electric vehicle design optimization: integration of a...

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Abstract—Simulation-based design optimization of an electric

vehicle (EV) propulsion system requires integration of a system

model with detailed models of the components. In particular, a

high fidelity interior permanent-magnet (IPM) motor model is

necessary in order to capture important physical effects, such as

magnetic saturation. The system optimization challenge is to

maintain adequate model fidelity with acceptable computational

cost. This paper proposes a design method that incorporates

high-fidelity motor, high-voltage power electronics, and vehicle

propulsion simulation models in a system design optimization

formulation that maximizes energy efficiency of a compact EV on

a given drive cycle. The resulting optimal design and associated

energy efficiency for a variety of drive cycles and performance

requirements are presented and discussed.

Index Terms— Electric vehicle, Vehicle electrification, Motor

design, Design optimization, Optimal design

I. INTRODUCTION

HE propulsion system design process requires

integrating sub-system (component) designs into an overall

system model in order to maximize the performance of a given

propulsion architecture [1]. Previous studies have shown that

vehicle fuel efficiency and performance depend substantially

on how the design problems are coordinated [2]. Good

integration requires coordination of sub-system models and

requisite model interfaces that enable the virtual integration of

all system elements.

In Battery Electric Vehicle (BEV) design, ideal integration

will capture inter-dependency between motor and vehicle

system design. Changes resulting from a new motor design are

analyzed and taken into account on the system design side, and

vice versa. For example, new motor performance with a new

motor stack length requires a new optimal final drive ratio,

This paper was first submitted on March 11, 2014 for review.

Copyright (c) 2013 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be

obtained from the IEEE by sending a request to [email protected].

Kukhyun Ahn was with the Mechanical Engineering Department, University of Michigan, Ann Arbor, MI 48109 USA (e-mail:

[email protected])

A. E. Bayrak is with the Mechanical Engineering Department, University of Michigan, Ann Arbor, MI 48109 USA (e-mail: [email protected])

P.Y. Papalambros is with the Mechanical Engineering Department and

Division of Integrated Systems & Design, University of Michigan, Ann Arbor, MI 48109 USA (email: [email protected])

which shifts motor operation points. On the motor design side,

stack length must be optimized again given the shifted

operation points.

In earlier integration efforts in BEV design, motor rating

optimization used scaled maps derived from a baseline map in

order to find an approximate motor rating given vehicle

propulsion system and performance requirements [3,4]. This

method, however, is limited in capturing detailed

electromagnetic characteristics and geometric information of a

motor design, thus confining its application to the early

conceptual design stage.

Practical electric propulsion system design typically requires

a high-fidelity motor model based on Finite Element Analysis

(FEA) or other analysis methods of comparable accuracy.

Some methods employ detailed FEA for high fidelity in motor

modeling [5-15], and other methods use non-FEA motor

analyses to reduce computation time for running a large number

of simulations [14-23].

While these modeling and analysis methods provide high

analysis accuracy and efficiency, direct integration of a motor

model into a system optimization model has high

computational cost. Thus, the motor design remains at the

sub-system level, only allowing for motor design changes given

vehicle system design.

Some integration strategies that address design

inter-dependency are based on decomposition. In a common

formulation, vehicle performance at the system level is

translated to motor target performance at the motor design level

[1,24]. Another common formulation bases motor design on

subsystem use information obtained from system-level

simulation [2]. In order for these formulations to capture design

inter-dependency, they require an iterative solution process,

such as Augmented Lagrangian Coordination and Analytic

Target Cascading [1,24]. The challenge for these integration

strategies is to coordinate the motor design requirements with

the overall system design requirements, maintaining

consistency in the boundary conditions across the elements of

the decomposed system.

In contrast to decomposition-based integration, All-in-One

(AIO) integration requires little coordination effort because the

entire system is simultaneously analyzed and optimized.

However, interfacing individual design spaces is difficult and

rarely discussed in the literature. A method that builds a

metamodel of a high-fidelity motor model and integrates the

Electric Vehicle Design Optimization:

Integration of a High-fidelity Interior

Permanent-Magnet Motor Model

Kukhyun Ahn, Alparslan Emrah Bayrak, and Panos Y. Papalambros

T

This is the author's version of an article that has been published in this journal. Changes were made to this version by the publisher prior to publication.The final version of record is available at http://dx.doi.org/10.1109/TVT.2014.2363144

Copyright (c) 2014 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing [email protected].

