returning a valuewhich indicates the performance of every possible design. O en f is defined asminimiza on problem (e.g. weight, compliance)

• Design variable x A func on that describes the design domain, and which can varyduring op miza on. It generally represents the geometry of the design domain.

• State variable y For a given design described by x, y is a func on that representsthe response of the structure. (e.g. stress, displacement)

Therefore, a general op miza on problem takes the form:

minimize f(x, y)

subject to

behavioral constraints on y

design constraints on x

equilibrium constraint

Most numerical op miza on methods are based on finite element analysis (FEA). Thatmeans the design domain is discre zed into a structure or mesh of discrete elements.Thus, the op miza on problem contains a equilibrium constraint of the form

K(x)u = F (x) (2.10)

where K(x) is the s ffness matrix of the structure depending on the design variable x, uis the displacement vector, while F (x) denotes the force vector which might also relateto the design variable.

Depending on the defini on of the design domain one can classify structural op miza onproblems into three categories [Par07]:

a) Size Op miza on In this case x represents some type of structural thickness, suchas the thickness of a plate or the cross-sec onal dimensions of trusses or frames.


Size op miza on is the simplest approach to improve structural performance, as thedesign domain is largely fixed throughout the op miza on process except for thevarying size variables.

b) Shape Op miza on Here, the design variable represents the form or contour of theboundary of the design domain, whereas the op miza on process cannot changethe connec vity of the structure or form new boundaries.

c) Topology Op miza on This is the most general type of structural op miza on. Fordiscrete structures such as trusses and frames, it takes the cross sec onal areasof frame members as design variables allowing them to become zero, which willeventually remove bars from the frame. Thus, it allows changes of the connec vity ofstructures. For Con nuum structures topology op miza on seeks to find the op maldesign by determining the best loca on and geometry of the material.

a)

b)

c)

Figure 2.14: Three types of structural op miza on. a) Size op miza on of truss structure,b) shape op miza on, c) topology op miza on. The le side represents ini al problemwhile the right shows the respec ve op mal solu ons

The graphic in Figure 2.14 is based on a similar illustra on in [Ben03] and compares thethree categories through the simple example of a can lever structure to be op mized.

2.5.2 Topology Op miza on

Topology op miza on of con nuum structures is by far the most challenging but at thesame me economically most rewarding of the three structural op miza on types [Hua10].It provides much more freedom, as it is not limited to simply changing sizes or shapesof structural components. The op miza on procedure is to find the material distribu onof a structure by determining which points in the design domain should be materialpoints (1) and which points should remain void (0), which eventually results in a 0-1problem. An abundance of publica ons have emerged on this general problem, star ngwith the groundbreaking paper of Bendsøe and Kikuchi (1988). As a result, many different


approaches to topology op miza on have been proposed, including the SIMP method, thehomogeniza on method and the ESO/BESO method. The term ESO stands for evolu onarystructural op miza on, which is a design method that starts from the full design domainand removes gradually inefficient material from the structure according to the stress orstrain energy levels of the discrete elements, while the bi-direc onal evolu onary structuralop miza on (BESO) method allows material to be removed and added simultaneously[Hua10]. The homogeniza on method along with the SIMP method are gradient basedand solve the 0-1 problem by replacing the integer variables with con nuous variables,while introducing some form of penalty that steers the element densi es to the discretevalues 0 and 1 [Ben03]. Therefore, each element of the design domain has an intermediatedensity lying on the con nuum between 0 and 1

x = xi ∈ [0, 1], ∀i = 1,...,N (2.11)

where N is the total number of finite elements in the design domain. The density of thei-th element is then given with respect to the full density of the material ρ0

ρ(xi) = xi ρ0 (2.12)

According to the earlier homogeniza on method each element is treated as homogeneousporous material with a microscale void. The local s ffness of such material depends on thesize, shape and orienta on of the voids, while the size of the void area varies according to theconcept of intermediate densi es between 0 and the full element size. This approach canrequire complicated mathema cal solu on algorithms. The SIMP method is considerablysimpler as it assumes that the s ffness of each element of the design domain is given by

ki(ρi) = (ρi)p k0 (2.13)

where k0 denotes the full ini al s ffness of the isotropic material and the exponent p

represents the penalty factor. Here, the current material s ffness is wri en as exponen alfunc on of the element density ρi and the ini al element s ffness, which greatly simplifiesthe solu on of topology op miza on [Zuo07]. The subsequent subsec on is concernedwith this approach into more detail, as the topology op miza on performed later in thiswork is based on the SIMP interpola on scheme.

2.5.2.1 The SIMP Method

The SIMP (solid isotropic material with penaliza on) Method “has been accepted by mostresearchers and engineers, and has been successfully used in many engineering fields”[Zuo07]. It allows to transform the design problem of op mal topology into a sizing problemby introducing an interpola on scheme that modifies the s ffness matrix in a way that itdepends con nuously on a func on which is interpreted as density of the material (see ρi


in eq. (2.13)) [Ben03]. In order to get a physically clear solu on, it is required that theop miza on results in a design which consists almost exclusively of regions of material (1)or no material (0). The SIMP method deals with this by penalizing intermediate elementdensi es with a penalty factor as exponent as seen in the propor onal s ffness model ofeq. (2.13). The penalty factor makes elements with intermediate densi es unfavorable forthe op mized solu on. The simplest type of op miza on problem formula on in termsof objec ve and constraint is minimizing the compliance C of a structure, which is whythis formula on is o en used to mathema cally express a topology op miza on problembased on the SIMP approach. In this case, the problem can be wri en as

minimize C = F TU = UTKU =N∑i=1

(ρi)p uT

i k0ui (2.14)

subject to

V = f · V0

F = KU

0 < ρmin ≤ ρi ≤ 1

where F is the force vector, U is the displacement vector, K is the s ffness matrix of thestructure. The lower case le ers denote the respec ve element characteris cs, which sumup to the global compliance of the structure, while the element s ffness a er op miza onis propor onate to the ini al element s ffness k0 through the penalized element density(ρi)

p (see eq. (2.13)). The minimiza on is subject to a volume constraint, which defines alimit of the structure volume a er op miza on V in rela on to the ini al volume of thestructure V0. In addi on, a lower bound of the element density is introduced with ρmin,which prevents singularity of the equilibrium constraint.

Implementa on of the Op miza on Procedure Topology op miza on, as it has beenintroduced here, is based on the numerical computa on of the globally best distribu onof the material density ρ according to the defined op mality condi ons. A computa onflow chart illustra ng the implementa on of such a topology op miza on procedure isshown in Figure 2.15. This procedure is preceded by the preprocessing of the modelgeometry and loadings, including the discre za on of the design domain and the setupof the op miza on responses and constraint. The first step is then the ini aliza on ofthe model followed by a finite element analysis of the structure in its ini al state. Thenext step is a sensi vity analysis for the displacements of each element based on the FEAresults. This means nothing else than finding the deriva ves of the element displacementswith respect to the element densi es. These gradients are necessary input for the actualop miza on step. Here, the density of each element is updated according to a numericalop miza on algorithm. At present, two op miza on algorithms are used in topologyop miza on: the op mality criteria (OC) approach and the method of moving asymptotes(MMA) [Zuo07]. The former, is usually deduced by a Lagrange func on and has a good


convergence as it is based on a heuris c formula on. However, it is difficult to apply inproblems with mul ple constraints. The MMA approach is a mathema cal programmingalgorithm which has wider engineering applica ons as it is suited for single and mul pleconstraints condi ons. The itera on loop is stopped when the current candidate designonly has a marginally improved compliance compared to the previous design. The finalstep is the post-processing and interpreta on of the results.

Initialize(Starting guess)

Finite element analysis

Sensitivity analysis(linearization)

Optimization algorithm

converged?

plot results/post-processing

stop

no

yes

Update element densities

Figure 2.15: Flow chart of computa ons performed for topology op miza on using thematerial distribu on method. (illustra on based on [Ben03] )

The described procedure does not require complex programming efforts in case of aminimumcompliance topology design problem. This is shownby the educa onalMatlab codefrom Sigmund (2000) [Sig01]. Here, a complete programme including FE analysis, filteringprocedures and plo ng commands for a rectangular design domain discre zed with squareelements is wri en in 99 lines. Another interes ng implementa on is the web GUI interfacefor a topology op miza on programme publicly accessible at http://www.topopt.dtu.dk.It provides a computer aided learning tool intended to “spread the concept and ideas oftopology op miza on among designers in various fields of engineering” [Tch01].

2.5.2.2 General Issues in Topology Op miza on

The following will discuss a few general issues that have a significant impact on thecomputa onal results of a topology op miza on process. This includes, the appearanceof checkerboards and the mesh-dependency of the resul ng topology, as two major


influence factors. In addi on, it is shown how the magnitude of the penalty factor andthe considera on of mul ple load cases affect the results. The demonstra on of theseeffects is performed on a simple C-shaped clip structure, which is loaded by two opposingforces and which is being op mized using Altair Op Struct. The C-clip is modeled with2D-shell elements (Figure 2.16) and the op miza on objec ve is minimizing the weightedcompliance due to the two loads considered as individual loading condi ons.

F2

F1

Figure 2.16: Example clip for demonstra on of topology op miza on issues

Mesh-Dependency Mesh-dependency concerns the effect that the solu on of a topologyop miza on process depends on the mesh refinement of the design domain. Ideally, afiner discre za on of the design domain should result in a be er finite element modellingof the same structure and thus in a be er descrip on of boundaries. However, in factqualita vely different solu ons are achieved for different mesh-sizes. Refining the finiteelement mesh ul mately leads to a much more detailed fine-scale structure. This effect isillustrated in Figure 2.17 for three different mesh sizes of the example clip. The reason forthis effect is that introducing more holes into a structure without changing its structuralvolume will generally increase the efficiency of the structure. Several techniques have beendeveloped to overcome this issue. These include adding constraints to the op miza onproblem, reducing the parameter space of the design domain or applying certain filters[Ben03].

Design History

Design History Design History

1720 elements 7800 elements 27800 elements

Figure 2.17: Demonstra on of the mesh dependency in topology op miza on


Checkerboard Problem Checkerboards in topology op miza on refer to the forma on ofareas with alterna ng solid and void or low density elements similar to a checkerboardpa ern. This is a result of errors in the finite element approxima on, that overes mates thes ffness of checkerboards [Ben03]. This problem can be avoided through the use of higherorder finite elements for the discre za on of the design domain. However, this leads to asignificant increase in CPU- me necessary for solving the FE-equilibrium equa ons, which isthe most me consuming part of the op miza on process. Therefore, other computa onallymore efficient methods have been proposed. These methods typically include a meshrelated filtering of the element densi es. Figure 2.18 illustrates the checkerboard effectusing the introduced example topology op miza on of a C-shape clip.

Design History Design History Design History

1720 elements 7800 elements 27800 elements

Figure 2.18: Demonstra on of checkerboard effect for three different mesh refinements

In this case, checkerboard pa erns especially appear in the center area of the structure,which makes it difficult to determine a clear op mized topology in these regions. For thedemonstra on of the mesh dependency (see Figure 2.17), filters were applied to preventthe development of checkerboards. Therefore, the op mized topology can be be erinterpreted, when applying measures to prevent checkerboards.

Penalty Factor The penalty factor p was introduced in the SIMP method to steer elementswith intermediate densi es towards the discrete values (1) and (0). In Op Struct, thepenalty factor is represented by the DISCRETE se ng, which can be found op controlpanel. Its default is set to 1.0, meaning the element densi es are not penalized. Raisingthe penalty factor leads to a more discrete solu on with most elements having densi esof either 1 or 0. However, a too severe penaliza on of the intermediate densi es canresult in topologies, which are very sensi ve to the choice of the ini al design domain, asthe op miza on itera ons might “jump” to quickly to a 0-1 design [Ben03]. Therefore,it is recommended to implement a con nua on method, which slowly raises the penaltyfactor through the computa on itera ons un l the procedure arrives at a sa sfying finaldesign. Figure 2.19 demonstrates the effect of the penalty factor on the resul ng topologyof the C-clip. Here, the density of each element is illustrated through a black and whitescale, where black refers to fully dense elements, white represents void elements and grayrepresents intermediate density elements. Good results were achieved with penalty factors


of about p = 3.0. It can be seen that a raised penalty factor leads to a more discretetopology, with most elements either being white (void) or black (full density). On the otherhand, large factors of p result in imprac cal results as in the right graphic of Figure 2.19.

Design History

Design HistoryDesign History

p = 1.0 p = 3.0 p = 7.0

Figure 2.19: Effect of the penalty factor on the resul ng topology

Mul ple Loads The op miza on results of a mul ply loaded structure depends on howthe loads are considered in the op miza on problem formula on. The introduced exampleproblem of a C-shaped clip contains two opposing loads. These two loads can be eitherregarded as single load case, which means both loads are considered to act simultaneouslyor as two individual load cases. If the structure is op mized for a single loading condi on,it might collapse in case the two loads act independently. To prevent this, the op miza onproblem is formulated in a way that the two loads are regarded as two separate loadingcondi ons. Therefore, the minimum compliance problem introduced in eq. (2.14) isformulated as minimiza on of the weighted average of the compliances for each of thetwo load cases:

minimize C =N∑k=1

ki Ci (2.15)

where N denotes the number of considered load cases. The previously pictured op mizedtopologies were based on a individual load case formula on. With this the op mizedtopology is stable for the loads ac ng both simultaneously and independently.

F2

F1

F2

F1

single load case mul ple load cases

Figure 2.20: Comparison of topology op miza on, using one or more load cases


Figure 2.20 compares the topology results for both load considera ons, where the graphicon the right side is derived from Figure 2.17. Here it becomes apparent that a mul pleload case considera on leads to stable structures based on triangular frames, while a singleload problem results in unstable square shaped frames.

2.5.3 Topology Op miza on Using Altair Hyperworks

The FE-based op miza on and analysis within the framework of this thesis is performedusing the so ware package HyperWorks from Altair Engineering Inc. This computer aidedengineering (CAE) so ware provides a wide range of analysis and op miza on modulesfor different engineering problems. This includes amongst others, linear and non-linearFE-analysis, topology, size and shape op miza on as well as mul -body dynamic simula on,while this work focuses on studying its capabili es of performing topology op miza onand linear FE-analysis. Like most FEA programmes [Fr5], HyperWorks follows a modularstructure consis ng of preprocessor, solver and postprocessor. The preprocessor module,called HyperMesh, enables the crea on of the FE-models (geometry, constraints, loads,mesh ect). It possesses several interfaces for the export of models to common external FEsolvers, such as ANSYS, ABAQUS, NASTRAN or LS-DYNA. Hyperworks also provides Altairexclusive in-house solvers like RADIOSS and Op Struct, while Op Struct is a solver that isspecialized on conceptual structural op miza on problems. All op miza on computa onsin this work have been performed using Altair Op Struct. For the visualiza on of theFEA results, Hyperworks provides with HyperView a comprehensive postprocessor module,which is also used here. Figure 2.21 illustrates the modular structure of Hyperworks,indica ng the modules primarily applied in this work.

Preprocessor Solver Postprocessor

modelingmodeling computationcomputation display resultsdisplay results

Figure 2.21: Altair modules applied in this work

3 Parameter Study for the Vehicle Range

One of the most considerable drawbacks of electric vehicles is their limited range. Forexample, an electric vehicle based on the VW Lupo equipped with 1000 modules of theadvanced lithium-ion ba ery, hardly exceeds 450km of range. Such a ba ery would weightover 1,110kg, which more than doubles the vehicle’s mass. Such an increase in mass has asignificant nega ve impact on the propulsive efficiency of the vehicle. Moreover, it wouldrequire notable addi onal material to strengthen the vehicle body for the accommoda onof such a high-weight ba ery. Hence, this configura on is unacceptable. If lead-acidba eries were to be used to achieve the same range, the situa on becomes even worsewith the ba ery mass reaching over 2.5 tons. A diesel version of the same car on theother hand, achieves double the range (900km) without technical difficul es [Sør10]. As aconsequence of the limited energy storage capabili es, the range of most electric vehicleslies well under 200km [WH10]. At the same me, the remaining chassis componentsrequire a par cular energy efficient design in order to compensate the limited energystorage and achieve an acceptable range.

The NUS City Car project is intended as pla orm for studying electric vehicle technologyin an urban environment. Since the project is presently s ll in its first design itera on,the primary concern is the design and implementa on of the chassis systems in order tobuild a func oning prototype. With this, the range of the vehicle itself is secondary in thecurrent stage. Nevertheless, it is important to es mate the achievable range of the currentconfigura on for two main reasons. Firstly, one wants to evaluate the performance ofthe current configura on by comparing the theore cally achievable range with the actualperformance. The ques on here is, do the components perform like expected? And if not,where do the inconsistencies come from? Secondly, such a evalua on helps to determineweak links in the system. This becomes par cularly important in prepara on of the nextdesign itera on. Determining the components or vehicle parameters, that contribute mostto the achievable performance is the first step in improving a system. Experience inthe transporta on industry shows that it is especially consequent lightweight design thatsignificantly improves the performance of vehicles in terms of energy consump on andrange (see 2.4). However, lightweight design has played a minor role in the developmentof the current NUS City Car prototype, which is why this is further inves gated in theframework of this thesis.

The objec ve of this chapter is therefore the development of a model that es mates therange of the NUS City Car depending on basic vehicle parameters such as weight, rolling

3.1 Parameter Model 28

resistance, aerodynamics and ba ery size. The resul ng model is the basis for the followingsensi vity analysis. Here, it is shown to what extent the different vehicle parametersinfluence the energy consump on and the range of the vehicle in urban driving condi ons.The objec ve is to es mate the poten al for extending the range of the NUS City Carthrough weight reduc on compared to the remaining parameters. In addi on, the modelis meant to provide a tool for future es ma on purposes, which is why it is implementedas graphical user interface.

3.1 Parameter ModelAs briefly discussed in sec on 2.3, the simula on of an vehicle’s powertrain is a crucialstep in the vehicle design process. As a result of this, several comprehensive simula ontools have been developed. An example is the Powertrain Systems Analysis Toolkit (PSAT) ,developed by the Argonne Na onal Laboratory in coopera on with the U.S. Department ofEnergy. Based on Matlab/Simulink, this so ware provides performance and fuel economysimula ons through a modular GUI interface, allowing parameter studies and comparisonof drivetrain configura ons [Arg07]. A similar so ware is the Advanced Vehicle Simulator(ADVISOR), which is also based on Matlab. The problem with these so ware packages isthat they require a license on top of the necessary Matlab license. Although the NUSpossesses a few licenses for the PSAT so ware, their availability is limited. In addi on, itrequires considerable familiariza on to navigate the so ware even with the model alreadyset up. Another problem that occurred while using the so ware is, that the basis ofthe computa ons for the simula on is not clearly stated, which leaves the user ratherunaware of what effects are considered and what are neglected. Finally, when buildingup the drivetrain, the user is limited to the components provided in the included library.Without matching components for the NUS City Car, the simula on results are likely tobe inaccurate. As a consequence, the benefits of using PSAT, more accuracy through theuse of an established so ware, seemed to be outweighed for the proposed applica onof a simple qualita ve parameter study on the vehicle’s range. This is why the decisionwas made to build up an easy to use Matlab model from the scratch. This ensures thatthe considered effects are clearly known as well as the model can be used without anylicense barriers for quick future es ma on purposes. The following paragraphs describethe development of such a model.

3.1.1 Modeling of Electric Components

Under 2.1, the electricmotor and the ba erywere pointed out as cri cal vehicle components.This status remains when it comes to modeling the range performance of electric vehicles.The proposed range es ma on model requires the modeling of these components in away that is compa ble with the quasista c approach of modeling the energy demand ofroad vehicles which was introduced in 2.3. Therefore, the needed modeling aspects ofboth the motor and the ba ery are described in the following.


3.1.1.1 Electric Motor

For the intended range es ma on model, the main concern is to study the energy lossesof the electric motor. The equipped motor of the NUS City Car is a brushed series-woundDC motor. The major energy losses in DC motors are the same as for all electric motors.They can be divided into four main categories [Lar03].

• Copper losses: Are caused by the electrical resistance of the wires and brushes,which results in energy dissipa on through heat. They are propor onal to the squareof the motor current and for DC motors it is therefore also propor onal to the squareof the motor torque. ∝ T 2

• Iron losses: Are caused by magne c effects in the iron of the rotor. The higher thefrequency of the changing magne c field, the higher the iron losses. ∝ ω

• Fric on and windage: Naturally, there is fric on in the bearings and brushes of themotor accompanied by wind resistance of the revolving rotor. While the fric on forceis roughly constant, the wind resistance increases with the square of the speed. Inorder to get the power losses from these resistance forces they have to mul pliedby the angular speed. Therefore, the fric on is ∝ ω, and the windage losses arepropor onal to the angular speed cubed ∝ ω3

• Constant losses: Eventually, there are constant losses that occur even when themotor is sta onary. This is a result of the power that has to be supplied to maintainthe magne c field or the electric control circuits.

All power losses combined can hence be wri en as

total losses = kc T2 + ki ω + kw ω3 + C (3.1)

where, kc, ki, kw and C are motor constants. This equa on is also a good approxima onfor all other electric motor types. With the equa on for all power losses, the motorefficiency yields

ηmot(T, ω) =output power

output power + losses=

T ω

T ω + kc T 2 + ki ω + kw ω3 + C(3.2)

Since the motor efficiency is a func on of the motor torque and angular velocity, it iscommon to plot the values of the efficiency on a torque-velocity graph. The result is theso called motor efficiency map, which gives an idea of the efficiency at any given opera ngcondi on. Figure 3.1 illustrates such a map.

3.1 Parameter Model 3076 4 Electric and Hybrid-Electric Propulsion Systems

0.7

0.7 0.7 0.7

0.8

0.80.8

0.8

5

0.85

0.85

0.9

!2 [rad/s]

T2 [N

m]

100 200 300 400 500 600 700

10

20

30

40

50

0.7

0.80.80.8

0.8

0.8 0.8

0.80.8

0.80.85

!2 [rad/s]

T2 [N

m]

200 300 400 500 600 700 800 900

20

40

60

80

100

120

Fig. 4.14. Efficiency maps for a 32 kW PM motor (top) and a 30 kW AC motor(bottom), with curves of maximum torque (dashdot).

by measuring the motor efficiency also in the generator range, and the differ-ence is typically more important for induction motors [10]. For example, themeasured efficiency map shown in Fig. 4.15 illustrates a case in which neitherthe efficiency nor the power losses are mirrored when passing from the motormode to the generator mode. A possible way to manage this general case con-

Figure 3.1: Efficiency map for a 32kW permanent magnet motor [Guz08]

It is obvious that the es ma on of the motor energy losses requires the knowledge ofthe respec ve motor constants kc, ki, kw and C for the equipped motor.

3.1.1.2 Electric Ba eries

Es ma ng the vehicle range requires to analyze the discharging of the equipped lead acidba eries. Therefore, the following paragraphs are centered around basic concepts neededfor the development of a simple quasista c discharge model.

Ba ery Capacity The capacity of a ba ery is usually expressed in ampere hours Ah andis determined with constant-current discharge/charge tests [Guz08]. A very importantphenomena occurring in ba eries is that the actual available capacity depends on the rateof discharge, which is why manufacturers always give the capacity of lead acid ba eries asrated capacity. That means a certain capacity is “guaranteed” if the ba ery is dischargedwith a reference discharge current. To illustrate this, lets assume an example ba ery islabeled as C0 = 30Ah ba ery with an hour ra ng of to = 10h. This translates into a ba erythat provides C = 30Ah when discharged over 10h with the discharge current Idis of

Idis =C0

t0=

30Ah

10h= 3A (3.3)

However, in case the ba ery is discharged at a higher rate, it will ul mately provide lesscapacity. This rela onship between actual capacity and discharge rate is described by thePeukert Law, which can be wri en as

Cp = C0 ·(IdisI0

)1−k

(3.4)

Here Cp is the nominal capacity, when discharged with the current Idis, while C0 denotesthe rated capacity at a given rated current I0. The exponent k is eventually the peukertcoefficient, which lies between 1.1 and 1.3 for lead acid ba eries [Lar03].


State of Charge The state of charge (SoC) of a ba ery is simply the ra o of the electriccharge Q that can be delivered to the nominal ba ery capacity Cp

SoC =Q

Cp

(3.5)

while SoC = 1 suggests a fully charged ba ery and SoC = 0 respec vely indicates anempty ba ery. Some mes the term depth of discharge (DoD) is used to refer to the ba erycharge status. It is equally meaningful, just that it describes the charge le in the ba eryas ra o between removed charge Qr to nominal capacity Cp, which means DoD = 1 refersto an empty ba ery. An important issue in this context is the fact that ba eries shouldnot be discharged much below a SoC of 20%. If they are discharged deeper, they arelikely take damage which results in a drama cally reduced longevity [Guz08]. This has tobe taken into account when es ma ng the range of a vehicle.

