numerical method for simulating tire rolling noise by … · tread surface. the tire structural...

International Journal of Automotive Technology, Vol. 18, No. 5, pp. 823−832 (2017)

DOI 10.1007/s12239−017−0081−x

Copyright © 2017 KSAE/ 098−08

pISSN 1229−9138/ eISSN 1976−3832

823

NUMERICAL METHOD FOR SIMULATING TIRE ROLLING NOISE BY

THE CONCEPT OF PERIODICALLY EXCITING CONTACT FORCE

Han-Wool Lee1), Jin-Rae Cho2)* and Weui-Bong Jeong1)

1)School of Mechanical Engineering, Pusan National University, Busan 46241, Korea2)Department of Naval Architecture and Ocean Engineering, Hongik University, Sejong 30016, Korea

(Received 3 January 2017; Revised 24 February 2017; Accepted 11 March 2017)

ABSTRACT−For the numerical simulation of tire rolling noise, an important subject is the extraction of normal velocity data

of the tire surface that are essential for the acoustic analysis. In the current study, a concept of periodically exciting contact

force is introduced to effectively extract the tire normal velocity data. The ground contact pressure within contact patch that

is obtained by the static tire contact analysis is periodically applied to the whole tread surface of stationary tire. The

periodically exciting contact forces are sequentially applied with a time delay corresponding to the tire rolling speed. The tire

vibration is analyzed by the mode superposition in the frequency domain, and the acoustic analysis is performed by

commercial BEM code. The proposed method is illustrated through the numerical experiment of 3-D smooth tire model and

verified from the comparison with experiment, and furthermore the acoustical responses are investigated to the tire rolling

speed.

KEY WORDS : Tire rolling noise, Periodically exciting contact force, Stationary tire, Tire body vibration, Normal velocity

extraction, Acoustic analysis, Sound pressure and power

1. INTRODUCTION

As the automobile manufacturing technology develops and

the public’s desire for better riding comfort increases,

automobile noise is becoming a bigger issue these days.

For this reason, all the car makers are devoting themselves

to the development of low noise automobiles. Among the

major automobile parts, tire is importantly considered for

the reduction of automobile noise because the noise caused

by tire takes a big part of the entire automobile noise

(Lelong, 1999). In particular, the tire labeling that was

institutionalized by EU requires the car maker to display an

item called pass-by-noise, in order to regulate the noise that

is emitted from tires of running automobiles (Maffei and

Masullo, 2014; Klein et al., 2015). The tire noise is induced

by several sources such as the tire body vibration, the tread

impact with the ground, the compression/expansion of air

within tire grooves (Iwao and Yamazaki, 1996) and the

torus resonance. The tire noise can be transferred to the

vehicle body through the suspension unit or radiated into

the surrounding air (Lee and Li, 1997; Guan et al., 1999).

Regardless of the type of tire noise transfer, the

evaluation of tire noise has been traditionally relied on the

experimental method (Guan et al., 1999). It is because the

tire noise is a complex phenomenon caused by the dynamic

excitation that is induced by not stationary but rolling tire

(Kim and Bolton, 2002). In other words, the dynamic

excitation force that is induced by rolling tire was difficult

to be accurately derived by analytical method in early days.

Only the limited analytical models by simplifying tire as a

thin elastic ring (Potts et al., 1977) or as a plate/shell

structure (Kropp et al., 2001) were presented. Meanwhile,

in the traditional experimental approach, a tire model was

manufactured first and then the measurement of tire noise

was conducted. However, this experiment-based evaluation

is not only time and cost-consuming, but it cannot provide

the sufficiently beneficial information to the designer at the

design stage of target tire model. In this context, a precedent

evaluation of tire noise using a reliable numerical method

at the design stage is highly desirable. Fortunately, thanks

to the rapid advances in computer modeling and simulation

technology, the useful numerical methods using FEM or/

and BEM have been introduced by the subsequent

investigators.