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metamodel directly into a system optimization model was

previously presented [2]. An alternative approach is proposed

in this paper referred to as an indirect integration strategy.

In this integration study, an IPM synchronous motor is

designed as part of a BEV propulsion system. The integrated

problem is solved in an AIO optimization formulation, where

an FEA-based high-fidelity motor model is incorporated into a

feed-forward vehicle simulation model. Key power electronics

devices are also modeled in order to include electric power

control decisions in the optimization problem. We discuss how

to integrate the motor and propulsion models and create a

unified design space where design variables of the motor,

power electronics, and vehicle propulsion models are

optimized simultaneously.

In Section 2, the sub-system and system models are

described. Section 3 details the method of creating a unified

design space for BEV propulsion. Optimization results are

presented in Section 4, followed by some discussion and

conclusions in Section 5.

II. BEV PROPULSION SYSTEM MODELING

In model-based system analysis and design of electric

vehicles, sufficiently high fidelity is required for key

sub-systems such as electric motors, power electronics, and

battery systems. Once an adequate level of model fidelity is

achieved, the challenge is to integrate the high-fidelity models

into a system-level vehicle model.

The modeling effort focuses on the IPM motor and the

vehicle, including the high-voltage electric drive, gear-train,

and resistive road loads. The schematic of the BEV propulsion

system is shown in Fig. 1. Dashed and solid lines represent

electrical and mechanical connections, respectively. The design

variables that represent the respective component models are

shown in parentheses.

A. IPM Synchronous Motor

The analysis of motor design here is based on SPEED

software [25]. Two-dimensional FEA is run using

parameterized templates of cross-sectional designs (magnet,

stator tooth, etc.) combined with phasor diagram analysis to

achieve reduced computational cost compared to that of

full-scale FEA. Fig. 2 shows the modeling and FEA simulation

of a motor design in SPEED.

Three-phase AC is fed to the machine by a DC-AC inverter,

whose modeling details are given in the following subsection.

The baseline design has eight poles for permanent magnet

blocks and 12 stator slots for concentrated winding. The outer

and inner diameters are 250 and 150 mm, respectively. The air

gap is 1 mm.

Two design variables were chosen for the motor: coil turns of

the three-phase concentrated winding, and lamination stack

length. After some preliminary exploration of the design space,

the first was set to vary between 102 and 110 turns, and the

second between 140 and 160 mm. Each variable was assigned

five equally-spaced levels to generate 25 full-factorial design

samples, which represent the motor subsystem in the vehicle

design space. This way, the high-fidelity motor model can be

integrated in the vehicle design process with reasonable

computational cost. Determining the sampling method and

sample size depends on the problem dimension and complexity.

Here, we found the full-factorial sampling with five levels for

two factors sufficient for the problem, as discussed in the

results section.

For each of the sample designs, magnetic circuit and

mechanical loss data ( , , , ) are collected in the

two-dimensional operation space of control current ( ) and

angle ( ). Fig. 3 shows a flux surface on the current-angle grid.

For the grid fineness shown in the figure, the analysis time for a

sample design is about half an hour.

Given a machine rotational speed ( ), the d, q-axis phasor

properties are calculated as,

, , (1)

, , (2)

, , (3)

where electric speed is calculated by for the 8-pole

machine and is the phase resistance.

Then, line-to-line voltage ( ), output torque ( ) and input

power ( ) are obtained as,

Fig. 1. Electric vehicle propulsion and design variables

Fig. 2. Finite element analysis of IPM motor



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,

(4)

, (5)

, (6)

where , accounts for iron (core)

loss, copper loss is calculated by

, and

inverter loss, , is calculated using the models described in

the next subsection. The fluxes and currents are RMS (root

mean square) values.

A set of control current and angle is found to minimize input

power for the target shaft torque ( ), maintaining line-to-line

voltage below the DC voltage ( ). The optimization problem

is formulated as,

with respect to

subject to . (7)

Repeatedly solving the optimization problem sweeping

machine speed and target torque, a pair of a full-load torque and

power loss maps are generated for a corresponding DC voltage.

