Sound Radiation Analysis for Structure Vibration Noise Control of Vehicle Tire under The Action of Random Moving Line Forces

2004년도 한국음향학회 학술발표대회 논문집 제23권 제2(s)호

Sound

Radiation

Analyses

for Structure

Vibration

Noise

C

이】

_tr

이

_of

_Vehi

이

_e

_Tire

_under

The Action

of

Random

Moving

Line

Forces

Kim, Byoung-sam

Dept, of Automobile & Machinery, Suncheon First College, [email protected]

불규칙

이동분포하중을

받는

차량 타이어의

구조

진동소음

제어를

위한

음향방사

해석

김 병 삼

순천 제일대 학 자동차기 계과

Abstract

A theoret ical model has been studied to descr ibe the so니nd radiat ion analysis for stnjct니「e vibration noise of vehicle t i res under the action of random moving Iine forces. When a t i re is analyzed, it had been modeled as curved beams with distr ibuted spr ings and dash pots that represent the radial, tangential st iffness and dam미ng of tire, respect ively. The reaction due to fluid loading on the vibratory response of the c니「ved beam is taken into account. The curved beam is assumed to occupy the plane y=0 and to be axially infinite. The curved beam material and elastic foundation are assumed to be lossless BernoulIi-Euler beam theory including a tension force, dam­ ping coeff icient and st i ffness of foundation wi11 be empIoyed. The expression for sound power is integrated numer ically and the results examined as a funct ion of Mach number, wave-number ratio and st i ffness factor. The exper imental invest igation for structure vibration noise of vehi이e t ire under the act ion of random moving I ine forces has been made. Based on the Spatial Transformation of Sound Field techniques, the sound power and sound radia-t ion are measured. Results strongly suggest that operation condition in the tire mater ial properties and design factors of the t i re govern the sound power and sound radiation character ist ics.

1.

Introduction

The tire noise in automobiles is one of the major sources of noise p이lution. Structural vibrat ion in a t i re exerts a great influence on automobile noise. Consider the aftermath of a survey about the correlat ion between t i re noise scarce and i ts

contr ibuting factors. In this paper, the t i re is assumed to be curved beam that is considered by basis hardness, basis damping, and tension. Reia-t ive sound power that radiates from the curved beam is interpreted when random moving distr ibution load acts to the curved beam. It is the pu「pose of this paper to examine sound radiation character istics from struct나「al vibrat ion in t ires

2.

Theoretical

Background

Fig. 1 shows a curved beam or ring model of the tire. The t i re is assumed to be a thin elastic ring, or the curved beam that sustains a tension of elast ics base.

Fig. 1 Curved beam or ring model fo「 a pneumatic tire The t i re model is considered carcass's steady­ state character istic on the soft surface. This study assumes that the vibration of the t i re excited by road surface, generates from plane, and assumes 이ane vibrat ion to the vibration of a

-circular beam. Ap이ying dam이ng and tension force

to the equation of motion by the rotation and centr ifugal in the radial direction. The problem of sound radiation is studied by using statist ically distributed force in the surface of the tire. The statistically distributed forces are expressed as the irregular random functions in the surface coordination on the tire.

Assuming an input function transmitted from road surface to stationary ergodic function, the input funct ion can be processed as a deterministic func­ tion in the frequency band. The q나ality of input funct ion inside concerned frequency band is road surface that is determined by roughness and the number of vibrations on irregular road surfaces.

Fig. 2 The mot ion of a random force F"

丿

(1+A/)

0 +

夕

(列]

<]早3

楸:+ 鼻疔_円乙„+깅

(2) According to the road

surface, power spectrum distribution load forced inverse proportion tothe It is shown in Fig. 3.

surface's propertyof road density of random moving tire was assumed to be in

square of the frequency.

S3=

윽

可初_

。

「荷

(牛

企+夕)

図(本비

必从疔 ' "읎勿

+師

尸]

父

For doing non-dimensional structure impedance in the wave number field in the equat ion (4). It can be wr i tten as equat ion (5).

1m

=以

时必

成

丿

㈣

厂｝

Fig. 3 Spectral density as a function of frequency

so,

n =

끄亶싀京히

poso

心J宀

说广）

(6)

By integraling the intensity in the surface over the whole t i re, the mean of the sound power is obtained I ike equation (1).

E\W]

=

Re

[

lim

y

(x,

)

(x,

(

(1)

The time mean of sound power radiation abo나 power spectrum density is eq바al to equation (2).

3. Numerical Analysis

Relative acoustic power was analyzed, according to the change for the factor of t ire vibration quality when the t ire sustained by elast ic-damping foundation, as we11 as acted by tension is vibrated by random Iine force at the fixed speed. The fl니id

loading as acoustic media which touch with the tire is considered divided into Iight fluid loading (For exam이e： air) or heavy fluid loading (For example： water). Acoust ic impedance in the process of num-er ical analysis also is ignored, because acoustic

impedance by t ire vibration is rmjch far less than structure impedance. I「「ewla「 load forcing tire was supposed to normal process. Also, the loss

n =

□爲

E

质冋

factor was considered by st「나ctu「al damping of tire. The sajnd waves that progress from the tire border to outside direction radiate acoustic energy

in the range, that the structural wave number is more than the acoustic wave number, but i t does not radiate acoustic energy in the range that the acoustic wave number is more than structure.

the ranges of the f「ec^jency of excitement from both t i re radius and road surface, the length of random moving Iine force, and the wave length, are equal to fol lowing when the vehi이e is dr iving at

40-]50 Km/h.