Equivalent Circuit A quasista c physical model of a ba ery can be derived by consideringan equivalent circuit as shown in figure 3.2. Here, the ba ery is reflected by an idealopen-circuit voltage Uoc in series with an internal resistance Ri.

4.4 Batteries 97

Q(t) = −I2(t) . (4.50)

In case of charge, the evaluation of the state of charge must take into accountthe fact that a fraction of the current I2 is not transformed into charge. Thisfraction is due to irreversible, parasitic reactions taking place in the battery.Often [65, 149, 129] such an effect is modeled by a charging or coulombicefficiency ηc,

Q(t) = −ηc · I2(t) . (4.51)

The combination of (4.50)–(4.51) yields a method to determine the state ofcharge by measuring the terminal current. This method, known as “Coulombcounting” has the advantage of being easy and reliable as long as the currentmeasurement is accurate. Practically, however, this method requires frequentrecalibration points, to compensate the effects neglected by (4.50)–(4.51) [193].Modern system for SoC determination attempt in some cases to estimatesome of these effects, namely, the charge “efficiency” during discharge, whichis due to reaction kinetics and diffusion processes, battery self-discharge, andcapacity loss as the battery ages [195].

More advanced methods of SoC determination include adaptive methodsbased on physical models of batteries [194, 193, 195]. If the state of charge is astate of the model, it can be estimated by comparing the measurements avail-able (terminal voltage, current), with the model outputs, using well-knowntechniques such as Kalman filtering.

Equivalent Circuit

A basic physical model of a battery can be derived by considering an equivalentcircuit of the system such as the one shown in Fig. 4.26. In this circuit, thebattery is represented by an ideal open-circuit voltage source in series withan internal resistance. Kirchhoff’s voltage law for the equivalent circuit yieldsthe equation

Uoc(t)−Ri(t) · I2(t) = U2(t) . (4.52)

The steady-state battery equivalent circuit has been applied mainly for variouslead–acid batteries [65, 75, 238, 129, 149], but also for nickel–cadmium, nickel–metal hydride and lithium-ion batteries [129].

U2

I2

R i

Uoc =

Fig. 4.26. Equivalent circuit of a battery.Figure 3.2: Equivalent circuit of a quasista c ba ery

Applying Kirchhoff’s voltage law yields the equa on for the terminal voltage U2

U2 = Uoc −Ri · I2 (3.6)

This simple model is not capable of describing the transient behaviour of the ba ery. Forthis, one has to consider a dynamic equivalent circuit that takes into account capaci veand induc ve effects. Detailed dynamic simula ons also require a thermal submodel,which evaluates how the ba ery temperature varies during vehicle opera on, since thetemperature affects many aspects of a ba ery’s opera on [Guz08]. The applied approachof a quasista c ba ery model, however, is sufficient for modeling the ba ery dischargingas part of a qualita ve es ma on of an electric vehicle’s range [Lar03].

The internal resistance Ri takes into account several phenomena, including the ohmicresistance in the electrolyte and electrodes as well as well as a charge transfer resistance. Aswith the equivalent circuit, proper considera on of all effects requires more sophis catedmodels for the internal resistance. However, Larminie and Lowry (2003) suggest the


following rule of thumb for a constant average resistance:

Ri = nCells · 0.022C0

Ω (3.7)

The chemical charging and discharging reac ons taking place in the ba ery involve changingthe concentra on of the electrolyte of the cells. Therefore, there is a small decrease in thevoltage produced by the cell as it discharges. Modern lead acid ba eries are characterizedby an approximately linear rela onship between DoD and Uoc, which can be wri en as[Lar03]:

Uoc = nCells · (2.15−DoD · (2.15− 2.00)) (3.8)

Ba ery Power Depending on the vehicle’s opera on the ba ery will be required to providea certain electric power to the motor. The power that is supplied by the ba ery yieldswith the circuit equa on (3.6)

Pb = U2 · I2 = (Uoc −Ri I2) · I2 = Uoc I2 −Ri I22 (3.9)

In order to determine the charge removed from the ba ery as result of the provided power,one has to determine the outgoing ba ery current I2 with respect to the demanded poweroutput. Therefore, equa on (3.9) is transformed as follows:

I2 =Uoc −

√U2oc − 4Ri Pb

2Ri

(3.10)

In case the ba ery is being charged by dissipa ng power into the ba ery, for instancethrough a regenera ve braking system, the current I2 is flowing into the ba ery. Equa on(3.10) has to be rewri en accordingly in order to get the charge current:

I2 = −Uoc +

√U2oc + 8Ri Pb

4Ri

(3.11)

Here, it is already accounted for the effect that the internal resistance is normally largerwhen charging as opposed to discharging the ba ery. Larminie and Lowry (2003) proposea value twice the size of the normal discharge resistance as first approxima on.

Charge and Discharge The charge is generally defined as current by me. In case ofdischarging a ba ery the Peukert law comes into play as follows:

Cr = T · Ik (3.12)

Since the discharge current varies throughout the opera on along with the demandedpower output, the ba ery discharge is modeled using a quasista c approach. This isexplained into more detail under 2.3. Essen ally, it is assumed that the ba ery discharge


is divided into discrete me intervals ∆t. For each me interval, it is calculated how muchcharge is removed depending on the present ba ery current Ii. Assuming that the meintervals are given in seconds the removed charge becomes:

Ci =∆t · Iki3600

Ah (3.13)

In me intervals where the ba ery is being charged, the Peukert correc on has to beremoved, as large ba ery currents do not have propor onally more effect than small oneswhen charing. Also when charging, the ba ery current Ii becomes nega ve meaning thatit is flowing into the ba ery. Therefore, the charge “removed” from the ba ery becomesalso nega ve which means it actually is a charge restored in the ba ery:

Ci =∆t · Ii3600

Ah (3.14)

The sum of all incremental charges eventually results in the total removed charge:

Cr =N∑i=1

Ci (3.15)

3.1.2 Model Development

The es ma on of the vehicle’s range is performed a er the quasista c method as introducedin sec on 2.3.2. The implementa on of this approach follows closely the descrip on ofGuzzella, Sciarre a (2008) [Guz08] and Larminie, Lowry (2003) [Lar03], which are verysimilar. There is only one notable excep on. These authors partly model the drivetrainthrough the es ma on of the necessary motor torque and sha speed, which enablesthe determina on of the quasista c motor efficiency using the respec ve efficiency map.The problem is that there is no efficiency map available for the motor of the NUS CityCar. Two op ons were considered to solve this problem. Firstly, one could try to findan efficiency map of a similar motor assuming that it sufficiently models the actual type.Secondly, the motor efficiency could be assumed to be constant modeled by an averagevalue. Eventually it was decided to simply assume a constant efficiency. This decision wasmade, because it was difficult to obtain efficiency maps of motors that could be certainlyiden fied as similar to the City Car motor. Moreover, a constant average motor efficiencybrings the benefit that the motor is modeled by only this one value instead of a complexmotor map, which makes it easier to include it into a parameter study. In addi on, thisassump on allows a considerable simplifica on of the model structure. And this is wherethe developed model differs from the above men oned authors.

Drivetrain characteris cs such as torques and sha speeds are not relevant under theassump on that drivetrain efficiencies are constant and the iner as of rota ng parts areapproximated (see eq. (2.5)). Thus, the drivetrain is not modeled explicitly. Instead, it is


bypassed, which leaves only two basic model steps. Firstly, the needed mechanical energyto be supplied at the wheels is determined. In the second step, this mechanical energyconsump on is directly translated into a reduc on of the available stored energy, whichin this case is electric energy. The drivetrain lies “in between” these two en es and isconsidered as blackbox, which is bypassed using a constant average efficiency to accountfor transmission losses. In addi on to the mechanical energy needed to move the vehicle,the ba ery has to provide energy for all accessories such as head light, radio or even aircondi on. For modeling purposes, these accessory losses are usually accounted for by aconstant addi onal energy consump on, which has to be supplied con nuously regardlessof the present vehicle opera on.

Frr

α

Fhc

Fad

Ftrac

Fla

Mg

+

-

Reduced stored electric energyNeeded mechanical energy

Drivetrain

bypass

Figure 3.3: Illustra on of the modeling approach of bypassing the drivetrain

With this simplifica ons, the quasista c simula on model runs through the followingprocedure. For each of the me intervals, the constant speed and accelera on requiredto follow the given driving cycle is calculated from the cycle input data with the equa onsin (2.8). With this informa on, the total trac ve force Ftrac that has to be ac ng on thewheels during the me interval is calculated using eq. (2.6). For the next step, the modeldis nguishes for each me interval between the different vehicle opera ng modes. In casethe vehicle is in trac on mode (Ftrac > 0), the motor is supplied with the necessary trac onpower, while the losses of the drivetrain are considered through average efficiencies (motorand gear efficiency). Hence, the power to be supplied to the motor yields

Pmot, in =Ftrac · v

ηmot · ηgear=

Ptrac

ηmot · ηgear(3.16)

In case the vehicle is coas ng (Ftrac = 0) or stopping (v = 0), Ptrac and thus Pmot, in

automa cally become zero, which means it is assumed the motor does not consume anyenergy in these opera ng modes. When the vehicle is braking (Ftrac < 0), the availablesurplus in kine c energy can be transformed back into electric energy should the vehiclebe equipped with a recupera on system. The NUS City Car does not have such a system inthe current design itera on, which is why regenera ve braking has not been studied intodetail in this work. However, in order to es mate the poten al of regenera ve braking in


terms of energy consump on, the model allows a simple considera on of a recupera onsystem. In case the motor is used to transform the available kine c energy into electricenergy, the drivetrain efficiencies work in the opposite sense compared to eq. (3.16).Therefore, the motor input power that can be u lized to recharge the ba ery yields

Pmot, in = Ftrac v · (ηmot · ηgear · ηrecup) = Ptrac · (ηmot · ηgear · ηrecup) (3.17)

where ηrecup denotes an addi onal recupera on efficiency, that represents the quality ofthe recupera on system. In case regenera ve braking is not considered, Pmot, in is set tozero for all braking intervals. In the next step, the average accessory power Pac is addedto the motor input power, which eventually results in the ba ery power Pb.

Pb = Pmot, in + Pac (3.18)

Since the present ba ery voltage correlates to the ba ery SoC, the voltage is calculatedwith the rela onship established in eq. (3.8), before with the ba ery power as input theba ery charge or discharge current is computed using eq. (3.11) or (3.10) (depending onweather Pb is posi ve or nega ve). In the next step the ba ery current is translated into acharge that is either removed or restored in the ba ery (eq. (3.13) or (3.14)). Eventuallythe state of charge is updated with eq. (3.15). This whole procedure is repeated un l theba ery reaches a SoC that is below the defined discharge limit, which is considered asempty ba ery.

A flowchart of the developed model helping to illustrate this procedure is pictured in figure3.4. The respec ve model is implemented in a Matlab script file. Besides the es ma on ofthe vehicle range, where the chosen driving cycle is repeated un l the ba ery is empty,the model also enables the analysis of a single driving cycle. This allows for the plo ng ofdifferent simula on parameters such as motor power, ba ery voltage/current or consumedenergy over the me history of a test cycle.

Capabili es and Limits The developed model is based on a quasista c method andenables the es ma on of the range of an electric vehicle depending on a few basic vehicleparameters such as rolling fric on, aerodynamic drag, weight or drivetrain efficiencies aswell as ba ery parameters like capacity and number of cells. Different driving pa ernscan be accurately simulated through the use of standardized test cycles. It allows a simpleconsidera on of a recupera on system, which restores some of the used energy whenbraking depending on the defined recupera on efficiency. The ba ery discharge is modeledupon the Peukert law based on a simple equivalent circuit. The applied approach is wellaccepted for op miza on and evalua on purposes ([Lar03, Guz08]). However, limita onsare especially induced by the fact that the drivetrain is not explicitly modeled. This leads toan inaccurate considera on of the motor efficiency, which can significantly vary throughouta driving cycle. Averaging the efficiency is likely to achieve good results for the overall energy


Initialize(set default values, load

driving cycle)

Compute present velocity and accelaration, update traveled

distance

Compute presenttractive force

Compute necessary motor input power

Compute batterydischarge/charge current

Compute available recuperation power

gearmot

tracinmot

PP

ηη ⋅=

,

0>tracF

Compute charge that is removed/restored in battery

0<tracF

Update State of Charge

)(, recupgearmottracinmot PP ηηη⋅=

Add average accessory power to get the battery power dd

bP

Battery empty?

Stop computation

no

yes

Update State of Charge

Figure 3.4: Flowchart of the developed range es ma on model

consump on, but it might be wrong for certain peak values of the necessary motor inputpower and current. In addi on, the ba ery model lacks the considera on of temperaturevaria ons during opera on. These can affect relevant aspects such as ba ery efficiencyand capacity. Lastly, the ba ery model is limited to lead-acid ba eries as this is currentlythe relevant ba ery type for NUS City Car. A comparison of different ba ery technologiesis currently not implemented.

Model Valida on In some first reference tests, the model delivered reasonable es ma onsfor the energy consump on and range of an electric vehicle. A small electric car from theMini or Fiat 500 class with a mass of 750kg and a 120 V lead-acid ba ery pack with 60Ah and 7.2kWh achieves about 80km of range [Hod01]. Assuming average values for allremaining model parameters, the model es mates a maximum range of about 85km ina driving pa ern without many braking and accelera on phases. However, such a quickplausibility evalua on is barely enough to declare the model a func oning basis for the


proposed parameter study. At the same me, its not necessary to a empt a completemodel valida on through experimental tests, since the model is not intended to accuratelysimulate the performance of the vehicle system. For a simple valida on, it would besufficient to simply run some simula ons with the developed model and compare basicsimula on parameters such as trac on force, motor input power, ba ery current or energyconsump on with a validated reference model.

Such a validated referencemodel has been found in the predefined powertrain configura onsof the PSAT so ware package, which was briefly introduced before. The procedure and theexact results of the performed valida on are summarized in appendix B. The outcome isthat the simplified model gives out very similar values for the overall energy consump onwith clearly visible devia ons only at the some peak values of the motor power. Thisdevia ons are also respec vely reflected in the ba ery current. This is assumed to resultfrom the simplified considera on of the motor efficiency as constant value. PSAT on theother hand considers that the motor efficiency actually varies considerably dependingon the opera on, which probably causes the men oned devia ons. Another differencethat became apparent when comparing both models is the ba ery discharge rate. Thedeveloped simple model seems to generally discharge the ba ery more rapidly, althoughit es mates a slightly higher energy demand than the PSAT model. The reason for thiscould not be determined with certainty because PSAT applies a considerably more complexba ery model which makes comparisons difficult. However, it could be established thatthis difference is rather an offset that occurred throughout all valida on runs to a similarextend. Overall, the developed model represents the same trends and similar absolutevalues in all simula on parameters, which clearly confirms the model as solid founda onfor the proposed parameter study.

3.1.3 GUI Interface

In order to ensure that the model can be applied without difficulty for future es ma onpurposes, it has been implemented in a Matlab graphical user interface (GUI) . Here, theuser simply keys in the vehicle and ba ery parameters at the le and chooses weatherregenera ve braking is to be considered. In the next step, the considered test cycle isselected in the upper center area, while it allows a preview of the velocity profile. Currently,there are five test cycles implemented, with four of them being urban drive cycles. Theremaining test cycle reflects an ideal con nuous low speed cycle, which is included toes mate the maximum range under ideal condi ons. With this setup completed, the usercan choose between analysing a single driving cycle (’Simula on of Single Test Cycle’) andes ma ng the total range (’Range Simula on’). The former allows to generate plots thatshow simula on parameters in the course of the selected driving cycle. The parameters tobe plo ed are selected via the respec ve radio bu ons. The range simula on bu on repeatsthe selected driving cycle un l the ba ery is considered discharged, while it automa callygenerates a results table with relevant values a er the simula on is completed (e.g. covered

3.2 Sensi vity Analysis 38

distance, average power, used energy).

Figure 3.5: GUI interface of the developed es ma on model

3.2 Sensi vity AnalysisA er the range es ma on model was successfully established and validated, it is nowapplied to derive the sensi vity of the energy consump on and the achievable range todifferent vehicle parameters. Since the model has been wri en as Matlab code fromscratch, it was comparably easy to modify the model in a way, that it can be included intoa global Matlab script that executes the sensi vity analysis automa cally and repeatablyfor all parameters. The results are exported to Excel to generate illustra ng graphs.

With regards to the intended lightweight design op miza on, it is especially of interest todetermine the impact of the vehicle mass on the range and the energy consump on. Theobjec ve is to eventually quan fy how much the range can be extended when the mass isreduced by a certain factor. At the same me, it is desired to determine the impact of theremaining vehicle parameters with respect to the vehicle mass. The assump on that thevehicle mass is a comparably significant influence factor for the energy consump on andthus the range, can be considered as one the star ng points for this work. This assump on


is to be confirmed through the following sensi vity analysis.

In order to study the rela ve impact of the relevant vehicle parameters, a base configura onis defined. This base configura on represents the current design of the NUS City Car. Therespec ve values have adopted from [Lar03], where they are similarly stated for a smallelectric car. However, the drag coefficient has been adjusted to the results of a CFD analysisfor the intended body shell design of the NUS City Car. This analysis was performed in theframework of a related student research project. For each of the relevant parameters, it isthen determined how a devia on of +5% to -5% around its base value affects the energyconsump on and the range. This span is established at such a comparably low level, sothat the efficiencies remain in realis c boundaries. The general trend of the sensi vityanalysis will be retained also for the low span of +5% to -5%. Table 3.1 summarizes thebase values along with the respec ve deviated values.

base +5% -5% base +5% -5%

Vehicle mass [kg] 500 525 475 No. of cells 60 63 57

Drag coeff. 0.6 0.63 0.57 Peukert coeff. 1.12 - -

Frontal area [m²] 1.5 1.575 1.425 Capacity [Ah] 66 69.3 62.7

Rolling resistence 0.01 0.0105 0.01 Hour rating [h] 10 - -

Gear efficiency 0.95 0.9975 0.903 Maximum DoD 0.8 - -

Motor efficiency 0.8 0.84 0.76

Accessory power [W] 200 210 190

Battery ParametersVehicle Parameters

Table 3.1: Base vehicle configura on of the sensi vity analysis

The simula on model is then run for each deviated parameter while all remainingparameters are kept at their base value. In order to study the sensi vity of both, theenergy consump on and the range, the performed sensi vity analysis is divided into twoparts. The energy consump on is determined for one single test cycle, while the range isobtained by repea ng the input test cycle un l the ba ery is discharged. The focus lies onstudying the vehicle parameters rather than the ba ery characteris cs, since the availableba ery is considered as fixed design constraint. Therefore, most of the ba ery parametersare excluded from the sensi vity analysis. Solely the number of cells and their capacityis considered in order to give a general idea of how the ba ery size affects the range incomparison to the vehicle parameters. At the same me, it is accounted for the inevitablechange of the total vehicle mass resul ng from varying the ba ery size. This is done bya simple propor onal rela onship between ba ery mass and capacity/cell number. It issimply assumed that an 5% increase in capacity or number of cells leads to a 5% increasedba ery mass. Apart from the change in the total vehicle mass, the ba ery size does notinfluence the energy consump on, which is why the ba ery parameters are completelyexcluded from the sensi vity study of the energy consump on.

In order to illustrate the impact of the driving pa ern on the sensi vity, the analysis is


performed for two different urban test cycles (NYCC and ECE1 Type1), while the ECE1 hasbeen doubled to so that both test cycles cover roughly the same distance. This makes surethat the absolute values of the energy sensi vity can be directly compared. All sensi vityanalysis results are summarized using tornado charts. A tornado chart is an efficient wayof illustra ng the sensi vity of an output parameter with respect to changes on all inputvariables simultaneously. This is achieved by plo ng the span between +5% and -5% foreach parameter as bar around its base value. The typical tornado shape results fromarranging the considered parameters in descending order according to the significance oftheir impact on the output.

The performed sensi vity analysis results in four tornado charts, energy consump onand range for two different driving pa erns, while the energy consump on charts onlyconsider the seven vehicle parameters. These charts are summarized together with thetwo considered driving pa erns in figure 3.6.

0 100 200 300 400 500 6000

5

10

15

time [s]

velo

city

[m/s

]

New York City Cycle

0 50 100 150 200 250 300 350 4000

5

10

15

time [s]

velo

city

[m/s

]2x ECE1 Type1

distance: 1.89 km, average speed: 11.4 km/h distance: 2.078 km, average speed: 18.7 km/h

Work [kWh]

Base Result: 137.347

Name Low High Delta

Accessory Power 136.2582072 138.435985

Rolling Resistance 135.945 138.749 #REF! #REF! #REF!

Frontal Area 135.7460582 138.948134

Drag Coeff. 135.7460582 138.948134 -2.804 42.374 39.570

Vehicle Mass 133.170 141.525 -8.355 45.149 36.794

Motor Eff. 143.430 131.844 -11.586 34.889 46.475

171 176 181 186

Frontal Area

Drag Coeff.

Rolling Resistance

Accessory Power

Vehicle Mass

Motor Eff.

Gear Eff.

Energy [Wh]

Electric Energy for Single NYCC

+5%

-5%

Motor Eff. 143.430 131.844 -11.586 34.889 46.475

Gear Eff. 143.430 131.844 -11.586 34.889 46.475

-5% +5%

131 136 141

Accessory Power

Rolling Resistance

Frontal Area

Drag Coeff.

Vehicle Mass

Motor Eff.

Gear Eff.

Energy [Wh]

Electric Energy for 2x ECE1 Type1

+5%

-5%

Work [kWh]

Base Result: 137.347

Name Low High Delta

Accessory Power 136.2582072 138.435985

Rolling Resistance 135.945 138.749 #REF! #REF! #REF!

Frontal Area 135.7460582 138.948134

Drag Coeff. 135.7460582 138.948134 -2.804 42.374 39.570

Vehicle Mass 133.170 141.525 -8.355 45.149 36.794

Motor Eff. 143.430 131.844 -11.586 34.889 46.475

171 176 181 186

Frontal Area

Drag Coeff.

Rolling Resistance

Accessory Power

Vehicle Mass

Motor Eff.

Gear Eff.

Energy [Wh]

Electric Energy for Single NYCC

+5%

-5%

Motor Eff. 143.430 131.844 -11.586 34.889 46.475

Gear Eff. 143.430 131.844 -11.586 34.889 46.475

-5% +5%

131 136 141

Accessory Power

Rolling Resistance

Frontal Area

Drag Coeff.

Vehicle Mass

Motor Eff.

Gear Eff.

Energy [Wh]

Electric Energy for 2x ECE1 Type1

+5%

-5%

48.0 50.0 52.0 54.0

Frontal Area

Drag Coeff.

Rolling Resistance

Accessory Power

Battery Capacity

No. Battery Cells

Vehicle Mass

Motor Eff.

Gear Eff.

Range [km]

City Car Range - NYCC

+5%

-5%

Drag Coeff.

Battery Capacity

No. Battery Cells

Vehicle Mass

Motor Eff.

Gear Eff.

City Car Range - ECE1 Type1

+5%

-5%

68.0 70.0 72.0 74.0 76.0

Accessory Power

Rolling Resistance

Frontal Area

Drag Coeff.

Battery Capacity

No. Battery Cells

Range [km]

+5%

-5%

48.0 50.0 52.0 54.0

Frontal Area

Drag Coeff.

Rolling Resistance

Accessory Power

Battery Capacity

No. Battery Cells

Vehicle Mass

Motor Eff.

Gear Eff.

Range [km]

City Car Range - NYCC

+5%

-5%

Drag Coeff.

Battery Capacity

No. Battery Cells

Vehicle Mass

Motor Eff.

Gear Eff.

City Car Range - ECE1 Type1

+5%

-5%

68.0 70.0 72.0 74.0 76.0

Accessory Power

Rolling Resistance

Frontal Area

Drag Coeff.

