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Abstract — Tariation) whiariation) and taper, in order tystem of an autnalysis progrependent charonsidered. BTxperiment is ensitivity analyiffness of a bus Index Terms —

ensitivity Anal

While drivinause vibrationhattering. Espotational vibraf a steering whrough the sus

These vibratrake disc anassengers. Inuspension and

Also this can chould be evaevelopment.

The brake juf brake forcenuniformity oontact pressuonditions are

Variation), iniventually, it

Variation) [1-2]To reduce su

he first way xciting vibraperation precis

Manuscript receJ. H. Lee is a ma

epartment at AjouT. W. Park is a p

jou University, x:+82-31-219-19S. P. Jung is

epartment at AjouW. H. Kim is

ngineering Depar

SCon

he cause of braich is resultethis phenomento analyze the tomotive is moram. Especiaracteristics ofTV measureapplied to

ysis of the susshing as a desi

— Brake Juddlysis, Brake To

I. INTR

ng a vehicle, fn and noise proecially, vibratation (nibble)wheel and puspension and stions that are d pad can g

n addition, id steering systcause of an acaluated and

udder is genere. This phenf the disc fric

ure between happened b

itial productiis the cause

]. uch brake judd

is to reduce ation forces sion of the bra

eived March 19, 2aster degree candu University (e-mprofessor with theSuwon, Republi65; e-mail:park@a PhD candidat

u University (e-ms a master degrtment at Ajou Un

Sensitinsideri

Jin

ake judder is Bed from DTVon affects the rtransfer mech

odeled using a ally, nonlineaf the bushingd from brathe simulatiospension systeign variable is

der, Transfer Morque Variation

RODUCTION

frequent and soblems like jution, called br, translationalulsation of a steering systemcaused by fri

give an unplf resonance tems can be ccident. Thereimproved du

rated from an nomenon is ution surface adisc and b

by the DTVon defects ae of the BT

der, there are tbrake torquefor exampl

ake disc, the fr

2010. didate student of Mmail:ljh1227@ajoe Mechanical Engic of Korea (Ph

@ajou.ac.kr) te student of M

mail: moonsejung@gree candidate sniversity (e-mail:s

ivity Aing Dyn Hee Lee, T

BTV (Brake ToV (Disc Thicride comfort. Ianism, a suspemultibody dyn

ar and frequg componentsake dynamomon model. Fiem which conscarried out.

Mechanism, Bun.

sudden brakinudder, shimmyrake judder, ol vibration (sh

brake pedal ms. iction betweeleasant feelinis occurred

severely damefore, brake juuring the ve

irregular variusually arise

and variation obrake pad. T (Disc Thickand disc runV (Brake To

two main mete variation due improving

friction materi

Mechanical Enginu.ac.kr)

gineering Departmhone:+82-31-219

Mechanical Engin@naver.com) student of Mechshornet@nate.com

AnalysiynamicTae Won Park

orque ckness In this ension namic uency s are meter inally, siders

ushing,

g can y and

occurs hake) pass

en the ng to , the

maged. udder ehicle

iation en by of the These kness n-out. orque

thods. ue to

g the als of

neering

ment at 9-2952;

neering

hanical m)

the frequsyste

InvibraAnd Espestiffnevalucan deve

II

A.To

dynasuspsuspstrutand conspropdesigmechmod

B.W

progHowelemand mThe

or flu

is of Trc Chara

k, Sung Pil J

brake pad, euency range em and frequen this paper, nation through the effect of

ecially, sensitiness is conducuation and deapply at the

eloping advanc

I. CONSTRUC

Vehicle Modo analyze dynamic analysis ension systemension system

t and each parbushings. Th

sist of 27 moperties of eachgn process. Phanism is ana

del is shown in

Bush ModelWhen the susgram, each pawever, the partment such as b

mounting pose actual bushiuid seal type.