In the case of low frequency (/«1)

쳐쁮窘

_{I 据}

(-a2 +i//2)yl^2 + 2

伽”"

户

<]

2

(1) In the case of the t i re under Iight fluid loading (%/尸《1) a

『

져쁴쏠끄

一

n~ r

例使&

(2) In the case of the t i re under heavy fluid loading (%/戶 그거 1)after assuming

n~f_—

一

丨

应

:

底版

项

］Fy

4.

Experiment

The t i re used in the exper iment for sMu(가니「al vibration noise measurement consists of both a radial t i re that is actually installed on a ca「and an experimental t ire that changes design factor in

Iimited extent. In addi t ion, the changed design factors in that the tire used in the experiment is a 195/65R14. Fig.4 is the schemat ic diagram of a t i re structural vibration noise test. Estab Iishing load condit ion after attaching the t i re loading equipment, we can control the travel speed of the t i re using a chassis dynamometer. The preliminary

operation is pract iced to sat isfy a fixed exper i- mental condit ion for Wminutes at 80 Km/h. Then, the microphone is installed at the point, 25 cmover the surface of land as we 11 as at horizontal dis­ tances, 1m from the tread center to measure sound pressure that radiates from t rre sidewa11. In the case of using the STSF Technique, a microphone is

installed at the point, 60cm, hor izontal distance from the sidewa11, 20cm over the surface of land, and its interval distance is 20cm.

Fig. 4 Schemat ic diagram of noise test

a t ire structural vibrat ion

In Fig.5, Mach number involved in velocity of random moving distribution load is 0.2, wave number ratio is 0.07, non-dimension damping coefficient is 0.025 and non-dimensional tension coefficient is 0.1,0.5,1.0,1.5. These are the result of numerical analysis of relative sound power about increment of cr i t ical acoustic relative acoustic power slightly increased as non-dimens ion tension coefficient increased； however, as the critical acoustic length increased relative acoustic power also increased. 타 om this viewpoint, we can assume that air 이tss나「e and load inside the t ire affect relative acoustic power.

Fig.6 is the relative sound power level of cri-t ical acoustic length (Mach number, M=0.2, non- dimensional damping coeff icient=0.025, wave number

「a니0=0.03, 0.05, 0.08, 0.11). When the wave number is in the region of low frequencies, relative sound power increases. Fig.7 is the relative sound power about increasing non-dimensional tension coeffici­ ent when Mach n니mber그0.2, non-dimensional damping coefficient=0.025, tension coefficient=0.1,0.5,1.0,

-1.5. Resonance radiat ion generated from the near wave number rat io=0.04, increases the relative sound power. = = -* , -'-4 # 1--•■c ? ' ,i,_芬 -, " -~

티g. 5 Relative sound power level versus critical acoustic-length

Fig. 6 Relative sound power acoustic-length

level versus cr it ical

懲獄、"gg隽表：£ 4 t I Fig. 7 Relative sound power level versus

wave-number ratio

5. Conclusions

The results of the study on structure vibration noise control of t i re forced random moving distribution load, and sound radiation analysis for

low noise t ire design shows the fol lowing. If non­ dimension tension coefficient involved with tire

inside air pressure is increased, relative acoustic power increased slightly. And according to increase cr i t ical acoustic length related to forced load of tire, relative acoustic power was decreased. But in the low frequency field, if the wave-number ratio increases, relative acoustic power increases as well. In the area of wave number rat io correspon­ ding to forced frequency involved with the running velocity of tire, the relative acoustic power for resonance radiation of t ire noise energy was increased significantly. Also wave number ratio produced resonance radiation moved when wave number ratio decreased. If the non-dimensional damping coefficient involved with tire of physical charac­ teristic is increased, relat ively acoustic power decreased significantly. 11 affected the tire ben­ ding tension and quantity of matter.

References

1. A. C. Eberhardt,"Investigation of the Truck Tire Vibrat ion Sound Mechanism11, Tire Noise Conference

1979, Stockholm, pp.153-168, 1979.

2. A. C. Eberhardt, "Truck Tire Vibration Sound", Inter-Noise Conference, Florida, pp.281-288, 1980. 3. A. C. Eberhardt, "The Truck Tire Vibrat ion Sound Mechanism", Ph. D. Dissertation, North Carolina University, Raleigh, North Carol ina, University MicrofiIms, Ann Arbor, Michigan, 1977.

4. W. F. Rei ter and A. C. Eberhardt, "자le Relation ship Between Truck Tire Vib「a니이i and Near and Far Field Sound levels", SAE Paper 762021, 1976.

5. W. F. Reiter, "Resonant Sound and Vibration Characteristics of a Truck Tire1', Tire Science and Technology, TSTCA, V이. 2, No. 2, pp.130-141, 1974. 6. W. F. Reiter, 11 Invest igat ion of Vi 바 ation in Truck Tire Noise Generation", Ph. 0. Dissertation. North Caiplina University, Raleigh, North Carol ina, University Microf iIms, Ann Arbor, Michigan, 1973. 7. M. Heck I, "Tire Noise Generation", Wear,113, pp..

157-170, 1986.

8. J. T. Tieiking, "Plane Vibration Characteristics of a Pneumatic Tire Mode I, '* SAE P叩e「650492, 1965. 9. S. H. CrandalI and W. 0. Mark, Random Vibrat ion

in Mechanical Systems, New York, London : Academic Press, 1963.