TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 11, Novembe
r
2014, pp. 76
6
8
~ 768
0
DOI: 10.115
9
1
/telkomni
ka.
v
12i11.62
11
7668
Re
cei
v
ed Ma
y 4, 2014; Re
vised July 1
9
, 2014; Accept
ed Augu
st 10
, 2014
Noise Analysis of wet Multi-disc Brake Used Complex
Eigenvalue
Tian-hon
g L
u
o
1
, Ting-qiong Cui
1
, De-shan Li
1
, We
n-jun Luo
2
, Chao Lin
2
1
Colle
ge of Me
chan
ics & Auto
mobil
e
Eng
i
n
e
e
rin
g
, Chon
gq
i
ng Jia
o
ton
g
Un
iversit
y
,
Cho
ngq
in
g, 40
007
4, Chi
n
a
2
T
he State Ke
y Labor
ator
y
of Mecha
n
ica
l
T
r
ansmissi
on, C
hon
gqi
ng U
n
iv
ersit
y
,
Cho
ngq
in
g 40
0
030, Ch
in
a)
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: 1029
92
594
8
@
qq.com
A
b
st
r
a
ct
T
h
is pap
er pr
opos
ed a
n
an
alysis
mo
del
and a c
o
mpl
e
x-eig
enva
l
u
e
-b
ased a
l
g
o
rith
m of w
e
t
mu
ltipl
e
d
i
sc b
r
ake (W
MDB)
nois
e
. F
i
rstly, the da
mpi
ng a
nd stiffness
b
e
tw
een the
br
ake d
i
sc a
nd t
h
e
friction plate w
e
re introduced based
on
the considerat
ion
of the sl
ight rotation
of t
he br
aking
system
and
da
mp
ing c
har
a
c
teristics of bra
k
e oi
l. T
hen, th
e fricti
on c
o
u
p
li
ng
math
e
m
atic
al
mo
del
an
d the fin
i
te e
l
e
m
e
n
t
mo
de
l (FEM)
of the braki
n
g
system
w
e
re establ
ishe
d. The occurr
enc
e
tendency
of brake sq
ue
al
w
a
s
jud
ged
accord
i
ng to the re
al
part (positiv
e
or neg
ativ
e
valu
e) of char
acterist
ic roots
of the compl
e
x
eig
enva
l
u
e
. T
he rel
a
tive err
o
r betw
een th
e
nu
meric
a
l
an
alysis res
u
lts
and th
e finit
e
ele
m
ent an
aly
s
is
results w
a
s
4%
, ind
i
catin
g
th
at braki
n
g
sp
eed
an
d br
aki
ng
pr
essure
ha
d
littl
e effect o
n
bra
k
e n
o
ise.
Duri
n
g
the br
aki
ng sy
stem des
ig
n, u
nder
the
pre
m
i
s
e that
th
e
br
akin
g p
e
rfor
ma
nce
is
not
affected, the
frictio
n
mater
i
al
w
i
th the l
o
w
e
r stiffness sho
u
l
d
b
e
used
as
possi
ble. Mor
eov
er, prop
erly
decr
easi
ng th
e fricti
o
n
coefficie
n
t bet
w
een the frictio
n
lini
ngs a
nd d
ual stee
l
disc w
ill red
u
ce the
b
r
ake no
ise. Therefore, the pr
ope
r
combi
natio
n of the para
m
ete
r
s
w
a
s deduc
ed to obtai
n the stabl
e fr
eq
uency res
pons
e of the braki
n
g
system
.
Ke
y
w
ords
:
auto
m
otiv
e
en
gin
eeri
ng, w
e
t
multi
p
le
d
i
sc
br
ake, c
o
mpl
e
x ei
genv
al
ue,
solid-
l
i
qui
d c
o
u
p
lin
g,
brake n
o
ise
Copy
right
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
With the a
n
ti-pollution p
e
rf
orma
nce, large br
aki
ng to
rque,
small
wear, lon
g
service life,
wet multi-disc b
r
a
k
e
s
a
r
e
widely
used
in en
gi
ne
eri
ng ma
chi
nery. Neverthel
e
ss,
bra
k
in
g n
o
ise
deterio
rate
d automobil
e
brakin
g stability
,
affe
cted occupant comfort
and re
du
ced
the com
pon
e
n
t
life [1].