Battery Capacity

No. Battery Cells

Range [km]

+5%

-5%

Figure 3.6: Sensi vity analysis results table for two different urban driving cycles


Energy Consump on Sensi vity As for the sensi vity of the energy consump on, thetornado charts indicate that the drivetrain efficiencies, notably motor and gear efficiency, arethe most influen al parameters. This is not surprising considering the fact that efficienciescontributedirectly tothenecessarypoweroutput througha inverselypropor onal rela onship(eq.(3.16)). Almost equally significant is the vehicle mass, while the remaining parametersplay a minor role compared to the three top parameters in the chart. This trend is valid forboth considered driving cycles. However, it becomes apparent that the rela ve impact ofthe vehicle mass decreases from NYCC to ECE1. This is expected due to the fact that theNYCC models a more severe urban driving pa ern with considerably more accelera on andbraking phases as well as lower average velocity. Therefore, the accelera on resistance,and thus the vehicle mass, contributes more to the overall energy consump on in case ofthe NYCC. The higher accelera on resistance in the NYCC also results in 23% more energyneeded to complete a single NYCC compared to comple ng two ECE1 cycles, even thoughboth pa erns cover roughly the same distance. In addi on, the higher average velocityof the ECE1 leads to a considerable increase in the rela ve impact of the aerodynamicparameters, frontal area and drag coefficient compared to the NYCC. The rela ve influenceof the accessory power decreases at the same me, since the accessories have to besupplied constantly regardless of the driving condi on. The more stopping phases thereare and the lower the average velocity, the bigger is the influence of the constant accessorylosses. The absolute impact of a decrease in mass on the energy consump on of bothtest cycles is summarized in the following table.

NYCC 2x ECE1 Type1Base Energy Demand: 178.4Wh 137.4Whwith 5% less mass: 171.8Wh 131.2WhEnergy Decrease: 3.7% 3.0%

Table 3.2: Impact of mass reduc on on energy consump on for both test cycles

Whereas a 5% decreased vehicle mass results in a 3.7% decreased energy demand whenfollowing the NYCC pa ern, the 5% mass decrease only leads to a 3.0% reduc on in energydemand in the ECE1 driving pa ern.

Range Sensi vity The achievable range of a vehicle is closely linked to its energyconsump on. Therefore, the sensi vity of the vehicle range reveals very similar results tothe energy sensi vity. The three most significant parameters in both driving pa erns arethe drivetrain efficiencies and the vehicle mass, while the rela ve impact of the vehiclemass is considerably lower when assuming the ECE1 driving pa ern. Noteworthy is the factthat the vehicle mass remains more influen al than the ba ery size in both test cycles. Thisis rather to be assessed as qualita ve observa on that is only valid for lead acid ba eries,since the es ma on model goes back to a very simple lead acid ba ery discharge model.However, it can be established with certainty that the vehicle mass holds up as decisive


parameter. Comparing the base range in both test cycles reveals a 28% gap between NYCCand ECE1, which is consistent with the results from the energy consump on analysis. Thepoten al for extending the range through weight reduc on is summarized in the followingtable.

NYCC ECE1 Type1Base Range: 51.4 72.0with 5% less mass: 54.0 75.1Range Increase: 5.4% 4.3%

Table 3.3: Impact of mass reduc on on vehicle range for both driving pa erns

5.4% and 4.3% increase in range as a result of a mass reduc on by 5%, roughly translatesinto 1% range extension with every percent vehicle mass saved. Through further tes ng,it could be established that this conclusion remains valid up un l a weight reduc on ofabout 40%.

Regenera ve Braking In addi on to the sensi vity analysis of the energy consump onand vehicle range, a brief es ma on of the range extension poten al through regenera vebraking is performed. Using the simple implementa on of regenera ve braking in thedeveloped model and assuming a recupera on efficiency of ηrecup = 0.6 it is examinedhow the ba ery state of charge develops in the course of the applied test cycles. In Figure3.7 the state of charge with and without regenera ve braking is contrasted for both testcycles respec vely.

0 100 200 300 400 500 6000.975

0.98

0.985

0.99

0.995

1

time [s]

Sta

te o

f Cha

rge

[%]

Impact of Regen. Braking on SoC − NYCC

Without Regen. BrakingRegen. Braking

0 100 200 300 4000.975

0.98

0.985

0.99

0.995

1

time [s]

Sta

te o

f Cha

rge

[%]

Impact of Regen. Braking on SoC − 2x ECE1 Type1

Without Regen. BrakingRegen. Braking

Figure 3.7: Impact of Regenera ve Braking on the SoC during NYCC and 2x ECE1 Type1driving cycles

It can be seen how the two graphs gradually separate the further the vehicle progressesin the driving cycle, with the gap between the two graphs being larger in case of the NYCC.This is again expected, as there are simply more braking phases in the NYCC, which meansthere is more dissipa ng energy that can be recovered by a recupera on device. Whenonly considering the green curve, it can also be seen that the graph slightly recovers at

3.3 Summary and Conclusion 43

mes, which represents the recharging of the ba ery in case of braking. The direct impactof regenera ve braking on the achievable range is summarized in Table 3.4.

NYCC 2x ECE1 Type1Base Range: 51.4km 72.0kmwith Regen. Braking: 59.6km 78.4kmRange Increase: 14% 9%

Table 3.4: Impact of regenera ve braking on achievable range

The poten al of regenera ve braking for extending the range is 50% higher whenconsidering the NYCC compared to the ECE1, which further supports the significance ofthe driving pa ern on the energy efficiency characteris cs.

3.3 Summary and ConclusionThe objec ve of this chapter has been analysing the performance of the current NUS CityCar design in terms of range and energy consump on under the assump on of an urbandriving environment. As such, it was of par cular interest to determine the influence of thevehicle mass on the vehicle range, as the inten on of this work is eventually the reduc on ofthe vehicle’s mass in order to maximize its range. Therefore, a simple energy consump onand range es ma on model has been developed. This model is capable of es ma ng therange of an electric vehicle with basic vehicle parameters and driving pa erns as input.The model has been validated through comparison with a reference model extracted fromthe PSAT so ware. The model indicates that the current configura on of the NUS City Caris able to achieve about 50km in an extreme urban driving pa ern, while this figure doesnot include a considera on of the grade level of the track.

Based on this model, a sensi vity analysis for the energy consump on and the vehicle rangehas been performed. Here, it was of interest on the one hand to determine the poten alof extending the range through weight reduc on. On the other hand, it was desired toillustrate the rela ve significance of the vehicle mass on range and energy consump oncompared to the remaining vehicle parameters such as aerodynamics and rolling fric on.Therefore, each relevant input parameter was varied by +5% and -5% of its base valueand the respec ve model output was computed with all remaining parameters remainingconstant. The result was illustrated by tornado charts. This analysis was done for twodifferent urban driving pa erns (NYCC and ECE1). The outcome of the parameter studyis that the drivetrain efficiencies are most influen al, with the vehicle mass being almostequally influen al especially when assuming the NYCC driving pa ern. All remaining vehicleparameters contribute only to a li le extend to the energy consump on and the achievablerange. The ba ery size on the other side can extend the range to considerable degree. Itcan also be concluded that the vehicle mass becomes more significant the more the drivingpa ern is characterized by frequent accelera on and braking phases. In other words, the


vehicle mass is most influen al when the vehicle is mainly operated in an highly urbanenvironment. On average, a remarkable 1% range extension can be achieved with everypercent vehicle mass saved. It was established that this rela onship remains linear up toroughly 40% weight reduc on, while one has to bear in mind that it is applies only for purecity driving condi ons. This conclusion is also valid for the drivetrain efficiency. However,it is considerably more difficult to improve the drivetrain efficiency by one percent thanreducing the weight by one percent. Therefore, the conclusion is drawn that reducing theweight is the most reasonable approach to improving the current NUS City Car design interms of energy consump on and range. The ini al assump on has hence been confirmed.

In addi on it was studied how regenera ve braking can contribute to an improvement ofthe vehicle’s range in a future design itera on. It could be established that a recupera ondevice with an efficiency of 0.6 can result in 9% - 14% range extension depending on thedriving pa ern.

4 Determina on of a Component for a Topology Op miza on

The sensi vity analysis performed in the previous chapter has illustrated how the totalweight significantly influences the energy consump on and the range of an electric vehicle.It was highlighted that in an urban environment, weight reduc on is the most promisingstar ng point for improving the range of the NUS City Car. Every percent that is saved intotal vehicles mass results in about 1% improved range, which means that the current NUSCity Car design can be improved from 51km to 54km just by reducing the total weight by5%. This would be a relevant improvement considering that there might be even moreweight reduc on poten al. In this context, the present work studies the weight reduc onpossibili es through structural op miza on of vehicle components. Therefore, this chapterdescribes the process of analyzing the present vehicle configura on and the selec on of apar cularly promising vehicle component for a subsequent structural op miza on.

4.1 Implementa on of the Selec on ApproachIn order to determine suitable components for a structural lightweight op miza on it isessen al to capture the current status of the chassis components in terms of individualweight. This gives a first reference to components that are worth to be inves gatedfurther due to their high contribu on to the overall vehicle mass. However, the componentweight cannot be the only criteria. When studying the composi on of the major chassiscomponents, it becomes quickly obvious that certain components might have a high massbut are simply not prac cal for a structural op miza on. This especially includes electricalcomponents, such as ba ery or controllers as well as mechatronical systems like the motor.Other components are generally suitable for an op miza on but might be already op mizedto some extent, which makes them generally less interes ng for this considera on, sincethey promise less poten al for a weight reduc on. The main objec ve of this thesisis the weight reduc on through structural op miza on of selected chassis components.Hence, it makes sense to put the captured components into categories that indicatetheir feasibility and poten al for structural op miza on. This second criteria is termedop miza on ap tude in the framework of this thesis. The result is a simple approachthat includes two criteria, component weight and op miza on ap tude, to determinesuitable components. In the following the implementa on of this approach is describedand the results subsequently visualized, using Treemaps and ABC-analysis. The results ofan internal PKT study, dealing with the development of methods for the integra on offunc ons for an op mized lightweight design, served as major input for this part [Pla10].

4.1 Implementa on of the Selec on Approach 46

The developed methods include the evalua on of the poten al of system components interms of func on integra on. In this work, these results are applied on the componentselec on for a structural light weight op miza on.

A cri cal step of the applied approach is the defini on of the ap tude categories. Havingonly a few categories that simply indicate verbally the degree of the op miza on ap tudebears the risk of biased results depending on how the components have been allocated tothe categories. Naturally, one would tend to allocate them according to “common sense“asa result of experience. However, this approach would favor components that have alreadybeen considered right from the beginning without applying any structured methods, whileother less obvious components might be overseen. Therefore, it is a empted to make thecategory defini on and alloca on less influenced by the personal percep on. In [Pla10]the component material is defined as major property influencing the poten al for weightreduc on. This is also a useful indicator for the purpose of structural op miza on. Thematerial not only indicates the component density, but also its structural proper es. Unlikein [Pla10] where each individual piece part of the analyzed system is considered, the analysishere is reduced to component level. This is necessary because the number of piece partsis comparably high due to the complexity of the vehicle system. Moreover, the focus ofthis work lies in the topology op miza on of vehicle parts not on a complete capture andanalysis of all vehicle components. A full scale piece part analysis including weighing eachpart is considered imprac cal within the work scope of this thesis. In addi on, severalvehicle parts are yet undefined or unfinished and their mass has to be guessed, whichmakes a full scale piece part analysis further unfavorable.

Since the components partly consist of mul ple parts, not every component can be clearlyassigned to one material. However, o en the components comprise only a few major partsthat represent the main share of the total weight. Therefore, the component material canbe s ll used as reference for crea ng op miza on ap tude categories. All componentsthat are mostly made of steel are generally considered to be highly suitable for structuralop miza on. This also includes components like the seats, since their weight is largelydefined by the steel structure rather than the cushions. Steel components are assigneda high ap tude because steel has a high density and high strength, which might not benecessary for certain components. Components made of aluminum or even carbon fibrereinforced plas cs (CFRP) suggest less poten al as they are less dense and might havebeen already lightweight op mized. For instance, the CFRP body shell does not hold muchpoten al, since the shape is predefined and the currently used material was already alightweight design driven choice (material lightweight design). In addi on to the material, itis also considered to what extent the design and the manufacturing of the components canbe influenced considering the available workshop and know-how. Therefore, specializedisolated components like brakes, shock absorbers or wheels are also considered as lesssuitable. These components are comparably complex and feature a high diversity ofmaterials and parts, which makes it difficult to perform a structural op miza on. Instead,

4.2 Visualiza on of Collected Data 47

these systems are considered fixed, as they are bought externally according to availabilityand budget. Lastly, there are electrical and mechatronical parts, like the motor, the ba eryor the motor controller, which are least applicable for structural op miza on because theyare also too complex and their design mainly depends on electronic requirements ratherthan structural ones. Hence, the defined categories sum up to five. The hierarchy of theseap tude categories is indicated by the legend in Figure 4.2. All components are addi onallyallocated to superordinated subsystems in order to further structure the collected data.The result is a table consis ng of 23 components organized in six superordinated assemblygroups, where each component has been weighted and assigned to an op miza on ap tudecategory based on the component material and complexity. The table can be found inAppendix C.

4.2 Visualiza on of Collected DataThe next step a er collec ng and structuring the data is the visualiza on. A well presentedillustra on of the database can significantly support the process of drawing conclusions.In [Pla10] several visualiza on aids are reviewed and evaluated, where the so calledTreemaps have been pointed out as par cularly capable illustra on tool for the proposedapplica on. Treemaps are also applied at this point. Another well established method forthe determina on of weak system links is the ABC-Analysis. In order to complement thevisualiza on through Treemaps, an ABC-analysis is addi onally performed.

Treemaps The principle of Treemaps originates from the development of a compactvisualiza on of directory tree structures in 1990. The objec vewas tomonitor the occupa onof shared hard disk space structured a er user, directory and file size as hierarchicalmeasure [Shn98]. The result was a algorithm that can hierarchically illustrate thousands ofdata entries along with addi onal proper es simultaneously on a limited surface area. Thealgorithm essen ally splits the screen into rectangles in alterna ng horizontal and ver caldirec on. Each rectangle reflects one data entry, while its size represents its hierarchicalvalue. A second dimension can be implemented through the use of colors indica ng theproper es of each entry. Out of this idea, a comprehensive tool that enables more func onsfor further manipula on of the visualiza on has been developed. Nowadays, Treemapsare a common way of illustra ng complex hierarchical data sets such as financial figures[Pla10]. The genera on of Treemaps can be performed without difficulty with the helpof the Treemap so ware provided by the University of Maryland [Shn98]. Therefore, thecaptured weight data (see Appendix C) is transfered into a compa ble database formatand subsequently imported into the Treemap so ware. Figure 4.1 illustrates the resultsof the Treemap algorithm for an one dimensional considera on. One dimensional meansthat the shown colors do not represent component proper es. Instead, they support theillustra on of the hierarchical order according to the component weight.


TreeMap_NUSCC.tm3

NUS City Car

Energy Storage

Battery Battery Battery

Battery

Battery

Battery

Battery Battery

Battery

Battery

Battery

Battery

Chassis Frame

Frame Body Shell Seat incl. Cushion

Seat incl. Cushion Wires

Power Train

Motor

MotorMount Drive

Gear

Controlle

Rear Assembly

Swingarm Wheel (rear) Sus

pen

sion

Bra

Front Assembly

Wheel

(front)

Wheel

(front)

Double

wishbo

ne

Double

wishbo

ne

Sus

pen

Sus

pen

Bra Bra

Controls

Steering

Wheel

Steering

Rag&Pinion

Braki

ng

Steerin

Emerg

Thrott

NUS City Car

Energy Storage


Battery

Battery

Battery

Battery Battery

Battery

Battery

Battery

Battery

Chassis Frame



Power Train

Motor

MotorMount Drive

Gear

Controlle

Rear Assembly


pen

sion

Bra

Front Assembly

Wheel

(front)

Wheel

(front)

Double

wishbo

ne

Double

wishbo

ne

Sus

pen

Sus

pen

Bra Bra

Controls

Steering

Wheel

Steering

Rag&Pinion

Braki

ng

Steerin

Emerg

Thrott

TreeMap_NUSCC.tm3

NUS City Car

Energy Storage


Battery

Battery

Battery

Battery Battery

Battery

Battery

Battery

Battery

Chassis Frame



Power Train

Motor

MotorMount Drive

Gear

Controlle

Rear Assembly


pen

sion

Bra

Front Assembly

Wheel

(front)

Wheel

(front)

Double

wishbo

ne

Double

wishbo

ne

Sus

pen

Sus

pen

Bra Bra

Controls

Steering

Wheel

Steering

Rag&Pinion

Braki

ng

Steerin

Emerg

Thrott

min max

Mass

Figure 4.1: Treemap for NUS City Car component weight

Each of the shown rectangles stands for one component, with its size indica ng theweight of the respec ve component, while the total area reflects the total weight of thevehicle. In addi on, bright rectangles indicate a heavy component while dark ones suggestlight ones. This illustra on clearly points out the chassis frame and the motor as theheaviest single components. Also apparent is the large share of the ba ery pack, whichmakes up more than half of the en re vehicle weight. However, as men oned before, theweight cannot be the only criteria taken into considera on.

Therefore, the colors are now u lized to illustrate a second dimension, in this case thepreviously defined op miza on ap tude based on the component material and complexity.Through the color code in Figure 4.2, it is possible to easily dis nguish the componentsaccording to their assigned op miza on ap tude category. The green rectangles representsteel components, which have the highest op miza on ap tude according to the previouslymade assump ons. The Treemap allows the comparison of the weight for each of thesecomponents with respect to the overall vehicle mass. Comparing the size of all steelcomponents reveals that the chassis frame together with the seats, suggest the highestweight reduc on poten al.


TreeMap_NUSCC.tm3

NUS City Car

Energy Storage


Battery

Battery

Battery

Battery Battery

Battery

Battery

Battery

Battery

Chassis Frame



Power Train

Motor

MotorMount Drive

Gear

Controlle

Rear Assembly


pen

sion

Bra

Front Assembly

Wheel

(front)

Wheel

(front)

Double

wishbo

ne

Double

wishbo

ne

Sus

pen

Sus

pen

Bra Bra

Controls

Steering

Wheel

Steering

Rag&Pinion

Braki

ng

Steerin

Emerg

Thrott

NUS City Car

Energy Storage


Battery

Battery

Battery

Battery Battery

Battery

Battery

Battery

Battery

Chassis Frame



Power Train

Motor

MotorMount Drive

Gear

Controlle

Rear Assembly


pen

sion

Bra

Front Assembly

Wheel

(front)

Wheel

(front)

Double

wishbo

ne

Double

wishbo

ne

Sus

pen

Sus

pen

Bra Bra

Controls

Steering

Wheel

Steering

Rag&Pinion

Braki

ng

Steerin

Emerg

Thrott

TreeMap_NUSCC.tm3

NUS City Car

Energy Storage


Battery

Battery

Battery

Battery Battery

Battery

Battery

Battery

Battery

Chassis Frame



Power Train

Motor

MotorMount Drive

Gear

Controlle

Rear Assembly


pen

sion

Bra

Front Assembly

Wheel

(front)

Wheel

(front)

Double

wishbo

ne

Double

wishbo

ne

Sus

pen

Sus

pen

Bra Bra

Controls

Steering

Wheel

Steering

Rag&Pinion

Braki

ng

Steerin

Emerg

Thrott

Steel Aluminum CFRP Fixed Electric

+ + + 0 - - -

Optimization

Aptitude

Figure 4.2: Treemap for NUS City Car component weight

This is somewhat expected, considering that the frame is the heaviest single componentand that the currently available seats have been obtained from a discarded compact car.These seats are designed to stand alone within the passenger compartment, holding thepassenger mainly independently from the surrounding chassis structure. This does notseem prac cal in case of a small two seater car. It appears that an integra on of theseat-backrest into the chassis frame has a significant weight reduc on poten al (systemlighweight design). Other steel components that stand out due to their rectangle sizeare the rear suspension swing arm, the motor mount and the doublewishbone assembly.The red rectangles represent electrical and mechatronical components, which have beendeclared as not applicable for structural op miza on. That means that the motor, as thesecond most heavy component is not further considered. The same applies for the ba erypack consis ng of 12 lead acid ba eries, which make up roughly half of the total vehiclemass. However, the illustra on through Treemaps further supports the conclusion that theba ery selec on plays a major role in defining the overall vehicle weight. Due to its largesurface area, the body shell (blue color) appears as another comparably heavy component.However, since it was already subject to material lightweight design by applying lightweightcarbon fibre reinforced panels, the body shell is also excluded. Due to the small rectangle


size of all remaining components, the Treemap indicates that these components only playa minor role in the overall vehicle mass, which is why they are not further discussed.

ABC-Analysis The ABC-Analysis is based on the assump on that in every considered seta small number of elements has a large share of the general appearance [Lin09]. Applyingthis concept on a weight analysis means, it is assumed that only a few vehicle componentsmake up a large share of the total weight. The objec ve of the ABC-Analysis is a simpleclassifica on of the considered components into classes according to their specific shareof the analyzed characteris c. Those components with the largest specific shares aregrouped in class A while those with the smallest shares form class C. In between lie thecomponents of class B. It is assumed that class A summarizes the components that arecharacterized by the most structural weak spots in terms of the analyzed characteris c.Therefore, it is these components that show the most poten al for an op miza on of theanalyzed product. However, in [Lin09] it is also pointed out that this conclusion has to beconfirmed for each individual component through single case qualita ve analysis, as theABC-Analysis only allows quan ta ve conclusions. The following procedure for performingan ABC-Analysis is suggested by [Lin09]:

• Determining the analyzed element characteris c• Ranking of the elements according to the analyzed characteris c• Grouping the components into the three classes: class A roughly comprises 20% ofthe elements with 80% of the analyzed variable while class C is made up by about50% of the elements with only 5% of the analyzed variable.

Applying this approach on the collected database of Appendix C leads to the followinggraph, at which mul ple components such as the ba eries are summarized to one element.

0

50

100

150

200

250

300

We

igh

t [

kg

]

ABC-Analysis for entire Vehicle

A -Class B -Class C -Class

Figure 4.3: ABC-Analysis for the collected data

The graph highlights similar rela onships as seen before in the Treemaps. The fourA-Class components comprise the ba ery pack as the dominant element along with thechassis, motor and seats. However, due to the nature of this quan ta ve illustra on, itdraws the a en on solely to these four components, while all other components remain


unrecognized. The Treemaps are therefore considered the favorable visualiza on aid asthey are not limited to emphasizing on a few elements. In addi on, they allow theillustra on of a second element property using different colors. Although, the graph fromthe ABC-Analysis could be also complemented by a color code, its general appearanceas bar chart makes it comparable hard to clearly dis nguish the colors. Hence, it is notpossible to indicate the second hierarchy of a second component feature.

However, the ABC-Analysis could be applied to support the results from the Treemapinterpreta on. During the capture of the database for this chapter, each componentwas categorized according to its ap tude for a structural op miza on, while basic steelcomponents were pointed out as most suitable. Due to this defini on, it can be assumedthat it is steel components that will be shortlisted as already seen in the interpreta onof the Treemaps above. Therefore, it makes sense to perform an ABC-Analysis just forall steel components of the database. In this case, the A-class elements comprise onlycomponents that are actually applicable for a topology op miza on. The drawback isthat one might lose track of all remaining components, while concentra ng solely on thecomponents with high ap tude. This could lead to an overes ma on of the overall weightreduc on poten al of the steel parts, which is why this addi onal ABC-Analysis is meantto complement and not replace the Treemaps. The ABC-Analysis for the steel componentsis shown in Figure 4.4. Here, it becomes apparent that it is the seats and the framethat are the most promising components. While the Treemaps also highlight these twocomponents, this addi onal ABC-Analysis allows a be er quan ta ve comparison of theshortlisted components from the Treemap interpreta on.

0

10

20

30

40

50

60

We

igh

t [k

g]

ABC-Analysis for Steel Components

A -Class B -Class C -Class

Figure 4.4: ABC-Analysis for steel components only

4.3 Summary and ConclusionThe objec ve of this chapter was to determine suitable vehicle components for a weightreduc on through structural op miza on. The component suitability was defined as acombina on of both component mass and op miza on ap tude, while the op miza on


ap tude was introduced as indicator for the weight reduc on poten al and op miza onfeasibility of a component. Therefore, all major vehicle components were weighted andput into an op miza on ap tude category. Simple components that are comparably heavyand made of high density material were considered highly suitable. Complex componentslike shock absorbers or electrical devices were declared as not prac cal for a structuralop miza on regardless of their mass or density, while components with low mass weregenerally excluded from a further discussion. The assembled database has been illustratedusing Treemaps and ABC-Analysis, while both methods deliver similar trends. However, theTreemaps appear to provide the more comprehensive visualiza on, due to their ability toillustrate the mass of all components and one of their proper es at the same me. Itwas also shown, that an ABC-Analysis can be applied to complement the results from theTreemap interpreta on.

The interpreta on of these visualiza on results suggests that it is the large basic steelcomponents, which are most suitable for structural op miza on. According to Figure4.4 this especially includes the frame and the seats of the vehicle. Out of these twocomponents, the frame contributes to most of the total weight, which is why the frame ischosen to be op mized using structural op miza on methods.

