Sensitivity Analysi s of Transfer Mechanism Con ng Dynamic ... · nsidered. BT periment is...
Transcript of Sensitivity Analysi s of Transfer Mechanism Con ng Dynamic ... · nsidered. BT periment is...
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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 [email protected]) student of [email protected]
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