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Measurement of the Tire Dynamic Transfer Stiffness at

Operational Excitation Levels

P. Kindt, F. De Coninck, P. Sas, W. Desmet

K.U.Leuven, Department of Mechanical Engineering,

Celestijnenlaan 300 B, B-3001, Heverlee, Belgium

e-mail: peter.kindt@mech.kuleuven.be

AbstractThe tire dynamic transfer stiffness describes how a displacement enforced at the tire contact patch results ina force at the spindle-wheel interface. The dynamic transfer stiffness is expressed as a function of frequency

and provides insight in the generation of vehicle interior structure-borne tire/road noise. The road surface

texture excites the tire at the contact patch, resulting in structural waves travelling around the circumference

of the tire. The tire sidewalls transfer these vibrations to the rim. The vibrational energy is then transmitted

through the spindle-wheel interface toward the suspension and vehicle body. The resulting body panel and

window vibrations cause noise radiation in the passenger compartment.

It is known that the tire dynamic properties are dependent on the vibration amplitude. Therefore, the ex-

citation levels during tire dynamic characterization tests should be similar as the excitation levels during

operation of the tire. This is not possible with the classic excitation devices such as hammer and electro-

dynamic shakers. This paper presents an experimental method to obtain the dynamic transfer stiffness ofa non-rolling tire which is excited at operational excitation levels. Therefore, a high-frequency 6-DOF hy-

draulic shaker table (CUBE R) is used to excite the tire. The shaker table provides the static preload and

excites the tire at the contact patch in the frequency range 20-235 Hz. The force at the fixed spindle is

measured by a piezo-electric dynamometer.

1 Introduction

The drivers subjective perception of a vehicle is strongly determined by its Noise, Vibration and Harshness

(NVH) characteristics. Well balanced vehicle NVH characteristics can enhance safety by reducing driver

fatigue and bring to the most modest of cars a perception of high quality. It is found that the vibro-acoustic

properties of a new vehicle have a very significant impact on the purchasing decisions. Consequently, the

NVH performance is an important design and marketing criterion for vehicle manufacturers.

Similar to the exterior vehicle noise, the main sources of noise inside the passenger compartment of a typ-

ical vehicle are: power unit, aerodynamics and tire/road interaction. Thestructure-borne tire/road noise

component originates from the tire vibrations that are generated by the tire/road interaction while driving.

This vibrational energy is transmitted through the suspension towards the vehicle body. The resulting body

panel and window vibrations cause noise radiation in the vehicle passenger compartment which is referred

to as structure-borne interior tire/road noise. Theairborne interior tire/road noise component originates

from the exterior noise that is generated by the tire/road interaction. The sound waves are then transmit-

ted through the air towards the windows and vehicle body panels. There are two paths along which soundcan be transmitted to the passenger compartment. First, the sound-induced vibrations of the vehicle body

panels cause noise radiation in the vehicle passenger compartment. Secondly, noise can enter the passenger

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compartment at places where there is a poor sealing between the interior and the exterior environment (for

instance, around door and window seals). The structure-borne contribution dominates the interior tire/road

noise below 500 Hz [1]. At higher frequencies, the airborne contribution is most significant.

In addition to the noise, the driver of a vehicle experiences vibrations at the seat and steering wheel. Depend-

ing on the amplitude and frequency content, these vibrations can reduce the drivers comfort significantly.

Vibrations are perceived as most uncomfortable in the frequency range of 4-8 Hz (whole-body vibration) and

18-200 Hz (vibration of individual body parts), or in the frequency range below 1 Hz, where dizziness and

motion sickness can appear. Additionally, blurring of vision can occur due to eyeball resonances in the range

20-70 Hz. For most road surfaces, the interaction between the tire and the road surface is a major source of

vibrations; which are then transmitted through the suspension towards the vehicle body.

Improving the NVH characteristics of a vehicle and its components requires a thorough understanding of

the different noise sources, vibration sources and transmission paths of structural and acoustic energy in

the vehicle. Consequently, there is a need for more accurate tire models to support vehicle NVH simulations

during the development process. This also involves more accurate testing methods which characterise the tire

under operational excitation levels in order to quantify non-linear dynamic behavior [2]. These experimentalmethods can either be applied to obtain an experimental model or to validate and parameterize a numerical

tire model. This paper focuses on the tire dynamic transfer stiffness, which describes how a displacement

enforced at the tire contact patch results in a force at the spindle-wheel interface. The dynamic transfer

stiffness is expressed as a function of frequency and provides insight in the generation of vehicle interior

structure-borne tire/road noise.