The two-stage map generation procedure is summarized in

Table I.

Setting five levels of DC voltages from 630 to 670 V

produced a total of 125 motor map pairs, representing a

three-dimensional design space of motor coil turns, lamination

stack length and DC operation voltage.

This indirect integration method enables virtual exploration

of the three-dimensional design space as a continuum and

avoids excessive computational cost. We discuss how the 125

map pairs are used to assess vehicle attributes and then build a

virtual continuum space in the vehicle propulsion analysis

subsection and optimization section further below.

B. High-Voltage Power Electronics Devices

The schematic of the circuit used in the power electronics

devices is shown in Fig. 4. The first two IGBTs (Insulated-Gate

Bipolar Transistors), Q1 and Q2, along with the capacitor and

inductor represent the DC/DC converter, and the other six

IGBTs represent the inverter. In the vehicle model, the power

electronics devices are modeled as loss components with a

simple input and output power relationship.

The losses at the power electronics stage are grouped into

switching and conduction losses. Switching losses consist of

three elements, turn-on and turn-off losses in the IGBTs and

turn-off loss in the diodes, each of which is a function of

switching voltage, current and frequency. The conduction loss

in the DC/DC converter is a function of battery current and duty

cycle, while the conduction loss in the inverter is a function of

peak current, modulation index and phase angle. Since only one

diode and one transistor from switches Q1 and Q2 conduct

during motor and generator operations, DC/DC converter loss

is calculated for a diode and a transistor [17]. The total loss in

the DC/DC converter is the sum of three switching losses

( ), conduction loss of a diode ( ), and conduction

loss of an IGBT ( ).

. (8)

The input and output power relationship is given by:

, (9)

where battery power ( ) and power at the DC-link ( ) are

negative in boost mode and positive in buck mode.

Similarly to the DC/DC converter, the inverter loss is

calculated for each transistor and diode pair and then multiplied

by six to obtain the total loss [17]. The total inverter loss is

given as follows:

=13( / ) , (10)

Fig. 3. Permanent magnet flux linkage

Fig. 4. Power electronics topology

TABLE I

MOTOR MAP GENERATION PROCEDURE

•Sweep control variables: Irms, γ •To obtain phasor properties

Stage 1: Finite element analysis

•Sweep operation variables: ωm, Tsh

•To obtain minimized power loss

Stage 2: Control optimization



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where are three switching loss components, and

and are conduction losses of an IGBT and a

diode in the inverter, respectively.

C. Vehicle Propulsion

A compact-sized vehicle model was built in the software

environment AMESim [26] (See Fig. 5). The 1-D multi-domain

vehicle model includes models of the driver, control unit,

battery, IPM motor, single-ratio transmission (final drive),

power electronics, and resistive loads of the vehicle body.

The dynamic propulsion model is solved in a feed-forward

manner with a driver control, and power losses are calculated

using static look-up maps or resistive models in mechanical and

electrical components. The traction motor solely propels the

vehicle with a single-ratio reduction gear that multiplies motor

traction torque. Gear losses are modeled using a damper with a

constant damping ratio. Road load components such as rolling

resistance and aerodynamic drag are included in the vehicle

model. The motor weight varies with the IPM motor design

variables and is added to the base vehicle weight. On the

electrical side, a DC-DC converter and DC-AC inverter are

placed between the high-voltage battery and the motor to

achieve power controls.

The converter, inverter, motor, and battery are integrated in

the propulsion system via static loss models; see Fig. 6 for a

motor loss map example. The first three were described in the

earlier subsections. The battery model is based on a fixed cell

design and the pack arrangement. Each cell is modeled using

open circuit voltage ( ), internal resistance ( ) and

filtering capacitance ( ). Given a current demand from a cell

( ), the output voltage of the cell ( ) is calculated by

solving the following dynamic equation:

, (11)

where and are functions of the state of charge ( )

and calculated using look-up maps. A fixed value of 50 F is

used in this study. Also is calculated as follows:

, (12)

where is the nominal battery cell capacity. The battery

information is shown in Table II along with some other vehicle

parameters.