Figure 4.5: Current chassis frame design before the op miza on process

Facts of the Current Design

• Welded tubular steel space frame• Combina on of rectangular and round tubes• Cross sec on diameter/widths: 12.5mm-38mm• Constant wall thickness: 2mm• Inside box measurements: 1875mm x 1220mm x 850mm• Total mass: 55kg

5 Structural Op miza on of the Chassis Frame

Reducing the mass of vehicles is an ongoing topic in the automo ve industry, in par cularamong manufactures that specialize in highly efficient low emission vehicles. Makingthe vehicle lighter not only improves its general handling and performance, but alsoreduces the energy consump on and the pollutant emissions in the overall energy balance.Furthermore, electric vehicles greatly benefit from weight reduc on in terms of achievablerange, especially when operated in city areas. This was studied extensively in Chapter 3based on the current NUS City Car design. At the same me, a reduc on of the vehiclemass is usually accompanied by a reduc on in the safety performance as less materialgenerally results in less structural strength. In Sec on 2.5, topology op miza on wasintroduced as useful tool to address this problem, making it possible to reduce the massof vehicle components with respect to given performance targets, for example in termsof s ffness, strength or crashworthiness. In the previous chapter, the chassis frame wasselected as the most suitable vehicle component for structural op miza on with regardsto feasibility and weight reduc on poten al. Many works revolving around applica ons ofstructural op miza on in automo ve design have emerged in the recent past, includingpublica ons that focus on the op miza on of vehicle body structures.

Yildiz et al. (2004) [Yil04] propose a general approach for topology op miza on of vehiclecomponents using the example of an engine mount bracket. Jang et. al (2010) [Jan10]address the op miza on of a flatbed trailer by maximizing its bending s ffness and torsionalfrequency through topology op miza on and subsequent thickness op miza on. Gauchiaet al. [Gau10] propose a structural op miza on of a real bus structure using gene calgorithms in combina on with the finite element method with the objec ve of reducedweight and improved torsional s ffness. Reed (2002) [Ree02] and Van Hooreweder (2008)[vH08] describe a very similar approach to designing a completely new vehicle frame basedon a previous design itera on. Therefore, various sta c load cases, including linearizedcrash situa ons, are considered and the weighted compliance of all load cases is beingminimized. Cavazzu et al. (2010) [Cav10] present a more advanced methodology, applyingtopology op miza on, topometry op miza on and size op miza on in cascade for reachingan op mum chassis configura on of an high performance vehicle. For the topologyop miza on a 3D design space is defined giving the op miza on process a maximum offreedom. Op miza on constraints include maximum displacements of certain chassis partsdue to bending, torsion and linearized frontal crash as well as the natural frequency ofrelevant mode shapes, while the volume is to be minimized.

5 Structural Op miza on of the Chassis Frame 54

The present work approaches the structural op miza on problem in four stages, beginningwith the iden fica on of the relevant load cases. Based on this load case analysis, theFE-model and the op miza on problem formula on is developed in the second stage. Here,general issues such as the ques on if a 2D or 3D element design space is to be used orhow the objec ve func on is to be defined are addressed. Building on these findings, thefinal op miza on setup is derived and the results are interpreted in the following stage.The results from the topology op miza on give a good picture of the op mal loca on ofthe chassis frame members. In order to also find the op mal cross sec onal dimensionsof the frame members, a size op miza on is lastly performed based on a beam model.

Figure 5.1: Different stages of performed structural op miza on

The proposed methodology follows a top-down approach in a way that the numberof design variables is gradually reduced according to func onal, physical (componentarrangement) or manufacturing requirements. This is done by gradually reducing the designspace freedom, first from 3D to 2D and eventually by adding more and more non-designelements where necessary. This ensures that the designer keeps track of the op malsolu on from a pure structural point of view, which could be u lized when defining therequirements in future projects (e.g. loca on of components). At the same me, thisapproach might inspire the designer to consider unconven onal designs, which would havebeen overseen when restric ng the design space too severely right from the start.

Before the op miza on process is described in the subsequent sec ons, a few relevantdesign requirements that influence the op miza on are summarized as follows:

• Like the current design, new frame is a welded tubular space frame• Two occupants can be accommodated comfortably• The exis ng vehicle components, such as suspension, pedals and steering arecompa ble with the new design

• Up to 12 ba eries of the standard SLI ba ery size can be accomodated

5.1 Iden fica on of Load Cases 55

• Material choice from supplier: ASTM A-500 tubing steel, aluminum alloy AA-6061 T6

5.1 Iden fica on of Load CasesThe star ng point for every structural op miza on is the iden fica on of all relevant loadcases (LC) . The resul ng structure is specifically op mized to sustain the defined loadcases, which means that an inaccurate or even incomplete load defini on is likely to leadto an insufficient and moreover inefficient material distribu on. It is therefore essen alto carefully study the possible load condi ons. The chassis frame of a road vehicle issubject to a great variety of sta c and dynamic loads. This includes global loads that areexerted on the en re structure through the suspension from standard driving situa onsas well as local loadings such as bracket forces, hinge loads or loads on suspension andcomponent moun ngs. In addi on, it is required that in the event of a crash, the passengercompartment suffers limited deforma ons to ensure the safety of the occupants. Dueto their non-elas c nature, crash situa ons have to be considered separately. Therefore,this sec on analyses basic vehicle load condi ons due to standard driving situa ons withreference to a three wheeled vehicle in the first part, The second part addresses theconsidera on of crash impacts in the context of structural op miza on.

5.1.1 Sta c and Dynamic Loads

An o en cited work on vehicle structures in an early design stage is Pawlowski (1969)[Paw69]. Though this work was not available in the framework of this thesis, it wasfound as reference in various reviewed publica ons (e.g. [Bro03, Hap01, Boo]). Theseauthors consider sta c global load cases that affect the whole vehicle structure and focuson determining the worst possbile loading that can be encountered in each load case.It is assumed that the structure also has sufficient fa gue strength when designed forwithstanding these maximum instaneous loads. Since a road vehicle structure generallysuffers dynamic loading with constantly changing load magnitudes and direc ons, it iscommon to adjust the determined sta c loads through dynamic load factors:

dynamic load = sta c load× dynamic load factor

The principal global road load cases as they are considered in this work are summarizedas follows:

• Ver cal loading: Caused by symmetric and asymmetric gravita onal forces• Longitudinal loading: Caused by breaking, accelera on or obstacles• Lateral loading: Caused by cornering or side wind

In the following, the basic global load cases are analysed by applying simple vehicledynamics and mechanics in order to determine reasonable maximum loads. The magnitudeof global vehicle loads is o en expressed as mul ple of the gravita onal accelera on g.These accelera ons are the basis for the transla on of iner a masses into forces ac ng


on the vehicle structure. In this context it is noteworthy that the unsprung masses suchas wheels, res, brakes, suspension arms and shock absorbers rest on the ground directly,without intervening the vehicle structure. As a result of this, they are not considered inthe following sec ons. That means all following references to the vehicle mass M denotethe sprung mass of the vehicle, which includes all components and subsystems that donot rest on the ground [Gen09a]. Moreover, the founda on of the following load caseanalysis is the determina on of the preliminary center of mass loca on of the vehicle. Thisis addressed in Appendix D under the considera on of the proposed new frame design.

5.1.1.1 Ver cal Loading

Ver cal loads resul ng from the weight of major vehicle components, passengers or payloadare generally considered as dominant load cases when designing a vehicle structure [Hap01].These loads can be significantly amplified due to dynamic vehicle behaviour as result ofuneven road surfaces or road bumps. Therefore, [Bro03] suggests a dynamic load factorbetweenK = 2.0− 3.0 for adjus ng the sta c loads. In general, it is dis nguished betweensymmetrical ver cal loading, also referred to as bending, and asymmetrical ver cal loadswhich results in torsion of the vehicle body. Figure 5.2 shows a free body diagram of thevehicle structure under pure ver cal loading.

x y

z

Fl

Fr

Rlh

Mg

lf + lh = wblf

Figure 5.2: Global ver cal loads on free body vehicle structure

Symmetric Load - Bending In a symmetric load case, the respec ve sta c axle loads arequickly determined through the sta c equilibrium equa ons:

F = Fr + Fl =e

lf + lh·M g Fr = Fl (5.1)

R =lf

lf + lh·M g (5.2)

Alterna vely, one could perform this analysis in more detail assuming eachmajor componentas individual center mass placed along the x-axis. This would allow to create bending


moment and shear force diagrams, which give a good first approxima on for the stresscondi ons of the structure along the x-axis [Bro03]. However, this is not done here, sincethis analysis primarily serves to explain general load condi ons.

Asymmetric Load - Torsion Asymmetrical ver cal load cases can arise from severalsitua ons. A simple example is when one wheel of the front wheel passes over a roadbump while the remaining wheels remain in their original posi on. As result of the upwardmovement of the single wheel, a torque around the x-axis is applied to the body structure.Since the city car is based on a three wheel concept, only the front axle can be subject toa torsional load due to standard driving condi ons. The three wheel design makes the cargenerally less recep ve for torsional loads from standard road condi ons if compared tostandard four-wheel cars. To illustrate this, the maximum sta c torque applied to one axleof a four-wheel vehicle is derived in the following:

When a single wheel of a standard passenger car is slowly passing over a bump, there isload transfer between the four wheels. Depending on the torsional s ffness of the en revehicle system and the bump height, one wheel is eventually being elevated above theroad surface. Noteworthy is that it is always one wheel of the lightest loaded axle whichli s off. This situa on can be easily simulated with an ordinary chair or similiar structures.In case one wheel of the lighter loaded axle passes over the bump, it is the oppositewheel that eventually li s off. In this situa on, the en re axle load rests on the wheel onthe bump imposing a torque around the x-axis. Figure 5.3 illustrates this situa on in asimplified scheme.

Vehicle Body

Heavy Axle

Light Axle

tr

Fr = 0 Fl = FAxle

Tmax

x y

z

Figure 5.3: Wheel loads and torque on axle when passing over road bump

Hence, the maximum sta c torque Tmax from standard driving condi ons results in:

Tmax = FAxle ·tr

2(5.3)

However, bumps have a different effect on three-wheel vehicle. Since the structure isalready supported by only three wheels, none of the remaining two wheels li s off in caseof a bump encounter. The occurring load transfer is just a result of the displaced vehiclecenter mass due to the bump eleva on and can be neglected. In addi on, the three wheel


design prevents the possible load case of two bumps eleva ng two diagonal wheels atthe same me. A three wheel vehicle is, however, subject to severe torsional loads whena single wheel of the two wheel axle strikes a road bump while the vehicle is movingwith a notable velocity. In this case, one side of the vehicle is accelerated ver cally bya shock load induced through the suspension system causing asymmetric bending on thestructure. A road bump hi ng the rear axle wheel or both front wheels on the other handonly results in a symmetric bending situa on of the chassis structure. However, dynamicbump encounters not only accelerate the structure ver cally. Due to the geometry ofbumps, they will also result in a longitudinal load. Since these dynamic bump loads areregarded as major vehicle loads, they are considered into more detail in Sec on 5.1.1.4.Another driving situa on causing torsional loads on the vehicle body is steady cornering.The centrifugal accelera on leads to a load transfer between the wheels on the front axle.In the extreme situa on of p over, the en re front axle loads rests on the outer wheel,simula ng the situa on described in Figure 5.3. Since cornering also causes severe lateralloads, it is analyzed into more detailed under 5.1.1.3. Ver cal loads, par cularly asymmetricones, are considered as prime vehicle loading condi on. Vehicle structure design is o encentered around achieving a high torsional and bending s ffness. On the one hand, thisis beneficial for the overall handling of the vehicle. On the other hand experience showsthat a vehicle body with high torsional and bending s ffness is sufficiently strong for allpossible load condi ons [Hap01].

5.1.1.2 Longitudinal Loading

Longitudinal vehicle loads primarily result from iner a forces generated by the accelera onor decelera on of the vehicle as well as from hi ng road obstacles. Addi onally, the vehiclestructure is affected by the drag force ac ng on the body shell. However, the magnitudeof the drag force is comparably small. Considering the vehicle parameters established inTable 3.1 and applying them to eq. (2.2), the drag force at maximum speed 22 m/s onlyadds up to:

Fdrag = 0.5 · 1.2 · 1.5 · 0.6 · 222 = 260N (5.4)

Hence, the drag force is neglected in the follwoing considera ons. Figure 5.4 displays thevehicle as rigid body under longitudinal and ver cal loads. The fric on force at the contactpatch area between re and road is propor onal to the ver cal axle load through thelongitudinal fric on coefficient µx.

Fx ≤ µx · F (5.5)

Since the center of mass of the vehicle is offset by the ver cal distance h from theroad surface, there will be a weight transfer from one axle to another under longitudinalaccelera on. While braking, the weight is transferred from the rear to the front wheelsand vice versa for the accelera on of the car.


x

z

R F=(Fl+Fr)

h Mg

Ma

FxRxlh lf

Figure 5.4: Global longitudinal loads on rigid vehicle structure

Experience shows that the maximum braking decelera on is eventually limited by thefric on coefficient between re and road surface [Hei08], whereas the peak accelera on ofthe examined car is mainly limited by the maximum power output of the motor. The fric oncoefficient is influenced by various parameters and cannot be easily determined analy cally.Therefore, a design decelera on is established which serves as upper limit for the brakingdecelera on provided by the braking system under ideal condi ons. Official regula ons forbraking systems imposed by transporta on authori es served as first reference for such amaximum decelera on. In the European Union, passenger cars are required to enable amean decelera on of at least 0.6g [Eur]. Similar values are regulated in US and Japanesedirec ves. However, car manufacturers generally design their braking systems well abovethis value in order to increase the safety [Hei08]. Brown (2002) [Bro03] makes furtherreferences to different authors ranging from 1.1 to 1.8 mes the gravita onal accelera onas peak braking load. Considering the city car is not designed for racing performance andthe regula ons require a comparable low minimum braking performance, a peak declara onof a = 1g is regarded as realis c maximum value for the final city car prototype. Usingthe nota on in Figure 5.4 the force and moment equilibrium equa ons lead to:

F =M g · lh +M a · h

lf + lhR =

M g · lf −M a · hlf + lh

(5.6)

Equa on (5.6) represents the load transfer between the two vehicle axles depending onthe magnitude and direc on of the vehicle accelera on. The reac on forces Fx and Rx asa result of the fric on between re and road can be derived for the border case when thewheels are just about the slip at the given peak braking decelera on a. Assuming that thelongitudinal fric on coefficient is equal at all wheels, the force equilibrium equa ons yield:

M g = F +R (5.7)

M a = µx · (F +R) (5.8)

With equa on (5.7) and (5.8), one can determine the fric on coefficient as ra o between


the gravita onal accelera on and the maximum vehicle accelera on in the border case.

M a = µx ·M g ⇒ µx =a

g(5.9)

Therefore, the maximum longitudinal reac on forces Fx andRx can be expressed as follows:

Fx =a

g· F Rx =

a

g·R (5.10)

For the accelera on of the car, the load condi ons are slightly different. Since it ischaracterized by a single wheel drive, only the rear wheel is subject to longitudinal loads.That means the longitudinal reac on force at the rear wheel simply wri en as:

Rx = M · a (5.11)

The ver cal wheel loads due to accelera on can be determined analog to the wheel loadsduring braking using eq. (5.6). The peak accelera on of the NUS City Car cannot bedetermined accurately at this point. Es ma ons indicate that it is about 2− 3m/s2, whichcan be translated into about 0.3g.

5.1.1.3 Lateral Loading

A typical driving situa on that causes lateral loads on the vehicle body is the cornering.The most extreme cornering situa on occurs when the vehicle is just about to p over.This situa on is generally considered as peak lateral loading condi on [Hap01]. The lateralaccelera on of the cornering vehicle results in a load transfer from the inner to the outerwheel of the front axle. In case of p over, the inner wheel load will eventually reach zero,which means that the en re front axle load is supported by the outer wheel. Appendix Adescribes this situa on into more detail as part of a discussion on the dynamic behaviourof three wheeled vehicles. Figure 5.5 illustrates the border case of the vehicle pping overfor a considera on of the occurring loads.

Figure 5.5: Tipping over due to lateralforce Figure 5.6: Vehicle top view

under lateral loads


For an es ma on of the peak cornering loads, it is assumed that the res cannot slide inlateral direc on (outer wheels are constrained sideways). This ensures that the simulatedsitua on also covers the possibility of striking a bump in lateral direc on while sliding. Theresul ng model delivers a good approxima on of the maximum sta c lateral loads on thevehicle structure due to normal driving condi ons. With the en re sta c front axle loadres ng on the outer wheel, the outer wheel reac on force yields with eq. (5.1):

Fl =lh

lf + lh·M g (5.12)

while the rear wheel load remains unchanged compared to the sta c bending case (eq.(5.2)). Therefore, the front axle is under asymmetric ver cal load as described in Figure5.3. The lateral reac on forces Fl y and Ry depend on the maximum lateral accelera onwhen the vehicle is about to p over. This p over accelera on ato is derived for threewheeled vehicles as mul ple of the gravita onal accelera on in equa on in Appendix A.Thus, the peak lateral force Flat is equivalent to the product of the unsprung mass andthe p over accelera on:

Flat = M · ato (5.13)

Through the moment and force equilibrium equa ons from Figure 5.6 the sta c lateralwheel loads yield:

Fl y =Flat · lhlf + lh

Ry =Flat · lflf + lh

(5.14)

As dynamic factor for lateral loading [Bro03] suggests a value of K = 1.75, which ismul plied with the calculated sta c loads in order to approximate the dynamic loads.

5.1.1.4 Bump Encounters

Asymmetric bump or pothole encounters as illustrated in Figure 5.7 lead to a very complexloading condi on on the vehicle structure. The ver cal and longitudinal forces exertedat one corner of the vehicle result in torsional loads about both x and z-axis. Intui ontells us that the magnitude of the applied forces depends on the vehicle speed at whichthe car is traversing over the obstacle as well as on its geometry. One would expect thatthe higher the bump and the faster it is taken, the higher are the resul ng loads on thevehicle body. Since the forces are exerted on the vehicle structure through the wheelsand the suspension system, the s ffness along with the damping of wheel and suspensionalso influence the loads on the structure. In addi on, the wheel mass and especially thevehicle body mass greatly influence the resul ng forces. Thus, it becomes obvious that anes ma on of the maximum bump loads on a car requires a comparable complex modelas well as reliable informa on on both the s ffness and damping characteris cs of wheel


and suspension.

Different approaches to developing a model for a vehicle going over a speed bump arestudied in the framework of a laboratory at the engineering faculty of the SwarthmoreCollege (Swarthmore, PA). The respec ve Matlab files are accessible on their homepage[Kad04]. These models enable an es ma on of the ver cal accelera on of the vehicle bodyfor a given bump geometry and car velocity depending on the wheel and vehicle massas well as wheel and suspension s ffness/damping. The problem is that the suspensionand damping coefficients of wheel and suspension are unknown for the examined car. Atthe same me experimen ng with the models from Swarthmore College revealed that thes ffness and damping characteris cs seem to have a significant impact on the ver calaccelera on of the vehicle body. With these informa on missing, it is difficult to get goodresults with these informa on lacking. However, instead of modeling the bump loads it iscommon to assume a ver cal accelera on as maximum design load based on experience.Depending on the applica on, suggested accelera ons vary from 4g− 7g [Gen09a, Bro03].Since the City Car is designed as low performance vehicle, a maximum ver cal accelera onof 4g is assumed. The resul ng horizontal load Lh is then determined under the assump onthat the wheel reac on force passes through the wheel center (see Figure 5.8),

Lh =Lv

tan(β) (5.15)

while β depends on the assumed bump height hb and the wheel radius r.

x y

z

Figure 5.7: Asymmetrical wheelload due to striking a road bump

2r

hb

β

L LvLh

v

Figure 5.8: Wheel striking bump ofheight hb

5.1.2 Crash Situa ons

Modern passenger vehicles are required to fulfill certain safety standards in a variety ofcrash situa ons (frontal, rear, lateral). This is regulated in guidelines such as the EuroNCAP. In order to guarantee maximum passenger safety, the vehicle structure should bevery s ff in some parts to prevent intrusions into sensi ve areas such as the passengercabin. But at the same me, it should be so in other areas to absorb the impact energybefore reaching the s ff parts [Ham05]. Computer aided crashworthiness analysis has


evolved into a mature tool that provides qualita vely as well as quan ta vely reliablepredic ons for the crush behaviour of structures [Sch92]. However, when consideringcrashworthiness in the context of this work, two main problems arise. Firstly, in order todraw clear conclusions on the passenger safety of a vehicle, one has to consider the en revehicle and perform a mul body crash simula on that includes all assemblies of the car.However, this work regards the chassis frame in a mostly isolated manner. Secondly, crashsimula ons require intensive dynamic non-linear finite element analysis, due to the highlynon-linear behaviour of crushing structures. However, structural op miza on methods asintroduced in 2.5 depend on the con nuous determina on of the structural performanceof the current candidate design through FEA. The heavy computa onal resources neededto perform non-linear FEA, lead to an imprac cal computa on me [Ham05].

This issue has been addressed by several publica ons. Fosberg and Nilsson (2006) [For07]present two alterna ve formula ons for topology op miza on based on the internal energydensity distribu on in the model. Park (2010) [Par10] proposes a non-linear structuralop miza on method where equivalent sta c loads are u lized for a linear sta c responseop miza on. However, the applied op miza on solver Op Struct does not have anynon-linear analysis func ons or simplifica ons implemented, which is why this ma er has tobe addressed differently in this work. Cavazzu et al. (2010) [Cav10] deal with this problemsimilarly to the approach of Park (2010). Here, iner al forces ac ng on the chassis aresubs tuted by suitable sta c forces applied at wheel centers, engine and seat moun ngs,while the structure is constrained in a row of elements at the side of the simulated impact.This simplified considera on is assumed to promote the forma on of longitudinal structuresin the op mized topology, that help to sa sfy the crash requirements. Such linearizeddummy loads are also proposed in [Gla05] and [vH08] to account for crash situa ons.Subs tu ng iner as by sta c forces requires an assumed maximum accelera on ac ng onthe vehicle in case of impact. Therefore, this approach is very similar to the considera onof the dynamic and sta c loads described before. However, it cannot be determined withcertainty what maximum accelera on is to be applied. In [Cav10] a high performancesports car is considered and therefore a high accelera on of 12g is assumed. [vH08] onthe other hand assume only 4g for their solar car chassis, as this is a requirement fromthe solar car challenge regula ons. The NUS City Car is a low performance vehicle whichshares many design features with solar challenge cars (max. performance, three wheels,space frame with CFRP body shell), which is why this work is orientated towards the workof [vH08]. However, in order to really verify the crashworthiness of the structure, a propernon-linear crash simula on would have to be performed a posteori a er the op miza onprocess. The implementa on of the linearized dummy load approach is illustrated intomore detail in the following sec ons regarding the model setup.

5.2 Modeling Considera ons 64

5.2 Modeling Considera onsWith the load cases iden fied, the next step is to setup the op miza on model accordingly.Topology op miza on is o en performed on basic structures which have clearly definedconstraints and load condi ons such as brackets or control arms. However, the chassis frameof a vehicle is by far more complex, which is why several general issues arise when se ngup the op miza on model. The chassis frame is not only characterized by a great varietyof different load condi ons but one also has to realize that it is not even a constrainedstructure in the conven onal sense. In addi on, one has to account for the non trivial loadtransmission from the road into the structure through the suspension system. Regardingthe op miza on setup, it is of importance to decide on a suitable objec ve formula on(min volume, max s ffness...) and on a appropriate design space defini on (2D elements,3D elements). All these issues are discussed in the following subsec ons.

5.2.1 Unconstrained Structures

As briefly men oned before, an important issue when dealing with the structural analysisof vehicle bodies is the fact that the structure is not clearly constrained. Strictly speaking,a car is only constrained by the road surface. Using the coordinate system of the freebody diagrams in the previous sec on, this means it is only constrained in nega ve z-axisdirec on. In posi ve z-direc on (li up) or bidirec onal on the x-axis (rolling) the vehiclecan be considered as free or unconstrained under most driving condi ons. In y-direc onthe vehicle is also unconstrained, apart from the lateral fric on in the contact patchbetween re and road. However, a conven onal structural analysis requires clearly definedconstraints in order to generate results in the first place. This problem does not apply forall load cases. For instance, in pure bending, there is only the gravita onal accelera onac ng on all iner a masses ver cally downwards where the structure is truly constrainedby the road surface. During accelera on and braking, one can assume that the structureis addi onally constrained in x-direc on due to the re fric on, which is equal to theiner a forces of the longitudinally accelerated component masses. That means for thesethree load cases the structure can be conven onally constrained without modeling theactual load condi on inaccurately. However, the situa on is completely different whenconsidering cornering and bump encounters, which have been pointed out as importantload condi ons in the previous sec on. It becomes obvious that the vehicle is simply notconstrained upwards and longitudinally when hi ng a bump. As for a cornering vehicle,one could assume at first glance that it could be modeled similarly to a braking vehicle as itis also constrained by the re fric on. However, this is not possible because in the extremecase of p over, the vehicle is only supported in two points: the outer wheel and the rearwheel, with the inner wheel assumed to be just li ing up. The vehicle is thus only held inbalance as a result of the dynamic moment equilibrium. This situa on cannot be modeledconven onally in the preprocessor simply because in a sta c analysis, a three-dimensionalstructure requires three transla onal supports. Otherwise, the equilibrium equa ons will


not lead to any results unless one of the supports can bear a moment, which would notrepresent the actual situa on.