The dynamic behavior of particle filled rubber strongly depends on the deformation magnitude, even for

small deformations. There are two stress-softening effects, known as the Payne effect [3] and the Mullins

effect [4], that occur in filled vulcanized rubber. The tire compounds consist generally of carbon black or

silica filled rubber. Consequently, these effects can be of importance. Another non-linearity of the tire is the

sidewall stiffness. It is well known that the tire sidewall stiffness depends on the sidewall deflection [5]. This

behavior is not material related, but rather a geometrical non-linearity since the sidewall can be approximatedas a pressurized curved membrane. As the sidewall deflection increases, the stiffness of the tire sidewalls

decreases.

Consequently, the excitation levels during tire dynamic characterization tests should be similar to the ex-

citation levels during operation of the tire. This is not possible with the classic excitation devices such as

hammer and electrodynamic shakers. This paper presents a measurement method to obtain the dynamic

transfer stiffness of a non-rolling tire which is excited at operational excitation levels. Therefore, a high-

frequency 6-DOF hydraulic shaker table (CUBE R) is applied to excite the tire. The shaker table provides

the static preload and excites the tire at the contact patch in the frequency range 20-235 Hz.

2 Test setup for tire dynamic transfer stiffness measurements

2.1 Test setup layout

Figure 1(a) shows the test-setup for the measurement of the dynamic transfer stiffness of a non-rolling tire

with the CUBE 6-DOF shaker table [6]. The tire (205/55R16 without tread pattern; steel wheel) is mounted

on a piezo-electric spindle dynamometer (fig. 1(b) ) which measures the vertical spindle force. The goal of

the setup is to measure the dynamic stiffness of a tire that is rigidly clamped at the spindle. This is achieved

by fixing the dynamometer onto a seismic mass (1250 kg) which is supported by four soft air springs (4 x

100 kN/m). The natural frequencies of this system are far below the frequency range of interest (20-235 Hz)

such that the spindle is sufficiently isolated from the ground vibrations. The ground vibrations are significant

due to the presence of the CUBE shaker table. Since the shaker table also provides a static preload to the tire,

a system of air springs and pneumatic control valves (fig. 1(a) ) provides a counteracting force and moment

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CUBE 6-DOFshaker table

Y

X

Z

seismic mass (1250 kg)on flexible air springs

seismic mass levelling and positioningsystem with air springs and pneumaticcontrol valves

z

(a) (b)

piezo-electricspindle dynamometer

acc. 4-y

acc. 1-z

acc. 2-z

acc. 3-z

acc. 4-x

Figure 1: (a) Test-setup for the measurement of the dynamic transfer stiffness of a non-rolling tire with the

CUBE 6-DOF hydraulic shaker table. (b) Position and direction of the 4 accelerometers on the shaker table

used for the Time Waveform Replication.

onto the seismic mass in order to keep the seismic mass leveled at a fixed position. Here, the static tire

deflection is 16 mm, which for this tire corresponds to a preload of 285 kg.

Figure 2 shows the acceleration transmissibility between the tire contact patch z-acceleration applied by the

CUBE and the tire spindle z-acceleration. This transmissibility shows that the z-component of the spindle

acceleration is at least a factor 0.054 (-25.3 dB) smaller than the z-component of the applied shaker tableacceleration. This proves that the spindle can be considered as rigidly clamped in the frequency range of

interest.

50 100 150 200 250 300-90

-80-70

-60

-50

-40

-30

-20

-10

0

frequency [Hz]

accelerationtransmissibility

[dB]

(SPINDLE z-acc.) / (CUBE z-acc.)

-25.3 dB

20

Figure 2: Acceleration transmissibility between the CUBE z-acceleration and the tire spindle z-acceleration.