The propulsion model predicts the vehicle’s 0-60MPH

acceleration time and charge depletions on test drive cycles for

a given set of propulsion design variables. Three drive test

cycles are used in this study: FTP75, NEDC and US06. Fig. 7

shows the battery state of charge simulated on US06, along

with the cycle’s speed profile.

III. OPTIMIZATION

The proposed design method enables integration of

high-fidelity motor and EV propulsion design, and achieves

system integration following a sequential procedure, whose

steps are summarized in the flow diagram in Fig. 8. Four design

variables are given in parentheses.

In the first step of the procedure, design samples are chosen

to represent the motor design space with two design variables.

When analysis results are produced for the samples, one design

variable is added to incorporate the high-voltage DC operation

decision. This decision assumes fixed voltage not considering

variable voltage control. After motor control optimization

post-processing, pairs of motor loss and capacity maps are

generated for all combinations of the three design variables. For

each motor efficiency/full-load map pair, representing one

motor design and its operation voltage, vehicle simulations are

run repeatedly for a set of final drive values to assess energy

efficiency and performance of the vehicle designs. In this study,

five levels were chosen for each design variable (stack length,

coil turns, DC voltage and final drive ratio), resulting in 625 EV

designs. Depending on the design goals, design variables,

sampling methods, and sample sizes can be selected to suit the

goals. For example, more advanced sampling techniques can be

Fig. 5. Vehicle simulation model in AMESim

Fig. 6. Motor power loss as function of speed and torque



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applied to find if they result in better model accuracy than the

full-factorial method that we chose here. Motor magnet shape

dimensions can be variables of choice instead of or in addition

to the current selection if design flexibility permits.

Battery charge depletions over NEDC, US06, and FTP75 are

calculated using AMESim vehicle simulation, as described in

an earlier section. The 0-60MPH acceleration time is also

simulated as a dynamic performance index. Based on the

simulation results, we build metamodels to represent the

function relationships between the design variables and the

corresponding vehicle attributes [3,4].

In the present study, we incorporate the motor

electromagnetic FEA and vehicle propulsion simulation into a

single AIO design space. This resolves the issue that both

high-fidelity analysis models are computationally too

expensive to be used for a large number of trial designs during

optimization. Although a limited number of design samples are

used, the built AIO surrogate design space performs as a

continuum, within which any design can be assessed at very

low computational cost. The key to validating the indirect

integration method is to ensure that prediction accuracy is

sufficiently high, as discussed in the results section.

For the metalmodels, we chose the RBF (Radial Basis

Function) interpolation after comparison with the quadratic

polynomial regression and the feed-forward artificial neural

network. The basis functions are multiquadrics and scaled to

minimize the mean leave-one-out error [27]. As shown in the

following section, the chosen metamodel is appropriate for the

complexity of the design space under consideration. More

sophisticated modeling and optimization techniques such as

Efficient Global Optimization (EGO) may be required if more

variables or model uncertainty were to be included in the motor

and vehicle design models [28-31].

Optimization is formulated as a bi-objective problem: the

two objectives are to minimize the battery charge depletion

over a cycle and to maximize 0-60MPH acceleration

performance at the same time. This is similar to a previously

proposed formulation, where one attribute is the sole objective

and the other is a constraint [2,32]. By repeatedly solving the

problem for several different bounds on the latter constraint, the

trade-off between the two attributes is found. Alternatively,

using Multi-Objective Genetic Algorithm (MOGA), the

bi-objective formulation gives a continuous view of the

trade-off frontier and design selections, as will be shown in the

next section. NSGA-II (Non-dominated Sorting Genetic

Algorithm-II) is employed [33, 34], and the initial population of

the sample designs is evolved through 10 generations. The four

design variables are motor armature coil turns, , stack

length, , operation DC voltage, , and final drive ratio,

. The optimization problem is formulated as,

with respect to

subject to the upper and lower bounds on , , , and

(13)

where and are the charge depletion and 0-60mph

acceleration time, respectively. The three test cycles are FTP75,

US06, and NEDC.