No
wad
a
ys, brake noi
se h
a
d
been exten
s
ively studied
. Shih-iti Kung [2] had cha
nged the
resona
nt freq
uen
cy by lowering
the
stiffness of the
bra
k
e di
sc
s,
thus wea
k
eni
ng the co
upl
ed
intera
ction
a
nd elimi
natin
g the dyn
a
m
i
c in
stabilit
y. T. S. Shi [3] had f
ound
that brake di
scs
prod
uced th
e low-fre
que
ncy no
rmal
squ
eal a
nd t
he hig
h
-freq
uen
cy tange
ntial sq
ueal
and
decrea
s
e
d
th
e brake n
o
ise by
cha
ngi
ng the
ge
om
etric structu
r
e, ch
oo
sing
suitabl
e fri
c
tion
material
s
an
d othe
r o
p
timization
met
hod
s. Júnio
r
MT [4] ha
d p
r
oved th
at wi
th the in
crea
sing
braking
pressure, the wear was
i
n
creased and the system instab
ility was
also increased. In
addition, the t
e
mpe
r
ature ri
se is
helpful t
o
impr
ove th
e system
sta
b
ility.
AbuBakar an
d Ou
-ya
n
g
[5-7] ha
d fou
nd that th
e
bra
k
ing
sy
ste
m
involved
with a
large
numbe
r
of n
online
a
r fa
ct
ors
inclu
d
ing non
-linea
r conta
c
t
stiffne
ss a
t
the
fric
tio
n
interface, ph
ysical
nonli
n
ear m
a
teri
al, the
friction
coefficient and the complex rel
a
tionship amo
n
g
load
s, spe
e
d
and tempe
r
ature.
Terry [8] found that wet brake
s
noi
se a
nd vibr
ation a
r
e ca
used by the “stick-sli
p” effect.
The n
egative
slop
e relatio
n
shi
p
bet
wee
n
the fri
c
tion
coeffi
cient a
nd the
rotati
on spee
d m
a
y
indu
ce
self
-e
xcited vib
r
ati
on. Dong
-Ye
Sun [9] h
a
d
discovered
th
at wh
en
the
ratio of th
e
static
friction
co
efficient to th
e kinetic fri
c
tion
coeffi
ci
ent was a
bout
1 a
nd the
se
co
n
d
braki
ng p
h
a
se
wa
s exten
d
e
d
, the vib
r
atio
n could
be
re
duced to
elim
inate the
noi
se. We
nqin
g
Z
hao [1
0-1
2
] h
ad
establi
s
h
ed t
he math
emat
ical mo
del fo
r wet br
a
k
e,
dedu
ce
d the
theoreti
c
al e
q
uation of b
r
a
k
e
noise ca
use
with the mo
d
a
l analysi
s
m
e
thod an
d
ex
ploited the g
e
neratio
n me
chani
sms,
rea
s
on
s
and facto
r
s
of brake noi
se. XueJie Fu
et al
[13] h
ad pro
p
o
s
ed
the complex
modal analy
s
is
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Noi
s
e Anal
ysi
s of wet Multi
-
disc Bra
k
e Used Com
p
lex Eigenvalue (Tian-hon
g
Lu
o)
7669
theory, an
alyzed
the m
a
i
n
influe
nce f
a
ctors
of b
r
a
k
e
noi
se, a
n
d
propo
se
d t
he me
asures of
redu
cin
g
brake noise.
The mo
dal chara
c
te
risti
c
s of wet disc b
r
akes
i
n
brake oil fluids
ha
ve not been
reporte
d
at home
an
d
abroad.
Co
mpared to
co
nventional
dry
bra
k
e
s
, wet bra
k
e
s
ope
rate it well in
the
clo
s
ed
oil spa
c
e. Th
e natu
r
al frequ
en
cy of solid m
a
te
rials in th
e liqu
i
d is different
from that in t
he
vacuum. To make
the
a
n
a
l
ysis re
sults close
to
the
re
al situatio
n, d
u
ring
the e
s
ta
blishm
ent of t
he
model, the
da
mping
and
sti
ffness bet
we
en
steel pl
ate
and
frictio
n
b
r
ake lini
n
g
s
were i
n
tro
duce
d
to con
s
ide
r
sli
ght rotation of
the braki
ng system.