2.2 Shaker table excitation

For the measurement of the tire vertical dynamic transfer stiffness, the shaker table should apply a purelyuniaxial excitation in the z-direction at the contact patch. Since the excitation force exerted by the shaker

table onto the tire has an offset with respect to the rotation centre of the shaker table, an open-loop control

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of the shaker table cannot ensure a purely uniaxial excitation. Especially at higher frequencies, rotational

motions of the shaker table can become significant, thus causing additional undesired excitations at the tire

contact patch. In order to ensure a purely uniaxial excitation at the contact patch of the tire, the motion of

the hydraulic shaker table will be monitored and controlled through a Time Waveform Replication (TWR)

algorithm [7]. The Time Waveform Replication is an advanced implementation of the off-line feedforwardcontrol strategy for a system with N input drives (= controlled DOFs of the shaker table) and M (= observed

DOFs) output signals (MN). The goal of the TWR algorithm is to make the response at the observed DOFs

to converge iteratively to the target behavior. This target behavior is defined as time domain responses of

target transducers, which most often are forces or accelerations.

Several accelerometers are attached to the shaker table surface. Figure 1(b) shows the position and direction

of these accelerometers. The acceleration perpendicular to the shaker surface (z-direction) is measured in

points 1, 2 and 3. In point 4, which is close to the tire contact patch, two perpendicular components of the

in-plane acceleration of the shaker surface are measured. A purely uniaxial excitation of the tire contact

patch in the z-direction is ensured when the z-acceleration at the points 1, 2 and 3 are equal and the x-

and y-acceleration at point 4 are equal to zero. Therefore, 5 acceleration target signals are defined in the

time domain, which comply with the above stated requirements to obtain an uniaxial excitation. These timedomain target accelerations will be reproduced by iteratively updating the shaker table drive signals. Here, 5

drive signals are selected, which correspond to the following 5 controlled DOFs of the shaker table: x-, y-,

z-displacement and rotations around the x- and y- axis.

frequency [Hz]100 120 140 160 180 200

-70

-60-50

-40

-30

-20

-10

0

10

20

Autopow

eracceleration(PSD)

[dB

-ref.1(m/s)/Hz]

acc. 1 - zacc. 2 - zacc. 3 - z

acc. 4 - xacc. 4 - y

24.4 24.45 24.5 24.55 24.6 24.65 24.7 24.75

-60

-40

-20

0

20

40

60

time [s]

Acceleration

[m/s]

acc. 1 - zacc. 2 - zacc. 3 - z

acc. 4 - xacc. 4 - y

(a) (b)

Figure 3: Measured accelerations on the shaker table after iteratively updating the 5 shaker table drives in

the frequency range 100-200 Hz. (a) section of the time signals, (b) autopower spectra

Figure 3 shows the 5 measured accelerations (time and frequency domain) on the shaker table after iteratively

updating the 5 shaker table drives in the frequency range 100-200 Hz. This figure clearly shows that theexcitation of the shaker table can be considered as purely uniaxial since 3 points of the shaker plane have an

identical acceleration and the in-plane motion of the plane is negligible compared to the out-of plane motion.

2.3 Operational excitation levels

It is known that the tire dynamic properties are dependent on the vibration amplitude. Therefore, the ex-

citation levels during tire dynamic characterization tests should be similar to the excitation levels during

operation of the tire. However, this is not possible with the classic excitation devices such as hammer and

electrodynamic shaker. The multi-axial hydraulic shaker table, which operates at an oil pressure of 280 bar

and which has a table dynamic mass of 590 kg, is able to exert dynamic forces up to 82 kN. The control

bandwidth for 6-DOF experiments was experimentally determined at 0-300 Hz. This makes the shaker ta-

ble appropriate for reproduction of road excitations which arise from driving on smooth and medium rough

roads [6].

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20 40 60 80 100 120 140 160 180 200 220 240-10

-5

0

5

10

15

20

frequency [Hz]

Autopower(PSD)acceleration

[dB

-ref.1(m/s

)/Hz]

cube acceleration acc.1 - z

freq. band 20-100 Hzfreq. band 100-200 Hzfreq. band 175-235 Hz

0

Figure 4: Autopower spectra of the CUBE z-acceleration (enforced tire contact patch acceleration) for the 3

different frequency bands.