None of the reviewed publica ons consider these loading condi ons explicitly, which couldbe the result of the just men oned problems. Instead, it is common to consider a globaltorsional load case. This load case is more or less modeled a er the industrial method ofmeasuring the global torsional s ffness of a vehicle body. Here, a sta c moment is appliedat the two front suspension supports, whereas the structure is constrained in the tworear suspension supports or at certain frame nodes in the rear. The torsion angle is thendefined as the resul ng deforma on angle between the front and rear supports [Hel10].As men oned before, the torsional s ffness of a vehicle has been established as reliablemeasure for the overall structural strength of a vehicle body. Since both, cornering andstriking a bump, result in a severe torsional load on the en re vehicle body, it is assumedthat the reviewed publica ons consider these two loading condi ons as covered by theglobal torsional load case. However, in this work it was aimed to study the considera onof the loads resul ng from cornering and striking a bump into more detail. Firstly, becausethey do not just lead to torsional loads but also longitudinal or lateral ones and secondly,because the constraints of the just described global torsional load case hardly reflect thereality. The vehicle is simply never clamped onto the road surface, which is implied bythis load case. When assuming such fixed constraints in a topology op miza on setup, theexerted torque at the front suspension will lead to the forma on of structures following theload path from the front suspension to rear constraint. Since this rear constraint does notexist in normal vehicle opera on, the resul ng op mized topology might be inappropriatefor the actual vehicle loads. Therefore, the objec ve was to find an alterna ve considera onof bump and cornering loads that is more realis c and might even replace the globaltorsional load case in the topology op miza on setup.

HyperWorks has a feature implemented that is specifically dedicated to the analysis ofunconstrained structures. This feature is called iner a relief and is very well explained inthe HyperWorks Users Guide [Alt09]:

Iner a relief allows the simula on of unconstrained structures. Typicalapplica ons are an airplane in flight, suspension parts of a car, or a satellite inspace. With IR, the applied loads are balanced by a set of transla onal androta onal accelera ons. These accelera ons provide body forces, distributedover the structure in such a way that the sum total of the applied forces on thestructure is zero. This provides the steady-state stress and deformed shape inthe structure as if it were freely accelera ng due to the applied loads. Boundarycondi ons are applied only to restrain rigid body mo on. Because the externalloads are balanced by the accelera ons, the reac on forces corresponding tothese boundary condi ons are zero.


Therefore, the iner a relief feature allows the applica on of bump loads as pictured inFigure 5.7 to an unconstrained vehicle body. In this way, the load path through the structuredoes not end in any fixed constraints. In order to illustrate the effect of iner a relief (IR) , asimple compara ve study was performed. A 2D shell-element structure that approximatesthe current chassis design was loaded with a single ver cal force at one corner, whilethe three remaining corners are constrained. It was compared how displacement andstress contours develop with both conven onal constraints and ac ve IR. The results arepictured in Appendix F.1. The outcome is that the absolute displacement of the structureis notably reduced in the iner a relief analysis, while the stress contours confirm theassump on of shortened load paths due to the missing fixed constraints. These differencesreflect the expecta ons and indicate that the iner a relief func on enables a more realis cconsidera on of bump and cornering loads.

5.2.2 Suspension Modeling

Modeling the load transmission through the suspension into the structure is crucial for thetopology op miza on of a chassis frame. An inaccurate or even incorrect considera on ofthe suspension system will inevitably result in the forma on of an unfavorable topology.One possibility to account for the load transmission is the manual calcula on of the loadsac ng on the structure through a free body diagram of the suspension. The calculatedforces could then be applied on the structure at the respec ve moun ng points of thesuspension. However, this method has one major drawback. The great number of differentload cases makes it cumbersome to calculate for each case the respec ve subs tute loadsat the mounts and apply then in the preprocessor model. This also makes it less flexiblein case of changes in the setup.

It becomes apparent that it would be favorable to simply model the suspension system andinclude it into the model setup. This would ensure that the load transmission is accuratelysimulated at all mes. The problem with this is that the model would become a mulbody system (MBS) , which complicates the op miza on procedure significantly. Although,a few applica ons of topology op miza on of MBS have been shown (e.g. [Alb05, Joh94]),it is a empted to avoid the considerable addi onal modeling effort.Therefore, it was experimented with 1D-elements that can be easily included into themodel without resul ng in a MBS. In order to model the suspension realis cally, it requiresjoints. The only way of including joints into a non-MBS model is through “ROD elements”.Per defini on ROD elements have a ball joint at each of their ends. Modeling thedoublewishbone front suspension en rely with ROD elements, results in a structure with akinema c behaviour that approximates the actual suspension very well. It is assumed that,if the kinema c behaviour of the suspension is reals cally modeled, the load transmissioninto the chassis structure will be also realis c. In a purely sta c situa on, the s ffness andthe damping of the shock absorbers do not influence the loads exerted on the structure.Since, all load condi ons are simulated by sta c subs tute loads, it is not necessary


to model the shock absorber as spring-damper unit, which makes ROD element also areasonable approxima on for the shock absorbers. The disadvantage of ROD elements is,that it is only possible to apply loads or connect them with other elements at their ends.However, the wheel is actually mounted in the center plane of the suspension model,which cannot be modeled with rod elements. Therefore, the outer ver cal rod has beenreplaced by two “BEAM elements”. In this way, the loads and constraints can be placed inthe center plane, while the overall kinema c behaviour of the structure remains the same.The result is a model that enables a very good approxima on of the load transmissionthrough the suspension, when applying a sta c force or constrain it at the point of thewheel suspension support, without having to set up a real MBS. Figure 5.9 illustratesthe HyperMesh preprocessor model of the described doublewishbone suspension modelconsis ng of ROD and BEAM elements. In addi on, the qualita ve displacement and stressunder a sta c ver cal load is shown. It can be seen that the model behaves very muchlike one would expect from the actual structure. The rear suspension swingarm has beenmodeled in a similar manner.

HM Model Qualita ve Displacement Qualita ve Stress

Figure 5.9: BEAM and ROD elements modeling the doublewishbone front suspension

Throughout the op miza on procedure, the suspension BEAM and ROD elements havebeen modeled as very s ff structures by alloca ng large cross sec on dimensions and ahigh young’s modulus. Hence, the en re deforma on resul ng from the applied loadstakes place in the design space and thus amongst the chassis frame members. This ensuresthat a worst case scenario is considered at all mes, as the suspension would normallyalso deform, which would reduce the overall displacement of the frame nodes.

5.2.3 Design Space Defini on

The design space defini on is another cri cal step in the op miza on setup. The designspace (DSP) , o en also called design domain, dictates where material can formate duringthe topology op miza on process. Therefore, one has to account for aesthe c, func onal


and manufacturing requirements already with the defini on of the DSP. At the same me,it is favorable to provide the op miza on process with a maximum degree of freedom byrestric ng the design domain only where necessary. This ensures that the resul ng topologytruly reflects the op mum within the set constraints. When dealing with three dimensionalstructures, one would naturally prefer a full 3D DSP consis ng of tetrahedron elements, asthis enables the u liza on of the en re available space. Another possibility is the defini onof a surface DSP consis ng of 2D shell-elements, that enclose the available space. Thisreduces the design domain significantly. But o en, such a surface DSP is sufficient becausefunc onal constraints demand a cage structure. For instance, the chassis frame of a car canbe generally put in this category. This is especially so in the passenger compartment, whichrequires spacious volume with no frame members cu ng through in any way. This appliessimilarly for the motor, energy storage and baggage compartment. As a result of this, bothapproaches are found in the literature. Cavazzu et al. (2010) [Cav10] work with a 3D blockas design space where only the passenger compartment is “carved” out. These authorsargue that the forma on of diagonal structures not necessarily collides with further spacerequirements for instance, in the motor compartment. In [vH08] a 2D shell-element designspace is defined, arguing that this reduces the necessary computa on me significantlywithout affec ng the results too severely. In order to acquire some own experiences onthis ma er and to help decide which is the more appropriate design domain defini on forthe present work, a brief comparison between the resul ng topology from a surface anda full 3D DSP is performed. The procedure of this compara ve analysis is summarized inthe following. Subsequently, the ini al design space used for the development of the finalop miza on setup is derived from the results of this compara ve study.

5.2.3.1 Comparison of Surface and 3D Element Design Space

In order to model the two design domains (full 3D and surface), the present chassis framewas imported into a CAD so ware and a full 3D block was modeled accordingly, leaving outmaterial only for the passenger compartment. The surface DSP was derived from this 3Dblock by extrac ng all outer surfaces and discre zing them with shell-elements. Therefore,both design domains look essen ally the same, just that the shell-element domain is hollow.One of the primary objec ves of this comparison was to find out if the 3D design domainresults in the forma on of structures in areas that are not captured by the shell-elementdomain. If this is not the case and the 3D domain leads to a cage structure similar tothe surface design domain, it can be assumed that a surface DSP is indeed sufficient forthis applica on. For this analysis, the number of considered load cases was reduced tojust three basic global loads. This was done to reduce the modeling and computa oneffort. These three load cases are considered as crucial global loads that affect the en restructure. Therefore, it was assumed that if diagonal forma ons develop at all, they wouldalready appear under the considera on of just these three load cases. These include aglobal bending and torsional load case as well as a linearized frontal crash. The defini on


of these load cases in the preprocessor is illustrated in Figure 5.10.

Global Bending Global Torsion Frontal Crash

Figure 5.10: Considered load cases for 2D/3D design space comparison

Here, the torsional load case was modeled conven onally with fixed constraints at thethree rear suspension moun ng points, since this appears to be the established method.For this side study, the bending load case included ver cal forces applied at the sills inthe center of the wheel base complemented by forces that load the roll hoop in the rear.Without these forces, the op mized topology would not have any material where the rollhoop should be located. The frontal crash was implemented as described in 5.1.2. Thesethree load cases essen ally reflect most of the load cases that have been considered in[Cav10]. The op miza on process was run for both design domains loaded with the threedescribed load cases with the objec ve of minimum weighted compliance. All three loadcases were weighted equally. The resul ng topologies are displayed in Figure 5.11.

2D element design space 3D element design space

90,400 elements | 1:44h CPU me 1,199,574 elements | 8:32h CPU me

Figure 5.11: Op mized Topology with surface and full 3D design space

What stands out immediately when comparing both resul ng topologies is, that they areactually very different. The full 3D design space looks generally unfavorable. It indicatesthat the en re front part is not necessary to sustain the defined loads, while the surfacedesign domain topology developed material in the front. It also becomes apparent that theshell-element design space is characterized by a strong triangulated topology as expected,


whereas this can barely be seen the in 3D element design space. Furthermore, the full3D-element DSP led to a few forma ons that literally stand out isolated without forming aclosed structure with other forma ons. Moreover, there are some very thick solid structuresthat are less feasible with a space frame. S ll, it can be established that there is nonotable forma on of diagonal structures in areas that are not captured by the surfaces ofthe shell element design space. In addi on, the 3D element design space reveals that theclearance area for the rear suspension can be modified by removing the frame membersthat currently enclose the rear swingarm on the side. This is something that cannot beseen from the surface design space defini on. Both design domains have been discre zedwith an average elements size of 10mm. This leads to over 12 mes more elements inthe full 3D design domain compared to the surface design space. As a result of this, thenecessary CPU me increases significantly to over 8h. The problem is that there was nopowerful worksta on available during the work on this thesis. Hence, CPU me was asevere limi ng factor. When considering the full range of the iden fied load cases, the CPUme is likely to rise again considerably. At the same me, the op miza on setup is largely

a trial and error process that requires numerous op miza on runs in order to se le downon the final se ngs. Due to the lack of CPU power, the full 3D design space setup wasnot inves gated further. However, it is possible that through further adjustments to theop miza on se ngs and formula on, a more favorable topology can be obtained from the3D element DSP. At the same me, a more detailed compara ve study on the applica onof surface and full 3D design domains is regarded as a very interes ng topic for futurework, as this has not been encountered during the literature review in the framework ofthis work.

5.2.3.2 Deriva on of the Ini al Design Space from the Current Design

As a result of the described problems with the 3D element design space, the furtherop miza on process was solely based on a surface DSP. Therefore, the surface DSP extractedfrom the 3D block was modified in order to suit the applica on be er. The center consolewas removed, since it is considered imprac cal to have frame members separa ng thepassenger compartment as this prevents the possibility of including a single bench insteadof two separate seats. In addi on, the two bo om surfaces were merged so that thereis only a single surface represen ng the bo om. For the first op miza on runs, thedesign space was not restricted at certain loca ons, for example by removing surfaces ordefining non-design elements. Applying the earlier men oned top-down approach meansthat the design space is only restricted when the resul ng topology violates any func onalrequirements. It is generally possible that the op mized topology fulfills these requirementswithout restric ng the DSP right from the start. If this is not the case, the design spaceis restricted accordingly and one has to keep in mind that limi ng the freedom of thedesign space always results in a less op mal solu on. The top down approach ensuresthat the designer is aware of the made trade-offs regarding the op mal structural design.


The ini al surface design space, which served as basis for all following op miza on runs,is illustrated in Figure 5.12 together with the current frame design.

Figure 5.12: Isometric rear view of the ini al surface design space enclosing the currentframe design (generated with CATIA V5)

It can be seen, that the design space partly differs considerably from the current design.The decision to op mize the chassis frame enables the implementa on of further changesto the general design. Therefore, several flaws of the current design can be addressedthrough the defini on of the design space. A main issue in this context is the very limitedcapacity of the current frame for the accommoda on of ba eries. The dynamic stability ofa three wheeled vehicle requires 2/3 of the vehicle weight to rest on the two-wheel-axle(see Appendix A). This is achieved by extending the en re vehicle and placing the ba eryin the front, which is reflected by the design space for the new frame. In addi on, thereare other adjustments to the current design, which are summarized as follows:

• The new frame is supposed to be slightly wider in order to accommodate twooccupants more comfortably than currently realised.

• The roll hoop is higher, since the current design does not provide enough protec onfor occupants above 1.80m of height.

• The wheel base is increased to increase the leg clearance for the occupants.• The rear has been modified in a way that the rear swingarm is no longer enclosed bythe frame structure (as suggested by the 3D element op miza on performed before).

As introduced in Sec on 5.1, vehicle loads can be divided in global load cases and localload cases. The considera on of local loads requires a rough idea of the loca on of themajor vehicle components within the design space. Each major vehicle components exertsiner a loads to the vehicle structure due to the external accelera on of the vehicle. Theseiner a forces are reflected by sta c loads, which are applied at the respec ve design spacenodes according to the expected loca on of the component. For the NUS City Car, fourmajor components have been iden fied. Their preliminary loca on in the ini al DSP isillustrated in Figure 5.13.


Motor

Assembly

Seat +

Occupant

Front

Battery Pack

Rear

Battery Pack

Design SpaceBelt

Frame members

Battery

Figure 5.13: Sec on view of ini al design space with loca on of major components

Here, it is also shown how the ba eries are supposed to be mounted onto the chassisframe. Using L-shaped profiles, the ba eries are kept in place through strained belts. Thisis considered as func onal constraint, which has to be accounted for in the followingop miza on process.

5.2.4 Op miza on Problem Formula on

The second crucial step in the op miza on setup is the formula on of the op miza onproblem and its implementa on using the defined design domain. In Sec on 2.5.2 theconcept of topology op miza on has been introduced using the standard formula on ofminimizing the compliance of the structure, while the volume frac on V /V0 of the designspace is limited to a certain level. This is a common method of se ng up an op miza onproblem and it is found in similar works, such as [vH08] and [Ree02]. However, this isnot the only applicable op miza on problem formula on for the proposed applica on. In[Cav10], the objec ve is defined as minimiza on of the total design space volume, while thedisplacement of individual nodes in the design space is constrained. Both of these methodsfocus on the s ffness of the structure either by minimizing the compliance or by constrainingthe displacement. In another different approach the op miza on formula on is based onlimi ng the stress in the structure, whereas the objec ve is to minimize the design spacevolume. However, none of the reviewed publica ons on vehicle body op miza on appliesthis formula on. This might be the result of the fact that the main concern of automobilemanufacturers is a high s ffness of the vehicle body (par cularly torsional s ffness). Asbriefly men oned before, experience shows that a vehicle body that meets the s ffnesscriteria is likely to have sufficient structural strength in general. This is reflected in thereviewed publica ons, which rely on s ffness related op miza on formula ons. However,in order to get an independent opinion on what op miza on formula on is the most


appropriate for the proposed applica on, all three men oned methods are studied in somemore detail. In the first step, it is compared how the op miza on problem formula onaffects the resul ng topology. The C-clip example op miza on problem (Figure 2.16) thatwas introduced in the second chapter is applied once again to illustrate this. In Sec on2.5.2 the C-clip was op mized using the minimum compliance approach. For a comparison,the clip is now addi onally op mized using the other two described problem formula ons.The three resul ng topologies and the respec ve key se ngs are summarized in Figure5.14.

Weighted Compliance Individual Displacement Global Stress Constraint

Design History

Design HistoryDesign History

Design History

responses weighted compliance (equal),volume frac on V /V0

disp. at loca on of applied forces,volume of design space

volume of design space, von misesstress

constraint upper value V /V0 = 0.25 upper value disp. = 0.2mm upper value stress = 150N/mm2

objec ve minimum weighted compliance minimum volume minimum volume

Figure 5.14: C-clip op mized topology with three different op miza on problemformula ons (the legend to the le indicates the density of each element)

With the indicated se ngs, all three methods essen ally result in the same topology.Therefore, it can be concluded that the op miza on problem formula on is actuallysecondary for the outcome of the op miza on process, at least in case of a simpleop miza on problem such as the introduced C-clip. It appears that each of the describedmethods is able to achieve the same op mized topology. It is simply a ma er of how toget there or what se ngs lead to that topology. Assuming that this finding is transferableto a more complex op miza on problem like the vehicle chassis frame, the most suitablemethod can be chosen simply by convenience and feasibility of the setup. In the eyesof the author, a convenient op miza on setup is characterized by a comparable smallnumber of state variables, such as displacements and their respec ve constraints. Thissimplifies changes to the setup, which are numerous during the op miza on procedure.At the same me, it is desirable to have only a few state variables of which the value isuncertain, as this prevents the necessity to determine their values through trial and error.

In order to decide on a suitable method, it was experimented with the three describedformula ons using a later stage of a 2D element design space similar as in Figure 5.12.The experiences made, are summarized in the following paragraphs.


WeightedCompliance Thewellestablishedapproachofminimizingtheweightedcomplianceproved to be very simple in its setup. It requires only two responses (volume frac on,weighted compliance) and one constraint (volume frac on) to define the op miza onproblem. However, since the s ffness is defined by a weighted compliance of all consideredload cases, one has to set a weigh ng factor for each load case. Firstly, it was experimentedwith equal weigh ng factors, which led to reasonable results. The weigh ng factors areaddi onal se ngs, that can steer the resul ng topology. They allow an individual adjustmentof the op miza on problem according to the importance of the load cases. The problem isthat one has to have a clear idea of what load cases are considered more important. Forthe vehicle body, it has been established that the bending and torsional loads are generallyconsidered as decisive load cases. However, the exact defini on of the weigh ng factorsremains more or less guessing and requires several test runs. To solve this ma er, Reed[Ree02] suggests an approach, where a separate op miza on is performed for each loadcase. Those load cases, which develop forma ons that are shared with many other loadcases are ranked higher and are being allocated a higher weigh ng factor. Although, fromthe view of the author of this work the weigh ng factors should not be overes mated intheir importance for the outcome of the topology op miza on. Since considerable mewas spent on the load case iden fica on and implementa on based on actual drivingsitua ons, the importance of each load case is already largely reflected by the magnitudeof the applied forces. This was also confirmed by brief sensi vity tests with the weigh ngfactors. Hence, the weigh ng factors are rather considered as complemen ng adjustments,which can help to reduce or enhance the contribu on of certain load cases if necessary.The volume frac on V /V0 as second response and only constraint is an important se ngof the weighted compliance method, especially with regards to lightweight design. Se ngthe volume frac on literally defines in advance how much the weight of the design spaceis reduced. The op miza on process then allocates the available material in a way that thecompliance is minimized. Hence, the resul ng topology largely depends on the defini on ofthe volume frac on. With regards to lightweight design, one could assume that the smallerthe volume frac on the be er is the result. Not surprisingly one also has to take intoaccount the feasibility and the achieved compliance of the candidate design. Dependingon the applica on, values between V /V0 = 0.05 to 0.4 appear to be appropriate star ngvalues. However, the final se ng has to be found through trial and error. It can beconcluded that this method is very appropriate for the proposed applica on, as it is notnecessary to have any knowledge of s ffness targets and the weight reduc on can besteered through the volume frac on. At the same me, it allows for a quick adjustmentof the op miza on se ngs, which is necessary to se le down on the final setup.

Individual Displacement It became quickly obvious that this method has its major drawbackwhen it comes to the setup. It requires the manual defini on of all displacement targets ofthe structure. Firstly, this is problema c because it is not trivial what nodes of the designspace should be constrained. Secondly, it is unknown to what extent the displacement of


the nodes should be constrained. Here, it would be useful to have certain guidelines orexperience from previous design itera ons, that help to define reasonable target values.Without it, it is difficult to find a start for the setup. In addi on, each load case wouldrequire several nodes to be constrained. This results in a very large number of op miza onresponses and constraints to be defined and thus in a very me consuming setup. As aresult of the men oned drawbacks in the setup, this method was not further inves gated.However, it is noteworthy that this approach is generally favorable for a light weight designop miza on should specific displacement targets be known beforehand. This is because itallows the direct op miza on of the volume with respect to the set s ffness targets.

Global Stress Constraint As men oned before, constraining the maximum allowable stressis a rather unusual approach to se ng up a topology op miza on of a vehicle bodystructure. However, a brief trial with the introduced C-clip problem revealed that such aformula on can deliver very similar results like the standard minimum compliance setup.Therefore, it was also experimented with the global stress constraint method. The outcomeis, that the achieved topology indeed resembles the the minimum compliance topology toa large extent. This could be confirmed for varying setups using different load cases to beconsidered. Regarding the setup, it can be said that it is similarly simple as the minimumcompliance approach. It only needs two responses (volume and stress) and one constraint(max. stress), while there is no need to guess weigh ng factors or the volume frac on.The op miza on algorithm simply distributes as li le material as possible in a way thatthe defined maximum stress value is not exceeded in any element, while all load casesare considered equally. The se ng for the maximum allowed stress can be used to steerthe final weight reduc on. A high maximum stress value expectedly leads to less materialin the structure, while reducing the value will add more material. The drawback is, thatthe op miza on of the structure is not related to its s ffness, which is generally desired.However, since both methods yield very similar op mized topologies, it can be concludedthat if the structure is op mized for maximum s ffness it actually also has a favorabletopology with regards to the stress in the structure. The same applies respec vely viceversa. In Appendix F.3 the op mized topologies of both methods are displayed underconsidera on of all iden fied load cases.

Summary All three described op miza on formula ons are applicable for the intendedtopology op miza on. However, the individual displacement method has been droppeddue to the laborious setup and the lack of reasonable s ffness targets. The weightedcompliance approach, as most widely used method, proved to be very simple to implement.The same applies for the global stress formula on. An interes ng fact was that bothof these methods achieve very similar topologies, which was not necessarily expected.However, due to the fact that the minimum compliance approach is the more establishedformula on, it is this method that was applied for the final op miza on setup. Table 5.1summarizes the experiences made while experimen ng with all three formula ons in a

5.3 Final Topology Op miza on Setup and Results 76

more compact form.

objective

+

-

application

constraints

• early design stage,

with knowledge from

previous design iteration

• early design stage,

without prior knowledge

of recommended design

targets

• later design stage,

for strength optimization

• fatigue optimization

• optim. for min vol.

• customized optim. to

meet displacement

requirements

• optim. possible without

known displacement targets

• simple setup

• well established

• optim. for min vol.