The a
nalysi
s
model
of wet brake noise vibratio
n
wa
s e
s
tabli
s
hed a
nd the
wet vibratio
n noi
se al
go
rithm ba
se
d
on complex
eigenvalu
e
s
wa
s
prop
osed. it
comp
ared
nu
meri
cal
analy
s
is with
finite
eleme
n
t a
n
a
l
ysis, ve
rified
the
relia
bility of
analysi
s
re
su
lts, studi
ed th
e effect
s of friction
c
oeffici
ent, bra
k
in
g
spe
ed, b
r
a
k
in
g pressu
re
a
nd
material
stiffness on the
braking system
stability.
2. Wet
Brak
e
Noise Gen
e
rate Me
chani
s
ms and Co
mplex Eigenv
a
l
ue Analy
s
is Theor
y
Primary b
r
a
k
e noi
se i
s
a
high-f
r
eq
uen
cy or lo
w-freq
uen
cy sq
ueal
. As for di
sc
bra
k
e
s
,
bra
k
e noi
se
mainly com
e
s from ci
rcu
m
ferential
a
n
d
axial vibration ca
used b
y
the friction
o
f
bra
k
e
discs a
nd the vib
r
ati
on of the
bra
k
e
calip
er
also strength
e
n
s
the sy
stem vibration.
Wh
e
n
the bra
k
e
be
gins to
wo
rk, unde
r the d
e
finite pr
e
s
su
re
, the moving
parts conta
c
t each othe
r a
n
d
are en
gag
ed i
n
the relative movement. T
he opp
os
ite
movement be
tween movin
g
parts p
r
o
d
u
c
e
s
friction, thu
s
stimulating
th
e moveme
nt
part to vi
b
r
at
e and
then
g
enerate n
o
ise
[14], as
sh
o
w
n in
Figure 1
.
In the p
ape
r, it a
nalyze
d
the
comple
x ei
gen
value to p
r
e
d
i
ct whethe
r th
e noi
se
wo
ul
d
occur o
r
not.
Figure 1. The
Link bet
wee
n
Compl
e
x Eigenvalu
e
s a
n
d
Brake Noi
s
e
Duri
ng
bra
k
in
g, modal
co
u
p
ling of
bra
k
i
ng comp
one
nts lea
d
s to
vibration, thu
s
ma
kin
g
the bra
k
e sy
stem un
stabl
e. Along with the modal
couplin
g of friction linin
gs, vibration
is
enha
nced. Under
wo
rki
n
g
conditio
n
s, the mod
a
l
vibration
of brake di
scs i
s
induced by
the
friction
ce
ntrifugal fo
rce an
d the mo
dal
cou
p
ling
bet
wee
n
b
r
a
k
e
discs
and
th
e frictio
n
lini
ngs
appe
ars, then low-frequ
en
cy noise
i
s
g
enerated. Th
e friction proces
s of conta
c
ted surfa
c
e
s
i
s
a
dynamics pro
c
e
s
s which
b
e
long
s to
the
transi
ent
m
o
d
e
. The
r
efo
r
e,
the tra
n
si
ent
vibration
mod
e
is
called
the i
n
stanta
neo
us vibration
mo
de. Since
the
co
ntact cha
r
acteri
stics
i
s
affected by
m
any
factors, such
as
co
ntact
sti
ffness, surface
rou
ghn
ess, pres
su
re, temperatu
r
e, spee
d, a
n
d
visco
us
dam
ping of b
r
a
k
e
fluid. The in
stantaneo
us
vi
bration
mod
e
is often
co
up
led with
syste
m
mode, di
sc
mode
and f
r
i
c
tion lini
n
g
s
mode. Th
e
continuo
us
en
ergy in
put a
nd a
c
cumul
a
tio
n
prod
uces the
resona
nce, as sh
own in Figure 2.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 11, Novem
ber 20
14: 76
68 – 768
0
7670
Figure 2. Bra
k
e Vibration
System
Introduc
e
the s
t
iffnes
s
mat
r
ix
]
[
f
K
of bra
k
e fri
c
tion amo
ng
parts of the
model; there
is
the equatio
n of motion for bra
k
e vibratio
n system.