The measurement of the dynamic transfer stiffness is performed in three frequency bands: 20-100 Hz, 100-

200 Hz and 175-235 Hz. Within each frequency band, the shaker table provides a random excitation at

the tire contact patch. Figure 4 shows the autopower spectrum of the shaker table z-acceleration for the

three different frequency bands. The excitation frequency range is divided in frequency bands such that

higher excitation levels can be obtained in the individual frequency bands, compared to an excitation over

the entire frequency band 20-235 Hz. The imposed contact patch acceleration in the frequency range 20-100

Hz causes spindle forces which are of the same level as measured during rolling on a rough road surface. For

the frequency range 100-200 Hz and 175 - 235 Hz, the obtained spindle forces are approximately 15 % of

the forces measured during rolling on a rough road surface.

20 40 60 80 100 120 140 160 180 200 220-150

-100

-50

0

50

frequency [Hz]

Autopower(PSD)acceleration

[dB-ref.1(m/s)/Hz]

CUBE excitation 20-100 HzCUBE excitation 100-200 HzCUBE excitation 175-235 Hzelectrodynamic shaker excitation

Z

X

F

55

6

Z

X

acc. response

acc. response

rigidsurface

Electrodynamic shaker(B&K 4809) excitation

contact patchexcitationwith CUBE

Figure 5: Autopower spectrum of the radial acceleration at a point on the tire surface due to the CUBE shaker

contact patch excitation and due to an electrodynamic shaker excitation.

Figure 5 shows the autopower spectrum of the radial acceleration at a point on the tire surface of a loaded tire

due to two different excitations. The first excitation is provided by the CUBE hydraulic shaker table and is the

excitation which is used to measure the dynamic transfer stiffness (fig. 4). The second excitation is provided

by an electrodynamic shaker (B&K 4809) which is typically used to measure frequency response functions

in order to determine experimentally the modal parameters of the loaded tire [8]. This figure clearly shows

that the CUBE excitation causes significant higher vibration levels. At 100 Hz and 200 Hz, a difference of

45 dB (factor 177) and 22 dB (factor 12), respectively, is observed between the response due to the CUBE

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and the electrodynamic shaker excitation. The largest difference between the two excitations appears at 20

Hz, where the response autopowers differ 96 dB.

3 Results tire dynamic transfer stiffness measurement

The measured dynamic transfer stiffness in the tire vertical direction is shown in figure 6. On this figure, the

three frequency bands corresponding to the excitations shown in figure 4, can be distinguished. At the edges

of the frequency bands, no significant discontinuities in the dynamic stiffness curve can be observed. This

indicates that the difference in excitation level between the different frequency bands is sufficiently small in

order to not cause significant changes of the system behavior.

50 100 150 20010

4

106

108

frequency [Hz]

AMPLITUDE[N

/m]

TIRE DYNAMIC STIFFNESS Fz / z

50 100 150 200

-15

-10

-5

0

5

frequency [Hz]

PHASE[rad]

LOG

98 Hz

127 Hz

156 Hz

190 Hz

222 Hz

230 Hz

20 235

20 235

Figure 6: Amplitude and phase of the measured tire dynamic transfer stiffness. Contact patch excitation and

spindle force measurement in the tire vertical (z-) direction.

The vertical dynamic transfer stiffness shows a peak at 98, 127, 156 and 190 Hz, which correspond to the

resonance frequency of the (1,0) vert., (2,0) extr., (3,0) extr. and (4,0) extr. structural tire mode, respectively.

Figure 7 shows some of the tire modes which have been obtained from an experimental modal analysis on

the loaded tire [2]. For each mode, the resonance frequency and modal damping ratio are indicated below

the mode shape. Figures 7 shows that the modes which determine the dynamic transfer stiffness, correspondto bending modes of the tire belt in which an anti-node is located in the contact patch (modes of fig. 7 (b),

(d), (f) and (h)). On the contrary, belt bending modes in which a node is located in the contact patch (modes

of fig. 7 (a), (c), (e) and (g)) have a much lower contribution to the tire dynamic transfer stiffness.

In addition to the structural modes, a peak appears in the dynamic transfer stiffness at 230 Hz, which corre-

sponds to the frequency of the first vertical acoustic mode of the air cavity. At this frequency, the acoustic

pressure variations in the tire air cavity are maximum near the contact area (see fig. 7 (i)). The peak in the

dynamic stiffness appears at 230 Hz, whereas, the frequency of the vertical acoustic resonance was deter-

mined at 227 Hz by the experimental modal analysis. This frequency difference is most likely caused by

a higher temperature of the air inside the tire air cavity during the dynamic transfer stiffness measurement.