• no guessing of weighting

factors, volume frac. or

displacement targets

• laborious setup

• displacement targets

have to be known a-priori

• guessing of upper

vol.frac. and weighting

factors of load cases

• compilance of resulting

design might be unsatisfying

• not a stiffness related

optimization

• not found in literature

max. allowed displacement

at specific locations

upper volume fraction

between 0.05 and 0.40

upper stress constraint for

defined design space

min volumemin weighted compilance min volume

Method 1 Method 2 Method 3

Weigthed Compilance Individual Displacement Global Stress Constraint

Table 5.1: Summary of the three reviewed op miza on problem formula ons

5.3 Final Topology Op miza on Setup and ResultsBased in the foregoing considera ons, the final op miza on setup was developed usingthe earlier described approach of gradually reducing the degree of freedom of the designspace un l no func onal or physical requirements are violated by the resul ng topology.The resul ng op miza on setup, including the final DSP and the exact implementa on ofthe load cases, is described in this sec on. Subsequently the results of the op miza onprocess are presented and discussed.

5.3.1 Final Design Space

As a result of the top-down procedure, several surfaces were cut or removed en rely toenable enough clearance for components and occupants. In addi on, some DSP elementswhere turned into so called “non-design” elements, meaning that these elements aredefinitely part of the op mized topology while the op miza on algorithm distributes thematerial around these elements. This was necessary to make sure the topology featuressuitable frame members for the accommoda on of the ba eries. Therefore, several framemembers are predefined by non-design elements in the bo om surface of the DSP.Considerable me was spent on discre zing the surfaces of the DSP. The mesh quality has


a significant impact on the solu on of the equilibrium equa ons of the sta c analysis.Therefore, the mesh was generated using the quality index op miza on func on ofHyperMesh. Subsequently the mesh was checked manually for elements that do not fulfillthe requirements in element size or aspect ra o. In addi on, it had to be ensured thatall elements are connected correctly. This was necessary because the design space hasbeen divided within the preprocessor into bo om elements and top surface elements.This enables to hide the top surfaces when applying the local iner a forces to the bo omdesign elements. Another issue in this context is the defini on of the mesh refinement. Ahigh number of elements generally leads to more discrete results, while one has to controlthe mesh dependency problem described in 2.5.2.2. At the same me the computa onme increases notably with the element number, which is a serious problem with regards

to the limited available hardware capacity. Experimen ng with different average elementsizes led to the establishment of 10mm as reasonable compromise between computa onme and discreteness of the resul ng topology.

Figure 5.15: Final preprocessor design space, number elements: 71400, element type:2D shell (mixed quads and trias), average elements size: 10mm, shell thickness: 2mm,material: steel

The considered material and thickness of the shell elements proved to be minor issuesin the op miza on setup. Though, one could further diversify the op miza on problemby alloca ng different shell thicknesses to certain surfaces of the DSP, the shell thicknesswas kept constant in all elements during the en re op miza on process. This was done,since there was no prior indica on that certain DSP surfaces require different thicknesses.With a constant thickness in all elements, the defini on of the thickness has no notableeffect on the resul ng topology, which was confirmed by respec ve test runs where thethickness has been varied between reasonable bounds (5-25mm). The same applies forthe allocated material of the elements. Tests with steel and aluminum as material did notlead to any no ceable differences in the resul ng topology. The final design space, as itwas defined in the preprocessor is illustrated in Figure 5.15.


5.3.2 Load Case Implementa on

The defini on and implementa on of the relevant load cases builds on the findings madein sec on 5.1. Therefore, the three load cases that already have been considered for thecomparison of surface and 3D element design space (Figure 5.10), are complemented byeight addi onal load cases, including other crash situa ons as well as the iner a reliefload cases described in 5.2.1. The total of eleven load cases can be categorized into threecategories according to their implementa on:

• Individual Load Cases: These include the standard bending as well as the accelera onand braking load cases. Here, each of the major components iden fied in Figure5.13 is represented by sta c forces applied at nodes at the respec ve loca on ofthe components. The structure is constrained in the wheel supports.

• Global Load Cases: The global load cases are characterized by sta c forces thatare solely applied at the wheel supports, while the structure is either constrainedconven onally (pure torsion) or by iner a relief supports at certain nodes of thedesign space or in the suspension supports. The applied forces simulate the globaldeforma on of the vehicle structure as the result of cri cal driving condi ons suchas cornering and striking a bump.

• Crash Load Cases: The considera on of crash loads follows the lineariza on approachdescribed in 5.1.2. The major components are reflected by sta c forces resul ngfrom the present external accelera on similarly to the individual load cases. Thedifference is that the structure is now constraint in a row of design space nodes atthe side of the simulated crash impact (side, rear, front and roof crush).

Figure 5.16 illustrates the implementa on of the load cases using one example load caseout of each category.

Individual Load Cases Global Load Cases Crash Load Cases

Bending Front Bump (IR) Side Crash

Figure 5.16: Load case defini on in the preprocessor HyperMesh

The preprocessor implementa on of the remaining load cases is illustrated in AppendixF.2. The magnitude of the applied individual forces was derived from the establishedmaximum vehicle accelera ons in each driving situa on. Each major component acts with


the product of present accelera on, component mass and dynamic factor on the structure.The magnitude of the global forces exerted at the suspension is based on the sta c wheelload. For example, the non-symmetric front bump encounter is simulated by an ver calupwards force, which is the product of the sta c front wheel load (roughly 1/3 of thetotal vehicle mass) and the assumed maximum ver cal accelera on resul ng from hi nga bump (4g). The magnitude of all forces applied for each of the considered load cases issummarized in Appendix E.

5.3.3 Op mized Topologies

Before the final op miza on setup and results are presented it is briefly discussed howthe different torsional load cases affect the resul ng topology. Under 5.2.1, two differentapproaches for the considera on of torsional loading condi ons were iden fied. Firstly,there is the well established pure torsion load case, where a torque is applied at the frontsuspension and a few nodes in the rear are constrained. Secondly, it was experimentedwith the iner a relief func on of HyperMesh in an a empt to reflect actual torsional loadcondi ons such as cornering and bump encounters more realis cally. In order to examinethe influence of both methods on the topology, the op miza on was run with iden calse ngs once with the pure torsion load case and once with the iner a relief cornering andfront bump load cases as torsional load cases. In addi on, the op miza on was performedunder the considera on of all eleven load cases.

Pure Torsion Iner a Relief - Cornering and Bump

All Load Cases

Figure 5.17: Comparison of different torsional load case considera ons


The three resul ng topologies are displayed in Figure 5.17. Both the iner a relief andpure torsion approach generally lead to similar topologies. However, there are no ceabledifferences. When the torsional loads are represented by the iner a relief cornering andbump load cases, there are more structural forma ons in the passenger compartment.These addi onal load paths are generally unfavorable and hardly to implement in a spaceframe design. On the other hand, when the pure torsion load case is considered, morestructures formate in the side surfaces, while the area of the front suspension mountslacks a clear feasible solu on.Under the considera on of all eleven load cases the resul ng topology combines thefeatures of both previous solu ons. It represents a good compromise, while it barelyfeatures the unfeasible forma ons of each of the previous topologies. Therefore, it is thisapproach that was applied for the final op miza on setup. In conclusion it can be said,that the developed iner a relief load cases do not appear to be appropriate to en relyreplace the established pure torsion load case. However, they can certainly complementthe pure torsion load case. Including the IR load cases leads to favorable structures at thefront suspension mounts. At the same me the severe load condi on of hi ng a bump isconsidered more realis cally.


Side ViewVolume Fraction

Min. Member-

size Control

Convergence

Tolerance

Number of

Load Cases

Bending 2.0

Braking 1.0

Accelerating 1.0

Front Bump 2.0

Rear Bump 2.0

Cornering 2.0

Pure Torsion 2.0

Front Crash 1.0

Side Crash 1.0

Rear Crash 1.0

Roof Crush 1.0

Memory Used

No. of Iterations

CPU Time

105

320 MB

13.5h

0.1

40

11

0.002

Weighting

Factors

Final Optimization Facts

Bo om View

Figure 5.18: Final result of topology op miza on using the minimum compliance approach

The final op miza on setup and the resul ng topology is illustrated in Figure 5.18. TheCPU me of 13.5h demonstrates that the available computa on capacity was a seriouslimita on throughout the work on this thesis, considering that it required a large numberof op miza on runs to establish this final setup.

5.4 Size Op miza on 82

5.4 Size Op miza onWith the final op mized topology established, the next step would be expor ng theresults into a CAD so ware and modeling a space frame accordingly. By doing so, itbecomes obvious that the obtained load paths cannot always be modeled one to one.The topology as suggested by the op miza on process is generally s ll too complicatedfrom a manufacturing point of view. Adjustments in form of simplifica ons were necessaryat various parts. This especially includes the transla on and merger of joints. The CADmodel of the frame was created using SolidWorks. Here, a space frame can be generatedconveniently by modeling a 3D wireframe consis ng of lines that mark the center axisof each frame member. This wireframe represents the topology of the new frame. Eachline of the wireframe is subsequently allocated a predefined cross sec on, which resultsin the desired 3D space frame model. The 3D wireframe also serves as basis for the sizeop miza on.

Op mized Topology 3D-Wireframe Model

Figure 5.19: Export of op mized topology and modeling of 3D-wireframe accordingly

However, the topology is only one criteria for a lightweight op mized structure. At thesame me, it is equally important to have an idea of the op mal size of the structure.In the case of a space frame, this means in par cular the cross sec onal dimensions.Lightweight design requires that the space frame members are designed in a way that theyare just strong enough to sustain the occurring maximum loads. However, the concept oftopology op miza on does not provide any indica on of the op mal cross sec on size. Asa consequence, it is common to perform a size op miza on subsequent to the topologyop miza on (eg. in [Cav10]). This ensures that the vehicle body not only has an op mizedtopology but also op mal tubular widths and thicknesses. This sec on describes the stepsof the performed size op miza on.

5.4.1 Foregoing Considera ons

In Sec on2.5, sizeop miza onwas introducedas the simplest formof structural op miza on.It is usually reduced to one design variable, which is o en some kind of structural thickness.That also means one has to predefine the shape of the structure unless a shape op miza on


was previously performed. Alhough this would be generally preferable with regards to anop mal lightweight design, it is not adequate for the here proposed applica on. A shapeop miza on could lead to cross sec onal shapes that require customized manufacturing,which is economically out of limits. In addi on, space frame designs have been successfullyimplemented in various engineering applica ons across different disciplines. In automo veengineering, it is a reoccurring topic especially in motor sports applica ons. Therefore,it is intended to resort to established accessible cross sec onal shapes used in similarapplica ons. Another non-trivial issue that has to be addressed is the finite elementmodeling of the space frame. Like topology op miza on, size op miza on is based on afinite element model of the structure. Several ways of discre zing a frame structure wereexamined before deciding on an adequate method. Both of these issues are subsequentlydiscussed.

5.4.1.1 Establishment of the Frame Cross Sec ons

During the literature review, numerous recent automo ve space frame designs origina ngfrom the FSAE Students Formula 1 compe on were encountered [GE07, Ril00, Bro09].All of these frames either consist en rely of thinwalled circular (round) tubes or they arebased on a combina on of rectangular and circular thinwalled tubes. The current CityCar frame design was derived from these FSAE space frames and is made of both circularand rectangular tubes. This concept is transfered to the new design. However, for thesetup of the size op miza on problem, it s ll has to be determined what frame membersfeatures a circular shape and what frame members have a rectangular cross sec on. Inthis context, the main considera on is that certain frame members are required to enablethe a achment of components. In addi on, one has to take into account the s ffness andstrength of both cross sec ons under the occurring loading condi ons (compression-tension,torsion and bending). The ques on if round or rectangular tubes are to be used for anautomo ve space frame is further discussed in Pashley (2008) [Pas08]. The pros and consof each tube type are accordingly summarized as follows.

Round Tubes Have the be er overall s ffness and strength per weight unit under universalloading condi ons (mul direc onal bending, torsion). A circular tubewith the cross sec onalarea A = 35mm2 is about 20% s ffer and 10% stronger than a square tube with the samesec on area. Here, structural strength is defined by the value of the occuring von Misesstress in the structure. These values were obtained from a quick FEA comparison of twobars with the respec ve cross sec ons. Therefore, round tubes are the best choice froma pure lightweight design point of view. However, there are several notable drawbackswhen working with circular tubes. This is especially with regards to the manufacturingprocess. Round tubes are considerably more complicated to align and clamp into posi onfor welding. Moreover, the required jigs and fixtures are much more complex and the jointsare harder to prepare. Lastly, it is more difficult to mount components onto circular tubes.


Rectangular Tubes Although rectangular tubes are generally less s ff and strong, theycan achieve a favorable structural performance for unidirec onal loads. A rectangularframe member with uneven side lengths is about 12.5% s ffer than a circular tube of thesame cross sec on area in the case of a force that is applied ver cally to the narrow sideof the frame member. This can be u lized to achieve a higher bending s ffness of thevehicle structure. However, one has to bear in mind that such a cross sec on leads to aless favorable structural performance when forces are applied in mul ple direc ons. Themain advantage of rectangular tubes is their considerably simpler manufacturing process ifcompared to round tubes. In addi on, they enable a simpler implementa on of the manybrackets needed to mount components such as suspension arms, seats, motor as well asthe body shell.

As a consequence, all frame members that have to enable the moun ng of components areallocated rectangular cross sec ons, whereas the remaining frame members are definedas circular tubes, as they promise the best structural performance per weight unit.

Another aspect of the size op miza on setup is the number of different cross sec ons tobe considered. On the one hand, it is desirable to have as li le different kinds of tubesas possible in the frame. This notably simplifies the structure, making it more feasiblein terms of both manufacturing and total costs. On the other hand, a high numberof different tubes allows to specifically op mize more frame members according to theoccurring loads, which reduces the number of over-dimensioned frame members. Hence,the more different tubes, the higher is the weight saving poten al. It becomes apparentthat one has to find a compromise between feasibility and costs and the weight savingpoten al. This problem was approached in mul ple size op miza on stages, while ineach stage the number of different cross sec ons was increased by one un l a reasonablecompromise was found. Star ng from two different tube types (one rectangular and onecircular) each cross sec on was allocated to one group of frame members, while it wasexperimented with numerous grouping constella ons in each op miza on stage. This isnecessary because it is hard to predict what frame members should have the same crosssec on. In addi on, it has to be considered that all tubes that coincide at one weldedjoint have to feature compa ble cross sec ons.

5.4.1.2 Finite Element Model of the Frame

Similar to the topology op miza on, the defini on of the design domain as finite elementmodel is crucial for the outcome of the size op miza on process. In the framework of thisthesis, three different methods of discre zing the frame structure were examined. Thesemethods are subsequently described.

Beam Model A simple and self-evident approach to modeling a space frame structureis the beam model. HyperWorks has the Timoshenko beam theory implemented. Usingthis theory, the space frame is discre zed with segments, also called elements, joining


two nodes with six degrees of freedom, to which the structural characteris cs (sec onarea and moment of iner a) of a body shell can be a ributed. The elas c and geometriccharacteris cs of the elements and thus the structure are solely defined by their crosssec ons. In HyperMesh, these elements can be defined with various different cross sec ons,while the cross sec on dimensions can be easily manipulated and also used as designvariables for a size op miza on. Another huge advantage is that the wireframe modelfrom the 3D-CAD model can be u lized without much addi onal modeling effort in thepreprocessor. Moreover, it allows to op mize the thickness and the diameter/width ofthe tubes at the same me. The drawback is the rela ve inaccuracy in the predic on ofthe stress in the structure. The beam model is only capable of indica ng the peak stressin each segment. The exact loca on of the stress contours on the surface of the tubesremains unknown.

Shell Model with RBE2 Nodes Another method of discre zing the space frame structureis by using shell elements based on the theory of plates and shells. This is valid sincethe frame members are made of thinwalled tubes where the thickness is small comparedto the planar dimensions of the tube. Hence, the tubes are reflected by surfaces with adiscrete thickness. There are different ways of modeling the joints of such shell elementframe members. One possibility is to connect the tubes with rigid RBE2 elements. Twonodes that are connected with RBE2 elements, are subject to equal displacements atall mes, while one can define which degrees of freedom should be affected by thisequaliza on. Modeling the joints with RBE2 elements enables the approxima on of anideal truss, similar to the beam model. This is illustrated in the middle graphic of Figure5.20. This method has been applied successfully in previous works at the Ins tut fürProduktentwicklung und Konstruk onstechnik. Its main benefit over the beam model isthat it enables the simula on of the loca on of the stress contours on the surface of thetubes. This informa on is necessary for the addi onal structural analysis of the weldedseams. However, a major downside of this method is the necessary modeling effort withinthe preprocessor environment. All nodes of each tube end have to be connected manuallywith the point of intersec on of the tube axes, using RBE2 elements. Moreover, thismethod requires an extra 3D-CAD model of the frame where all tubes are not connectedat the joints. The process of genera ng an extra CAD model and manually connec ng eachtube is extremely tedious considering the number of joints in the space frame. In addi on,if one would want to change the diameter or width of the tubes, one would have to startfrom scratch and model everything again. Lastly, it only enables the op miza on of thetube thickness, while the remaining cross sec onal dimensions have to be predefined.

Pure Shell Model The last examined approach is very similar to the previous shell elementmodel. The difference is, that the joints are modeled one to one from the generated3D-CAD frame by discre zing all outer surfaces with shell elements. In this way, thelaborious setup of connec ng all tubes with RBE2 elements at the joints does not apply.


While, the previous two methods assume the joints to be rigid, this method models thejoints as they are defined in the 3D-CAD model. However, this would neglect the influenceof the welded seams that are not included in the CAD. This problem does not apply for thepreceding methods, as they do not a empt to model the contact area between the weldedtubes. In addi on, the pure shell element model is limited to op mizing the thicknessonly, like the previous shell element model.

Beam Model RBE2 Shell Model Pure Shell Model

Figure 5.20: Different approaches to modeling the space frame

The implementa on of all three methods is illustrated in Figure 5.20, using an examplejoint that is modeled once with each method. In Appendix F.4 it is compared how thedisplacement and stress contours of these methods develop, when all three joint modelsare loaded with one and the same loading condi on. The outcome of this comparison isthat the pure shell model proves to be inadequate for the size op miza on as well as alater structural analysis. This is because the mesh quality in the area of the joint is verypoor when using the “automesh” func on of HyperMesh. Hence, it would again requireaddi onal modeling effort to manually adjust the mesh. Furthermore, it appears that themissing considera on of the welded seams leads to a joint model that is not s ff enough.As a consequence, the stress contours peak in a few elements in the joint area, reachingvalues that are three mes larger than the maximum stresses from the other two methods.The beam model and the rigid shell model, on the other hand, lead to very similar resultsin both displacement and stress contours, while the beam model tends to predict largervalues.

As a result of experimen ng with all three methods, it was decided to apply the beammodelas design space for the size op miza on. Its advantages over the shell element modelwith rigid joints are simply too overwhelming. It allows the simultaneous op miza on oftube thickness and diameter/witdh, it is significantly simpler in the setup and leads to verysimilar results in the stress and displacement if compared to the rigid shell model. Thedisadvantage that the beam model does not indicate the stress contours on the perimeterof the tube, is less of an issue in the size op miza on stage. It could be shown that thebeam model predicts reasonable stress values, which is sufficient for a size op miza on.However, for the structural analysis of the final design, the more laborious rigid shellelement approach appears to be useful to verify the stress contours of cri cal single joints


(see Sec on 6.2).

5.4.2 Final Size Op miza on Setup and Results

The final size op miza on problem was based on a beam model consis ng of two differentround and four different rectangular cross sec ons. Therefore, the 3D-wireframe wasimported into HyperMesh and discre zed with PBARL elements. Each group of framemembers that share the same cross sec on was allocated a dis nct color and PBARLproperty. The resul ng preprocessor model, including the suspension system, is displayedin Figure 5.21, while the PBARL property defini on is illustrated at the side.

Figure 5.21: HyperMesh PBARL-element model used for the size op miza on, number ofelements: 4921, number of nodes: 4826

The requirement that the frame is to be welded considerably limits the material op ons.The current frame is made of ASTM A500, which is a cost effec ve and very commonstructural tubing steel. In addi on, the NUS has some experience with the AA6061 T6aluminum alloy, which has been successfully applied in similar research car projects. Bothmaterials are widely available by suppliers in Singapore, which is factor that has to beconsidered when deciding on a material. Naturally, the aluminum alloy promises the largerweight saving poten al. However, it is also by far the more expansive choice, which isone of the main reasons why the current frame was made of steel. Due to an unknownfuture budget development, it is not decided yet if the new design can be implementedusing aluminum alloy tubes. However, from this point onwards, it does not require muchaddi onal effort to consider both materials in parallel in two separate op miza on models.This is done in the following. Hence, the size op miza on process will result in two designsugges ons for the new chassis frame, one aluminum and one steel frame. The materialcharacteris cs of both materials can be found in various openly available material factsheets [Lea09, Alc02]. Relevant characteris cs are summarized in Table 5.2.


ASTM A500 AA6061 T6Density [kg/dm3] 7.9 2.7

Young’s modulus [GPa] 210 75

Shear modulus [GPa] 81 28

Tensile strength [N/mm2] 427 262

Yield strength [N/mm2] 345 241

Table 5.2: Material characteris cs for ASTM A500 steel and AA6061 T6 aluminum alloy

The size op miza on problem is generally very similar to the previously performedtopology op miza on. The main difference is the considerably reduced freedom of thedesign space. That means the op miza on problem formula ons that were reviewed in5.2.4 can be adopted for the size op miza on. However, for the size op miza on, theglobal stress constraint seems to be the most adequate method. Since the result of thesize op miza on is already very close to the final design, it makes sense to constrainthe stress in the cross sec on with the objec ve of minimizing the volume of the en restructure. This ensures that the op miza on process leads to the minimum cross sec onaldimensions which are required to withstand the maximum loads in each loading condi on.Hence, the op miza on results automa cally fulfill the maximum stress limita ons of thematerial. Applying the minimum compliance approach would require the guessing of anappropriate value for the volume frac on V0/V , while there is no control of the absolutestress in the structure. As a consequence, the size op miza on was only performed usingthe global stress constraint method.

The yield strength of the material was used as reference for the stress constraint of theop miza on setup, while a moderate factor of safety was applied in order to account forremaining uncertain es in the actual maximum loadings as well as hardly predictable fa guefailures. Brown [Bro03] suggests to apply a safety factor of 1.5 for vehicles body structures.It is noteworthy, that the applica on of a safety factor is generally undesired in lightweightdesign. Applying a safety factor is always rather inaccurate and leads to less weight savingpoten al. Lightweight design largely depends on the exact knowledge of the occurringloads as well as failure mechanisms and designing the system in a way that it is just strongenough to guarantee a safe opera on. However, in automo ve engineering, it is o endifficult to determine the exact loads. This especially applies when, data or experience fromprevious design itera ons is missing, like in the case of the NUS City Car project. In addi on,the strength of the structure is not the only structural requirement for a vehicle body.As it was men oned before, the chassis s ffness is the more important structural criteria[Bro03, Hap01]. Applying a safety factor not only accounts for uncertain es in the maximumloading and fa gue behaviour, it also increases the s ffness of the structure. Under thesecircumstances, the applied safety factor is considered reasonable. The established stresslimits including safety factor are stated in Table 5.3

5.5 New Design Sugges on 89

ASTM A500 AA6061 T6Stress limit [N/mm2] 230 160

Table 5.3: Established stress limits for the size op miza on and strength analysis

The size op miza on was performed with a reduced number of considered load cases.Most notably, the ini ally developed linearized crash load cases were excluded. These weredeveloped specifically for the topology op miza on process to promote the forma on ofstructures that increase the global s ffness of the structure in the case of crash impacts.However, the objec ve of the size op miza on was to find the minimum cross sec onaldimensions of the frame members, so that standard driving situa ons do not result in aplas c deforma on or failure of the vehicle body. Severe crash situa ons, on the otherhand, are required to result in limited plas c deforma ons of the body, in order to protectthe occupant by absorbing kine c energy. Therefore, a crashworthiness analysis wouldrequire a proper non-linear FEA, which is not part of this thesis. As a result, only the sixload cases that model actual driving condi ons were considered in the size op miza on(front bump, rear bump, cornering, braking, accelera ng and bending). These cover avariety of both global and local loads and represent a good approxima on of the maximumloads resul ng from the vehicle opera on.

The resul ng op miza on problem consists of 20 design variables (4 for each rectangularand 2 for each round cross sec on). HyperMesh allows to define upper and lower boundsfor each design variable. This was u lized to limit the thickness, diameter and width ofthe design cross sec ons according to the available cross sec ons found in the suppliercatalogues. For both materials, the op miza on process leads to cross sec ons thatconsequently feature the minimum thickness that was set using the lower bound func on,while the widths and diameters are comparably large. This is consistent with the fact thatthe area moment of iner a of a thinwalled cross sec on is larger than the moment ofiner a of a full or thicker cross sec on of the exact same area. With the results from thesize op miza on process, the cross sec ons for each frame member group were selectedfrom the supplier catalogue. Since, the tubes are only available in incremental size steps,the op miza on results could not be implemented one to one. In the case a cross sec onwas not available as suggested by the op miza on results, the next larger available sizewas selected.