According to our literature survey, Zhang et al. (1998)

introduced a complete finite element tire model for the tire

and vehicle NVH studies. The tire vibration analysis in the

time domain was conducted by the explicit nonlinear LS/

DYNA3D, and the vibration modes were decomposed

using the fast Fourier transformation. Larsson and Kropp

(2002) proposed a double-layer smooth tire model to

analyze the high-frequency structure-borne noise, in which

the tangential contact force and the local deformation of the

tread were taken into consideration. Kim et al. (2006)*Corresponding author. e-mail: [email protected]

824 Han-Wool Lee, Jin-Rae Cho and Weui-Bong Jeong

numerically investigated the air-pumping noise of tire by a

three-stage hybrid technique, and they found that the

nonlinearity of air-pumping noise generation mechanism

affects both the noise characteristics in the frequency

domain and the directivity pattern. Brinkmeier et al. (2008)

proposed a finite element approach for simulating the

radiation noise of smooth tire using a modal superposition

method. They introduced a detailed finite element model

for the tire/road system, and the excitation by the real road

textures is modeled by the deterministic multi-frequency

harmonic functions.

For the numerical simulation of tire rolling noise, an

important part is the extraction of normal velocity data of

the surface of rolling tire. In order to extract such time-

dependent data by reflecting the tire rolling effect, one may

employ either the transient dynamic rolling analysis or the

stationary rolling analysis (Nackenhorst, 2004; Cho et al.,

2013). However, these numerical approaches are not only

time-consuming but also painstaking in dealing with the

numerous time-dependent normal velocity data. In this

context, the purpose of this study is to introduce and

validate a new numerical method for simulating the

radiation noise of smooth rolling tire, in which the normal

velocity data of tire surface is extracted by introducing the

concept of periodically exciting contact force. The

frequency of interest in this study is less than 600 Hz,

because the tire model is smooth without pattern blocks. In

patterned tire model, the noise sources associated with

pattern blocks, such as air pumping and pattern block

impact, produce the sound pressure higher than 1 kHz. But,

in case of smooth tire model, a main noise source is the

low-frequency tire body vibration caused by the belt-

bending at the leading edge of the contact patch.

In this approach, the ground contact pressure within the

tire contact patch is computed by the static tire contact

analysis, and the ground contact pressure is taken as the

external exciting contact force. And then, a sequence of the

ground contact forces a time delay corresponding to the tire

rolling speed are periodically excited on the whole tire

tread surface. The tire structural vibration analysis is

performed by the conventional mode superposition in the

frequency domain, and finally the radiation noise of rolling

tire is predicted by commercial BEM code. The present

method is illustrated through the rolling noise simulation of

3-D smooth tire and verified from the comparison with

experiment, and furthermore the acoustical responses are

investigated with respect to the tire rolling speed.

The organization of this paper is as follows: Following

the introduction, the tire radiation of tire rolling noise is

briefly described in Section 2. The simulation procedure

and the concept of periodically exciting contact force are

addressed in Section 3. The illustrative numerical

experiment, the comparison with experiment and the

parametric investigation to the tire rolling speed are given

in Section 4, and the final conclusion is made in Section 5.

2. RADIATION OF TIRE ROLLING NOISE

Tire noise is mostly distributed at frequencies below 3,000

Hz, and can be classified into structure-borne and air-borne

according to its source. The structure-borne noise is

generated by the vibration of tire body, due to the

interaction between the tire and the ground, and includes

bending-restoring (Jennewein and Bergmann, 1985), block

impact, and texture impact. The noise caused by the

bending-restoring of tire is occurred when a tire portion

within the contact patch is bended and restored according

to the rolling under the self weight of tire. The block impact

noise is generated when the tread pattern blocks hit the

ground, while the texture impact noise is generated when

the rough particles on the ground hit the tire tread surface.

