Run Flat Tires Versus

Conventional Tires A Model Based Comparison

L.W.L. Houben DCT 2006.112

Internal Traineeship Supervisors: Dr. Ir. A.J.C. Schmeitz Prof. Dr. H. Nijmeijer Eindhoven University of Technology Department of Mechanical Engineering Dynamics and Control Technology Group Eindhoven, September 2006

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Summary Run Flat Tyres vs. Conventional Tyres, a model based comparison – L.W.L. Houben Tyres play an important role in comfort, handling and safety of a vehicle. They are the key link in the force transmission between the road and the vehicle. During their lifetime tyres are exposed to many different road and environmental conditions. Most flat tyres are the result of (slow) leaks that go unnoticed and allow the tyre's air pressure to drop. This pressure drop has serious consequences for the comfort, handling and safety of a vehicle. One of the technologies used to help maintain vehicle mobility when a tyre is punctured, are self-supporting tyres (so called Run Flat Tyres). In this study a model based comparison is made between a vehicle model equipped with Run Flat tyres and a vehicle equipped with conventional tyres. Run Flat Tyres feature a stiffer internal construction compared with conventional tyres, resulting in a non-linear tyre stiffness. This has an effect on the handling behaviour and the ride comfort of the vehicle. The subject of this research is to investigate the difference in ride comfort of a vehicle equipped with both types of tyres. To achieve these results a half vehicle model is used to simulate the vehicle behaviour when driving over an uneven road surface. This vehicle model is equipped with a special tyre model that can simulate the enveloping behaviour of the tyre. Because this tyre model has originally been developed for conventional tyres, the model has to be validated for use with Run Flat tyres. Measurements are done to investigate the tyre behaviour and the tyre model is then fitted to these measurements. If the model fits these measurements, the model is suitable for predicting the enveloping behaviour of the tyre. In this case all performed model fits agree rather well, so the model can be used for the Run Flat tyres. Before comfort analyses can take place test conditions have to be determined. For this research it is chosen to test the model on a road surface of 1.2 km that has a surface quality that can be compared to a highway. To test the comfort on a complete range of road surfaces of different quality the basic surface is scaled up to four different roads of different quality. The ride comfort of the vehicle is analysed by the vertical accelerations of the sprung mass at the centre of gravity. Those accelerations are then compared with each other for the different test conditions and the different tyres. To assess the ride comfort of the vehicle the ISO comfort index is introduced. This comfort index exists of several weighting functions that account for the human body sensitivity for specific frequencies. A total value of this comfort index can be used as an indication of the comfort in a vehicle. Remarkably the vertical accelerations of the sprung mass as well as the comfort index showed no important difference in the ride comfort of the vehicle with Run Flat tyres. A closer look at the suspension system does show an increase in the vertical load of the tyres and in the accelerations of the unsprung masses for the vehicle with Run Flat tyres. This indicates that the increase of the load on the suspension system is larger than the increase of the load on the sprung mass. So the suspension system can absorb the effects of the Run Flat tyres but at the cost of a higher work load. Therefore further research can be done to investigate the effect on suspension durability.

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Samenvatting Run Flat banden vs. conventionele banden, een vergelijk op modelniveau – L.W.L. Houben Banden spelen een belangrijke rol in het comfort, het weggedrag en de veiligheid van een voertuig. Bij de krachtoverdracht tussen wegdek en voertuig zijn banden dé koppeling. Tijdens hun levensduur worden banden blootgesteld aan verschillende wegdek- en omgevingscondities. Veel platte banden zijn het resultaat van (kleine) lekkages die onopgemerkt blijven en ervoor zorgen dat de luchtdruk in de band daalt. Deze daling van de bandenspanning heeft ernstige gevolgen voor het comfort, het weggedrag en de veiligheid van een voertuig. Eén van de technologieën die gebruikt wordt om de voertuigmobiliteit te waarborgen als een band lek raakt, zijn zelfondersteunende banden (zogenaamde Run Flat Banden). In dit onderzoek is een vergelijk gemaakt tussen een voertuigmodel uitgerust met Run Flat banden en een voertuigmodel uitgerust met conventionele banden. Run flat banden bezitten, in vergelijking met conventionele banden, een stijvere interne constructie welke resulteert in een niet lineaire band stijfheid. Deze stijvere interne constructie heeft invloed op het weggedrag en het rijcomfort van een voertuig. Het onderwerp van dit onderzoek is om te kijken welke verschillen er ontstaan in het rij comfort van een voertuig uitgerust met de verschillende banden. Om tot dit resultaat te komen wordt er gebruik gemaakt van een half voertuig model om het gedrag te simuleren wanneer een voertuig over een wegdek rijdt met oneffenheden. Dit voertuigmodel is uitgerust met een speciaal bandmodel dat in staat is om het gedrag van de buitenkant van de band te beschrijven. Omdat dit bandmodel oorspronkelijk is ontwikkeld voor conventionele banden is het noodzakelijk om het model eerst te verifiëren voor Run Flat banden. Dit gebeurt door eerst metingen te verrichten van de Run Flat banden en vervolgens het bandmodel te fitten op de meetdata. Dit fit proces verloopt prima en de gemeten waarden komen goed overeen met de waarden van het model. Het model kan dus ook worden gebruikt voor Run Flat banden Voordat er kan worden begonnen met het analyseren, moeten er eerst diverse test condities worden vastgesteld. Voor dit onderzoek is er gekozen om het voertuig te testen op een wegdek van 1.2 km met een kwaliteit die kan worden vergeleken met een snelweg. Om verder de tests zo kompleet mogelijk te maken wordt het wegdek opgeschaald tot vier wegdekken van verschillende kwaliteit. Het rijcomfort van het voertuig wordt geanalyseerd aan de hand van de verticale versnellingen in het zwaartepunt van de afgeveerde massa. Om het rijcomfort goed te kunnen beoordelen wordt er een ISO comfort index geïntroduceerd. Deze comfort index bestaat uit een aantal weegfuncties die rekening houden met de gevoeligheid van het menselijk lichaam voor bepaalde frequenties. Een totale waarde van deze comfort index geeft een indicatie van het rijcomfort. Opmerkelijk genoeg zijn er zowel in de versnellingen als in de comfort index nauwelijks verschillen op te merken voor de Run Flat banden. Er zijn echter wel verschillen merkbaar in de verticale belasting van de banden en in de versnellingen van de onafgeveerde massa’s. Deze zijn namelijk hoger voor de Run Flat banden. Dit geeft aan dat de belasting op de wielophanging groter is dan het effect van de Run Flat banden op het rijcomfort. Daarom lijkt het van belang om in de toekomst meer onderzoek te verrichten naar het effect van Run Flat banden op de levensduur van de wielophanging.

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Table of contents Summary .................................................................................................................................. 2 Samenvatting.............................................................................................................................3 List of symbols...........................................................................................................................5 1 Introduction...................................................................................................................... 6

1.1 Motivation and background..................................................................................... 6 1.2 Aim and scope ...........................................................................................................7 1.3 Contents.....................................................................................................................7

2 Modelling.......................................................................................................................... 8 2.1 Vehicle model ........................................................................................................... 8 2.2 Tyre model ................................................................................................................ 9

2.2.1 Basic function and two-point follower ............................................................ 9 2.2.2 The tandem model with elliptical cams.........................................................10

2.3 Road surface ............................................................................................................12 2.4 Models combined ....................................................................................................14

3 Model Parameters .......................................................................................................... 16 3.1 Vehicle parameters................................................................................................. 16 3.2 Vertical tyre stiffness.............................................................................................. 16 3.3 Tyre model parameters ........................................................................................... 17

3.3.1 Cleat measurements ........................................................................................... 17 3.3.2 Effective contact length ...................................................................................... 19 3.3.3 Tyre model fit ..................................................................................................... 20

4 Analysing the Model Response ......................................................................................21 4.1 Vehicle response......................................................................................................21 4.2 Ride comfort ............................................................................................................21

5 Conclusions and Recommendations ............................................................................26 5.1 Conclusions ............................................................................................................26 5.2 Recommendations ................................................................................................. 27

References .............................................................................................................................. 28 Appendix 1 Vertical Stiffness ............................................................................................29 Appendix 2 Contact Length ................................................................................................ 31 Appendix 3 Model Fit Results ............................................................................................ 33

A3.1 Results Dunlop SP sport 2000*E ..............................................................................34 A3.2 Results Bridgestone Turanza RFT............................................................................. 35 A3.3 Results Michelin Pilot HX......................................................................................... 36 A3.4 Results Goodyear Eagle NCT5 EMT..........................................................................37

Appendix 4 Vehicle Response to Road Surfaces ...................................................................38 A4.1 Dunlop SP sport 2000*E.......................................................................................... 39 A4.2 Bridgestone Tarunza RFT.........................................................................................40 A4.3 Michelin Pilot HX.......................................................................................................41 A4.4 Goodyear Eagle NCT5 EMT...................................................................................... 42