IV. RESULTS

Fig. 9 shows the attribute space in the case of the NEDC

cycle. The dots represent the attribute pairs of the 625 sample

EV designs. The lower charge depletion on the y-axis indicates

TABLE II

VEHICLE SPECIFICATIONS

Initial battery voltage 350 V

Pack configuration 90 cells in series, 2 modules in parallel

Battery cell capacity 33.1 Ah

Base vehicle weight 1521 kg

Frontal area 2.27 m2

Drag coefficient 0.29

Tire radius 0.316 m

Fig. 7. Vehicle velocity and battery state of charge

Fig. 8. Motor and EV propulsion integrated design flow



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higher vehicle energy efficiency, and the smaller acceleration

time to 60 MPH on the x-axis indicates better performance. The

relationships between the designs and attributes, when captured

in a metamodel, led to Pareto-optimal solutions (solid curve),

found by the MOGA method. The curve represents the

marginal attribute pairs that the EV can achieve within the

given design constraints.

On the design space side, the solutions that correspond to

Pareto-optimal solutions in Fig. 9 are plotted in Fig. 10.

Along the Pareto frontier, each variable shows a noticeable

trend although discontinuity is observed due to local optima.

For example, higher DC voltage and final drive ratio contribute

to better performance but cause lower energy efficiency. We

can also infer that allocating more space for the motor in the

axial direction is likely to lead to a better BEV design.

However, these trends may not be perceived as separate

phenomena because they come from simultaneous interaction

among the four variables. Based on the obtained Pareto

frontiers, MPGe (Miles Per Gallon equivalent) has been

calculated for five performance target levels in the three cycle

cases [35]. Fig. 11 summarizes the optimization results.

As described earlier, optimization was based on prediction of

the vehicle attributes (acceleration and MPGe’s on three

cycles), and the prediction models (metamodels) need to be

checked for their validity. From the 15 optimal solutions in Fig.

11, 12 are from the metamodel prediction. When we performed

simulation for these 12 optimal designs, virtual and real

attributes matched closely, as can be seen in Fig. 12. The

percentage errors did not exceed 0.42 and 0.053 in the cases of

acceleration and MPGe, respectively. This indicates the

proposed approach represents motor performance with

sufficiently high accuracy in the integrated design space.

V. CONCLUSIONS

We proposed a method that integrates a high-fidelity motor

and vehicle analysis model for optimizing the IPM motor and

vehicle propulsion design simultaneously. Without actually

running a costly FEA simulation for every trial design, the

motor design space was accurately captured and efficiently

incorporated in the propulsion design space, i.e., high fidelity

was maintained for both motor and vehicle models.

Metamodel-based design optimization allowed for the

multi-domain analyses to be integrated: IPM motor FEA,

power electronics steady-state simulation and EV propulsion

forward-facing dynamic simulation. Once the functional

relationship from the design space to the attribute space is

modeled, the cost of exploring the integrated design space is

significantly reduced. We performed an extensive search using

MOGA and obtained the Pareto-optimal solutions for two

vehicle attributes, energy efficiency on US and European test

cycles and 0-60MPH acceleration performance. Driveability,

NVH, and safety metrics can be additionally taken into design

consideration in the form of objectives or constraints in this

optimization framework. Tracing the changes in optimal design

variable values as the objective changes showed how individual

variables affect the optimal design.

This integration study suggests that the approach used here

may also work for problems of higher complexity. Future

Fig. 9. Charge depletion on NEDC against acceleration

Fig. 10. Normalized optimal design solutions

Fig. 11. Energy efficiency on three test cycles



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research can address inclusion of additional motor design

variables, such as radial dimensions (rotor, air gap and stator),

magnet block arrangements and stator tooth dimensions, as

well as power electronics and battery design variables. The

methodology can also be applied to integrate more detailed

electromagnetic analysis models or vehicle packaging

optimization models. To address higher design space

dimensionality, the number of motor design samples must be

significantly increased. Rapid motor analysis methods, such as

Output Spacing Mapping, may serve well for this purpose.

More sophisticated metamodel types can also be examined to

replace the RBF interpolation method used here to capture the

increased complexity.

