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Operational Modal Analysis of tyre road interaction using

Abaqus Explicit and Operational Modal Analysis

P. Sakthivel1, K. V. Narasimha Rao

2, R. Krishna Kumar

1

1Indian Institute of Technology Madras, Engineering Design Department

Chennai 600036, Tamilnadu, India

e-mail: [email protected]

2JK Tyre and Industries Ltd., RPSCOE for Tyre & Vehicle Mechanics,

IIT Madras, Chennai 600 036, Tamilnadu, India.

AbstractModern vehicles have well established control mechanisms for power unit noise reduction. On the other

hand, noise due to tyre road interaction has become a significant contributor of vehicle interior and

exterior noise. Understanding tyre structural dynamics is very important to mitigate the tyre/road noise

problem. The objective of this work is to establish a procedure to acquire vibration response data for

Operational Modal Analysis (OMA), using a dynamic finite element (FE) analysis. This has been

achieved in two stages. Firstly, the experimental procedure is replicated using Abaqus Explicit, a

commercial dynamic FE analysis software. Secondly, the tyre dynamic characteristics are determined

through Operational Modal Analysis by integrating the explicit FE analysis results with LMS Test Lab

software. The modal parameters of the rolling tyre are extracted by the use of polyreference least squares

complex frequency domain (LSCF) approach.

1 Introduction

Tyre/road interaction is the main source for tyre vibrations. The spindle force due to this interaction

attains its maximum value at the occurrence of structural resonance of tyre wheel assembly. It is further

transmitted to the vehicle body through the suspension sub system. This body force excitation is

responsible for structure borne interior noise (for a comprehensive account of tyre noise, refer to Sandberg

and Ejsmont [1]).

Modal frequencies, damping and mode shapes describe the dynamic behaviour of a tyre. Traditionally

these quantities are found from Experimental Modal Analysis and/or finite element analysis of a non-

rolling tyre with the basic assumption of system linearity and reciprocity. Extraction of these quantities isobtained from the estimation of Frequency Response Functions for the known dynamic excitation force.

In reality, it is impractical to measure the excitation force of a rolling tyre from the tyre road interface.

Under this situation, Operational Modal Analysis (OMA) can be used for modal analysis [2].

The modal parameters obtained from the Experimental Modal Analysis of a stationary tyre may be

modified during rolling, though the static mode shapes are useful to understand the mode shapes obtained

from the Operational Modal Analysis. Excitation of a rolling tyre over a cleat gives relatively a flat

spectrum and is preferred for the measurement of acceleration responses.

The procedure developed in this paper is useful to carry out a parametric study to understand the influence

of driving speed, cleat dimension, inflation pressure, static preload etc.

Peter Kindt et al. [3,4] have extracted modal parameters of a rolling tyre, using tyre on tyre over a circular

cleat. Laser Doppler Vibrometer was used to measure the acceleration response of the smooth tyre atvarious points on the tread and sidewall and used as an input for Operational Modal Analysis.

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Peter Willem Anton Zegelaar [5] showed that the modes of vibration of tyre strongly depend on tyre

construction, rotational velocity, spindle boundary conditions and contact patch boundary

conditions.Modal parameters are extracted from the measured frequency response functions that describe

the dynamic response of the structure to a known dynamic excitation force. The tyre is excited at one

point and the acceleration responses are measured in several points on the tread and sidewall and wheel.

L. H. Yam et al. [6] have obtained three dimensional mode shapes (radial, tangential and lateral directional

modal parameters) of a tyre using Experimental Modal Analysis.

Operational Modal Analysis provides a complete modal model under operating conditions. Sum of

Crosspower spectrum is used to extract the modal parameters of rolling tyre. T. Lauwagie et al. [7] have

done a comparative study of modal parameter extraction procedure viz., Operational Modal Analysis,

Experimental Modal Analysis and combined Operational and Experimental Modal Analysis on a small

hydraulic crane modal analysis study.

Modal analysis results of a tyre have significant contribution in tyre/road interaction noise prediction.

Tyre modal data are used directly in Boundary Element Method and Infinite Finite Element Method based

tyre models. Nakajima et al. [8] have used the tyre modal analysis results to define the surface vibrational

boundary conditions for predicting air borne noise fields. Michel Constant et al. [9] have studied the

vibro-acoustic interaction between tyre and car sub systems and identified the main suspension parts

affecting the structure borne interior noise. Operational deflection shapes of tyre wheel subsystem were

used by Ichiro Kido [10] to quantify the force transmitted through suspension sub system to the vehicle

body, to address the structure borne interior noise of the vehicle. In-spite of the importance of the rolling

tyre modal analysis, very few attempts has been made in this direction.