Appendix 5 Comfort Numbers ...........................................................................................43 A5.1 Comfort numbers for a sprung mass of 520 kg....................................................... 44 A5.2 Comfort numbers for a sprung mass of 670 kg......................................................46

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List of symbols Symbol Description Unit a distance front axle to centre of gravity [m] a half of the (effective) contact patch length [m]

ea ellipse length [m]

b distance rear axle to centre of gravity [m]

eb ellipse height [m]

ec ellipse power [-]

1 2,s sd d suspension damping [Ns/m]

zd vertical deflection [m]

bf basic curve (function) [m]

axF longitudinal component of spindle force [N]

azF vertical component of spindle force [N]

zF vertical force [N]

bh (elementary) basic curve height [m]

steph step height [m]

yI moment of inertia vehicle body [kgm²]

1 2,s sk k suspension vertical stiffness [N/m]

tk tyre vertical stiffness [N/m]

bl length of basic curve [m]

sl tandem base length, length of the two point follower [m]

L wheel base [m]

1 2,a am m unsprung masses [kg]

sm sprung mass [kg]

0r unloaded, free tyre radius [m]

V vehicle forward velocity [m/s] w effective height [m] x distance to local x-axis [m] X distance to global x-axis [m] z distance to local z-axis [m]

1 2,a az z vertical displacement unsprung masses [m]

bz vertical displacement centre of gravity sprung mass [m]

ez vertical distance between a point of the ellipse and [m] the local x-axis

1 2,r rz z vertical displacement tyre contact points (road input) [m]

Z distance to global z-axis [m]

yβ effective forward slope [rad]

ϕ body pitch angle [rad]

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1 Introduction The research described in this report is a follow up of an earlier research [4]. Therefore a lot of information is taken from that research and although this report is written so that it can be read without special knowledge, it is useful to keep [4] at hand for more background information. In the first chapter of this report the motivation, background, aim and scope of the project are presented. At the end a brief outline of the contents is given.

1.1 Motivation and background Tyres play an important role in comfort, handling and safety of a vehicle. During their lifetime tyres are exposed to many different road and environmental conditions. There are basically three elements of a tyre which determine the load capacity of the tyre and maintain the contact patch: the size of the air chamber between the tyre and the rim, the strength provided by the tyre construction and the amount of air pressure in the tyre. Most flat tyres are the result of (slow) leaks that go unnoticed and allow the tyre's air pressure to drop. There are three technologies used to help maintain vehicle mobility when a tyre is punctured. These are self-sealing tyres, tyres supported by an auxiliary system and self-supporting tyres (so called Run Flat Tyres). Self-sealing tyres are designed to fix most tread-area punctures instantly and permanently. In Auxiliary supported systems, the flat tyre's tread rests on a support ring attached to the wheel when the tyre loses pressure [4]. Run Flat Tyres feature a stiffer internal construction. These kinds of tyres are used during experiments in this project. Run Flat Tyres are capable of temporarily carrying the weight of the vehicle, even after a tyre has lost all air pressure. To provide "self-supporting" capability, rubber inserts are attached next to or between layers of heat-resistant cord in the sidewalls to help prevent breaking the reinforcing cords if air pressure is lost, (Fig. 1.1). They also feature specialized beads that allow the tyre to firmly grip the rim even in the event of air loss. In practice, run flat tyres can operate with maximum 80 km/h for 80 km in the event of air loss [4]. Fig. 1.1, Sidewall distortion conventional tyre and run flat tyre [4]

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1.2 Aim and scope In and earlier research [4] it is proven that due to the stiffer internal construction of the Run Flat Tyres, the vertical stiffness of the tyres rises much more progressive in comparison to conventional tyres. This might have its effect on the ride comfort of a vehicle equipped with Run Flat tyres. Therefore it is of interest to investigate the difference in vehicle comfort with both types of tyres. So the aim of this project is:

• To investigate the ride comfort of a vehicle equipped with Run Flat Tyres and a vehicle equipped with conventional tyres.

To achieve this aim the following approach is used:

• First, a complete vehicle model is built; this model consist of a half vehicle model, a tyre model able to simulate the enveloping behaviour of tyres and various road surfaces to have specific testing conditions.

• Second, the model parameters are determined; especially the parameters for the tyre model need to be found to know if the tyre model is able to simulate the enveloping behaviour of Run Flat tyres.

• Third, simulations are made for different testing conditions to analyse the model behaviour and the effect of different tyres on vehicle comfort.

1.3 Contents This report covers the research that has been done to achieve the aim described above in the following outline. Chapter 2 describes the vehicle model, the tyre model and the road that will be used to do the analysis. In chapter 3 explanations of all the model parameters are given. It is also described how these parameters can be calculated or determined from experiments. Next the results of the research are presented in chapter 4. Finally, the summation of the conclusions and the recommendations is given in chapter 5.

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2 Modelling In this chapter, the vehicle model, the tyre model and the road surface are explained which are used in the analyses.

2.1 Vehicle model To get basic insight in the relevant vehicle dynamics, the well known ‘Half Vehicle Model’ is used in this research (fig 2.1).

Fig. 2.1, Half Vehicle Model. [2]

As can be seen in the figure the half vehicle model consists of a single body representing the sprung mass of the vehicle and one front and one rear wheel suspension. These front and rear wheel suspensions are consisting of spring-damper elements representing the suspension main spring and damper, masses representing the suspension unsprung masses and springs to represent the tyre vertical stiffness. The road input is simulated via the tyre contact points by a vertical displacement 1rz for the front wheel and 2rz for the rear wheel. In the list below, the symbols are explained. L Wheel base [m] b Distance rear axle to centre of gravity [m] a Distance front axle to centre of gravity [m] V Vehicle forward velocity [m/s]

bz Vertical displacement centre of gravity sprung mass [m]

1 2,a az z Vertical displacement unsprung masses [m]

1 2,r rz z Vertical displacement tyre contact points (road input) [m] ϕ Body pitch angle [rad]

1 2,s sk k Suspension vertical stiffness [N/m]

tk Tyre vertical stiffness [N/m]

1 2,s sd d Suspension damping [Ns/m]

sm Sprung mass [kg]

1 2,a am m Unsprung masses [kg]

yI Moment of inertia vehicle body [kgm²]

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The equations of motion of this system read [2]:

2 2 1 1

2 2 1 1

( ) ( )( ) ( )

s s s s a s s a

s s a s s a

m z d z b z d z a zk z b z k z a z

ϕ ϕϕ ϕ

= − + − − − −− + − − − −

(2.1)

1 1 2 2

2 2 1 1

( ) ( )

( ) ( )y s s a s s a

s s a s s a

I ad z a z bd z b z

bk z b z ak z a z

ϕ ϕ ϕ

ϕ ϕ

= − − − + −

− + − + − − (2.2)

1 1 1 1 1 1 1 1( ) ( ) ( )a a s s a s s a t a rm z d z a z k z a z k z zϕ ϕ= − − + − − − − (2.3)

2 2 2 2 2 2 2 2( ) ( ) ( )a a s s a s s a t a rm z d z b z k z b z k z zϕ ϕ= + − + + − − − (2.4) These equations are implemented in a Matlab Simulink model to do further analyses.

2.2 Tyre model The only tyre information that is implemented in the vehicle model explained above is the tyre stiffness. However, to correctly investigate the effect of a tyre rolling over a realistic uneven road surface, more information about the deformation of the tyre is needed. The vehicle model used is two-dimensional; therefore the ‘Tandem model with elliptical cams’ [1] is chosen to represent the tyre behaviour. In this paragraph, this model will briefly be explained to understand how it describes the enveloping behaviour of the tyre. For more detailed or background information it is advised to read [1].

2.2.1 Basic function and two-point follower This tyre model consists of a basic curve replacing the obstacle and a two-point follower moving over the basic curve. Consider a tyre rolling quasi-statically with constant vertical load over a step obstacle as depicted in figure 2.2.

basic curve

vertical axle displacement= effective height ( )w

Fa

quartersine wave

identicalquartersine waves

effectiveforward

slope ( )�ylb

h

hstep

b=

lf

lb ls

½hstep

hstep

ls

X

lb

Fig. 2.2, Representation of the basic function and two-point follower models. [1]

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In the figure the vertical displacement of the wheel centre equals the effective height (w ). The curve of the effective height may be represented by the summation of two identical basic functions that are shifted a certain longitudinal distance sl . For instance, the curve might be represented by a summation of two identical quarter sine waves see figure 2.2. However, the curve for the effective height can also be obtained by moving with a two-point follower with length sl over a single basic curve bf with full height bh . When this is done the midpoint of the follower describes the curve that represents the effective height. The problem with using a sine wave for the basic curve is that its shape depends on the height of the step. This of course does not correspond to the curve the tyre will make since for example the tyre does not know the depth of a hole until the bottom is hit. This situation of different step heights for a tyre rolling over a downward step is illustrated in figure 2.3.

hstep

hstep

hsteppath lowestpoint ofrigid wheel

curves arenot identical

quarter sinebasic curves

Fig. 2.3, Quarter sine basic curves for three downward steps. [1] So the two-point follower model with a quarter sine wave as a basic curve might be used for known single step profiles, but it certainly not holds for an arbitrarily shaped road profile.