Fig. 1 Ve

ransferacterisJung and Wo

etc. The otheof natural fr

ency of the branumerical mothe suspensiovibration on

ivity analysis cted and the iesign improve initial desigcement is pos

CTION OF TRAN

del namic behaviprogram is u

m is assumedm of the vehiclrt is connectehe suspensionoving parts. Th part of the sPerformance oalyzed for the n Fig. 1.

ling pension systeart can be cos of actual vehushing. Tableition used in f

ing componenSuch material

ehicle Multibo

r Mechstic of aook Hyeon K

er way is to frequency of ake judder. odel is develon system and the vehicle bodue to changeinfluence is anement in virtugn process, risible [3].

NSFER MECHA

ior on judderused. The brad as a rigid ble consists of d by joints, sp

n and steeringThe dimensionsystem are obof the brake front suspensi

em is modeonstrained as hicles are conse. I shows the front suspensints consist of rls have viscoe

ody Dynamic

hanisma Bush

Kim

differently the suspensi

oped to find orubber bushinody is analyzee of the bushinalyzed. If suual environmeide quality a

ANISM MODEL

r, the multiboake module abody. The frothe Macphersprings, dampeg system modns and mater

btained from tjudder trans

ion. An analy

led in analyan ideal joi

strained by fortype of bushi

ion. rubber, urethaelastic behavio

Model

m hing

set ion

out ngs. ed. ing uch ent and

ody and ont son ers del rial the fer

ysis

ysis int. rce ing

ane or.

Proceedings of the World Congress on Engineering 2010 Vol II WCE 2010, June 30 - July 2, 2010, London, U.K.

ISBN: 978-988-18210-7-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

WCE 2010

1

2

34

BcoonmmSpjuIndefubyfodevachofthMca

WandifrusnoFichco

FiA

1 Sub Fr

2 Lower

3 Stabiliz4 Sprin

ecause bushinonstrain the mn ride quality

more accuratelmodeling of d

pecially, bushudder. So this n the bushinependent chaunctions. The y applying exporce accordingependent charariable x as a haracteristic cuf the frequencyhe transfer fu

Maxwell modealculating stati

Where, x is a fnd d are coeffiisplacement. Tequency funcsing experimeonlinear bushiig. 3 shows haracteristic oefficients.

ig. 2 ExperimArm Mounting

Table. I BushItem

rame Mountin

r Arm Mountin

zer Bar Mountng Upper Stru

Tota

ng componentmovement of e

, driving staby evaluate chdetailed bushhings affect tdynamic char

ng model, staracteristics nonlinear chaperimental datg to displacemacteristic, the frequency funurve. In othery dependent cunction formel is used. Eic bushing for

F G

filtered displacicients of the tTo use staticction, appropntal data. Fig.ing force accocharacteristicobtained tu

ental Non-LinFR bushing

hing Informati

ng Bushing

ng Bushing

ting Bushing ut Bushing al

ts support theeach part, it hability, etc. Thehassis as a trahing compontransmit of loracteristic is netatic nonlineaare included

aracteristic of ta using a spli

ment. In othermethod that f

nction is applir words, to expcharacteristic o

mula based onquation (1) irce.

G a x

cement value, transfer functic displacemenriate fitting p 2 is the experording to the c of the frequning the

near Static Stif

ion Location

FR RR FR RR

- -

e vehicle bodyas a decisive eerefore, in ordansfer mechan

nents is invoow frequencyeeded to incluar and frequd using spestiffness is crine curve - bur case as frequfilters displaceied using the press characteof a rubber bun the generais the formul

x x. aion and a is int variable x process is nerimental data tdisplacement.quency depentransfer fun

ffness of Low

No.2 2 2 2 2 2

12

y and effect der to nism,

olved. y like ude. uency ecific reated ushing uency ement static

eristic ushing, alized la for

(1)

a, b, c initial

as a eeded that is . And ndent

nction

wer

Fig.Stiff Con

behathan

C.In

repreand Tabltest d

IDisc

Max

3 Experimentfness of Lower

nsidering onlyavior because

40Hz.

BTV Measurn developed vesent the brakpad. BTV is

le. II shows tedynamometer

ItemInitial ang. velc Thickness V

PressureDynamic RadEffective Rad

x Friction CoeContact Stiffn

F

tal Frequency r Arm Mounti

y 1st order is frequency ran

rement virtual simulatke judder, BTV

measured at est conditionsand measured

Table. II TeU

locity RVariation μ

Ndius dius efficient

fness N

Fig. 4 Brake D

Dependent Ding FR Bushin

sufficient to enge of the brak

tion environmV is inputted bthe brake dyn

s. Fig. 4 and Fd BTV, respec

est Condition Unit

Rad/s μm /m 2m m 0-

N/m 1.