Meanwhile, the air-borne noise, which is mainly caused by

the compression/expansion of air within tire grooves,

includes air-pumping noise (Brinkmeier et al., 2008) and

pipe resonance (Sakata et al., 1990). The air pumping noise

is a compression-expansion burst as air volume within tire

grooves is rapidly emitted to the outside while the tire

pattern is in contact with the ground. On the other hand, the

pipe resonance is generated when an empty space with the

shape of a pipe that is formed between tire tread and

ground resonates.

The current study deals with the radiation of structure-

borne noise of smooth rolling tire which is mainly due to

the bending-restoring of tire. Then, it becomes a 3-D

coupled structure-acoustic problem in which a rolling tire

and the surrounding air are interacted, as represented in

Figure 1. The tire body with its surface SN is in

contact with the infinite ground SR. Meanwhile, the semi-

infinite air domain is divided into the interior

domain and the exterior infinite domain based on

the finite boundary ΓX which is truncated for computation.

The dynamic displacement field u(x;t) of rolling tire is

interacted with the acoustic velocity field V(x;t) of air

through their common interface SN such that .

Then, the time-harmonic acoustic pressure field

within the air domain Ωa that is induced

by the structural vibration of rolling tire B is formulated as

follows: Find the acoustic pressure p(x;t) such that

(1)

for every admissible pressure field q(x;t). Where, κ = ω/c is

the wave number with ω and c being the angular frequency

and the speed of sound, and ρ is the air density. Equation

(1) could be derived by taking the variational formulation

to the Helmholtz equation equipped with the associated

Neuman, Robin and Sommerfeld conditions (Brinkmeier et

al., 2008). This problem can be numerically implemented by

B ℜ3

∈

Ωa ℜ3

∈

Ωa,I Ωa,∞

V n⋅ = u·– n⋅

p x;t( ) = p x( ) eiωt

⋅

Ωa

∫ ∇p ∇q⋅ κ2pq–( )dV =

SN

∫ iρωu·n0qds

− ΓX

∫ iκp O Xd 1–( )/2–

( )–( )qds

NUMERICAL METHOD FOR SIMULATING TIRE ROLLING NOISE BY THE CONCEPT OF PERIODICALLY 825

various methods, among which the finite element method,

combined finite/infinite element method and the boundary

element method (BEM) are widely employed (Astley,

2000; Wrobel, 2002).

In the current study, the above vibro-acoustic formulation

(1) is basically solved by the boundary element method.

But, the normal velocity on the tire surface, a source of

tire noise, is calculated by the concept of periodically

exciting contact force, which will be addressed in Section

3. According to this concept, the structural vibration field

of rolling tire is approximated by making use of the

FEM-based mode superposition method in the frequency

domain.

3. SIMULATION PROCEDURE AND PERIODICALLY EXCITING CONTACT FORCE

3.1. Numerical Simulation Procedure

A first step of the numerical simulation of radiation noise is

to obtain the distribution of normal velocity on the tire

surface, which serves as a boundary condition for the

acoustic analysis. When the tire is rotating, the tire vibrates

due to the interaction with the ground. Here, since the tire

contact region is continuously varying with the tire

rotation, the tire contact patch shown in Figure 2 (a) is also

continuously varying. In the figure, the left and right edges

of the contact path are called the bending and restoring

fronts respectively. By virtue of this fact, the dynamic tire

rolling analysis is thought to be vital to obtain the normal

velocity data. But, in the current study, the static tire

contact analysis illustrated in Figure 2 (b) is utilized. As

will be explained in the next section, the contact pressure

within the contact patch is to be periodically applied to the

whole tread surface instead of making the tire rotate.

Next, the modal analysis is performed to obtain the

mode shapes of tire in the deformed configuration by its

vertical contact force Fc and the internal pressure pint. And,

the periodically exciting contact force that was obtained by

utilizing the static tire contact analysis and the mode

superposition are performed in the frequency domain.

Then, the normal velocity distribution on the tire surface is

to be extracted in the frequency domain. Finally, the

computed normal velocity data are to be mapped into the

BEM mesh of smooth tire model and the acoustic analysis

is to be performed.