2.2.2 The tandem model with elliptical cams The solution for the problem of finding a basic curve that holds for any step is found by using an elliptical cam that moves over the step creating a basic curve that corresponds to the path of the lowest point of the elliptical cam. The basic idea is illustrated in figure 2.4.

pathellipsecentre

path lowestpoint ellipse= basic curve

lb

hstep

ae

be

correspondsto basic curve

x

z

XG

ZG

ze

Xstep

Fig. 2.4, Generation of the elementary basic curve with an elliptical cam. [1]

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The elliptical cam has three shape parameters ea , eb and ec which form the base of the generalised super ellipse equation:

1e ec c

e e

x za b

⎛ ⎞ ⎛ ⎞+ =⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠ (2.5)

The equation for the length bl of the curve reads:

1

1 1e ec c

stepb e

e

hl a

b

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟= − −⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠

(2.6)

For the distance ez between the local x-axis and the ellipse:

1

1e ec c

e ee

xz b

a

⎛ ⎞⎛ ⎞⎜ ⎟= − ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

(2.7)

And now to express the elliptical basic curve in terms of the global X-coordinate:

1

1e ec c

stepstep e e b step step

e

X XZ h b b if l X X X

a

⎛ ⎞⎛ ⎞−⎜ ⎟⎜ ⎟= − + − − + < <⎜ ⎟⎜ ⎟

⎝ ⎠⎝ ⎠

(2.8)

Now the basic curve is known, it can be used with the two-point follower to obtain the effective road surface. However, now it is also possible to create a full geometrical model since the elliptical cams, which are creating the basic profile, are moving over the actual road profile. This configuration is called the tandem model with elliptical cams and is depicted in figure 2.5.

x

zr

XG

xf

z

b x ae

e f e

=

| (1-(| |/ ) ) |c 1/c

xf

ZG

Z X xroad f f( + )

zf

X

ls

w X( )

XfXr

Zf

ae

be

-�y

Zr

ellipticalcam

Fig. 2.5, The tandem model with elliptical cams. [1]

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In this configuration the effective height (w ) can be calculated with:

( )2

f re

Z Zw X b

+= − (2.9)

where fZ and rZ can be calculated according to equation 2.8 for a step obstacle. The

inclination angle of the tandem rod corresponds to the effective forward slope tan yβ :

tan r fy

s

Z Zl

β−

= (2.10)

The shape of the effective road profile depends on the shape of the ellipse and the length of the tandem rod. The shape of the ellipse depends on the parameters ea , eb , ec and the

length of the rod depends on the contact length ( 2a ) of the tyre. These parameters are transformed into the following dimensionless parameters:

/ 2ls sp l a= (2.11)

0/ae ep a r= (2.12)

0/be ep b r= (2.13)

ce ep c= (2.14) The advantage of using dimensionless parameters is that the results for various tyres can be easily compared and that all parameters are of equal order of magnitude. With these parameters the model can be tuned to fit any tyre. For the tyres used in this research the determination of the parameters is explained in chapter 3.

2.3 Road surface The road on which the vehicle is tested is a random signal measured from an actual road during a distance of 1.2 km and a sample interval of 0.05 m. In figure 2.6 the road profile is depicted and it can be seen that the road height is varying between –0.02 and 0.04 m. This may seem a lot for a road surface but since the variation is spread over a distance of 1.2 km the road is actually of a quite good quality.

0 200 400 600 800 1000 1200−0.05

0

0.05Road Profile

road

hei

ght [

m]

425 430 435−15

−10

−5

0

5x 10

−3

longitudinal position [m]

road

hei

ght [

m]

Fig. 2.6, Measured road profile.

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Road profiles are commonly presented by their displacement power spectral densities (PSD) and the quality of the road can be classified according to ISO 8608:1995(E) in class limits A-H. Class type A is the best road profile and class type H the worst. In figure 2.7 the power spectral density of the measured road profile is given and in addition the ISO road class limits are shown. This proves that the measured road profile is around A and B, which is very good and can be compared to highway quality.

10−2

10−1

100

101

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

spatial frequency n=1/λ [1/m]

pow

er s

pect

ral d

ensi

ty S

zr [m

3 ]

A

B

C

D

E

F

G

H

Fig. 2.7, Displacement power spectral density of the measured road. Obviously it is not only of interest to test the Run Flat Tyres on a good road, but it is also of interest to test the tyres on a road surface of less quality. Therefore the measured road surface will be scaled with a constant number to reach other ISO class limits. Figure 2.8 shows the power spectral densities of the scaled road surfaces.

10−2

10−1

100

101

10−8

10−7

10−6

10−5

10−4

10−3

10−2

10−1

spatial frequency n=1/λ [1/m]

pow

er s

pect

ral d

ensi

ty S

zr [m

3 ]

A

B

C

D

E

F

G

H

A

B

C

D

E

F

G

H

A

B

C

D

E

F

G

H

Fig. 2.8, Road surfaces scaled up to various ISO classes. From now on, the original road surface is indicated with road type 1. The scaled road surfaces are indicated with road type 3 to 5, where road type 3 is of class B and 5 of class E.

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2.4 Models combined The last step to complete the model is to combine the vehicle model with the tyre model, which basically means that the vehicle model as depicted in figure 2.1 has to be extended with the tyre model as depicted in figure 2.5. However, using the tandem model with elliptical cams in the vehicle model means that the basic profile, which originates from the elliptical cam moving over the road profile, has to be calculated four times, while only one time should be sufficient. Therefore it is useful to split this part from the vehicle model into a separate calculation, and thus reduce the calculation time of the model itself. As explained in paragraph 2.2.2 the shape of the effective road profile depends on the shape of the ellipse and the length of the tandem rod. The shape of the ellipses depends on the type of tyre used, and the length of the tandem rod depends on the effective contact length of the tyre, which in a dynamic situation depends on the vertical load of the tyre. In other words the ellipses don’t change during a simulation and the length of the tandem rod does because of changing vertical loads. This allows a split up of the tyre model into two parts. The first part takes only one ellipse and moves this ellipse over the road surface creating a basic curve for that road surface, see figure 2.9 top left.

basic curve

effective height

two-point follower

=

X

cam camwheel centre line

X

cam

Fig. 2.9, Instead of using a complete tandem model it is possible to

use one single cam and a two point follower. [1] This basic curve is simply the trajectory the lowest point of the cam will follow when the cam moves over the step obstacle. Since the front and the rear cam of the tandem model are identical they will both follow the same path and therefore creating the same basic curve. The second step uses the tandem rod as a two point follower that moves over the basic curve created by the elliptical cam. The midpoint of the rod then describes the effective axle height just as for the complete tandem model, see figure 2.9 bottom right. The single ellipse can then be used to recalculate the road profile into a basic curve with equation 2.8. The recalculated road profile will now be used as the road height input in the vehicle model, which is now equipped with the two-point follower explained above, see figure 2.10. This way the basic curve only has to be calculated one time before the simulation instead of four times during the simulation.

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Fig. 2.9, The vehicle model with two-point followers on the front and rear.

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3 Model Parameters Before the model can be used for the analyses, all model parameters need to be determined. In this chapter all parameters needed to run the model are explained, especially the tyre parameters, which are obtained from experiments.

3.1 Vehicle parameters For the vehicle model, as shown in figure 2.1, a constant set of parameters needs to be determined like dimensions, weight and mass. These constants are chosen in such a way that the model represents an actual vehicle and are shown in table 3.1. Symbol Amount Unit Description L 2.6 [m] Wheelbase a 1.0 [m] Distance from c.o.g. to front axle b 1.6 [m] Distance from c.o.g. to rear axle

sm 520 [kg] Half vehicle body mass

yI 1000 [kgm²] Moment of inertia vehicle body

1am 45 [kg] Unsprung mass front, 47.5 for R.F.T.

2am 40 [kg] Unsprung mass rear, 42.5 for R.F.T.

1sk 24000 N/m Front suspension stiffness

2sk 21500 N/m Rear suspension stiffness

1sd 1800 Ns/m Front suspension damping

2sd 1500 Ns/m Rear suspension damping

Table 3.1, Constant vehicle parameters.