There are various modal identification techniques for extracting the modal parameters using Operational

Modal Analysis [11,12]. They are grouped as follows: (1) Time Domain approach, (2) Frequency Domain

approach and (3) Time-Frequency plane approach. The time domain approach includes Natural Excitation

Technique (NExT), Auto Regressive Moving Average technique (ARMA) and Stochastic Subspace

Identification technique (SSI). The frequency domain approach includes Frequency Domain

Decomposition (FDD) and Enhanced Frequency Domain Decomposition (EFFD) techniques. Time

Frequency plane is the Wavelet Transform Technique. In the present work LMS Test Lab softwareimplementation of PolyMAX algorithm has been used to extract the modal parameters. Initially the

method has been developed for classical modal analysis that uses measured frequency response functions

as primary data and the theory behind the method can be found in P. Guillaume et al. [13] and B. Peeteers

et al. [14]. Later it has been proved by B. Peeteers et al. [15] that the LMS PolyMAX estimator can also

be used effectively in Operational Modal Analysis. The following section describes the finite element

modeling of tyre and the procedure of integrating the results of finite element analysis with LMS Test Lab

software to carry out the Operational Modal Analysis.

2 Finite element model and modal extraction

Rao K. V. N. et al. [16] have used a finite element tyre model to study cornering, braking and cornering-

cum-braking dynamic behaviour of tyre. The detailed model, based on a hyperelastic material, includes

all the reinforcements of the tyre. Their approach is adopted to develop a finite element model of a

205/55R16 tyre.

Explicit dynamic rolling of finite element model over a semicircular cleat of 25 mm radius has been

carried out. This numerical simulation replicate the experiments followed by Peter Kindt et al. [3,4]. The

same inflation pressure of 220 kPa and driving speed of 28.3 kmph are used to compare the results.

Figure 1a shows the axi-symmetric half finite element tyre model that has been used to generate the full

tyre model. The colour group describes the various components and constructional details of the tyre.

The tyre includes two belts and one ply and one protection ply.

Figure 1b shows the 3D finite element model, rolling over a semi-circular cleat. Smooth tyre has beenconsidered to eliminate the influence of tread pattern vibrations and tread groove resonances over the

whole tyre vibrations. The spindle force and tyre structural vibrations responses were obtained from the

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simulation results. These measurements were made with the sampling frequency of 2048 Hz. The

spectral content of the spindle force were obtained from its power spectral density function.

Figure 1: (a) Axi-symmetric half tyre model Figure 1: (b) Tyre rolling over a cleat

The numerical simulation has been completed in two stages. In the First stage, the inflation and loading of

the finite element tyre and rim assembly has been simulated. The inflation pressure of 220 kPa was

defined and a pre load of 2930 N was given by lifting the road, which is modeled as a rigid surface. All

the six degrees of freedoms (dof) of the tyre rim spindle point were arrested. All degrees of freedom

except the vertical translation of the rigid road were arrested. In the second stage, rolling of the tyre over a

cleat has been simulated. The following boundary conditions were ensured. Except the longitudinal

translation and rotation about spindle axis of the tyre rim assembly, rest of the dofs were arrested. For the

road with the lifted position all the degrees of freedom were arrested to simulate the straight rolling oftyre. The acceleration responses in x, y and z directions with respect to the global Cartesian reference, at

240 points in four circles of tyre, two on tread and one each on right and left side wall respectively were

written as an output during the simulation.

These response results were communicated to the LMS software by defining appropriate header

information that describes the data characteristics, sampling rate and number and name of the channels

and database information. Thus the data input to the software is given as if they have been acquired

through data acquisition system and stored as throughput data format. The tyre geometry was created

using the 240 measurement points as shown in Figure 3. Tyre right hand tread leading edge node point

named RTD72074 is highlighted in the Figure 3. The vertical direction acceleration response of this node

was chosen to be the reference signal for auto and crosspower function calculations.

Figure 3: Tyre Modal Model Geometry

FP7 IAPP TIRE-DYN TYR E / ROAD NOISE AND EXPERIMENTAL VALIDATION 1605

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The auto and crosspower functions of output responses were determined for the modal parameter

extraction. Further the LMS Test Lab implementation of PolyMAX algorithm in frequency domain was

used to formulate the least squares problem to estimate the mode shapes. The advantage of using the

frequency domain implementation is that the start and end frequencies can be specified and that residual

effects of modes outside the band can be taken into account. Also the closely spaced poles are well

identified. Crosspower function plays a similar role in Operational Modal Analysis as that of Frequency

Response Function in case of Experimental Modal Analysis. Crosspower sum of all the signals is shown

in Figure 4. The peaks in the crosspower sum represent the modal frequencies and the sharpness of the

peaks decides the corresponding damping value.