3.2. Periodically Exciting Contact Force

One of most important subject for the reliable numerical

simulation of radiation noise of rolling tire is the

identification and application of excitation force. To

identify the excitation force acting on the rolling tire, one

may consider the transient dynamic rolling analysis.

However, it is highly time-consuming as mentioned above,

and furthermore commercial acoustic simulation code like

MSC/Sysnoise cannot be applicable to the rolling tire

model. For this reason, an alternative way is to utilize the

static tire contact analysis, as illustrated in Figure 2, where

the ground contact force at the bending front would be

taken as an excitation force. It is because the vibration of

rolling tire is mostly caused by the impact while tire is

bending at the bending front. But, this simplification

cannot be acceptable in two aspects. One is that the effect

of tire rolling is neglected, and the other is that the

magnitude of excitation force is different from the total

excitation force that is exerted on the whole tire body

during a revolution. In order to resolve this problem, the

concept of periodically exciting contact force, which is

illustrated in Figure 3, is introduced for the current study.

The tire is kept stationary but the ground contact force is

periodically applied to the entire tire tread surface with a

time delay. Here, the ground contact force Fgc means the

contact pressure within the contact patch. The direction of

u· n

u x;t( )

Figure 1. Structure-acoustic interaction problem composed

of a rolling tire and the surrounding air.Figure 2. (a) Bending and restoring fronts within the

contact patch; (b) Static tire contact analysis.

Figure 3. Ground contact force within contact patch and

schematics of periodically exciting contact force.


periodically exciting contact force is opposite to the

direction of tire rolling.

Referring to Figure 4 (a), the total of M circular paths is

defined on the tire tread surface which passes through the

tire contact patch. For each circular path, the total of N

finite element nodes are assigned, as represented in Figure

4 (b). And, the N finite element nodes are assigned side by

side with those on the remaining circular paths, as shown in

Figure 4 (a). Furthermore, it is assumed that a finite

element mesh is uniform in both the axial and

circumferential directions such that the circular paths and

the nodes are well defined. Then, the total number of

nodes where the periodically contact force is applied

becomes .

For the precise analysis, one should consider the rolling

tire as a moving sound source, but we in this study compute

the acoustic pressure by simplifying the rolling tire as a

fixed sound source. This simplification is based on the fact

that the surface velocity of rolling tire leads to extremely

low Mach number. For example, if the tire rolling speed is

60 km/h, then the peak tire surface velocity reaches to

33.4m/s which is less than Mach number of 0.1.

Next, we compare the total contact force exerted on the

whole tire tread surface between the rolling tire and the

stationary tire subject to periodically exciting contact force.

Letting fk,1 be a nodal ground contact force acting on the k −

node on the bending front (i.e., the nodal ground contact

force acting on the path k when the path passes through the

bending front), then the magnitude of the total impact force

that is exerted on the bending front becomes

(2)

And, the magnitude of the total impact force that is

exerted on the entire tread tread surface during a revolution

of rolling tire becomes

(3)

This total contact force is also conserved for the stationary

tire subject to periodically exciting contact force if the

following two are simplified and assumed. The flat contact

area is replaced with the undeformed circular one which

would be acceptable when the length of contact patch is

much smaller than the tire radius.

Next, in case of stationary tire, let T be the time period

during a revolution of rolling tite. Then, the time interval Δt

between two adjacent nodes shown in Figure 4 (b) on the

same path k becomes Δt = T/N. With respect to the node Pk,1

on the bending front, the j − th node on the same path has

the time delay Δtj given by

, j = 1, 2, ..., N (4)

Then, in the concept of periodically exciting contact force,

the nodal ground contact force that should be applied to the

j − th node on path k is defined by

, j = 1, 2, ..., N (5)

And, the total magnitude of periodically exciting

contact forces is calculated as

(6)

which becomes identical with Equation (3). Thus, it has

been justified the the total contact forces are the same for

the rolling tire and the stationary tire subject to periodically

exciting contact force. Figure 5 represents a sequence of

periodically exciting nodal contact forces fk,j along the

circular path k. Where, Pk,j and Δtj indicate the applying

nodes and corresponding time delays.