3.2 Vertical tyre stiffness In table 3.1 one can see that the vertical tyre stiffness tk is not added. The reason for this is that the tyre stiffness is not constant but nonlinear with the tyre deflection. Therefore, an equation is needed that gives the relation between the tyre deflection zd and the vertical

force zF . This relation has already been determined in a previous research [4]. The results have been obtained by measuring the vertical stiffness of a rolling tyre. Subsequently a polynomial fit equation of the following form,

21* 2*z z zF P d P d= + (3.1) is used to fit the measuring results. Here P1 and P2 are the fit parameters and zd is the tyre deflection. In appendix 1 the figures of the measurements and the polynomial fit equations with parameters P1 and P2 are given.

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3.3 Tyre model parameters As explained in paragraph 2.2 the tyre model has several shape parameters that together determine the shape of the effective height curve. When the model is tuned correctly this curve corresponds to the curve measured at the wheel centre of the tyre when the tyre is rolling over an obstacle. So the model parameters can be determined by an optimization routine minimizing the error between model results and measurements using the dimensionless parameters as the minimizers. So, in order for the optimization routine to succeed, the following data is needed:

• Measuring results of the tyre rolling over step obstacles. • The effective half contact length a which is needed for the length of the tandem

rod, see equation 2.11. • The unloaded tyre radius 0r , see equation 2.12 and 2.13, which can be found in the

table below.

Code Tire Unloaded radius [mm] GE Goodyear Eagle NCT5 EMT 317 BT Bridgestone Turanza RFT 319 DS Dunlop SP Sport 2000*E 314 MP Michelin Pilot HX 318

Table 3.2, Unloaded tire radius. [4]

3.3.1 Cleat measurements In order to determine the tyre model parameters cleat measurements are carried out to compare model behaviour with the actual tyre behaviour. These measurements are carried out at the so called Flat Plank tyre test facility. Since measurements on the Goodyear Eagle and the Michelin Pilot tyres have already been done in an earlier research [4], explanation of the measurements in this report is restricted to the theory only. For detailed information on the Flat Plank tyre test facility it is referred to [1] or [4]. The results of the measurements are given in the last paragraph of this chapter, together with all the fitted model results (appendix 3). The cleat measurements are carried out with step obstacles of three different heights (10, 20 and 30) millimetres as can be seen in figure 3.1.

Fig. 3.1, Cross sections of step obstacles used for cleat measurements. Each tyre is rolled over the cleats with a constant vertical load. In total three different vertical loads are used: 2000, 4000 and 6000 N.

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The results of the cleat measurements with the step obstacles are post-processed and expressed in two characterizing variables, namely the effective height (w ) and the effective forward slope ( yβ ). Both variables are defined in one point: the wheel centre, and are used

to describe the so-called effective road plane. The position and orientation of the two-dimensional effective road plane is defined such that the resulting force that acts upon the wheel axle is directed perpendicularly to the effective road plane [4], see Figure 3.2. Assumed is that the friction may be neglected.

Fig. 3.2, The wheel rolled over an obstacle at constant vertical load to establish the two-dimensional effective road surface. The spindle force (Fa) acts from the tyre on the wheel axle. [4]

The effective height (w) is defined as the distance over which the wheel centre has to move vertically in order to keep the vertical load constant when rolling over an obstacle:

w z= Δ (3.2) where ( zΔ ) is the measured vertical axle displacement to keep the vertical load constant. The effective forward slope (βy) is defined as the longitudinal spindle force (Fax) divided by the constant vertical spindle force (Faz):

tan axy

az

FF

β = (3.3)

The following equations apply:

sinax a yF F β= (3.4)

cosaz a yF F β= (3.5)

Now, with the effective height (w ) and the forward slope ( yβ ) known, equations 2.8

through 2.14 can be used to fit the measurement results.

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3.3.2 Effective contact length In order to know the length ( sl ) of the tandem rod depicted in figure 2.5, the effective

contact length ( 2a ) of the tyre needs to be determined. The problem however is that the effective contact length of the tyre varies with the vertical load and seems to be nonlinear. So, as for the vertical tyre stiffness, a combination of measuring and fitting will give an equation that returns the effective contact length for any vertical load. The first step in this process is to take footprints of the different tyres at again the loads of 2, 4 and 6 kN. This has already been done in previous research [4]. For convenience, the footprints are shown in appendix 2. These measurements show that the shape of the contact patch changes from an oval shape at very low values of vertical load to a more rectangular shape at higher values of vertical load. To represent the shape of the contact area an elliptical shape is used with the following equation:

1c c

c c

x ya b

⎛ ⎞ ⎛ ⎞+ =⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠ (3.6)

in which ca denotes half the contact length, cb half the contact width, x and y the envelope of the contact area and c the power of the ellipse. The shape factor c provides a smooth transition between the oval and the rectangular shape as shown in figure 3.3.

Fig. 3.3, The general shape of the contact area. [3]

To fit this ellipse on the footprints, a Matlab optimization routine is used that can load the footprint and fit the ellipse using pixel information. The output of this routine is the effective half contact length a which belongs to the vertical load of the footprint. When for all measured contact pressures the effective contact length is known, a polynomial can be fitted through the measured data.

1 2a z a za q F q F= + (3.7)

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Where 1aq and 2aq are the coefficients of the polynomial, zF denotes the vertical load and a is the effective half contact length. In figure 3.4 the contact length as function of the vertical load is depicted for all four tyres.

0 1000 2000 3000 4000 5000 60000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Vertical load Fz [N]

Effe

ctiv

e ha

lf co

ntac

t len

gth

[m]

MichelinBridgestoneGoodyearDunlop

Fig. 3.4, The effective contact length as function of the vertical load.

The polynomial coefficients 1aq and 2aq are given in table 3.3.

Tyre 1aq 2aq

Goodyear Eagle NCT5 EMT 51.0889 10−− × 0.0020 Bridgestone Turanza RFT 51.6407 10−− × 0.0023 Dunlop SP Sport 2000*E 51.3214 10−− × 0.0022 Michelin Pilot HX 51.3050 10−− × 0.0021

Table 3.3, Polynomial coefficients for the contact length.

3.3.3 Tyre model fit Now all data needed to fit the tyre model are known, the optimisation routine can fit the tyre model onto the cleat measurements using the tyre model parameters. The results of this process are shown in appendix 3. The figures showed, display the cleat measurements as explained in paragraph 3.3.1 together with the fit results of the tandem model with elliptical cams. Per tyre one set of optimized parameters is used. Finally, each experimental condition such as cleat height and vertical load gives a different set of parameters. The final set of parameters for one tyre is obtained by taking the average value of each parameter for the different experimental conditions. These final values can be found in table 3.4. model parameter values tyre

lsp aep bep cep

Goodyear Eagle NCT5 EMT 0.6131 1.9073 1.0845 1.3909 Bridgestone Turanza RFT 0.5057 1.4403 1.7568 2.0774 Dunlop SP Sport 2000*E 0.5696 1.3396 1.6708 2.1101 Michelin Pilot HX 0.5470 1.9397 1.1174 1.4176

Table 3.4, Estimated parameter values for the tandem model with elliptical cams.

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4 Analysing the Model Response The vehicle model is now completed and is ready to be used to investigate the influence of the different tyres. In this chapter the results of the model are discussed in two steps. First the response of the vehicle driving over different road surfaces is discussed and second the vehicle response is transformed into so called ride comfort numbers. These numbers give a better understanding in what is experienced as being comfortable and what is not.

4.1 Vehicle response The vehicle model as explained in chapter 2 is driven with four different tyres over 4 different road surfaces. The Goodyear Eagle and the Bridgestone Tarunza are tyres with Run Flat technology; the Dunlop SP sport and the Michelin Pilot are conventional tyres. The speed with which the vehicle drives over a road surface depends on the quality of that surface. Obviously it is less interesting to investigate the behaviour of the vehicle driving over a highway with 30 km/h since no one would drive that slow and in the same sense it is of no use to drive with 120 km/h over a very bad road surface. Therefore, the choice is made to drive over each surface with two different speeds. The combinations of road type and speed can be found in table 4.1.

Road type ISO class Speeds (km/h) 1 A/B 100 120 2 B/C 80 100 3 C/D 50 80 4 D/E 30 50

Table 4.1, Various combinations of road surfaces and speeds.

Since the aim is to investigate the ride comfort, the response of the vehicle model is presented in power spectral densities (PSD) of the vertical body accelerations. The accelerations are measured in three different points: the vertical body acceleration above the front and the rear axle and the vertical body acceleration at the centre of gravity (c.0.g.) of the sprung mass. The figures of the various testing conditions are presented in appendix 4.