5.5 New Design Sugges onWith all cross sec ons selected, the final 3D CAD model of both frames could be modeled.Both resul ng frames, steel and aluminum, look very similar from the outside, since theouter diameters and widths of the tubes only differ slightly. The main difference is that thesteel frame generally features thinner tubes. The two frames models are illustrated in Figure5.22 and 5.23 respec vely. Here, all displayed measurements are given in millimeters.


25

2

12.5

2

38

38

2

25

38

2

2

45

64

25

38

1

Figure 5.22: Design sugges on using aluminum alloy tubes, mass: 23.5kg

25

1

12.5

1

38

38

1.2

25

38

1

1.6

38

64

19

38

1

Figure 5.23: Design sugges on using steel tubes, mass: 40.8kg

Remarkable is the large single rectangular tube in the back (green), which has to sustainthe forces transmi ed by the single rear shock absorber. It also becomes apparent that theop miza on led to rectangular cross sec ons rather than square ones for several framemembers. This includes the central frame members that support the si ng occupants aswell as the frame members that accommodate the brackets for the suspension arms. Thisis a result of the mainly unidirec onal loads ac ng on these frame members. The achievedweight reduc on and the resul ng range extension for both op mized frame designs issummarized in Figure 5.24. In order to demonstrate the increased dimensions of the newdesign if compared to the current state, both frames are addi onally displayed one upon


the other.

Aluminum Steel

Frame Mass [kg] 23.5 40.7

Mass Reduction [kg] 31.5 14.3

Relative

Reduction of

Frame Mass

% 57.3 26.0

Relative

Reduction of

Vehicle Mass

% 6.0 2.7

Range Extension [km] 3.01 1.32

Current design (55kg)

New design

Figure 5.24: Comparison of the weight saving poten al of the two new design sugges ons

Despite the fact that the new design is considerably larger and has been designed forsignificantly higher loadings than the current design, it could be achieved to reduce theframe mass by respectable 57% in case of the aluminum sugges on and 26% when assumingsteel. The reason for this notable weight reduc on in spite of the increased global size,is the comparable large wallthickness of the current frame, which consists exclusively of2mm steel tubes. In contrast, the new steel design features way thinner tubes whichcompensates the increased global dimensions. With regards to the total vehicle mass, thenew design sugges ons would respec vely contribute to a 6% and 2.7% weight reduc on.This translates into a 3km increased range in case of the aluminum frame and 1.3km morerange if the steel frame is considered.

6 Structural Analysis of the New Design

The structural op miza on process performed in the previous chapter resulted in two designsugges ons for the chassis frame of the NUS City Car, depending on weather the frame isto be implemented as steel or aluminum frame. In the last step, both design sugges onsare subjected to a structural strength analysis, which is described in this chapter. Sincethe performed size op miza on was based on constraining the maximum stress in thestructure and the cross sec ons were selected according to the size op miza on results,it could be expected that the final frame designs remain below the stress limit in allloading condi ons. However, the following detailed strength analysis will point out cri calload cases as well as cri cal joints and frame members in each loading condi on. Thestrength analysis is mainly based on the beam model that has been introduced in the sizeop miza on process. The disadvantage of the beam model is that it lacks the indica on ofstress contours on the perimeter of the tubes. In order to compensate this, a method thatallows a quick and reliable recalcula on of cri cal joints and frame members is addi onallydemonstrated. Lastly, the torsional s ffness of both frames is compared using the torsionalload case introduced in Sec on 5.2.

6.1 Strength Analysis Based on the Developed Beam ModelSimilar to the size op miza on, the ques on of the best discre za on method of the framestructure also arises when performing the strength analysis of the final design. Consideringthat the design is finalized and that further changes to cross sec on diameters or widthsare unlikely, the shell model with RBE2 nodes appears to be more reasonable in this finalstage if compared to the previous size op miza on stage. However, the modeling effort iss ll very high and since the beam model performed very similar to the RBE2 shell model interms of maximum stress (see Appendix F.4), it was decided to apply the developed beammodel (Figure 5.21) once again as modeling founda on. Therefore, the cross sec ons ofeach final frame design were a ributed to the PBARL elements of the beam model viathe property manager of the preprocessor. The considered load cases were adopted fromthe size op miza on process. The three global load cases (cornering, front bump, rearbump) could be iden fied as cri cal load cases. The stress contour plots of these threeload cases are displayed in the following for both the steel frame (Figure 6.1) and thealuminum frame (Figure 6.2). The stress contours of the remaining load cases (bending,braking, accelera ng) are displayed in Appendix F.5. The strength of the chassis frameis checked using the von Mises yield criterion, which suggests that yielding of a duc le

6.1 Strength Analysis Based on the Developed Beam Model 93

material does not begin before an equivalent tensile stress reaches a cri cal value. Thisequivalent tensile stress σv approximates mul -axial stress condi ons through a scalarvalue that can be computed from the stress tensor in the cross sec on. Therefore, thefollowing plots display the von Mises stress in the structure.

Front Bump

Steel Frame - Front Bump

SUB5 - bump_L Von Mises Stress

> 2.09e+02< 2.09e+02< 1.83e+02< 1.57e+02< 1.31e+02< 1.05e+02< 7.85e+01< 5.23e+01< 2.62e+01< 5.28e-10

Max = 2.36e+02Min = 5.28e-10

X

Y

Z

Cornering Rear Bump

Steel Frame - Cornering

SUB8 - cornering_L Von Mises Stress

> 2.10e+02< 2.10e+02< 1.83e+02< 1.57e+02< 1.31e+02< 1.05e+02< 7.86e+01< 5.24e+01< 2.62e+01< 0.00e+00

Max = 2.36e+02Min = 3.27e-09

X

Y

Z

Steel Frame - Rear Bump

SUB7 - bump_rear Von Mises Stress

> 1.87e+02< 1.87e+02< 1.64e+02< 1.41e+02< 1.17e+02< 9.37e+01< 7.03e+01< 4.69e+01< 2.34e+01< 0.00e+00

Max = 2.11e+02Min = 1.82e-10

X

Y

Z

Figure 6.1: Steel Frame - v. Mises stress contours in cri cal load cases (unit: N/mm2)

The stress contour plots of both frames look very similar in each loading condi on withthe only difference being the absolute stress values. This was expected, as the crosssec ons of both frames were selected using the same size op miza on procedure. Sincethe cornering and the front bump load case both lead to considerable torsional loads onthe structure, the stress distribu on in these two load cases resemble each other. Here, thejoints adjacent to the front suspension mounts can be pointed out as cri cal. The rear bumploading condi ons yields maximum stress in the single horizontal back frame member. Thestress values of these cri cal load cases reach or even match the defined stress limits fromTable 5.3. This supports the successful applica on of the size op miza on process, whichled to the required cross sec onal dimensions in a very efficient way. However, at this

6.1 Strength Analysis Based on the Developed Beam Model 94

point, it is again referred to the compromise made by adjus ng the maximum allowablestress with a safety factor. The lightweight design poten al could be increased by rulingout the uncertain es in the loading which were the reason for the considera on of safetyfactors. Therefore, it would require further tests and study. This especially includes cyclicloadings that result in material fa gue. However, in the current applica on, the safetyfactor is not only applied in an a empt to account for the loading uncertain es but alsoto increase the s ffness of the structure, since this is the prime structural property of avehicle body [Bro03, Hap01].

Front Bump

Alu Frame - Front Bump

SUB5 - bump_L Von Mises Stress

> 1.26e+02< 1.26e+02< 1.11e+02< 9.48e+01< 7.90e+01< 6.32e+01< 4.74e+01< 3.16e+01< 1.58e+01< 0.00e+00

Max = 1.42e+02Min = 6.28e-10

X

Y

Z

Cornering Rear Bump

Alu Frame - Rear Bump

SUB8 - cornering_L Von Mises Stress

> 1.17e+02< 1.17e+02< 1.03e+02< 8.79e+01< 7.33e+01< 5.86e+01< 4.40e+01< 2.93e+01< 1.47e+01< 0.00e+00

Max = 1.32e+02Min = 5.70e-09

X

Y

Z

Alu Frame - Rear Bump

SUB7 - bump_rear Von Mises Stress

> 1.32e+02< 1.32e+02< 1.16e+02< 9.92e+01< 8.27e+01< 6.61e+01< 4.96e+01< 3.31e+01< 1.65e+01< 0.00e+00

Max = 1.49e+02Min = 1.90e-10

X

Y

Z

Figure 6.2: Aluminum Frame - v. Mises stress contours in cri cal load cases (unit:N/mm2)

6.2 Recalcula on of Cri cal Frame Members 95

6.2 Recalcula on of Cri cal Frame MembersIt was shown that the maximum stress values indicated by the beam model are almostequal to the peak stress in the RBE2 shell element model, which was the reasoning forapplying the easily implemented beam model as basis for the strength analysis. However,it is possible that it is required to determine the exact loca on of the maximum stresson the outer surface of the frame members. This is for example necessary for a detailedanalysis of the welds or for the evalua on of the impact of addi onal bore holes in certainframe members. As it was discussed in 5.4.1, the RBE2 shell model is capable of such aconsidera on. In order to avoid the considerable modeling effort of discre zing the en reframe with shell element tubes, it was experimented with extrac ng certain frame membersfrom the beam model and remodeling these joints with the shell element method in anisolated manner. This ensures that only those frame members are subject to a detailedRBE2 shell element analysis, that are of par cular interest. The idea was to read out theforces and moments in the boundary nodes of the examined frame members from thebeam model analysis, and create the same loading condi on on an isolated shell elementmodel of the same frame member with the extracted forces and moments. In the isolatedmodel, the respec ve forces and moments are applied at one end of the frame member,while the opposing end is constrained in all six degrees of freedom. The result is a freebody diagram of the examined frame member which approximates the actual loading inthe vehicle body. This method was tested using the example of a cri cal joint in the frontbump loading condi on. The tes ng procedure is as follows:

1. Run FEA with beam model and highlight the stress contours of the examined framemembers

2. Extract the forces and moments in the end nodes of each frame member

3. Cut the examined frame members from the full beam model and apply the extractedforces and moments (free body diagram)

4. Run FEA with isolated beam model and compare with the highlighted stress contoursof full beam model

5. Model the examined frame members using the RB2 shell element method and applythe extracted forces and moments (free body diagram)

6. Run FEA with isolated RBE2 shell element model and compare the peak stress valueswith the isolated beam model

This procedure along with the generated models and stress contour plots are illustrated inFigure 6.3.

6.2 Recalcula on of Cri cal Frame Members 96

Front Bump Loading Cri cal Joint - Beam Model Cri cal Joint - Shell Model

Figure 6.3: Development of the recalcula on of cri cal joints/frame members

The outcome of this test is, that the proposed procedure qualifies as complemen ngmethod for backing the strength of cri cal frame members or for the indica on of the exactstress contours on the tube perimeter if necessary. Comparing, the isolated beam modelwith the highlighted frame members of the full model, shows that the extracted forcesand moments are sufficient to create a loading condi on that yields the same qualita vestress like the full beam model. The only difference is that the absolute stress valuesof the isolated model lie about 5-10% below the original model. However, this can beneglected, since the peak stress is already known and the purpose of this procedure isthe iden fca on of the qualiata ve stress contours, which is given by the isolated beammodel. Based on this finding, the same frame members were modeled using the RBE2shell element method and the same loading condi on is simulated with the extractedforces and moments. The resul ng stress contours peak slightly under the maximum stressof the isolated beam model. This further confirms the assump on, that the beam modelgenerally indicates the same or slightly larger maximum stress like the beam model. Inaddi on, the shell model finally indicates the aimed stress distribu on on the tube surface.

The proposed procedure has proven that it is possible to combine the advantages of boththe beam model and the RBE2 shell element model without notably compromising neitherthe accuracy of the shell model nor the convenience of the beam model. Using this method,addi onal cri cal frame members can be easily examined if needed at some point.

6.3 Torsional S ffness Comparison 97

6.3 Torsional S ffness ComparisonAs it was discussed in Sec on 5.1, the torsional s ffness of vehicles structures is one ofthe main structural performance criteria. However, the requirement of high body s ffnessgenerally clashes with the concept of lightweight design. The topology op miza on processled to a s ffness and lightweight op mized structure. However, the size op miza on processand the strength analysis were based on a safety factor adjusted maximum allowablestress. This safety factor decreases the lightweight op miza on poten al of the structureconsiderably. However, at the same me, it increases the s ffness of the vehicle body byincreasing the cross sec onal dimensions, which is also much desired. This is the reasonwhy a safety factor was eventually applied, despite the fact that some weight savingpoten al is dissipated.

In addi on to the safety factor, the material plays a major role when it comes to thevehicle body s ffness. Two designs based on different materials were suggested. Due tothe larger young’s modulus of steel, the steel frame is expected to lead to a notably largers ffness if compared to the aluminum frame. This sec on compares the torsional s ffnessof both final design sugges ons, based on the established FE beam model. In addi on,a beam model of the current frame was generated in order to contrast the achieveds ffness of the new designs with the current design. All three beam models were loadedwith the torsional load case applied in the topology op miza on process. This load caseis illustrated in Figure 6.4 along with the geometry behind the s ffness calcula on. Thismethod resembles the common prac ce of measuring the torsional s ffness of vehiclebodies. In the pictured equa ons, KT denotes the torsional s ffness, T the applied torqueand Θ the resul ng deforma on angle. The necessary displacements ∆y1 and ∆y2 weremeasured in the postprocessor HyperMesh.

KT = TΘ

KT = F ·Ltan−1(∆y1+∆y2

2L )

F

Δy1

Δy2

L

FΘ

Figure 6.4: Method of measuring the torsional s ffness of the chassis frame

The calcula on of the torsional s ffness of the three frame designs using the describedmethod is summarized in the following table.

6.3 Torsional S ffness Comparison 98

Values Aluminum Steel Current

Delta Y1 [mm] 9.0 5.3 21.1

Delta Y2 [mm] 8.8 5.3 18.5

L [mm] 750 750 714

Applied Force [N] 1000 1000 1000

Angle [deg] 0.68 0.41 1.59

Torque [Nm] 750 750 714

Stiffness [Nm/deg] 1104 1842 450

Torsionnal Stiffness

Table 6.1: Calcula on of the torsional s ffness according to the described method

It can be established that the steel frame is 2/3 s ffer than the aluminum frame.Considering that the weight advantage of the aluminum frame over the steel frame is 72%,it can be concluded that both frames feature roughly the same s ffness performance ifmeasured in mass/s ffness. Therefore, the steel frame remains the be er choice whenthe main criteria is torsional s ffness, as it provides the higher absolute s ffness at lowercost. However, both new design sugges ons exceed the torsional s ffness of the currentframe many mes over. In case of the aluminum frame, the s ffness is increased by morethan two mes, while the steel design exceeds the current s ffness about four mes.

7 Summary and Conclusions

The main objec ve of this study was the op miza on of the lightweight design of the NUSCity Car using finite element based structural op miza on. This objec ve was approachedin three parts.

In Chapter 3, it was studied how the vehicle’s mass affects the energy consump onand the range of the vehicle. This was approached by developing a simple quasista cparametric model that es mates the energy consump on and the range of the City Carunder the considera on of basic vehicle characteris cs such as vehicle mass, rolling fric on,aerodynamics or ba ery size as well as the driving pa ern of the vehicle opera on. Thismodel was wri en in Matlab and could be validated through comparisons with a referencemodel of a similar configura on, which was available from the powertrain simula onso ware PSAT. The developed model was the founda on of a parametric sensi vity analysis,which studied how changes of +5% and -5% to each model parameter influence the rangeof the vehicle. The result of this parameter study is that the drivetrain efficiencies have thelargest impact. However, the vehicle mass is almost equally influen al, especially whenassuming a severe city driving pa ern. The remaining parameters have a comparable li leinfluence on the range, while the rela ve impact of the vehicle mass decreases as thedriving pa ern shi s towards higher average veloci es. However, in average city cyclecondi ons, it could be concluded that a 1% reduc on in the vehicle’s mass translates intoa notable 1% increase in the achieveable range, while the absolute range of the currentvehilce configura on is about 50km. This rela onship remains linear up un l a weightreduc on of 40%. Considering the fact that 1% saving in the vehicle mass is by far morerealis c than the improvement of the drivetrain efficiency by 1%, it could be established thatlightweight design is indeed the most reasonable approach to op mizing the performanceof the NUC City Car in terms of energy consump on and range. The developed parametricrange es ma on model was addi onally implemented as Matlab GUI. This enables itsuser-friendly usage for quick future es ma on purposes within the NUS City Car project.

Supported by this conclusion, the current vehicle configura on was analyzed in Chapter4 with the objec ve of selec ng one vehicle component that is par cularly suitable forreducing its weight through structural op miza on. Therefore, all major vehicle componentswere weighted and captured in a database. In addi on, each component was allocated afeature that indicates its poten al and feasibility for structural op miza on. For instance,basic steel components with high density and simple structure were defined as highlysuitable, whereas complex electric components such as ba eries were declared as least

7 Summary and Conclusions 100

suitable, irregardless their high absolute weight. The resul ng database was put into graphsthrough ABC-Analysis and Treemaps. Here, the Treemaps proved to be an especially usefultool for the visualiza on of the database content. The interpreta on of the performedcomponent analysis concluded in the selec on of the chassis frame as heaviest of thebasic steel components.

With the chassis frame chosen asmost suitable component, the last andmost comprehensivepart of this work revolved around the finite element based structural op miza on consis ngof both topology and subsequent size op miza on of the chassis frame (Chapter 5). Thefirst step of the op miza on process was the iden fica on of all relevant load cases. Theframe, as central component that holds everything together, is subjected to a mul tude oflocal and global loads. Based on the performed literature review, 11 load cases resul ngfrom all possible driving situa ons were eventually determined. These not only includestandard driving situa ons, such as braking, cornering or striking a bump, but also crashsitua ons, which were approximated by linearized iner a forces. Before the topologyop miza on problem was implemented based on the iden fied load cases, considerableme was spent on several side studies that were conducted to back the made decisions

regarding the FE-modeling as well as the op miza on setup. This includes a compara vestudy on the implementa on of dynamic load cases such as cornering and bump encounters,where it was established that the iner a relief func on of HyperWorks is suitable to modelbump forces exerted at the unconstrained vehicle structure. Moreover, different op onsfor the approxima on of the load transmission through the suspension system into thevehicle body were inves gated. This inves ga on led to the successful implementa on ofa simple suspension model consis ng of 1D ROD and BEAM elements.Regarding the topology op miza on setup, another study regarding the op miza onproblemformula on was performed. Three different methods of defining the op miza on problemwere examined. It was shown that the same op mized topology can be achieved with allthree methods. However, the global stress constraint and the minimum compliance methodturned out to bemore convenient in the setup than the individual displacementmethod. Thefinal op miza on setup was eventually implemented using the well established minimumcompliance method. Following that, the design space of the topology op miza on setupwas developed using a top down approach, where the design space freedom is graduallyreduced un l the resul ng topology is compa ble with all func onal and manufacturingrequirements of the chassis frame. This approach ensures that the achieved topology trulyreflects the op mum within the present constraints. As a result, a full 3D-element designspace proved to be computa onally too intense for the available hardware. However, itcould be shown that a 2D-surface design space is also sufficient for the proposed applica on.The resul ng op mized topology of the final op miza on setup, was then exported intoSolidWorks and reproduced as 3D-wireframe, while a few simplifying changes had to bemade in order to keep the design feasible. This 3D-wireframe served as basis for thesize op miza on and the final 3D CAD model. The next step was the setup of the size


op miza on problem, with the objec ve of finding the op mal cross sec onal dimensionsof the frame members.In support of the size op miza on setup, a compara ve study on different ways of modelingthe frame members was conducted. This study concluded in the selec on of a simple beammodel consis ng of PBARL elements as best op on. Such a beam model proved to haveseveral decisive advantages such as its simple setup using the 3D-wireframe model, itshigh flexibility regarding changes to the setup and its capability to simultaneously op mizethe thickness and the diameter/width of frame members. At the same me, it could beshown that the beam model is sufficiently accurate when it comes to indica ng the peakstresses in the structure.The size op miza on was formulated as minimiza on of the volume while the stress in thestructure was constrained (global stress constraint method). This appeared to be the bestformula on, since the maximum allowable stress is known from the material fact sheet ofthe supplier and no op miza on se ngs have to be guessed. The size op miza on processwas performed in parallel under the considera on of both available material op ons, astandard tubing steel as in the current design and a lighter weldable aluminum alloy. Hence,the size op miza on stage was characterized by the incorpora on of material lightweightdesign principles. The stress limit for the op miza on setup was defined by adjus ngthe yield strength of each material with a safety factor of 1.5, despite the fact that thismeasure possibly leads to was ng some weight reduc on poten al. At the same me, itincreases the vehicle s ffness as the prime structural criteria for a vehicle body. This iswhy a compromise was made between the weight reduc on poten al and the s ffness ofthe vehicle structure by applying a safety factor. In the last step of the size op miza onsetup, the cross sec onal shape of all frame members had to be defined. Like the old framedesign, the new frame was to be made of a combina on of round and rectangular tubes,while all frame members that have to enable the moun ng of components were allocatedrectangular cross sec ons. The remaining frame members were defined as round tubes,as they have the be er overall s ffness and strength per weight unit. In order to findthe op mal number of different frame tubes to be considered, the size op miza on wasperformed mul ple mes with each base material, while the number of different tube typeswas gradually increased un l a good compromise between the weight reduc on poten aland the frame complexity was achieved. The final size op miza on setup comprised 2different circular and 4 different rectangular tube types. Since the material suppliers onlyprovide incremental tube sizes, the final cross sec ons for each group of frame memberswere selected according to availability. With the selected cross sec ons, both the steeland the aluminum frame were modeled accordingly in SolidWorks.Hence, the structural op miza on process concluded in two design sugges ons for the newchassis frame of the NUS City Car. If the op mized design was to be made of the suggestedaluminum alloy, the weight can be reduced by over 50% to just 24kg. This translates into a6% reduc on of the total vehicle mass, which leads to 3km more range compared to thecurrent configura on. Considering the steel frame design sugges on, the weight reduc on


yields 25% with a op mized mass of about 40kg. Hence, the total vehicle mass would bereduced by 2.7% leading to a range extension of 1.3km. Remarkable is that, this weightreduc on was achieved despite the fact that the new design features considerably largerdimensions and was designed to accommodate a notably heavier ba ery pack.

Both design sugges ons were subjected to a structural strength analysis in the final Chapter6. Here, it was proven that the two designs remain below the defined stress limits withthe global dynamic load cases (cornering, front bump, rear bump) being the most severeloading condi ons. The joints adjacent to the suspension moun ngs could be pointed outas cri cal. The strength analysis was based on the developed beam model from the sizeop miza on. However, such a beam model is not capable of indica ng the loca on ofthe peak stress contours on the outer surface of the tubes. Therefore, a procedure wasproposed that allows a quick recalcula on of cri cal frame members, based on an isolatedfree body diagram of the examined frame members. In this free body diagram, the framemembers are discre zed with shell elements, allowing to simulate the stress contours onthe tube perimeter. The needed forces and moments can be extracted from the full beammodel. Lastly, the torsional s ffness of both design sugges ons as well as the currentframe was es mated, based on beam models. It could be established that both new designsugges ons feature a tremendously increased torsional s ffness if compared to the currentframe design. The steel frame design sugges on exceeds the s ffness of the current frameby more than 400%, while the aluminum design sugges on is superior by about 250%.Hence, the structural op miza on process not only led to a significant weight reduc onbut also to a remarkable improvement of the torsional s ffness of the chassis frame.

Future Prospects

During the process of this work, several issues that appear to have poten al for future studieswere encountered. This especially includes issues regarding the structural op miza onprocedure but also the general lightweight design approach. A few promising ma ers aresummarized in the following.

The present thesis approached the lightweight design op miza on mainly from a structuralpoint of view. However, the weight reduc on poten al can be increased when systemand material lightweight design concepts are incorporated to a larger extent. Therefore,it is suggested to perform a more detailed component analysis, where all componentsare captured down to piece part level, before further lightweight design measures areimplemented on the current NUS City Car. If this analysis was performed under theconsidera on of all lightweight design concepts, several new star ng points for furtherweight reduc on measures can be expected.