4. NUMERICAL EXPERIMENTS

An automobile tire model P205/60R15 is taken for the

numerical simulation, and only a main groove is

considered for its finite element model shown in Figure 6

(a) by neglecting the detailed tread pattern. The width and

depth of the main groove are 6 and 4 mm respectively, and

the frictional coefficient between the tire surface and the

ground is set by 0.8. Referring to the previous Figure 2 (b),

the tire model is inflated by the internal pressure pint of

206.84 kPa and compressed by the vertical force Fc of 475

kgf. The main grooved smooth tire model is uniformly

discretized with the total of 28,800 C3D6H and C3D8H

finite elements that are provided by Hibbitt, Karlsson &

Sorensen Inc. (2007). With the generated tire FEM model,

ℵimp

ℵimp = M N×

f BF

tot

f BF

tot = f1,1 + f2,1 +…+ fM,1

f RT

tot

f RT

tot = N f BF

tot×

Δtj = j 1–( )Δt = j 1–( )

N---------------T

fk,j t( ) = fk,1 δ⋅ t Δtj–( )

f PE

tot

f PE

tot =

j=1

N

∑k=1

M

∑ fk,1 δ t Δtj–( ) = N ×

k=1

M

∑ fk,1⋅

Figure 4. Definition: (a) Circular path k on the tire tread

surface; (b) Finite elemenet nodes along the path k.Figure 5. Sequence of periodically exciting nodal contact

forces that are excited along the path k.


the static tire contact analysis was performed to obtain the

deformed tire configuration and the contact pressure within

the contact patch. The deformed tire configuration is used

for the modal and acoustic analyses.

Referring to Figure 6 (a), the total number M of circular

paths is 34 and each circular path contains 256 nodes.

Thus, the total number of nodes where the nodal

contact forces are to be applied becomes 34 × 256 = 8,704.

The total nodes 256 along the circular path was cosen

based on the wavelength and the frequency of interest. The

frequency of interest in this study is 600 Hz, as addressed

in Introduction, and we will extract tire modes up to 900

Hz for the mode superposition. Since the tire diameter D is

595 mm, 256 nodes lead to the wavelength λ equal to 14.56

mm. For the tire rolling speed of 60 km/h, this wavelength

leads to the appropriate frequency range up to 1,147 Hz.

Figure 6 (b) represents the distribution of ground contact

force Fgc within the contact patch when the tire tread

surface is unfold., where two axes indicate the path number

and the rotation angle from point P, respectively. Each

nodal force within the ground contact force becomes the

nodal contact force fk,j which was defined in the previous

Section 3.2. It is observed that the ground contact force Fgc

is symmetric with respect to path 17 and the magnitudes of

nodal contact forces fk,j within the ground contact force are

shown to be different for different circular paths. Referring

to the previous Figures 3 and 4 (b), the nodal contact forces

are applied to all the 8,704 nodes for which the application

time for each nodal contact force depends on the relative

position of each node on the circular path and the tire

rolling speed. The concept of time delay in applying the

nodal contact force is explained below.

In case of tire at rest, the width of a specific nodal

contact force Fgc is identical with the width of contact

patch. But, if the tire is rolling, the time duration required

to pass through such a relative distance (i.e., the width of

contact patch) would be different for different tire rolling

speeds. Figure 7 (a) represents the time histories of a

ground contact force for four different tire rolling speeds,

which are reproduced by converting the relative distance

into the time interval. The horizontal axis indicates the

lapse of time starting from the top point P in Figure 6 (a),

and which illustrates the time delay when the ground

contact force is applied to the bottom point R. Figure 7 (b)

represents the frequency responses of ground contact force,

which are obtained by the discrete Fourier transform. The

faster the velocity, the higher the frequency wherein the

excitation can occur, vice versa.