4.2 Ride comfort As said before, the aim of this research is to investigate the difference in ride comfort of a vehicle equipped with Run Flat tyres or a vehicle equipped with conventional tyres. The only problem with answering this is that the definition of comfort is not quite clear and can be different for every person. Therefore an ISO standard has been made to give a better understanding in what is uncomfortable for the human body.

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According to [ISO 2631-1, 1997] ride comfort is assessed in the 0.5 to 80 Hz range. Above 80 Hz the human body is not very sensitive to vibrations. In the 0.1 to 0.5 Hz range, vibrations may cause motion sickness. Because the human body is more sensitive to specific frequencies, weighting functions ( )isoH f are applied to the vertical, longitudinal and lateral accelerations. Figure 4.1 shows the distribution of the weighting functions. It basically means that all vibrations in the frequency range of 0.1 to 80 Hz have to be multiplied by the value of the weighting function.

Fig. 4.1, Acceleration weighting functions according to [ISO 2631-1, 1997]. [2] As can be seen in the figure, different weighting functions for horizontal and vertical accelerations as well as for motion sickness are used. For the power spectral density in the vertical direction this means that:

2

, ,( ) ( ) ( )s sz iso iso z zS f H f S f= i (4.1)

It is also possible to calculate the weighted RMS acceleration, for acceleration in one direction this is the same as the mean square value obtained from the weighted acceleration PSD:

2

, ( ) ( )siso z za H f S f= i (4.2)

This value is also called the comfort index.

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In table 4.3 the comfort indexes for all vehicle test conditions measured at the centre of gravity of the vehicle are shown.

Tyre Conditions Michelin Dunlop Bridgestone¹ Goodyear¹

Road type Speed [km/h] Comfort index at c.o.g. [m/s²] 120 0,643 0,643 0,644 0,643 1 100 0,528 0,528 0,527 0,527 100 1,204 1,202 1,196 1,198 2 80 1,037 1,057 1,024 1,027 80 2,186 2,219 2,152 2,163 3 50 1,455 1,442 1,392 1,435 50 2,821 2,792 2,679 2,773 4 30 1,851 1,820 1,821 1,850

¹ Tyres with Run Flat technology Table 4.3, Comfort index at c.o.g. for all test conditions.

The results for the comfort index presented in table 4.3 are quite remarkably because it was expected that the Run Flat tyres due to a stiffer internal construction have a bad influence on the comfort. However, the comfort indexes show very little difference for all the tyres. This corresponds to the results presented in appendix 4. The PSD’s also show very little difference for the different tyres. So the question rises what kind of influence the Run Flat tyres do have? In figure 4.2 the vertical tyre stiffness of all four tyres is depicted. The figure shows that when the vertical load on the tyres exceeds about 4000 N the Run Flat tyres enter the nonlinear stiffness range.

0 5 10 15 20 25 30 350

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000Vertical load vs. vert displacement (non−rolling)

Vert. disp [mm]

Fz [N

]

GEBTDSMP

Fig. 4.2, Vertical tyre stiffness for the conventional and the Run Flat tyres.

Since no difference can be found in the comfort behaviour of the vehicle one would expect that the vertical tyre loads do not enter the nonlinear area of the Run Flat tyres. A closer look at the suspension system gives a better insight of the forces and accelerations acting on the unsprung mass. In appendix 5 the RMS values for the vertical accelerations of the sprung mass at the c.o.g., for the dynamic wheel loads, for the vertical accelerations of the unsprung masses and the comfort index for the sprung mass at the c.o.g. are given. Furthermore, the average is taken for the conventional tyres, (Michelin and Dunlop) and for the Run Flat tyres, (Bridgestone and Goodyear). From these averages the difference in percentage is calculated to get a good comparison between the conventional and the Run Flat tyres.

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The total differences between the different tyres can also be found in table 4.4, where a positive number indicates the increase of the Run Flat tyres with respect to the conventional tyres. To complete the comparison all calculations have also been carried out with a sprung mass of 670 kg to simulate the effect of a vehicle loaded with passengers.

Sprung mass 520 kg Sprung mass 670 kg RMS acc. sprung mass 2.50 % 2.28 % Comfort index -1.61 % -1.81 % Front Rear Front Rear Dynamic wheel load 13.7 % 10.9 % 16.6 % 12.8 % RMS acc. unsprung mass 15.1 % 8.7 % 18.7 % 11.5 %

Table 4.4, The change in % between conventional and Run Flat tyres

Before conclusions on the vertical loads of the tyres can be drown, the static loads on the wheels need to be known:

• Static load front wheel unloaded vehicle: 3580 N • Static load rear wheel unloaded vehicle: 2354 N • Static load front wheel loaded vehicle: 4515 N • Static load rear wheel loaded vehicle: 2949 N

Tables A5.3 and A5.7 show that the vertical load on the tyres increase by more than 10% when the vehicle is equipped with Run Flat tyres instead of conventional tyres. The average RMS value lays around 1500 N but in some situations even an RMS value of 2700 N can be found. Adding these values to the static load gives the load a tyre experiences while driving over the road surface, and as can be seen in figure 4.2 in almost every situation this means that the Run Flat tyres enter the non-linear stiffness area. Apparently the increase in vertical load does not affect the ride comfort of the vehicle, since table A5.1 and A5.5 show only a small (2.5%) increase in vertical accelerations. Calculating the comfort index one even gets a stranger result because it says that the run flat tyres would be a little more comfortable (-1.8%) than the conventional tyres. This is strange since the comfort index is calculated by the vertical accelerations of the sprung mass and these indicate an increase in accelerations. An explanation for this result can probably be found in the weighting of the accelerations to obtain the comfort index. The small difference in vertical accelerations can also be explained by calculating the total stiffness of the tyre and suspension combined. The total stiffness is calculated by the following equation:

s ttot

t s

k kkk k

=+

(4.3)

in which sk is the constant suspension stiffness and tk is the tyre stiffness according to appendix 1.

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In figure 4.3 the total stiffness is given for the suspension system in combination with a Run Flat tyre and with a conventional tyre.

0 1000 2000 3000 4000 5000 6000 7000 8000−0.5

0

0.5

1

1.5

2

2.5

3

Vertical load Fz [N]

diffe

renc

e [%

]

Conventional tyre is 100%

Fig. 4.3, (left) The total stiffness of suspension and tyre for Run Flat and conventional Fig. 4.4, (right) The difference in total suspension stiffness with Run Flat or conventional tyres, conventional is 100% As can be seen in figure 4.4 the difference between the total stiffness with a Run Flat tyre and the total stiffness with a conventional tyre is very small. The difference that occurs is about 2.5% which strokes with an average increase of the vertical accelerations of 2.5%. In table A5.4 and A5.8 the accelerations of the unsprung masses are given and these show as expected an increase of 10 to 18% for the Run Flat tyres with respect to the conventional tyres. The situation of the loaded vehicle does not seem to affect the vehicle comfort. The only differences found are the changes in vertical load and accelerations of the unsprung masses, but this is rather logical since the vertical load increases with the mass of the sprung body. These results prove that using Run Flat tyres instead of conventional tyres has a larger effect on the suspension system, (higher forces and accelerations) than it has on the ride comfort of the vehicle. So the suspension system is able to filter most of the effects of the Run Flat tyres.

0 1000 2000 3000 4000 5000 6000 7000 80002.1

2.15

2.2

2.25x 10

4

Vertical load Fz [N]

Stif

fnes

s [N

/m]

total stiffness with Run Flat tyretotal stiffness with conventional tyre

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5 Conclusions and Recommendations In this chapter the main conclusions of the research are summed and some recommendations for further research are formulated. The aim of this project was to investigate the ride comfort of a vehicle equipped with conventional tyres and Run Flat tyres. The stiffer internal construction of the Run Flat tyres results in a nonlinear tyre stiffness that increases more progressive than the stiffness of conventional tyres. This is expected to result in a less comfortable ride and therefore worth investigating. To achieve these results a half vehicle model equipped with an enveloping tyre model has been used. This tyre model first had to be verified for use with Run Flat tyres because it was initially developed for conventional tyres.

5.1 Conclusions The following conclusions have been drawn during the research:

• The tandem model with elliptical cams can be used for Run Flat tyres as well as for conventional tyres. To validate the tyre model for Run Flat tyres, measurements were taken and the tyre model was fitted onto the measured data by changing the parameters of the model. The fit process succeeded very well and figures of the model and measurements showed a very similar enveloping behaviour as for conventional tyres.

• To analyse the comfort behaviour of the vehicle, the vertical accelerations of the

vehicle sprung mass are analysed using power spectral density diagrams. These diagrams show the relation between the amplitude and the frequency of the accelerations and are made for every test condition. Comparing these accelerations for each tyre and test condition shows very little difference between the use of conventional or Run Flat tyres. Especially at the centre of gravity, which roughly corresponds to the seating position of a person, the differences in vertical accelerations are small.