The CUBE shaker table has during operation a surface temperature of approximately 40oC. The tire acoustic

resonances frequencies are more sensitive to changes in the tire temperature, compared to the structural tireresonances [2]. A higher temperature causes an increase of the acoustic resonances. At 222 Hz, a small peak

is visible in the dynamic transfer stiffness curve. This frequency corresponds to the first vertical acoustic

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Z

Y

X

Z

X

Y

X

Y

Z

(3,0)0: 142.56 Hz; 2.87%

Z

Y

X

Z

X

Y

X

Y

Z

(4,0)0: 172.66 Hz; 2.89%

Z

Y

X

Z

X

Y

X

Y

Z

(1,0)vert.: 98.22 Hz; 4.09%

Z

Y

X

Z

X

Y

X

Y

Z

(2,0)extr: 126.74 Hz; 3.18%

Z

Y

X

Z

X

Y

X

Y

Z

(3,0)extr: 156.03 Hz; 2.75%

Z

Y

X

Z

X

Y

X

Y

Z

(4,0)extr: 189.10 Hz; 2.86%

+p

-p

0Z

X

acoustic vert.: 227.35 Hz; 0.43%

(a) (b) (c)

Z

Y

X

Z

X

Y

X

Y

Z

(1,0)hor.: 82.15 Hz; 5.42%

Z

Y

X

Z

X

Y

X

Y

Z

(2,0)0: 117.94 Hz; 3.43%

(g) (h) (i)

(d) (e) (f)

Figure 7: Tire modes obtained from an experimental modal analysis on the loaded tire. (a)-(h): structural

modes; (i): acoustic mode.

mode of the air cavity. This mode exhibits no acoustic pressure variations in the tire air cavity near the

contact area. Consequently, this mode is poorly excited by an excitation at the contact patch.

4 Numerical prediction of the tire dynamic transfer stiffness

In this section, the dynamic transfer stiffness of the same tire is numerically predicted. This prediction is

base on the structural tire model described in [9].

4.1 Tire model description

The structural tire model, which is implemented as a finite element model, is based on a three-dimensional

flexible ring on an elastic foundation. The ring represents the treadband and the elastic foundation represents

the tire sidewall. The model is valid up to 300 Hz and is able to predict the response of the tire treadband,

wheel and air cavity. The parameterization of the model, which does not require detailed knowledge of thetire construction, is based on the main geometrical properties of the tire and a limited modal test on the

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unloaded tire. Figure 8(b) shows the different submodels of which the tire model is composed. The different

submodels will hereafter be briefly discussed.

Y

Z

X

(4)

Z

XY

(1)

(3)

(2)

b

h

treadband ring cross-section

(a) (b)

(c)

Figure 8: (a) Cross-section of the ring which represents the tire treadband. (b) Different submodels of the

tire-wheel model: (1) treadband ring, (2) wheel, (3) tire sidewall, (4) air cavity (for clarity, the cavity model

is shown separately). (c) Tire-wheel model at the end of the loading simulation.

The treadband is modeled as an isotropic, homogeneous three-dimensional ring. The ring cross-section is

shown in figure 8(a). Despite this drastic simplification, the tire model exhibits acceptable accuracy in the

frequency range of interest. The non-linear static material behavior of the ring is described by the Neo-

Hookean hyperelastic material model. The dynamic material properties of the treadband (described by a

complex Youngs modulus) are considered to be frequency independent. The reference surface of the ring

is discretized in the finite element model by linear 4-node shell elements (ABAQUS S4R elements). These

elements allow transverse shear deformation (Kirchhoff constraint is not enforced; however, it is assumed

that a plane section remains plane) and account for finite membrane strains and arbitrarily large rotations.

The wheel submodel is a finite element model of the steel 16 wheel (discretized by 4-node shell elements).

The model does not include a damping definition and the geometry of the wheel is modeled in detail since

the flexibility of rim and disk are highly influenced by their complex shape.