ACKNOWLEDGMENT

This work was partially supported by the Automotive

Research Center, a US Army Center of Excellence in Modeling

and Simulation of Ground Vehicle Systems headquartered at

the University of Michigan. The LMS International and

CD-adapco provided academic support for the use of the

AMESim and SPEED software, respectively. This support is

gratefully acknowledged. The findings of this work reflect only

the opinion of the authors.

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Kukhyun Ahn received his B.S. (2000),

M.S. (2002) and Ph.D. (2007) degree in

mechanical engineering at Seoul National

University, Seoul, South Korea.

He was research faculty in Mechanical

Engineering at the University of Michigan,

Ann Arbor, USA and a visiting researcher

at General Motors Global R&D, Warren,

USA before joining Research and

Advanced Engineering at Ford Motor Company, Dearborn,

USA. His research interests include a wide range of topics in

vehicle electrification, such as hybrid electric propulsion

architectures, propulsion system energy management and

design optimization.

Alparslan Emrah Bayrak was born in

Aksehir, Konya, Turkey in 1988. He

received the B.S. degree in mechatronics

engineering from Sabanci University,

Istanbul, Turkey in 2011 and M.S. degree

in mechanical engineering from the

University of Michigan, Ann Arbor, MI, in

2013.

Since 2011, he has been a Research Assistant with the

Optimal Design Laboratory at the University of Michigan.

Since 2013 he has been a PhD candidate in mechanical

engineering at the University of Michigan. His research

interests include optimal design and control of electric and

hybrid electric powertrain architecture, modular vehicle design

and crowdsourced design with gaming platforms.

Panos Y. Papalambros is the James B.

Angell Distinguished University

Professor and the Donald C. Graham

Professor of Engineering. He is a

Professor of Mechanical Engineering,

Professor of Architecture, and Professor

of Art and Design; and serves as the

founding Chair of the Integrative

Systems & Design Division, College of

Engineering, at the University of Michigan.

Born in Patras, Greece, he attended the National Technical

University of Athens and earned a diploma in Mechanical and

Electrical Engineering in 1974. Moving to California he

attended Stanford University and earned his M.S. degree

(Mechanical Engineering) in 1976 and Ph.D. degree (Design

Division, Mechanical Engineering) in 1979. At Michigan he

has served as a faculty member since 1979. During his tenure at

Michigan he served as mechanical engineering department

chair (1992-98, and 2007-08) and was the founding director of

Optimal Design (ODE) Laboratory (1980-); Design Laboratory

(1990-92); Ford Durability Simulation Center (1992-94);

Automotive Research Center (1994-2003); General Motors

Collaborative Research Laboratory (1998-2002); the Antilium

Project (2003-2008), and the Ford BlockM Sustainability

Laboratory (2006-2009); he served as the founding chair and

director of the University of Michigan interdisciplinary Design

Science Doctoral Program (2006-2011). His research interests

include design science and optimization, with applications to

sustainable design of products, automotive systems, such as

hybrid and electric vehicles; design of complex engineered

systems; and architectural design. With D. J. Wilde, he

co-authored the textbook Principles of Optimal Design (1988,

2000). He has published over 320 articles in journals,

conference proceedings, and books.

He is a member of ASME, INFORMS, MOS, SME, SAE,

ISSMO, AIAA, AAUP, ASEE, IEEE, INCOSE and serves as

Vice President on the Board of Management of the Design

Society. He served as Chief Editor of the ASME Journal of

Mechanical Design (2008-2012) and as associate editor of the

Journal of Mechanisms, Transmissions and Automation in

Design, Journal of Global Optimization, Computer-Integrated

Engineering, and the Japan Society of Mechanical Engineers

International Journal. He currently serves on the editorial

boards of the journals Artificial Intelligence in Engineering

Design and Manufacturing, Engineering Design, Engineering

Optimization, Structural and Multidisciplinary Optimization,

Journal of Reliability and Safety and Product Development.

He is a Fellow of ASME and SAE, and the recipient of the

ASME Design Automation Award (1998), ASME Machine

Design Award (1999), Japan SME Design and Systems

Achievement Award (2004), ASME Joel and Ruth Spira

Outstanding Design Educator Award (2007), and the Stephen

S. Attwood Award (highest engineering honor in the University

of Michigan, 2009).



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