• To get a better insight in the meaning of ‘comfort’ an ISO standard is used to

calculate the comfort index. This standard uses weighting parameters to account for the human body’s sensitivity to accelerations in a certain frequency range. This comfort index also shows no difference in the ride comfort with Run Flat tyres or conventional tyres. In fact at some point it even shows that the Run Flat tyres are a little more comfortable than the conventional tyres. However, this difference is about 1.5% and since the magnitude of the weighting parameters are frequency dependent, the comfort index might give a misleading result. In other words there are vertical accelerations taking place with a frequency where the amplitude of the weighting parameter is low, resulting in a lower comfort index.

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• A closer look at the suspension system gives better insight in the differences

resulting from the different tyres. The RMS values of the dynamic wheel loads show an average increase in vertical load of 13% for the Run Flat tyres. This is easily explained by the nonlinear tyre stiffness of the Run Flat tyres. The increase in vertical load on the tyres also results in an increase of the vertical accelerations of the unsprung masses.

• The final conclusion that can be drawn from these results is that the effects of the

Run Flat tyres reach up to the suspension system but not up to the sprung mass of the vehicle. In other words: the load on the suspension system increases but not the load on the sprung mass of the vehicle. Therefore, no difference can be found in the comfort behaviour of the vehicle.

5.2 Recommendations The following recommendations can be made for future research:

• In this research a half vehicle model was used to do the simulations. The limitation of this model in terms of comfort is that comfort can only be analysed in the vertical direction. However, a full vehicle model will make it possible to also investigate the horizontal and lateral accelerations and thus the comfort in horizontal and lateral directions. Furthermore, with a full vehicle model vibrations resulting from the tyre stiffness are inserted in the sprung mass on four points instead of two, this might result in different vibration behaviour on the seating surface.

• Instead of changing the vehicle model it is also possible to change the tyre model.

In this research the tandem model with elliptical cams is used to simulate the enveloping behaviour of the tyre. This model however, does not include any information on the vibration modes of the tyre. Actually the main information used to predict the effect on the comfort behaviour is the nonlinear tyre stiffness while other factors may also play an important role in the comfort behaviour of the tyre.

• Other road surfaces might be used to test the vehicle comfort. Although the road

surface used in this research was scaled up to different types of quality, the structure of the road surface remains the same. Scaling only changes the amplitude of the surface but not its frequency spectrum. Therefore, using a completely different type of road surface might give a change in resulting vibrations of the sprung mass.

Finally, all the recommendations made above are made for further research on the influence on vehicle comfort with Run Flat tyres. However, the results of this research show that the impact of Run Flat tyres on the suspension system is worse than the influence they have on the ride comfort. Therefore, it is of interest to investigate the effect of Run Flat tyres on the durability of the suspension system.

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References [1] Schmeitz, A.J.C. (2004), A Semi-Empirical Three-Dimensional Model of the

Pneumatic Tire Rolling over Arbitrarily Uneven Road Surfaces, PhD Thesis, Delft University of Technology, Delft, The Netherlands, ISBN 90-9018380-9, 2004

[2] Introduction to Automotive Technology (4N820), Schmeitz, A.J.C., Besselink, I.J.M., e.a. Eindhoven University of technology, Eindhoven The Netherlands [3] Zegelaar, P.W.A. (1998), The dynamic response of tyres to brake torque variations and road unevennesses, Dissertation, TU Delft, 1998 [4] Veld op het, I.B.A.(2006), Run Flat Tires vs. Conventional Tires ‘An experimental

comparison’, Internal traineeship, Eindhoven University of technology, Eindhoven, The Netherlands, DCT 2006.042

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Appendix 1 Vertical Stiffness As described in section 3.2 the vertical tyre stiffness for all the test tyres is determined in previous research [4]. These results are presented below in the form of figures that show the measured as well as the fitted force versus deflection characteristics. In figure A1.1 the results of the Goodyear Eagle EMT are depicted.

Fig. A1.1, Measurements (thin) and quadratic fit (thick) Goodyear Eagle EMT. [4] In figure A1.2 the results of the Bridgestone Turanza RFT are depicted.

Fig. A1.2, Measurements (thin) and quadratic fit (thick) Bridgestone Turanza RFT. [4]

−5 0 5 10 15 20 25 30 350

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

(Tire: GE)Quadratic fit of vertical stiffness (rolling)

Relative vert. disp [mm]

Fz [N

]

−5 0 5 10 15 20 25 30 350

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

(Tire: BT)Quadratic fit of vertical stiffness (rolling)

Relative vert. disp [mm]

Fz [N

]

2

5

5

5

: 2.9707 176.21

: 5.9414 176.21

2[ ] , 9.75[ ] 2.34 10 [ / ]

4[ ] , 17.52[ ] 2.80 10 [ / ]

6[ ] , 24.19[ ] 3.20 10 [ / ]

9[ ] ,

z z z

zz z

z

z z z

z z z

z z z

z z

fit equation F d ddFstiffness equation C ddd

F kN d mm C N m

F kN d mm C N m

F kN d mm C N m

F kN d

= +

= = +

= = ⇒ = ⋅

= = ⇒ = ⋅

= = ⇒ = ⋅

= 532.87[ ] 3.72 10 [ / ]zmm C N m= ⇒ = ⋅

2

5

5

5

: 3.6167 161.94

: 7.2334 161.94

2[ ] , 10.08[ ] 2.35 10 [ / ]

4[ ] , 17.70[ ] 2.93 10 [ / ]

6[ ] , 24.09[ ] 3.36 10 [ / ]

9[ ] ,

z z z

zz z

z

z z z

z z z

z z z

z

fit equation F d ddFstiffness equation C ddd

F kN d mm C N m

F kN d mm C N m

F kN d mm C N m

F kN d

= +

= = +

= = ⇒ = ⋅

= = ⇒ = ⋅

= = ⇒ = ⋅

= 532.29[ ] 3.96 10 [ / ]z zmm C N m= ⇒ = ⋅

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In Figure A1.3 the results of the Dunlop SP Sport (conventional) are depicted.

Fig. A1.3, Measurements (thin) and quadratic fit (thick) Dunlop SP Sport. [4] In Figure A1.4 the results of the Michelin Pilot (conventional) are depicted.

Fig. A1.4, Measurements (thin) and quadratic fit (thick) Michelin Pilot. [4]

−5 0 5 10 15 20 25 30 35 40 450

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

(Tire: DS)Quadratic fit of vertical stiffness (rolling)

Relative vert. disp [mm]

Fz [N

]

−5 0 5 10 15 20 25 30 35 40 450

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

(Tire: MP)Quadratic fit of vertical stiffness (rolling)

Relative vert. disp [mm]

Fz [N

]

2

5

5

5

: 2.8423 188.52

: 5.6846 188.52

2[ ] , 9.30[ ] 2.41 10 [ / ]

4[ ] , 16.91[ ] 2.85 10 [ / ]

6[ ] , 23.50[ ] 3.22 10 [ / ]

9[ ] ,

z z z

zz z

z

z z z

z z z

z z z

z z

fit equation F d ddFstiffness equation C ddd

F kN d mm C N m

F kN d mm C N m

F kN d mm C N m

F kN d

= +

= = +

= = ⇒ = ⋅

= = ⇒ = ⋅

= = ⇒ = ⋅

= 532.15[ ] 3.71 10 [ / ]zmm C N m= ⇒ = ⋅

2

5

5

5

: 3.5637 163.99

: 7.1274 163.99

2[ ] , 10.02[ ] 2.35 10 [ / ]

4[ ] , 17.63[ ] 2.90 10 [ / ]

6[ ] , 24.04[ ] 3.35 10 [ / ]

9[ ] ,

z z z

zz z

z

z z z

z z z

z z z

z

fit equation F d ddFstiffness equation C ddd

F kN d mm C N m

F kN d mm C N m

F kN d mm C N m

F kN d

= +

= = +

= = ⇒ = ⋅

= = ⇒ = ⋅

= = ⇒ = ⋅

= 529.66[ ] 3.75 10 [ / ]z zmm C N m= ⇒ = ⋅

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Appendix 2 Contact Length Figure A2.1 to A2.3 show the footprints of the contact patches for the different vertical loads. Notice that all the footprints are scaled with the same scaling factor; dimensions of the depicted footprints are reduced to 15 percent of the actual dimensions. Fig. A2.1, Footprint contact patch at vertical load of 2 kN. [4] Fig. A3.3, Footprint contact patch at vertical load of 4 kN. [4]

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Fig. A3.3, Footprint contact patch at vertical load of 6 kN. [4] Observation of the footprints shows that the contact patches are quite similar for the run flat tires and the conventional tires. Only the Dunlop tire differs a bit due to other tire dimensions.