Next, the modal analysis was performed with the smooth

tire model in the deformed state, and the total of 3,000

modes were extracted up to 900 Hz. The mode shapes of

three lowest natural frequencies are represented in Figure

8. The radial deformation is dominated and the deformed

configuration is simple at low frequencies, but the

deformation configuration becomes complex and the

lateral deformation appears as the frequency goes up.

ℵimp

Figure 6. (a) Bending front and circular paths (180o rotated

for the sake of representation); (b) Ground contact force

Fgc within the contact patch when the tire tread surface is

unfold.

Figure 7. Variation to the tire rolling speed: (a) Ground

contact force Fgc; (b) Discrete Fourier transform.

Figure 8. Lowest mode shapes of the deformed tire: (a) 45

Hz; (b) 103 Hz; (c) 119 Hz.


Figure 9 (a) shows the 3-axis effective masses of natural

modes, where three axes x, y and zare defined in Figure 6

(a). It is observed that the first mode takes a large portion

and the contribution of modes higher than 750 Hz is

negligible. Figure 9 (b) represents the modal participation

factors, where those in the z − axis are excluded because

those are almost the same with ones in the x − axis. Both

the effective mass and the modal participation factors were

computed by the method in Hibbitt, Karlsson & Sorensen

Inc. (2007) which utilizes the influence vector. In case of

the x − axis, the lowest modes show relatively higher

values, but in case of the y − axis, the relatively higher

values appear at the intermediate modes near 700 Hz. It is

consistent with fact that the lowest modes are dominated by

the radial deformation in the x − and z − directions, while

the lateral deformation in the y − direction is dominated by

the relatively higher modes.

The structural vibration responses of the smooth tire at

rolling speed of 60 km/h were obtained by the mode

superposition method, for which all the natural modes were

taken and the modal damping ratio of 0.03 was applied.

Figure 10 represents the frequency responses of normal

velocity at three different points A, C and E on the tire

shoulder which are indicated in the next Figure 11 (a). The

responses are relatively larger at the frequencies lower than

250 Hz, because the ground contact force itself prevails at

low frequencies, as represented in the previous Figure 7

(b). This trend is also observed from Figure 10 (b) for other

three points B, C and D which are aligned in the lateral

direction. It is also found that the response at the tire rim

(i.e., at point D) is much smaller than the responses at the

tire tread. In other words, the tire structural vibration is

dominated by the radial deformation of tire tread.

It can be clearly observed from Figure 11 showing the

frequency-wise normal velocity distributions of tire, that

the structural vibration of tire is dominated by the tread

radial deformation.

Figure 12 represents the one-third octave band spectrum

of normal velocity at point A with respect to the tire rolling

Figure 9. (a) Modal effective masses; (b) Modal

participation factors.Figure 10. Normal velocity response spectra at 60 km/h:

(a) Points A, C and E; (b) Points B, C and D.

Figure 11. Normal velocity distributions at 60 km/h: (a) 45

Hz; (b) 167 Hz; (c) 190 Hz; (d) 206 Hz.


speed. It is observed that the normal velocity increases as a

whole in proportional to the rolling speed. However, owing

to the frequency response characteristic of ground contact

force shown Figure 7, it is also observed that higher speed

rather produces lower normal velocity and vice versa at

several frequencies. For example, near 42 Hz, the normal

velocity of 100 km/h is much lower than those of 60 and 80

km/h, and at 125 Hz, the normal velocity of 100 km/h is

higher than that of 120 km/h. Of course, this inconsistent

normal velocity trend to the rolling speed is dependent of

the measurement position on the tire surface as well as the

frequency.