With regards to the performed structural op miza on, it can be pointed out that thiswork did not include the considera on of cyclic loading condi ons or the modal frequencyresponse of the vehicle body. However, these are two important aspects in the design of


road vehicles. In a con nua ve work, it could be examined if the inclusion of these factorsin the topology op miza on formula on has a notable effect on the resul ng topology. Thesame applies for a more comprehensive incorpora on of crashworthiness concepts. In thiscontext it would be also interes ng to perform a subsequent non-linear crash simula onin order to evaluate the crashworthiness of the op mized design.

Lastly, it can be pointed out that the performed topology op miza on was based on areduced shell element design space mainly because of the limited computa on rate ofthe available hardware. Although it could be shown that such a surface design space issufficient for the proposed applica on, it would be worth studying if a full 3D elementdesign space can result in new aspects regarding the op mal topology. Especially withregards to remaining small scale vehicle components with high poten al for structuralop miza on such as the rear swingarm, it is suggested to focus on a 3D element designspace, if the needed CPU power is accessible. This ensures that the op miza on algorithmu lizes the en re available space.

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A Dynamic behvaiour of Three Wheeled VehiclesThe dynamic behaviour of three wheeled vehicles is notably different if compared toconven onal four wheel passenger cars. It is important to keep this in mind when designinga three wheel pla orm. Therefore, this appendix summarizes the basics of non- l ngTWV dynamics. In this context, two benchmark characteris cs are presented to help toevaluate the dynamic stability of TWVs. A comprehensive paper on designing stable TWVswas found in Starr (2006) [Sta06]. This work served as guideline and main input for thefollowing indica ons.

The dynamic behaviour of TWVs is closely related to the loca on of the center of mass(CM) of the vehicle. For non- l ng TWVs it is recommended to include the posi on ofthe CM into the design specifica ons in order to achieve a stable vehicle response. Itsloca on directly influences the vehicle’s stability in terms of:

• Resistance to rota ng about the ver cal axis through the CM, due to side loads• Resistance to pping over when cornering or encountering road obstacles• Resistance to a swapping rear in case of hard breaking due to weight transfer fromthe rear to the front

Out of these three stability characteris cs the focus lies in the former two, as a swapping rearis generally a less severe criteria for stability compared to steering and pping behaviour.

Yaw Response The tendency of a road vehicle to rotate about its ver cal axis is referredto as yaw response. It is required that the vehicle can undergo side loads as in turningor due to side wind without tendency to spin. The yaw response of the vehicle not onlydepends on the posi on of the CM. It also relates to the cornering s ffness of the resand to the suspension characteris cs. The suspension will mainly cause a delay of theresponse rather than a significant change in its tendency. To simplify ma ers, the impactof the suspension is hence neglected in the following. The cornering s ffness of the reson the other hand is needed to establish rela onships between the CM loca on and thevehicle stability. This results from the effect, that the actual travel direc on of a laterallyloaded rolling re is deflected from the direc on in which the re is headed. The angle ofdeflec on is generally known as slip angle α and depends on the cornering s ffness ofthe re as well as on the magnitude of the lateral load. For more detailed explana ons ofthis effect, it is referred to Chapter 9 of Popp und Schiehlen (2010) [PK10].

The following figures (A.1 - A.3) picture the top views of a simplified road vehicle model,which is generally known as bicycle model. In the model, the rectangles at each end reflectthe wheels of the two vehicle axles. Applying this model on the NUS City Car meansthat the front rectangle represents the two front axle wheels while the rear rectanglereflects the single rear wheel of the City Car. Assuming that all three res have the same

A Dynamic behvaiour of Three Wheeled Vehicles 110

cornering s ffness, the front wheel of the bicycle model has double the cornering s ffnessof the rear wheel. The vehicle center mass is assumed to be on the center line, whilethree different loca ons of the vehicle CM are considered (CM1, CM2, CM3). FigureA.1 shows the vehicle traveling at constant speed along a certain path without any sideload. The veloci es of the two vehicle axles are denoted as vf and vr, and have the samemagnitude and direc on as the vehicle velocity, when there is no side load applied. Themodel neglects the trac on force at the driving wheel as well as the aerodynamic dragforce along with the rolling resistance. These forces are assumed to be along the vehicle’spath summing up to zero.

path

CM1

CM3

CM2

vf

vr

lf

wb

Cf = C + C

Cr = C

Figure A.1: Bicyclemodel moving straight

LNSPCM1 Flat

Flat

Flat

αf

path

αr

Fr

vf

vr

Ff

CM3

CM2, NSP

Figure A.2: Bicyclemodel, laterally loaded

orig. path

Θ

Flat

Flat

Flat

SM > 0

SM < 0

CM2, NSP

CM3

lateralmotionfrom Flat

CM1

Figure A.3: Response tolateral load

Figure A.2 illustrates the bicycle model under the lateral load Flat. In this case, theres deflect according to their cornering s ffness resul ng in the slip angles αf and αr

respec vely at the rear and front axle. Therefore, the axle veloci es vf and vr also deflectfrom the original path. Figure A.3 shows the vehicle response due to the applied side load.For this illustra on, the reac on forces at the res as well as the slip angles have beenremoved for clarity. The vehicle response is a lateral movement of the CM off the originalpath and an angular movement about the vehicle’s CM, indicated by the angle Θ. Thepicture also shows the neutral steer point (NSP) of the vehicle. This point coincides withCM2 and describes the point at which a lateral load does not cause any yaw response.The loca on of the NSP with respect to the front axle depends on the total cornering


s ffness at each axle:LNSP =

(Cr

Cf + Cr

)· wb

The posi on of the NSP rela ve to the center mass of the vehicle defines the characterof the yaw response. Therefore, the distance from the CM to the NSP divided by thewheelbase wb is defined as sta c margin (SM) and serves as indicator for the yaw responseof vehicles:

SM =

(Cr

Cf+Cr

)· wb− lf

wb=

Cr

Cf + Cr

− lfwb

With the previously made assump on of equal cornering s ffness at all res the sta cmargin of a three wheeled vehicle in tadpole configura on can be rewri en as:

SMTWV =1

3− lf

wb

In case the CM coincides with the NSP, the sta c margin yields SM = 0 meaning that alateral load will not result it any yaw response. Thus, the vehicle will only slip laterallywith front and rear slip angle being equal (αf = αr). This yaw response is also referred toas neutral steer. In case the CM is ahead of the NSP, shown as CM1, the sta c marginbecomes posi ve with the front slip angle being larger than the front (αf > αf ) and thevehicle undergoes a rota on where the vehicle front heads off in direc on of the appliedforce. This yaw response is termed undesteer and is considered as stable. This is becausea posi ve SM leads to a slightly self-correc ng yaw response during steady cornering. Ifthe CM is located behind the NSP, as it is shown with CM3 in Figure A.3, the rear slipangle becomes larger than the front (αf < αf ), leading to an unstable yaw response, whichis also called oversteer. For more informa on on this effect it is referred to Popp (2010)[PK10]. As result of this, posi ve or zero values of SM are desirable. According to thepaper from Starr (2006) [Sta06] typical vehicles have small posi ve values of SM in therange of +0.05 to +0.07, while an SM up un l −0.01 is s ll acceptable. This sugges onroughly translates into an even weight distribu on of the total mass on the three wheelsin a sta c bending situa on.

Tipping Threshold Another important stability criteria for road vehicles is the resistanceto pping over. The pping situa on can be analysed through a simple quasi-sta c vehiclemodel represen ng the vehicle under such a lateral load that just causes the inside wheel(s)to have zero ver cal load. The respec ve lateral load is the pping threshold, here denotedas ato, and is o en expressed as a mul ple of the gravita onal accelera on. For a standardfour wheeled vehicle, the described model leads to a pping threshold dependent onlyon the vehicle track (tr) and the height of the CM above the road level (h) [Hap01]:

ato, 4W =tr

2 · h


For a TWV, this value is addi onally dependent from the longitudinal loca on of the CM,which is derived in the following. Figure A.4 shows a three wheeled vehicle under lateralload indicated by the ppover accelera on ato. The vehicle wheelbase is denoted as wb

and the front track as tr, with lf being the distance from the front axle to the CM, whilethe CM lies on the longitudinal center line. The reac on forces in the contact patchesbetween res and road are represented by F and R. In case of p over, the wheel loadson the right front wheel (Fr) become zero due to the load transfer resul ng from thelateral load ato poin ng to the le side.

R

Fl

Fr=0

gato

lf

wb

tr

h

Rx

Flx

Frx=0

Figure A.4: TWV under lateral load in the moment of pping over

For this considera on, it is assumed that the res cannot slip before the vehicle psover. The actual maximum lateral reac on force in the contact patch between road andre depends on the respec ve lateral fric on coefficient. Assuming that the res are

constraint sideways ensures that the model also accounts for extreme situa ons such asbump encounters while sliding. Solving the sta c equilibrium equa ons for the free bodydiagram in Figure A.4 leads to the following expression for ato:

ato =tr · (wb− lf )

2 · wb · h

The larger the value for ato is, the higher is the resistance of the vehicle to pping over,while Starr (2006) [Sta06] suggests a target value of ato = 1.0.

B Valida on of the Parameter Model through PSATIn order to validate the range es ma on model developed in Sec on 3.1, a few main modeloutput parameters were compared to the output of a reference model provided by thePSAT so ware package. The powertrain configura on of the reference model is illustratedin the following figure, which has been extracted directly from the PSAT interface.

Figure B.1: Mass centers of individual components in xy-plane

The assigned powertrain components are stated within PSAT as follows:

Vehicle mass = 500kg, Frontal area = 1.5, Drag coeff = 0.6

Wheel Represents PNGV goal, wheel radius 0.26, 1st rollingresistance coeff = 0.01

Motor MY04 Toyota Prius Mobility - con nuous Power = 25kW,Peak Power = 50kW

Ba ery Pb 12V, Capacity = 66h, Cell number = 60ElectricalAccessories

accessory power losses = 0W

Based on this reference model, the valida on procedure is subsequently summarized,while the New York City Cycle (NYCC) has been selected as reference driving pa ern.

• Perform simula on of single NYCC with PSAT reference model• Extract average motor efficiency from PSAT results table• Adjust input parameters of developed model according to PSAT model input (includingextracted average motor efficiency)

• Perform simula on of single NYCC with developed model• Plot results of both models upon each other

B Valida on of the Parameter Model through PSAT 114

The PSAT so ware does not provide an op on that directly determines the achievablerange. Therefore, the development of the SOC during the test cycle simula on is compared.This valida on procedure was performed for different overall vehicle masses. All valida onruns led to qualita vely similar results regardless the assumed vehicle mass. As a result ofthis, only the results of the valida on run with an assumed vehicle mass of M = 500kg

are illustrated.

0 100 200 300 400 500 600−10

−5

0

5

10

15

time [s]

Pow

er [k

W]

Comparison of Traction Power

PSATDeveloped Model

0 100 200 300 400 500 6000

5

10

15

20

time [s]

Pow

er [k

W]

Comparison of Motor Input Power

PSATDeveloped Model

0 100 200 300 400 500 6000

50

100

150

200

time [s]

Cur

rent

[A]

Comparison of Motor Input Current

PSATDeveloped Model


0 100 200 300 400 500 6000

10

20

30

40

50

60

time [s]

For

ce [N

]Comparison of Rolling Resistance

PSATDeveloped Model

0 100 200 300 400 500 6000

20

40

60

80

100

120

time [s]

For

ce [N

]

Comparison of Aerodynamic Resistance

PSATDeveloped Model

0 100 200 300 400 500 6000

50

100

150

200

time [s]

Ene

rgy

[Wh]

Comparison of Accumulated Energy Demand

PSATDeveloped Model


0 100 200 300 400 500 60096

97

98

99

100

time [s]

Sta

te o

f Cha

rge

[%]

Comparison of State of Charge Development

PSATDeveloped Model

Through these plots, it can be concluded that the developed simplified model deliversoverall very similar results if compared to the reference model. The developed model notonly reflects the trend of the reference model in all simula on parameters, it also achievesvery similar absolute values. It could be shown that the developed model sufficientlyes mates the energy consump on and ba ery discharge of an electric vehicle. Therefore,it is considered a reasonable founda on for the sensi vity analysis on the vehicle’s range.

C Component Weight and Op miza on Ap tude Database

Assembly Group Weight [kg] QuantityTotal

Weight

Aptitude/

Material

Chassis Frame

Wires 5 1 5 Electric

Frame 55 1 55 Steel

Body Shell 20 1 20 CFK

Seat incl. Cushion 19 2 38 Steel

Sum 118

Controls

Steering Unit 4.5 1 4.5 Steel

Steering Gear 1.3 1 1.3 Al

Steering Wheel 4.7 1 4.7 Steel

BrakingPedal 3.3 1 3.3 Steel

Throttle Pedal 1.1 1 1.1 Electric

Emergency Stop 1.2 1 1.2 Electric

Sum 16.1

Energy Storage

Battery 23 12 276 Electric

Sum 276

Power Unit

Motor 45 1 45 Electric

Motor Controller 1.6 1 1.6 Electric

Rear Gear 2.7 1 2.7 SteelRear Gear 2.7 1 2.7 Steel

Motor Mount 10.2 1 10.2 Steel

Sum 59.5

Rear Assembly

Rear Wheel 11 1 11 Fixed

Rear Suspension 2.5 1 2.5 Fixed

Rear Swingarm 14.5 1 14.5 Steel

Rear Brake 1.1 1 1.1 Fixed

Sum 29.1

Front Assembly

Front Wheel 7.5 2 15 Fixed

Front Suspension 1.5 2 3 Fixed

Front Brake 0.8 2 1.6 Fixed

Doublewishbone 4.3 2 8.6 Steel

Sum 28.2

Total Weight 526.9

D Center of Mass and Dynamic Stability

D.1 Determina on of preliminary CMThe center of mass (CM) is a crucial parameter when it comes to monitoring the globalvehicle loads and the dynamic stability of the car. The determina on of the expectedmaximum loads on the vehicle structure based on the theore cal background establishedin Sec on 5.1 requires the knowledge of the preliminary CM of the vehicle. At the sameme, it is par cularly important to keep track of the CM loca on of three wheeled vehicles

in order to ensure stable dynamic vehicle behaviour (see appendix A). Therefore, the futurecenter of mass of the final vehicle design is es mated in the following.In order to es mate the center of mass, the en re vehicle system has been divided intoseven major subassemblies. These subassemblies have been placed as simplified modelsinto the CATIA surface model used as design space for the topology op miza on. Itis assumed that the overall vehicle CM is equal to the weighted mean loca on of theconsidered subassemblies. Figure D.1 illustrates the es mated future posi on of thesesubassemblies in a sec on view of the surface model.

Front Wheel

Assembly

Chassis Frame

Front

Battery Pack

Seat + Occupant

Rear

Battery Pack

Motor Assembly

Rear Wheel

Assembly

x

z y

Figure D.1: Mass centers of individual components in xy-plane

Assuming a symmetric mass distribu on around the x-axis, the center of mass lies in thexz-plane. Therefore, it is only required to determine the x and z-coordinates of the CM.This simplified approach is assumed to predict the posi on of the CM of the final vehicleaccurate enough in the framework of this thesis. For monitoring of the vehicle stability interms of oversteering and pping over, the CM of the en re vehicle system is of concern.However, for the determina on of the loads ac ng on the vehicle structure during normaldriving condi ons, the CM of the sprung mass is the decisive parameter. Considering theestablished subdivision of the vehicle system, the sprung mass includes all subassemblies

D.1 Determina on of preliminary CM 119

except the front and rear wheel assemblies, as they rest on the ground directly withoutinterfering with the vehicle structure. Figure D.2 shows the xz-plane of the CATIA modelwith the qualita ve posi on of each individual mass center.

x

Mb1 Mm

z

Mc

Md

Mb2 Mr Mf

Figure D.2: Mass centers of individual components in xy-plane

Table D.1 summarizes the posi on and weight of the considered vehicle subassemblies.The average of their posi ons ri, weighted by their individual masses mi represents thecenter of mass of the simplified vehicle system.

Mv =

∑mi · ri∑mi

Mass Descrip on x-coord[mm]

z-coord[mm] weight [kg]

MrRear wheel assembly, includingrear swingarm 105 310 37

Mm Electric motor assembly 410 360 51

Mb1Rear ba ery pack, op onaladdi onal energy source 650 270 96

Md Seat and Occupant 1250 520 191

McChassisframe, includingsteeringassembly 1420 390 140

MfFrontwheel assembly, includingsuspension 2050 270 28

Mb2Front ba ery pack, primarypropulsion energy source 2200 270 192

Table D.1: Loca on and weight of single center masses

With these values, the loca on of the CM of the total vehicle mass and of the sprungmass result in:

D.2 Check of Dynamic Stability Criteria 120

Mass Descrip on x-coord[mm]

z-coord[mm] weight [kg]

CMvCenter of mass of the en revehicle 1354 366 734

CMsCenter of mass of the vehiclesprung mass 1394 373 669

Table D.2: Result of center mass calcula on

D.2 Check of Dynamic Stability CriteriaWith the es mated CM of the final vehicle design, one can determine the dynamic stabilitycriteria established in A, namely the sta c margin and the pping threshold. Therefore,the CM of the total vehicle mass CMv is taken into account. The wheelbase of the finaldesign is es mated with wb = 2050mm, while the track is assumed to be tr = 1800. Thesevalues are based on the current design under the considera on of some minor changespar cularly in the overall length of the vehicle in an a empt to increase the leg space forthe occupants. With these values the SM yields:

SM =1

3− lf

wb=

1

3− 696

2050= −0.0065

Thus, the sta c margin is just within acceptable limits. Although it is concerning that italmost falls into a range where there is no stable steering behaviour guaranteed. Thissitua on would be even worse if the main ba ery pack was placed in the center of thevehicle, which clearly shows the necessity of placing the main ba ery pack in front. Thedetermined SM assumes an addi onal ba ery pack in the back of the vehicle. However, ithas not been decided yet if the final design really includes this extra ba ery pack. Whenassuming the final design does not feature this extra ba ery, the SM changes along withthe CM of the vehicle as follows:

SMsingleBat =1

3− lf

wb=

1

3− 590

2050= 0.045

Under this assump on, the SM would indicate a sufficiently stable steering behvaiour. Itcan be concluded that a final design without addi onal ba ery is very likely to have astable behaviour. The addi onal ba ery pack, however, brings the design close to a pointwhere oversteering beavhiour can be expected. In this case it would be advisable to furtherinves gate possibili es to distribute more weight to the front of vehicle to compensatethe extra ba ery.

D.2 Check of Dynamic Stability Criteria 121

The pping threshold turns out to be a minor issue for the NUS City Car. This is a resultof the comparable large track of the car. The pping threshold yields

ato =tr · (wb− lf )

2 · wb · h=

1800 · (2050− 696)

2 · 2050 · 373= 1.64

, which is well above the recommended minimum value of ato = 1.0.

E Summary of the Applied Forces in the Preprocessor ModelThe following tables summarize all forces that have been applied to the preprocessormodels throughout this thesis. In addi on, all preliminary vehicle dimensions along withall considered accelera ons and dynamic factors are displayed, as they were applied forthe calcula on of these forces.

mass [kg] lh [mm] lf [mm] h [mm] tr [mm] wb [mm]

669 1394 656 373 1800 2050

Bending Braking Acceler. Cornering Bump Crash

Accel. [g] 1.0 1.0 0.3 1.0 4.0 4.0

Dynamic F. 2.5 1.75 1.75 1.75 - -

Wheel Loads F_r [N] F_l [N] R [N]

static 2231 2231 2100

Cornering F_out [N] R [N] F_out_y [N] R_y [N]

static 4462 2100 4462 2100

dynamic 7809 3676 7809 3676

F_y [N] F_z [N] R [N] R_z [N]

dynamic 8925 6515 8402 6133

Torsion F_r [N] F_l [N]

static -2231 2231

Major

ComponentMass [kg]

No. Forces

in Model

Bending

Forces [N]

Braking

Forces [N]

Acceler.

Forces [N]

Battery 23 2 282 197 59

Front Bump Rear Bump

Sprung Mass, CM Location and Base Geometry

Max Vehicle Acceleration and Dynamic Factors

Global Forces Exerted at Suspension

Bumps

Inertia Forces from normal Vehicle Operation

•Cornering

•Front Bump

•Rear Bump

•Pure Torsion

•Bending

Load Cases

Load Cases

Battery 23 2 282 197 59

Occupant 90 4 552 386 116

Motor 45 1 1104 773 232

Major

ComponentMass [kg]

No. Forces

in Model

Crash

Forces [N]

Battery 23 2 451

Occupant 90 8 441

Motor 45 1 1766

Inertia Forces from Crash Impact

•Braking

•Accelerat.

•Front Crash

•Side Crash

•Roof Crush

•Rear Crash

Load Cases

F Complementary HyperWorks Illustra ons

F.1 Compara ve Study - Iner a ReliefThe following study was performed in the framework of Sec on 5.2.1 on page 64. Theobjec ve was to get an idea of the effect of the iner a relief func on of HyperWorks. Aboxed shell element structure is loaded with a asymmetric ver cal force (torsion). Theresul ng displacement and stress contours of the structure for both conven onal andiner a relief constraints are contrasted in the following.

Figure F.1: Prepocessor shell element model as basis of the comparison

Conven onal Iner a Relief

Analysis Results Analysis Results


Figure F.2: Comparison of iner a relief constraint and conven onal constraint on a 2Dshell-element structure

F.2 Considered Load Cases in the Topology Op miza on Setup 124

F.2 Considered Load Cases in the Topology Op miza on Setup

Bending Braking Accelera on

Front Bump (IR) Rear Bump (IR) Cornering (IR)

Pure Torsion Frontal Crash Side Crash

Rear Crash Roof Crush

see Sec on 5.3.2 on page 78

F.3 Comparison of Topologies from Examined Op miza on Formula ons 125

F.3 Comparison of Topologies from Examined Op miza on Formula onsIn Sec on 5.2.4, different op miza on formula ons are compared. It could be establishedthat both the global stress constraint and the minimum compliance method lead to roughlythe same op mized topology for the chassis frame. In the following figure both resul ngtopologies are contrasted.

Global Stress Constraint Weighted Compliance

F.4 Comparison of Different Approaches to Modeling Frame Nodes in FEA 126

F.4 Comparison of Different Approaches to Modeling Frame Nodes in FEA

1232

2

Displacement Contours [mm] v. Mises Stress Contours[

Nmm2

]Beam Model


Shell Model with RBE2 Nodes

Analysis ResultsAnalysis Results

Pure Shell Model

Analysis ResultsAnalysis Results

F.5 Stress Contours of Non-Cri cal Load Cases 127

F.5 Stress Contours of Non-Cri cal Load Cases

F.5.1 Steel Frame

Steel Frame - Vertical Bending

SUB1 - bending Von Mises Stress

> 9.43e+01< 9.43e+01< 8.25e+01< 7.07e+01< 5.89e+01< 4.71e+01< 3.53e+01< 2.36e+01< 1.18e+01< 0.00e+00

Max = 1.06e+02Min = 2.53e-02

X

Y

Z

Steel Frame - Braking

SUB13 - braking Von Mises Stress

> 1.56e+02< 1.56e+02< 1.37e+02< 1.17e+02< 9.75e+01< 7.80e+01< 5.85e+01< 3.90e+01< 1.95e+01< 0.00e+00

Max = 1.76e+02Min = 2.49e-01

X

Y

Z

Steel Frame - Acceleration

SUB14 - acceleration Von Mises Stress

> 8.58e+01< 8.58e+01< 7.51e+01< 6.44e+01< 5.36e+01< 4.29e+01< 3.22e+01< 2.15e+01< 1.07e+01< 0.00e+00

Max = 9.66e+01Min = 9.32e-12

X

Y

Z

F.5 Stress Contours of Non-Cri cal Load Cases 128

F.5.2 Aluminum Frame

Alu Frame - Vertical Bending

SUB1 - bending Von Mises Stress

> 7.03e+01< 7.03e+01< 6.15e+01< 5.27e+01< 4.39e+01< 3.51e+01< 2.64e+01< 1.76e+01< 8.78e+00< 0.00e+00

Max = 7.91e+01Min = 4.36e-02

X

Y

Z

Alu Frame - Braking

SUB13 - braking Von Mises Stress

> 9.95e+01< 9.95e+01< 8.71e+01< 7.46e+01< 6.22e+01< 4.98e+01< 3.73e+01< 2.49e+01< 1.24e+01< 0.00e+00

Max = 1.12e+02Min = 2.79e-01

X

Y

Z

Alu Frame - Acceleration

SUB14 - acceleration Von Mises Stress

> 5.38e+01< 5.38e+01< 4.71e+01< 4.03e+01< 3.36e+01< 2.69e+01< 2.02e+01< 1.34e+01< 6.72e+00< 0.00e+00

Max = 6.05e+01Min = 2.26e-11

X

Y

Z

All stresses are given in Nmm2

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