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Appendix 3 Model Fit Results In this appendix the plots of the fitting process for the tyre parameters are depicted. Each paragraph displays all test conditions for one tyre; so for cleat heights of 10, 20 and 30 mm and constant vertical loads of 2000, 4000 and 6000 N. The model is fitted on the effective height (w ) and the longitudinal force ( axF ) which are two of the outputs of the Flat Plank tyre tester. The longitudinal force can be used to calculate the effective forward slope as explained in paragraph 3.3.1. In the figures, the thin (blue) lines represent the measured data and the thick (red) lines represent the model results. Below, some comments for each of the tyres are made. Dunlop SP sport 2000*E The tyre model fits the enveloping behaviour of the tyre very well, especially the effective height of the model fit well with the measured data. Only at a vertical load of 6000 N there seems to be a small difference in reaching the maximum height of the cleat. The most logical explanation for this is that the measuring facility has some trouble of keeping the vertical load constant. Furthermore some large differences can be seen in the longitudinal force at a cleat height of 30 millimetres. Especially when the vertical force is low the differences seem larger; this again can be explained by the fact that the measuring facility has more trouble in keeping the vertical force constant. Only this time the force is too low and the cleat is quite large, so a rapid response in compensating the rising vertical force is needed. Bridgestone Tarunza RFT Again the model fits the measuring data quite well. Even at high loads the effective height reaches its maximum. A comment on this difference with the Dunlop tyre is that the Bridgestone and the Michelin tyres where measured a few months before the Dunlop and the Goodyear. Therefore the setup of the Flat Plank might not exactly be the same and some differences could be experienced. The difference in the longitudinal force at the cleat height of 30 millimetres will have the same explanation as for the Dunlop tyre. Michelin Pilot HX The results for the Michelin tyre do not differ much from the previous tyres. The model fits quite well, although some more differences can be found in the effective height. The model does not seem to behave as fluently as the measured data does, since this is a conventional tyre it might be a little bit to soft or the tyre pressure might be a bit low. Goodyear Eagle NCT5 EMT Like the other tyres the model fits well and differences can be explained as above. Finally, there seems to be no difference between a tyre equipped with Run Flat technology or not. The model fits all tyres equally well.

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A3.1 Results Dunlop SP sport 2000*E

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−5

0

5

10

15x 10

−3

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−5

0

5

10

15x 10

−3

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−5

0

5

10

15x 10

−3

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

2000 NazF = 4000 NazF = 6000 NazF =

Step

10

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St

ep 2

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Step

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m]

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[m]X [m]X [m]X

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A3.2 Results Bridgestone Turanza RFT

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−5

0

5

10

15x 10

−3

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−5

0

5

10

15x 10

−3

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−5

0

5

10

15x 10

−3

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

2000 NazF = 4000 NazF = 6000 NazF =

Step

10

mm

St

ep 2

0 m

m

Step

30

mm

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m]

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m]

Fax [

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[m]X [m]X [m]X

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A3.3 Results Michelin Pilot HX

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−5

0

5

10

15x 10

−3

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−5

0

5

10

15x 10

−3

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−5

0

5

10

15x 10

−3

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

2000 NazF = 4000 NazF = 6000 NazF =

Step

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mm

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ep 2

0 m

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m]

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[m]X [m]X [m]X

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A3.4 Results Goodyear Eagle NCT5 EMT

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−5

0

5

10

15x 10

−3

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−5

0

5

10

15x 10

−3

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−5

0

5

10

15x 10

−3

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

−0.2 −0.15 −0.1 −0.05 0 0.05 0.1−1500

−1000

−500

0

2000 NazF = 4000 NazF = 6000 NazF =

Step

10

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St

ep 2

0 m

m

Step

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m]

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Appendix 4 Vehicle Response to Road Surfaces In this appendix the results for the vehicle model driving with different speeds over several types of road surfaces are depicted. The figures presented are the power spectral density diagrams of the vertical body accelerations measured above the front and rear axle and at the center of gravity (c.o.g.). The thick solid line (blue) represents the accelerations at the center of gravity, the thin solid line (black) represents the accelerations at the front axle and the thin dashed line (black) represents the accelerations at the rear axle. As explained in chapter 4 each tyre is tested on four different road surfaces with two different speeds. In the title of each graph the information about the test condition can be found. For instance, the first graph says:

DSroadAV100

• DS: stands for the Dunlop tyre. • roadA: stands for road type 1, which is the best road surface. • V100: stands for a vehicle forward velocity of 100 km/h

The names for the other tyres are built up the same; only the tyre indications differ:

• BT: Bridgestone • MP: Michelin • GE: Goodyear

As can be seen in the figures of the results, no real differences between the tyres can be found. As expected, vibrations get worse when the vehicle speed is higher or the road surface gets worse. Obviously it is better for a passenger to sit around the centre of gravity, instead of sitting above the front or the rear axle, but this applies for the Run Flat Tyres as well as for the conventional tyres.

12

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A4.1 Dunlop SP sport 2000*E

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (DSroadAV100)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (DSroadAV120)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (DSroadBV80)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (DSroadBV100)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (DSroadCV50)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (DSroadCV80)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (DSroadDV30)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (DSroadDV50)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

12

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A4.2 Bridgestone Tarunza RFT

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (BTroadAV100)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (BTroadAV120)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (BTroadBV80)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (BTroadBV100)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (BTroadCV50)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (BTroadCV80)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (BTroadDV30)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (BTroadDV50)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

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A4.3 Michelin Pilot HX

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (MProadAV100)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (MProadAV120)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (MProadBV80)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (MProadBV100)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (MProadCV50)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (MProadCV80)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (MProadDV30)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (MProadDV50)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

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A4.4 Goodyear Eagle NCT5 EMT

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (GEroadAV100)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (GEroadAV120)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (GEroadBV80)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (GEroadBV100)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (GEroadCV50)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (GEroadCV80)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (GEroadDV30)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

100

101

102

10−6

10−5

10−4

10−3

10−2

10−1

100

101

Vertical body acceleration (GEroadDV50)

Frequency [Hz]

PS

D [m

2 /s4 /H

z]

front axlerear axlec.o.g.

12

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Appendix 5 Comfort Numbers In this appendix the calculated RMS values for the dynamic wheel loads, the vertical accelerations of the unsprung masses, the vertical accelerations of the sprung mass at the c.o.g. and the comfort index at the c.o.g. of the sprung mass are presented in tables for each test condition. All values for the unsprung masses are given for the front as well as for the rear wheel. Furthermore the average is taken for all RMS values of the Michelin and the Dunlop tyre, which are conventional tyres, and the average for the Bridgestone and the Goodyear tyre, which are Run Flat tyres. For these average values the difference in percentage is calculated to get a clear comparison between Run Flat and conventional tyres. In appendix A5.1 the results for the vehicle with a sprung mass of 520 kg are given. In appendix A5.2 the results for the vehicle with a sprung mass of 670 kg are given to simulate the effect of a loaded vehicle.

12

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A5.1 Comfort numbers for a sprung mass of 520 kg

Tyre Conditions Michelin Dunlop Bridgestone* Goodyear*

Road Speed RMS value vertical accelerations sprung mass 120 1,13 1,15 1,29 1,27

1 100 0,99 1,00 1,05 1,05 100 2,22 2,24 2,35 2,35

2 80 1,76 1,80 1,78 1,79 80 3,59 3,65 3,63 3,65

3 50 2,35 2,33 2,34 2,42 50 4,32 4,27 4,22 4,39

4 30 2,91 2,85 2,93 3,00

Average values Run-Flat and conventional Difference Conditions MP + DS BT + GE [%]

Road Speed Average RMS values vert. acc. 120 1,14 1,28 12,3

1 100 0,99 1,05 5,9 100 2,23 2,35 5,3

2 80 1,78 1,78 0,4 80 3,62 3,64 0,6

3 50 2,34 2,38 1,7 50 4,29 4,31 0,3

4 30 2,88 2,97 2,9 Total 19,28 19,76 2,50

Table A5.1, RMS values of the vertical accelerations of the sprung mass at c.o.g.

Tyre Conditions Michelin Dunlop Bridgestone* Goodyear*

Road Speed Comfort index at c.o.g. 120 0,643 0,643 0,644 0,643

1 100 0,528 0,528 0,527 0,527 100 1,204 1,202 1,196 1,198

2 80 1,037 1,057 1,024 1,027 80 2,186 2,219 2,152 2,163

3 50 1,455 1,442 1,392 1,435 50 2,821 2,792 2,679 2,773

4 30 1,851 1,820 1,821 1,850

Average values Run-Flat and conventional Difference Conditions MP + DS BT + GE [%]

Road Speed Average comfort index 120 0,64 0,64 0,1

1 100 0,53 0,53 -0,2 100 1,20 1,20 -0,5

2 80 1,05 1,03 -2,1 80 2,20 2,16 -2,0

3 50 1,45 1,41 -2,4 50 2,81 2,73 -2,9

4 30 1,84 1,84 0,0 Total 11,71 11,52 -1,61

Table A5.2, Comfort index of sprung mass at c.o.g.