Next, the acoustic analysis was performed by

Virtual.Lab with a BEM mesh of main grooved smooth tire

model (LMS International NV, 2012). Referring to Figure

13 (a), the BEM mesh was generated with the outer surface

of tire FEM mesh and the field point mesh having the

radius of 1.5 m. The ground is modeled as an infinite

acoustic-reflecting plate and forced to be in contact with

the tire BEM mesh. The structural vibration data on the tire

surface was mapped into the tire BEM mesh, and the

acoustic simulation was carried out up to 900 Hz with the

frequency interval of 5 Hz.

The sound pressure distribution on the field points at 105

Hz is represented in Figure 13 (a), where the sound

pressure is shown to be relatively higher in the direction of

tire rolling. Figure 13 (b) represents the frequency response

of total sound power at the rolling speed 60 km/h. The total

sound power prevails at low frequencies below 250 Hz and

it shows a gradual decrease with the frequency from 250

Hz. This trend is consistent with the normal velocity

response shown in Figure 10, because the ground contact

force itself prevails at low frequencies, as shown in Figure

7 (b).

Figure 14 represents the sound pressure distributions in

the region between the tire surface and the field points at

four different frequencies. First of all, the relatively high

sound pressure is observed around the tire contact patch,

regardless of the frequency. The space between a main

groove and the ground forms a narrow pipe with a

rectangular cross section, and the compression and

expansion of air within this pipe by the structural vibration

of a main groove produces relatively high pressure.

Meanwhile, it is observed that the sound pressure

distributions are different for different frequencies because

the sound pressure distribution is characterized by the tire

vibration pattern. The peaks are also observed around the

tire surface, which is solely due to the radial vibration

Figure 12. One-third octave band spectrum of normal

velocity at node A to the tire rolling speed.

Figure 13. Acoustic analysis for 60 km/h: (a) Sound

pressure distribution on the field points at 105 Hz; (b)

Total sound power.

Figure 14. Sound pressure distributions at 60 km/h: (a) 50

Hz; (b) 130 Hz; (c) 190 Hz; (d) 230 Hz.


pattern of tire natural modes.

Figure 15 (a) represents the one-third octave band

spectrum of sound pressure at 60 km/h that is measured at

point Q on the field points. As indicated in Figure 13 (a),

point Q is located 5 m high above the ground and aligned at

45o right from the tire moving direction. The sound

pressure is negligible at low frequencies below 20 Hz,

while it uniformly increases up to 200 Hz and decreases

thereafter. It is consistent with the previous sound power

response shown in Figure 13 (b), and it is found that the tire

radiation noise is highest at frequency near 200 Hz.

The acoustic analysis was also carried out four different

tire rolling speeds, in order to investigate the effect of tire

rolling speed on the radiation noise. In the current study,

the tire rolling speed is reflected by adjusting the time

delay for applying the periodically exciting contact forces

on the tire surface, as addressed in Section 3.2. The total

sound powers are compared in Figure 15 (b), where the

total sound power increases with the tire rolling speed as a

whole. However, at some frequencies, rather lower speed

produces higher sound power, owing to the response

characteristic of normal velocity shown in Figure 12 to the

tire rolling speed.

The one-third octave band levels at point Q are

compared in Table 1. As a whole, the sound pressure shows

an increase with the tire rolling speed and reaches its

highest level at 125 ~ 250 Hz depending on the tire rolling

speed. Meanwhile, it is also observed that lower speed

produces higher sound pressure level at some frequencies.

Next, the experiment was also performed in anechoic

chamber shown in Figure 16 (a) in order to verify the

numerical study. A test smooth tire model shown in Figure

16 (b) with a central main groove was manufactured, and it

was inflated and loaded by the same internal pressure pint

and the vertical load Fc as for the numerical simulation.

Tire is forced to be rolled on the drum that is rotating with

the constant rolling speed, and two different tire rolling

speeds 60 and 80 km/h were taken for the experiment. A

microphone is located 5 m high above the ground and

oriented at 45o right from the tire axis (i.e., point Q in the

previous Figure 13 (a)), and it is aligned to direct the center

of tire. The radiation noise was measured during 240 sec,

and the measured data were post-processed by the linear

amplitude averaging and the Hanning window.