Figure 4: Crosspower sum

Curve fit of the sum of all the crosspower functions for the required modal orders has been obtained from

the stabilization diagram. The selection of stable poles that gives the correct modal parameters from the

stabilization diagram is a challenging task. Selecting the poles by visual inspection requires experience

and skill, as the selection is based on similarity in frequency, damping ratio and/or mode vector between

poles belonging to subsequent modal orders. Hence LMS Test Lab Automatic Modal Parameter Selection

(AMPS) tool was used to select the stable poles.Figure 5 shows the stable poles picked from the stabilization diagram for the frequency band of 2 Hz to

250 Hz and the modal order of 106. The vertical lines represent the physical stable pole. There are peaks

that are not picked by AMPS tool between 67 Hz to 84 Hz as they represent unstable mathematical modes.

The main advantage of using the AMPS tool is that it selects only the correct physical stable poles for any

number of repetition of modal picking on the stabilization curve and gives user independent results. Thus

the Operational Modal Analysis of tyre road interaction of finite element model of 205/55R16 tyre has

been completed using LMS Test Lab Operational Modal Analysis Module.


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Figure 5: Stabilization diagram and pole selection by AMPS

Figure 6a shows the contact pressure distribution just before the cleat impact. The symmetric contour

profile describes the steady state straight rolling of tyre and Figure 6b shows the contact pressure

distribution at the instant of cleat impact and it represents the impulse excitation which is responsible for

flat excitation spectrum.

Figure 6: (a) Contact pressure of rolling tyre Figure 6: (b) Contact pressure during cleat impact

Figure 7 shows vertical spindle force excitation of the rolling tyre and it is clearly seen that the impulse

excitation peak resulted due to the cleat impact excitation.


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Figure 7: Vertical Spindle Force due to cleat impact excitation

3 Results and discussion

Figure 8 shows acceleration response in x, y & z directions of a node point that was located on the right

side leading edge tread of the tyre. The peak response of acceleration at 1.04sec clearly shows the instant

of the cleat impact on the tyre. Minimum response of lateral acceleration ensures the straight rolling of

tyre and shows the insignificant excitation in lateral direction. The periodic zero response in all three

directional responses represent the tyre tread contact point with the road during every revolution.

Figure 9a shows the spindle force response due to cleat impact on rolling tyre in all the three directions.

These plots are plotted from just before the cleat impact instant. The vertical spindle force includes bothstatic pre-load and the dynamic response force due to cleat impact. The longitudinal and lateral spindle

forces are the dynamic response forces alone. Dynamic spindle force response in lateral direction states

the negligible energy content of lateral excitation.

The frequency content of these spindle forces, shown in Figure 9b was obtained from their power spectral

density functions. The correlation of the spectral content of the spindle force with the modal frequencies

validates the results. The power spectral density plots of vertical and longitudinal spindle force represents

significant energy content up to 250 Hz, which is responsible for structure borne interior noise. The effect

of power spectral density function of lateral force to structure borne interior noise needs to be investigated.


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Figure 8: Acceleration response of a node point in X, Y & Z directions

obtained from Finite Element Analysis


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Figure 9: (a) Spindle force excitation Figure 9: (b) PSD of spindle force excitation

Figure 10a and Figure 10b shows the correlation obtained between the original operational crosspower

spectra and the synthesized crosspower spectra of well correlated signal for two different inflation

pressure respectively. The error between the spectra did not affect the stable poles selected. For all the

extracted frequency values very good correlation between the spectra is obtained. Also it gives an

immediate visual assessment of the accuracy of the modal parameter estimation procedure.


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Figure 10: (a) Comparison of operational and synthesized crosspower for tyre inflation pressure 220kPa

Figure 10: (b) Comparison of operational and synthesized crosspower for tyre inflation pressure 270kPa

The results of the modal parameters and the operational mode shapes are arranged in Figure 11. Since the

measurement points of acceleration responses obtained from the finite element model are more than the

measurement points considered in [3], structural resonance frequency upto (10,0), the circumferential belt

modes are obtained. These results are extracted for a driving speed of 28.3 kmph which corresponds to

the tyre free rolling speed of 25 rad/sec, inflation pressure of 220 kPa and the static preload of 2930 N.


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Figure 11: Operational mode shapes of 205/55R16 tyre due to tyre/road interaction

The modal frequencies and damping values of the current results are compared with the published results

of Peter Kindt et al. [3] in Table 1. Though the mode shapes match, the frequency and damping values do

not match. The variation in the natural frequency values may be due to the difference in the geometry and

properties of the tyre. It is proposed that these limitations will be overtaken in the ongoing research work.