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Tyre Michelin Dunlop Bridgestone* Goodyear*

Conditions RMS value dynamic wheel load Road Speed Front Rear Front Rear Front Rear Front Rear

120 647 602 662 624 803 727 785 707 1 100 531 491 541 505 628 572 623 565

100 1203 1069 1220 1094 1406 1222 1398 1209 2 80 933 835 960 865 1082 950 1078 942

80 1875 1595 1906 1642 2116 1774 2129 1773 3 50 1280 1105 1270 1111 1422 1212 1489 1261

50 2294 1870 2263 1867 2461 1981 2584 2064 4 30 1557 1375 1520 1357 1712 1484 1776 1530

Average values Run-Flat and conventional Difference Run-Flat versus

MP + DS BT + GE conventional [%] Conditions Average RMS values dyn. Wheel load

Road Speed Front Rear Front Rear Front Rear 120 655 613 794 717 21,3 16,9 1

100 536 498 625 568 16,6 14,0 100 1211 1082 1402 1215 15,7 12,4 2

80 947 850 1080 946 14,0 11,3 80 1890 1619 2122 1773 12,3 9,5 3

50 1275 1108 1455 1237 14,2 11,6 50 2279 1869 2522 2022 10,7 8,2 4

30 1538 1366 1744 1507 13,4 10,3 Total 10331 9004 11745 9986 13,7 10,9

Table A5.3, RMS values of the dynamic wheel loads for the front and rear axle.

Tyre Michelin Dunlop Bridgestone* Goodyear*

Conditions RMS value vertical accelerations unsprung mass Road Speed Front Rear Front Rear Front Rear Front Rear

120 12,15 13,28 12,48 13,83 14,95 15,53 14,57 15,06 1 100 9,81 10,66 10,04 11,03 11,51 12,07 11,39 11,89

100 22,15 23,09 22,57 23,75 25,68 25,62 25,50 25,31 2 80 16,55 17,58 17,11 18,32 19,28 19,60 19,17 19,38

80 32,70 32,96 33,32 34,12 37,03 35,90 37,23 35,80 3 50 21,28 22,43 21,18 22,71 24,20 24,26 25,50 25,32

50 36,68 36,59 36,13 36,74 40,28 38,19 42,58 39,92 4 30 24,36 25,48 23,70 25,24 27,62 27,47 28,94 28,50

Average values Run-Flat and conventional Difference Run-Flat versus

MP + DS BT + GE conventional [%] Conditions Average RMS values vert. acc.

Road Speed Front Rear Front Rear Front Rear 120 12,32 13,56 14,76 15,30 19,8 12,8 1

100 9,92 10,85 11,45 11,98 15,4 10,4 100 22,36 23,42 25,59 25,47 14,4 8,8 2

80 16,83 17,95 19,23 19,49 14,2 8,6 80 33,01 33,54 37,13 35,85 12,5 6,9 3

50 21,23 22,57 24,85 24,79 17,1 9,9 50 36,40 36,66 41,43 39,05 13,8 6,5 4

30 24,03 25,36 28,28 27,99 17,7 10,3 Total 176,10 183,90 202,71 199,91 15,1 8,7

Table A5.4, RMS values of the vertical accelerations of the unsprung masses.

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A5.2 Comfort numbers for a sprung mass of 670 kg

Tyre Conditions Michelin Dunlop Bridgestone* Goodyear*

Road Speed RMS value vertical accelerations sprung mass 120 0,96 0,97 1,08 1,07

1 100 0,81 0,82 0,85 0,85 100 1,85 1,86 1,94 1,94

2 80 1,44 1,46 1,45 1,46 80 3,00 3,04 3,02 3,04

3 50 1,98 1,96 1,96 2,04 50 3,71 3,66 3,62 3,77

4 30 2,35 2,30 2,36 2,43

Average values Run-Flat and conventional Difference Conditions MP + DS BT + GE [%]

Road Speed Average RMS values vert. acc. 120 0,96 1,07 11,4

1 100 0,81 0,85 4,8 100 1,86 1,94 4,4

2 80 1,45 1,45 0,2 80 3,02 3,03 0,3

3 50 1,97 2,00 1,7 50 3,68 3,70 0,4

4 30 2,32 2,40 3,2 Total 16,08 16,45 2,28

Table A5.5, RMS values of the vertical accelerations of the sprung mass at c.o.g.

Tyre Conditions Michelin Dunlop Bridgestone* Goodyear*

Road Speed Comfort index at c.o.g. 120 0,608 0,608 0,602 0,606

1 100 0,485 0,484 0,482 0,482 100 1,111 1,110 1,102 1,103

2 80 0,923 0,942 0,914 0,915 80 1,963 1,995 1,937 1,945

3 50 1,358 1,348 1,295 1,339 50 2,620 2,596 2,484 2,573

4 30 1,549 1,525 1,520 1,543

Average values Run-Flat and conventional Difference Conditions MP + DS BT + GE [%]

Road Speed Average comfort index 120 0,61 0,60 -0,7

1 100 0,48 0,48 -0,6 100 1,11 1,10 -0,7

2 80 0,93 0,91 -1,9 80 1,98 1,94 -1,9

3 50 1,35 1,32 -2,6 50 2,61 2,53 -3,0

4 30 1,54 1,53 -0,4 Total 10,61 10,42 -1,81

Table A5.6, Comfort index of sprung mass at c.o.g.

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Tyre Michelin Dunlop Bridgestone* Goodyear*

Conditions RMS value dynamic wheel load Road Speed Front Rear Front Rear Front Rear Front Rear

120 669 624 678 641 836 759 821 741 1 100 542 501 548 512 647 587 643 581

100 1241 1124 1251 1144 1469 1297 1465 1288 2 80 947 869 969 898 1119 1003 1118 997

80 1956 1718 1970 1754 2241 1933 2265 1940 3 50 1309 1178 1289 1176 1491 1309 1569 1370

50 2389 2065 2338 2047 2638 2212 2780 2314 4 30 1595 1433 1548 1403 1792 1565 1867 1627

Average values Run-Flat and conventional Difference Run-Flat versus

MP + DS BT + GE conventional [%] Conditions Average RMS values dyn. Wheel load

Road Speed Front Rear Front Rear Front Rear 120 674 632 828 750 22,9 18,6 1

100 545 507 645 584 18,3 15,2 100 1246 1134 1467 1292 17,8 14,0 2

80 958 884 1118 1000 16,8 13,2 80 1963 1736 2253 1937 14,8 11,6 3

50 1299 1177 1530 1340 17,8 13,8 50 2363 2056 2709 2263 14,6 10,1 4

30 1571 1418 1830 1596 16,4 12,5 Total 10619 9544 12380 10761 16,6 12,8

Table A5.7, RMS values of the dynamic wheel loads for the front and rear axle.

Tyre Michelin Dunlop Bridgestone* Goodyear*

Conditions RMS value vertical accelerations unsprung mass Road Speed Front Rear Front Rear Front Rear Front Rear

120 12,48 13,67 12,69 14,12 15,60 16,21 15,27 15,79 1 100 10,01 10,81 10,16 11,11 11,92 12,37 11,84 12,22

100 22,91 24,18 23,15 24,73 27,05 27,23 26,94 26,99 2 80 16,98 18,11 17,42 18,81 20,23 20,62 20,19 20,45

80 34,70 35,17 34,91 36,06 39,95 39,05 40,42 39,16 3 50 22,28 23,57 21,90 23,63 26,05 26,10 27,58 27,43

50 39,49 39,77 38,43 39,53 44,78 42,50 47,54 44,64 4 30 25,65 27,08 24,73 26,50 29,81 29,67 31,37 31,08

Average values Run-Flat and conventional Difference Run-Flat versus

MP + DS BT + GE conventional [%] Conditions Average RMS values vert. acc.

Road Speed Front Rear Front Rear Front Rear 120 12,59 13,89 15,43 16,00 22,6 15,2 1

100 10,09 10,96 11,88 12,29 17,8 12,2 100 23,03 24,45 27,00 27,11 17,2 10,9 2

80 17,20 18,46 20,21 20,54 17,5 11,2 80 34,80 35,62 40,18 39,11 15,5 9,8 3

50 22,09 23,60 26,82 26,76 21,4 13,4 50 38,96 39,65 46,16 43,57 18,5 9,9 4

30 25,19 26,79 30,59 30,38 21,4 13,4 Total 183,95 193,43 218,27 215,77 18,7 11,5

Table A5.8, RMS values of the vertical accelerations of the unsprung masses.