The tire sidewalls are approximated by distributed linear spring-damper systems in radial, tangential and

axial direction. An experimental modal analysis on an unloaded tire, clamped at the spindle, shows that the

first three resonances can be considered as resonances of a spring-mass system in which the sidewall acts

as a spring and the treadband as a mass. The sidewall spring stiffness and damping are derived from the

experimentally determined modal parameters of the first three tire modes. The sidewall model is based on

the assumption that the dynamic behavior of the sidewall is independent of the treadband dynamic behavior.

For the cross-sectional bending modes of higher order (above 300 Hz for this tire), the sidewall dynamic

behavior deviates too much from a spring-damper system and a more detailed description of the sidewall isrequired.

The tire air cavity is discretized by 8-node linear brick acoustic elements (ABAQUS AC3D8 elements) and

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is coupled to the structural mesh of the wheel and treadband ring. The sidewalls of the cavity are considered

to be acoustically rigid.

After assembling the different submodels, a simulation of the tire inflation is performed. The wheel centre

is clamped and the tire is inflated to 2.2 bar in a geometric non-linear static analysis. The inflation pressure

is applied to the rim outer surface and the treadband ring inner surface. This pressure loading induces a

circumferential pretension in the ring. Besides the circumferential tension, the tire treadband is also subjected

to an axial tension. This tension is not induced by the inflation pressure in the presented model and therefore

the axial tension will be applied through an external tensile load.

4.2 Simulated tire dynamic transfer stiffness

The above presented model of an unloaded tire-wheel assembly provides a physical description of the dy-

namic behavior of the belt, wheel and air cavity and their mutual interactions. Therefore, the model is also

able to describe the dynamic behavior of a tire at other operating conditions, such as loading. In order to

compare the measured and numerically predicted transfer stiffness, the same boundary conditions as duringthe experiment have to be enforced on the tire-wheel assembly model. Therefore, the model of the unloaded

tire-wheel assembly is subjected to a static deformation of 16 mm due to the contact with a rigid, flat road

surface. The loading is achieved by clamping the wheel at the wheel-spindle interface and imposing a ver-

tical displacement on the rigid road surface towards the tire. The contact between the treadband and road,

the large deformations of the treadband and the hyperelastic material definition introduce non-linear effects

during the loading of the tire. Therefore, a non-linear FE method is required that solves the problem incre-

mentally. A Coulomb friction coefficient of 0.5 is used in the simulation. Figure 8(c) shows the tire model

at the end of the loading simulation.

0 50 100 150 200 250 30010

0

102

104

106

108

frequency [Hz]

AMPLITUDE

[N/m]

TIRE DYNAMIC STIFFNESS

0 50 100 150 200 250 300-30

-20-10

0

frequency [Hz]

PHAS E

[rad]

Fz / z Fy / z Fx / z

LOG

Fx

FyFz

z

Figure 9: Amplitude and phase of the simulated vertical, longitudinal and axial dynamic transfer stiffness

for a vertical footprint displacement.

Next, the tire dynamic transfer stiffness is calculated. Therefore, the steady-state reaction forces at the

spindle-wheel interface are calculated due to a harmonic displacement of the rigid surface with an ampli-

tude of 0.1 mm. The response of the loaded tire is calculated in a steady-state harmonic analysis whichassumes linear dynamic behavior of the tire in its loaded state. Figure 9 shows the amplitude and phase of

the simulated vertical, longitudinal and axial dynamic transfer stiffness for an enforced harmonic footprint

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displacement in the vertical (z) direction. The dynamic transfer stiffness is calculated up to 300 Hz. Since

the contact patch excitation is purely in the vertical direction, the vertical spindle force component is the

most dominant.

4.3 Validation

Figure 10 compares the numerically predicted and measured vertical dynamic transfer stiffness (Fz/z). The

agreement is good, except for the frequency shift on some of the peaks of the dynamic stiffness curve. As

can be observed from table 1, there is a difference between the measured resonance frequencies and the

resonance frequencies predicted by the loaded tire model. The majority of the predicted natural frequencies

are within 5 % of the measured natural frequencies. The predicted resonance frequency of the (2,0) extr. and

(3,0) 0 mode deviate -6.2 % and -5.3 % with respect to the measured value, respectively.