0
}
]{
[
}
]{
[
}
]{
[
u
K
K
u
C
u
M
f
(1)
Whe
r
e: M, C, K and
f
K
res
p
ec
tively, for the s
y
s
t
em mass
matrix, damping matrix, s
t
iffnes
s
matrix and fri
c
tion stiffne
s
s matrix; u represents the
v
e
ctor of the system. The st
iffness mat
r
ix is
as
ymmet
r
ic
due to fric
tion s
t
iffnes
s
matrix
]
[
f
K
of the formula (1
). Th
e cha
r
a
c
teri
stic matrix
stiffness is fai
ling to symm
etric b
e
cau
s
e
of as
ymmetri
c
stiffne
ss m
a
trix, and the
eigenvalu
e
will
be pl
ural
un
der
ce
rtain
con
d
ition
s
in
duced
by
a
symmetric ma
trix. Whe
n
t
he real
pa
rt of
eigenvalu
e
is
positive, the system tend
s to be un
stable
.
i
i
i
i
j
2
1
,
（
n
i
,
,
1
）
(2)
Whe
r
e:
i
a
represents the
mod
a
l dam
ping,
i
mean
s n
a
tural freq
uen
cy
of i ord
e
r
mo
dal. Each
compl
e
x eige
nvalue corre
s
pond
s to a feature vecto
r
,
reflectin
g
the real pa
rt of the bra
k
e sy
ste
m
stability, if
i
a
is positive
，
th
e
n
the i
o
r
de
r mo
dal
da
mping
ratio
i
s
n
egative, t
he a
m
plitude
increa
se
s wit
h
time, cau
s
i
ng t
he brake system in
sta
b
ility, vibr
ation and noi
se.
Noi
s
e freq
ue
ncy
depe
nd
s on
modal natu
r
al
frequen
cy of the bra
k
e in
stability.
3. Analy
z
e the Model of
We
t Vibratio
n Noise
3.1. The Esta
blishment of the We
t Vibration Nois
e Analy
s
is Model
Figure 3. The
Equivalent Model of Wet B
r
ake System
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Noi
s
e Anal
ysi
s of wet Multi
-
disc Bra
k
e Used Com
p
lex Eigenvalue (Tian-hon
g
Lu
o)
7671
The followi
ng
equation
s
are obtaine
d by Newto
n's
se
con
d
law:
For m1:
1
1
12
1
2
12
1
2
1
1
12
1
2
12
1
2
1
11
11
mx
P
k
x
x
c
x
x
m
y
kxx
c
x
x
ky
c
y
(
3
)
For m2:
2
2
12
1
2
12
1
2
23
3
2
23
3
2
2
2
2
2
2
2
12
1
2
12
1
2
1
22
22
2
3
3
2
2
3
3
2
2
xx
yy
m
x
kxx
c
x
x
kx
x
c
x
x
k
x
c
x
m
y
kxx
c
x
x
ky
c
y
k
x
x
c
x
x
(4)
For m3:
1
3
23
2
3
23
2
3
1
1
2
3
23
2
3
23
2
33
33
mx
P
k
x
x
c
x
x
my
k
x
x
c
x
x
ky
c
y
(
5
)
Make the foll
owin
g assum
p
tions: wh
ere
3
,
1
m
m
repre
s
ent the mass of dual steel plat
es;
2
m
is
the ma
ss of
the fri
c
tion li
ning
s;
3
1
,
k
k
is the
stiffness
bet
wee
n
the
ste
e
l plate
an
d
the b
r
ake
hou
sing;
3
1
,
c
c
are the dampin
g
betwe
en the steel
plate an
d the bra
k
e h
ousi
ng;
23
12
,
k
k
are t
h
e
stiffness of dual steel pl
at
e and the friction lining;
23
12
,
c
c
are the stiffness between th
e friction
lining an
d dri
v
e shaft in th
e x-dire
ction
and y-di
re
ctio
n;
y
x
c
c
2
2
,
r
e
pr
es
e
n
t
th
e
s
t
iffn
es
s
be
tw
e
en
the d
r
ive
sha
ft and fri
c
tion
lining
s
i
n
th
e x-di
re
ction
and y
-
directio
n;
p
i
s
th
e b
r
akin
g p
r
e
s
sure
applie
d on th
e steel plate.