Dynamometer

Dynamic ng

express dynamke judder is le

ment, in order between the dnamometer teFig. 5 show tctively.

Value 67.4

8 1 x 10 0.330 0.1336 0.435 .5 x 10

mic ess

to isc

est. the

Proceedings of the World Congress on Engineering 2010 Vol II WCE 2010, June 30 - July 2, 2010, London, U.K.

ISBN: 978-988-18210-7-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

WCE 2010

A

tedeofcrit Plannedemparuthca

eapakex

coofm

to

Fig. 5

A. TheoreticSensitivity is

erms of designesign parametf the characterreate a Placketis widely usedlackett-Burmand the interaeglected. n+1esign variable

multiple of 4 arameters. In uns is used. Thhe characteristan be derived

where x is

ach experimenarameters, y

k is the numbxpressed in a m

According

oefficients ( βf error. The sq

matrix form.

EE T

The error is

o B. This leads

5 Measured B

III. Sensit

cal Backgrouns the derivativn parameters. ters, which havristic value, tott-Burman desd as a design tan design is aaction betwee experiments

es. The numband set accorthis study, th

he relationshiptic value, whicas (2).

+=y 0β

the level of nt condition, is the charactber of designmatrix form a

Y =

to the leaβ ) can be calcquare of error

YYE T −= 2

s eliminated bys to

YX T

rake Torque V

tivity Analysi

nd ve of the charSensitivity anve a serious ef

o be selected. sign than the otable for sensita 2-level desien design p are carried er of experimrding to the he Plackett-Bup between desch is called the

∑=

++k

iii x

1εβ

design paramβ is the coe

teristic value, n parameterss (3).

EXB +

ast square mculated by minr can be writte

BYXB TT +2

y differentiati

XBX T=

Variation

s

racteristic valnalysis allows ffect on the chSince it is eas

orthogonal arrativity analysisign of experimarameters caout in terms

ments is equalnumber of durman designign parametere response fun

ε

meters accordiefficients of dε is the erro

s. Equation (

method, recunimizing the sqen in the follo

XBXB TT

ing (4) with re

lue in main

hange sier to ay [4], s. The ments an be

of n l to a

design n of 8 rs and nction,

(2)

ing to design or and (2) is

(3)

ursive quare

owing

(4)

espect

(5)

Tobtai

The desigvalu

B.Th

bushcompbushx, y systethe slowevariacarrithe edesigon eperfoobjecrotatmaxiExpePlacksimuof dexpe

Nam

DV

DV2

DV3

DV4

DV5

Therefore, a ined as

magnitude ofgn parametere [5].

Sensitivity Ahe sensitivityhings which ponents are t

hing. And totaland z directio

em is symmetrsame value. Fer arm mountiables and levied out. The stexperimental rgn variables iseach design vormed using tctive of sensittional accelerimum acceleeriment for sekett-Burman d

ulations – expdesign variaberiment.

Fig. 6 Low

T

me De

1Lower a

FR2

3

4 Lower aRR5

set of recurs

XB T(=

f recursive coes affect the

Analysis of Busy analysis is

significantly the sub framl 5 design varion of each bury, stiffness o

Fig. 6 shows ing bushing anvel of bushingtiffness of eacresult of hardns initial value variable, totathe multibodytivity analysisration at the eration is obensitivity analdesign table. Feriment 3 and

bles and the

wer Arm(LH)