The comparison of the frequencies in table 1 and the peaks in figure 10 clearly shows that both the predicted

and measured dynamic stiffness curve are mainly determined by the (1,0) vert., (2,0) extr., (3,0) extr. and

(4,0) extr. structural tire mode. In addition, the first vertical acoustic tire mode significantly contributesto both the measured and predicted dynamic stiffness. The experimental modal analysis on the loaded tire

shows that the (4,0) extr. mode and the rim pitch mode both appear at 190 Hz. For the model, these two

resonances are predicted at 185 Hz and 189 Hz, respectively. This explains the more smeared out peak in

the calculated dynamic stiffness curve around these frequencies. Figure 10 also indicates that the model

overestimates the static tire stiffness.

50 100 150 200

104

106

108

frequency [Hz]

AMPLITUDE

[N/m]

TIRE DYNAMIC STIFFNESS Fz / z

50 100 150 200-20

-10

0

frequency [Hz]

PHA

SE

[rad]

Fz / z MODELFz / z TEST

20 235

20 235

LOG

98 Hz96 Hz

119 Hz127 Hz

149 Hz 156 Hz

189 Hz190 Hz

185 Hz

228 Hz230 Hz

Figure 10: Amplitude and phase of the simulated and measured vertical dynamic transfer stiffness for a

vertical footprint displacement.

5 Conclusions

This paper presents a measurement method to obtain the dynamic transfer stiffness of a non-rolling tire

which is excited at operational excitation levels. The excitation amplitude is particularly of importance when

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TEST MODEL

mode freq. [Hz] [%] freq. [Hz] [%]

(1,1) hor. 51.9 1.97 50.1 1.50

(1,1) vert. 64.8 2.48 62.1 1.73

(1,0) hor. 82.2 5.42 82.0 4.81(1,0) vert. 98.2 4.09 96.5 3.13

(2,0) 0 117.9 3.43 123.6 3.54

(2,0) extr. 126.7 3.18 118.9 3.09

(2,1) 0 102.1 2.78 101.48 2.85

(2,1) extr. 87.0 2.46 84.06 2.28

(3,0) 0 142.6 2.87 135.0 3.07

(3,0) extr. 156.0 2.75 149.2 3.04

(3,1) 0 * * 199.0 5.38

(3,1) extr. 162.4 2.78 162.3 4.39

(4,0) 0 172.7 2.89 164.5 3.43

(4,0) extr. 189.1 2.86 184.9 3.74

1st rim bending 0 183.1 2.53 179.7 3.51

1st rim bending extr. 183.1 2.53 179.9 3.54

rim pitch 0 189.6 1.15 188.7 1.44

rim pitch extr. 189.6 1.15 189.3 1.71

(4,1) 0 236.6 2.38 246.0 6.88

(4,1) extr. 225.2 1.44 224.6 6.02

(5,0) 0 205.1 3.10 202.0 4.28

(5,0) extr. 222.1 2.79 225.2 5.03

1st acoustic hor. 219.0 0.69 219.2 1.48

1st acoustic vert. 227.4 0.43 229.3 1.94

Table 1: Comparison between measured and calculated modal parameters of the loaded tire. ( indicates a

not experimentally identified mode)

dealing with non-linear systems, as the system behavior varies with the energy content of the input. It has

been shown that the tire vibration levels are significantly higher in the presented testing method, compared

to the classical experimental tire dynamic characterization methods.

The experimentally obtained dynamic stiffness has been validated by comparison with the numerically pre-

dicted dynamic stiffness. This comparison, combined with the results of an experimental modal analysis,

showed that the experimental and numerical dynamic stiffness are both dominated by the same structural

and acoustic tire modes.

Deviations between the predicted and measured dynamic transfer stiffness are most probably caused by the

tire sidewall description of the model. The used sidewall model is a linearised approximation of the sidewall

dynamic behavior for a tire in its unloaded state.

A next step in the ongoing development of the test setup is to extend the frequency range of the dynamic

stiffness measurement up to 300 Hz. Currently, a setup resonance starts to influence the measurements in

the frequency range above 235 Hz. An envisaged application of the presented measurement method is to

quantify the excitation amplitude non-linearity of a tire at operational excitation levels.

TYR E/ROAD NOISE AND EXPERIMENTAL VALIDATION 4001

7/25/2019 Qgkls

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Acknowledgements

Part of the research reported is funded by a PhD grant of the Institute for the Promotion of Innovation through

Science and Technology in Flanders (IWT-Vlaanderen).

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