11
22
a
a
-
-
(4)
10
2
1
20
2
3
vy
y
vy
y
(5)
Whe
r
e
2
1
,
u
u
are
th
e frictio
n
coef
ficient bet
we
en the fri
c
tion
lining
and
st
eel di
sc,
2
1
,
are the an
gul
ar velocity which the fri
c
tion lining com
pare
d
with d
ual steel pl
ate ,
a
u
stan
ds fo
r
the static fri
c
t
i
on co
efficien
t,
u
is the rate
of chan
ge of
friction
coeffi
cient,
a
v
means the initial
velocity of the friction pai
r.
3.2. Numerical Solution of the Model for Wet Vibration Noise
The form
ula (1), (2
) and (3) are written in
matrix:
M
XC
X
K
X
F
(
6
)
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14: 76
68 – 768
0
7672
There are:
111
11
1
222
222
333
333
,,
x
xx
yyy
x
xx
XX
X
yyy
x
xx
yy
y
，
1
2
3
4
5
6
0
0000
0
0000
0
0
000
00
0
0
0
00
0
0
0
0
0
000
m
m
m
M
m
m
m
，
12
12
11
2
1
11
2
12
12
23
2
2
3
11
2
1
1
2
2
2
3
2
2
2
3
23
23
22
3
2
2
3
3
00
0
0
00
0
00
0
00
00
0
0
00
0
x
y
cc
cc
c
cc
c
c
c
C
cc
c
c
c
cc
cc
c
12
12
11
2
1
11
2
12
12
23
2
2
3
11
2
1
1
2
2
2
3
2
2
2
3
23
23
22
3
2
2
3
3
00
0
0
00
0
00
0
00
00
0
0
00
0
x
y
kk
kc
k
kk
k
k
k
K
kk
k
k
k
kc
kk
k
000
0
Fp
p
T
11
2
1
3
1
4
1
52
6
2
7
2
8
2
9
3
10
3
1
1
3
12
3
,,
,
,
,,
,
,
,,
,
,
zx
z
x
z
y
z
y
zx
z
x
z
y
z
y
z
x
zx
zy
z
y
Assu
me that the state vect
or is:
1
23456
78
9
1
0
1
1
1
2
,,
,,
,
,
,
,
,
,
,
T
Z
zz
z
z
z
z
z
z
z
z
z
z
Get system
state equatio
n:
Z
AZ
BV
(7)
A is the Ja
co
bi matrix of the system:
)
12
,
12
(
)
12
,
2
(
)
12
,
1
(
)
2
,
12
(
)
2
,
2
(
)
2
,
1
(
)
1
,
12
(
)
1
,
2
(
)
1
,
1
(
Z
Z
Z
Z
Z
Z
Z
Z
Z
A
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Noi
s
e Anal
ysi
s of wet Multi
-
disc Bra
k
e Used Com
p
lex Eigenvalue (Tian-hon
g
Lu
o)
7673
1
1
2
2
3
3
0
1/
0
1/
0
1/
0
1/
0
1/
0
1/
0
0
m
m
m
B
m
m
m
T
V
=
0
P
00
00
00
0
-
P
0
0
Matrix A is th
e Jacobi matrix of
the syst
em who
s
e ei
genvalu
e
pre
d
ict wheth
e
r the bra
k
e
pro
c
e
ss
stabl
e or not, thro
ugh the re
sult
s of the real p
a
rt of eigenva
l
ues.
4. Analy
z
e the We
t Bra
ke
Noise
using
Finite Element Method
Becau
s
e th
e
natural freq
uen
cy
]
15
[
of the solid i
s
different in liquid
s
and the vacuum,
analyzed th
e
wet b
r
a
k
e
di
sc in
the
brake fluid
und
er
the pa
rticular wo
rking
con
d
itions,
obtai
ned
the vibration frequ
en
cy of wet multi-pl
ate disc
bra
k
e
s
and extracte
d the compl
e
x eigenvalue
s.