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Published results Current results

Mode Shape Frequency

(Hz)

Damping

(%)

Frequency

(Hz)

Damping

(%)

Mode: (0,0) * * 4.067 6.34

Mode:(1,1)horiz 77.15 6.01 * *

Mode:(1,0)vert 81.83 4.34 59.933 0.38

Mode: (2,0)0 102.98 3.02 84.733 0.3

Mode: (2,0)extr 113.94 3.66 * *

Mode: (2,1)0 96.09 3.41 * *

Mode: (2,1)extr 91.29 2.79 * *

Mode: (3,0)0 124.09 2.6 96.791 0.33

Mode: (3,0)extr 139.33 3.87 109.124 0.06

Mode: (4,0)0 151.76 2.62 116.956 0.28

Mode: (4,0)extr 167.52 3.29 129.534 0.14

Mode: (5,0)0 182.7 3.71 133.41 0.18

Mode: (5,0)extr 199.88 1.5 141.44 0.14

Mode: (6,0)0 * * 161.859 0.31

Mode: (6,0)extr * * 170.993 0.23

Mode: (7,0)0 * * 186.817 0.18

Mode: (7,0)extr * * 195.055 0.21

Mode: (8,0)0 * * 199.18 0.26

Mode: (8,0) * * 210.699 0.35

Mode: (8,0)extr * * 218.567 0.23

Mode: (9,0)0 * * 224.237 0.32

Mode: (9,0) * * 228.929 0.33

Mode: (9,0)extr * * 232.632 0.29

Mode: (10,0) * * 241.992 0.25

* indicates missing modes and published results are taken from Peter Kindt et al. paper [3]

Table 1: Results of modal parameters of 205/55R16 tyre rolling over 25mm semi circular cleat

In order to understand the influence of inflation pressure the same procedure was repeated for inflation

pressure of 270 kPa keeping the same driving speed, cleat dimension and static deflection. The radial

preload is increased due to the inflation pressure as the static deflection is kept a constant. There is a positive frequency shift of the structural resonances observed due to increase in inflation pressure. The

shift is resulted due to increase in tyre dynamic stiffness. There is also a noticeable change in damping

values due to inflation pressure variation. The modal parameters values of these two cases are tabulated in

Table 2.

From Table 2 it is observed that there is a 6 to 15 Hz positive frequency shift of structural resonance

frequencies due to an increase in the inflation pressure. This is due to an increase in the belt and sidewall

stiffness due to higher inflation pressure. This trend matches with the results published by Peter Kindt et

al. [3,4]. Also it is observed that there is a rise in radial preload of the tyre. This is due to the fact that in

the finite element simulation the road lift is maintained for both inflation pressure cases to have the same

static deflection of the tyre.


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Inflation pressure 220 kPa Inflation pressure 270 kPa

Mode Shape Frequency

(Hz)

Damping

(%)

Frequency

(Hz)

Damping

(%)

Mode: (0,0) 4.067 6.34 4.0593 5.87

Mode:(1,1)horiz * * * *Mode:(1,0)vert 59.933 0.38 65.5958 0.47

Mode: (2,0)0 84.733 0.3 90.6120 0.36

Mode: (2,0)extr * * * *

Mode: (2,1)0 * * * *

Mode: (2,1)extr * * * *

Mode: (3,0)0 96.791 0.33 102.6674 0.23

Mode: (3,0)extr 109.124 0.06 * *

Mode: (4,0)0 116.956 0.28 * *

Mode: (4,0)extr 129.534 0.14 139.2683 0.12

Mode: (5,0)0 133.41 0.18 143.2273 0.07

Mode: (5,0)extr 141.44 0.14 151.3242 0.10

Mode: (6,0)0 161.859 0.31 173.7737 0.28

Mode: (6,0)extr 170.993 0.23 182.3514 0.27

Mode: (7,0)0 186.817 0.18 201.6263 0.25

Mode: (7,0)extr 195.055 0.21 209.0481 0.29

Mode: (8,0)0 199.18 0.26 214.5045 0.10

Mode: (8,0) 210.699 0.35 216.9282 0.19

Mode: (8,0)extr 218.567 0.23 225.2255 0.21

Mode: (9,0)0 224.237 0.32 232.6206 0.31

Mode: (9,0) 228.929 0.33 * *

Mode: (9,0)extr 232.632 0.29 239.1948 0.07

Mode: (10,0) 241.992 0.25 * *

* indicates missing modes

Table 2: Results of modal parameters for different inflation pressures

4 Conclusion

This paper demonstrated the procedure developed for conducting the Operational Modal Analysis of

tyre/road interaction using Abaqus explicit finite element code and LMS Operational Modal Analysis.

The repeatability and accuracy of the simulation procedure leads the way to do parametric study

effectively. In this paper only the influence of inflation pressure on tyre vibration characteristics has been

presented. It is proposed to carry out detailed parametric study of the influencing factors affecting the

operational modal parameters in the ongoing research work.

Acknowledgements

Research work was supported by Raghupati Singhania Centre of Excellence for Tyre & Vehicle

Mechanics, sponsored by JK Tyres and Industries at IIT Madras, Chennai, India.


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