Table. III Desi

esign Variable

arm mountingR bushing

arm mountingR bushing

sive coefficie

YXX TT 1)−

efficients indichange of th

shing Componimplementedaffect vibra

me and loweriables are cho

ushing. Due toof left and righthe coordinatnd table. III reg that sensitih design varianess 60 and 7of the nonlinel 8 times of

y dynamic vehs is to minimiz

steering whbtained by thlysis is carrieFig. 7 shows

d 4. Table. IV simulation r

and Coordina

ign Variable

s Sti

Min

g x 38

y 14

z 25

g x/y 15

z 24

ents, B, can

(

cates how muhe characteris

nent d for 4 of ations. Selectr arm mountisen - stiffness

o the suspensiht variables hate system of tepresents desiivity analysis able is applied70. Each level ear curve. Basf simulation ahicle model. Tze the maximuheel. Therefohe simulation

ed out using tthe result of tshows the lev

results of ea

ate of bush

ffness(kgf/mm

n(-1) Max(+

8.4 64.6

40.6 282.0

5.2 44.4

50.0 296.2

4.0 48.6

be

(6)

uch stic

12 ted ing s of ion ave the ign

is d at

of sed are

The um ore, ns. the the vel ach

m)

+1)

6

0

4

2

6

Proceedings of the World Congress on Engineering 2010 Vol II WCE 2010, June 30 - July 2, 2010, London, U.K.

ISBN: 978-988-18210-7-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

WCE 2010

Fig. 7 Steering Wheel Angular Acceleration–exp.3 and 4

Table. IV Experiment Table and Result Row DV1 DV2 DV3 DV4 DV5 Result

1 +1 +1 +1 -1 +1 0.342 2 -1 +1 +1 +1 -1 0.213 3 -1 -1 +1 +1 +1 0.345 4 +1 -1 -1 +1 +1 0.130 5 -1 +1 -1 -1 +1 0.256 6 +1 -1 +1 -1 -1 0.286 7 +1 +1 -1 +1 -1 0.146 8 -1 -1 -1 -1 -1 0.288

Through the 2-level experiments, coefficients of response function in the form of polynomial function can be approximated. Equation (7) represents the response function. Sensitivity of bushing components is shown in Fig. 8. Change of the radial stiffness of the lower arm front and rear mounting bushing have a significant effect on the suspension system.

1 2 3 4 50.2508 0.0247 - 0.0565 0.01558 - 0.0255 - 0.0108y x x x x x= + + (7)

Fig. 8 Bush Sensitivity Analysis

IV. Conclusion

In this paper, using the multibody dynamic automotive model, the method which finds out influence of the brake judder is proposed in the virtual environment. The Mcpherson type suspension model is created and chassis performance is evaluated as a judder transfer path. Especially,

a rubber bushing which plays an important role as vibration isolation is modeled in more detail. Nonlinear stiffness according to the displacement and frequency dependent characteristics are modeled applied actual experimental data. Applying a judder to brake system in the virtual model is carried out using BTV from the actual dynamometer. Through input BTV generated by judder phenomenon, the rotational acceleration is calculated. In order to find out impact judder on the transfer mechanism, sensitivity analysis due to change of the bushing stiffness is conducted for a lower arm mounting bushing. Sensitivity due to change of the each directional stiffness is analyzed using Plackett-Burman design table through 8 times simulation.

In order to verify results of this research, the vehicle test should be accompanied in the same environment. Furthermore, if sensitivity analysis which considers not only stiffness of bushings but also geometry of the suspension can be conducted, more useful analysis result can be obtained for the transfer mechanism. Finally, improvement of the vehicle ride quality is expected to contribute through optimization design for the suspension system and bushing components based on this result.

REFERENCES [1] A.de. Vries and M. Wagner, “The Brake Judder Phenomenon,”SAE

930803, 1993. [2] G. Stefan and G. E. Hans, “Excitation and Transfer Mechanism of

Brake Judder,” SAE 931880, 1993. [3] I. J. Hwang, “System Mode and Sensitivity Analysis for Brake Judder

Reduction,” Transactions of KSAE, vol.13, No.6, 2005, pp. 142-153. [4] Plackett, R., Burman, J., “The Design of Optimum Multifactorial

Experiments,” Biometrica, vol. 33, 1946, pp. 305-325. [5] S. P. Jung, “An Optimum Design of a Gas Circuit Breaker using

Design of Experiments,” International Journal of Precision Engineering and Manufacturing, vol.8, No.1, July. 2007, pp. 1-5.

Proceedings of the World Congress on Engineering 2010 Vol II WCE 2010, June 30 - July 2, 2010, London, U.K.

ISBN: 978-988-18210-7-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

WCE 2010