The sound pressure was measured by the microphone

and compared with that obtained by the numerical

simulation. Figures 17 (a) and (b) compare the frequency

responses of sound pressure between numerical and

experiment at the tire rolling speeds 60 and 80 km/h,

respectively. A reasonably good agreement is observed up

to 350 Hz, and the numerical simulation is shown to predict

lower sound pressure at high frequencies. However, it is

Figure 15. (a) One-third octave band spectrum of sound

pressure at point Q at 60 km/h; (b) Comparison of total

sound power to the tire rolling speed.

Table 1. Comparison of one-third octave band levels (N/m2,

dBA) of sound pressure at point Q for four different tire

rolling speeds.

Frequency(Hz)

Tire rolling speed (km/h)

60 80 100 120

31.5 20.28 26.47 27.82 24.36

63 35.18 42.86 49.15 48.94

125 44.90 56.53 66.17 67.65

250 51.46 57.83 52.63 62.22

500 38.11 46.40 53.66 58.29

Figure 16. (a) Test setup for the tire noise measurement;

(b) Main grooved smooth tire.


because various surrounding noise sources, such as the

mechanical vibration of rotating drum, are included in the

experiment. By considering this fact, it has been verified

that the proposed numerical method can accurately predicts

the tire sound level and successfully account for the tire

rolling speed. Thus, the validity of the proposed numerical

method for predicting the tire radiation noise has been

justified.

Next, the tire structural velocity between simulation and

test was compared, because the similar noise level between

simulation and test does not necessarily mean the similarity

in the tire structureal vibration. Figures 18 (a) and (b)

comparatively represent the frequency responses of normal

velocity at point A (indicated in Figure 11) on the tread

surface at 60 and 80 km/h, respectively. Since we were not

able to directly measure the tire structural velocity, the

normal velocities at point A were indirectly predicted using

the transfer function between the normal velocity at point

A and the sound pressure at a microphone. A reasonably

good agreement is observed up to 350 Hz, but the test

shows the normal velocity higher than the simulation at

high frequencies. It is because the surround noise that is

included in the measured acoustic pressure at high

frequencies leads to higher normal velocity at high

frequencies, in the transfer process of the acoustic pressure

to the normal velocity.

5. CONCLUSION

In this paper, a new numerical method for simulating the

radiation noise of smooth rolling tire with a main groove

has been introduced. This method utilizes the simple static

tire contact analysis and introduces periodically exciting

contact force. Furthermore, the proposed method can

predict the variation of tire radiation noise with respect to

the tire rolling speed. The ground contact force within the

contact patch was obtained by the static tire contact

analysis, and it was periodically applied to the whole tread

surface of stationary tire. A sequence of periodically

exciting contact forces were applied to the tire surface with

appropriate time delays in order to take the tire rolling

effect into consideration. The structural vibration of rolling

tire was obtained by the mode superposition using the tire

natural modes in the deformed configuration and a sequence

of periodically exciting contact forces. The acoustic analyses

were performed for different tire rolling speeds and the

verification experiment was also performed. From the

comparison with the experiment, it has been justified that

the proposed numerical method successfully simulates the

radiation noise of smooth rolling tire with the reasonable

numerical accuracy. From the numerical results, it was

found that the sound power and pressure reach their highest

levels at the frequency range of 125 ~ 250 Hz, depending

on the tire rolling speed. Furthermore, it was found that the

Figure 17. Comparison of sound pressure at a point of

microphone: (a) 60 km/h; (b) 80 km/h.

Figure 18. Comparison of normal velocity at point A on

tire tread surface: (a) 60 km/h; (b) 80 km/h.


total sound pressure and power as a whole increase with the

tire rolling speed, but at some frequencies, lower speed

produces higher sound pressure and power and vice versa.

ACKNOWLEDGEMENT-The financial and technical support

for this work by Kumho Tire Co. is gratefully acknowledged.

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