4.1. Finite Element Mod
e
ling Wet
Brak
es
The
simplifie
d model
of fri
c
tion p
a
ir of
wet b
r
a
k
e i
s
sho
w
n i
n
Fig
u
re 4. Befo
re
dividing
the gri
d
, accordin
g to the
cha
r
a
c
teri
stic and th
e loa
d
boun
da
ry co
ndition
s of th
e wh
ole m
o
d
e
l,
some sm
all chamfers, hol
e, boss
and fillister
whi
c
h
have little im
pact on the
study of brake
noi
se
were app
ro
pri
a
tely negle
c
ted. The wh
ol
e finite eleme
n
t model is shown in Figu
re 5.
Figure 4. The
Simplified Model
Figure 5. Finite Element Model of the Wet Brake
4.2. Material
Propertie
s o
f
We
t Br
ake
Parts
Variou
s
com
pone
nts of
wet bra
k
e
mat
e
rial
pro
perti
es a
r
e
sh
own in Ta
ble 1.
Frictio
n
lining is
a co
mposite
mate
rial, steel
plat
e co
re i
s
65
Mn.The
re a
r
e
coatin
gs
whi
c
h b
e
long to
the
anisotropi
c material
s,
wh
ose su
rface have
pap
er
-
b
a
s
ed
fr
ic
tion ma
te
r
i
a
l
s
wh
ic
h
ab
se
nc
e o
f
asb
e
sto
s
.Duri
ng a
nalysi
s
p
r
ocessin
g
a
b
o
ve mate
ri
al
are
re
pla
c
ed
by linea
r m
a
terial
and
g
a
ve
the app
ro
pria
te Young'
s
modulu
s
a
n
d
Poisson'
s
ra
tio.8th tran
smissi
on
oil (40
℃
)
is
us
ed
a
s
bra
k
e
fluid, t
he d
e
n
s
ity is 852
kg. m
3
, the
spe
c
ific h
eat is
stetted
to 2
131
J.
(kg.
℃
), the
r
m
a
l
c
o
nduc
tivity i
s
s
e
tted to.138W.(m.
℃
), the vis
c
o
s
i
ty is
s
e
t to 52.18
mm
2
.s
1
.
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0
7674
Table 1. Mate
rials Prope
rti
e
s of Wet Bra
k
e Part
s
Parts
Y
oun
g’s
modulus/Mpa
Densit
y
/
kg·m-
3
Poisson’s
rati
o
Material name
Dual steel
plates
175000
7228
0.3
65Mn steel
Friction linings
175000
7228
0.3
65Mn steel
Friction
materials
1500
1450
0.25
Paper based f
r
iction material w
i
th
out
asbestos
4.3. The Bou
ndar
y
Conditions
Duri
ng braki
n
g, structu
r
al
comp
one
nts
of wet multiple disks prod
uce
coupli
n
g
modes
among va
rio
u
s
comp
one
n
t
s. Espe
cially
the friction
p
a
ir p
r
odu
ce
s
cou
p
ling m
o
d
e
s b
e
cau
s
e
o
f
excitation force, whi
c
h m
a
ke
s the brake to prod
uce
vibration noi
se. Since friction conta
c
t i
s
a
time-varia
nt
dynamic pro
c
e
ss, the
co
ntact relati
on
ship
between
the frictio
n
l
i
ning
s an
d st
eel
plates
sho
u
ld
be taken int
o
con
s
id
erati
on. It anal
yze
d
nonlin
ear p
r
e-stre
ss of friction pai
rs a
n
d
obtaine
d the
conta
c
t state
s
of the fri
c
tion. Then
it a
nalyze
d
the p
r
est
r
e
s
sed m
ode o
n
the b
a
si
s
of
modal ana
lysis system. The st
atic m
e
ch
ani
cal a
n
a
lysis
bou
nd
ary condition
s a
r
e p
r
ovide
d
as
follows. Fixed co
nstraints are im
po
sed
on ra
dial fri
c
tion lini
ngs
while th
e axi
a
l and ta
nge
ntial
movement
s
are free
and
the spee
d i
s
3
rad/
s.
Fi
xed co
nst
r
ain
t
s are imp
o
sed on
du
al steel
plates in
radi
al an
d tan
gen
tial dire
ction
while
t
he
axial moveme
nt i
s
free. Th
e 4
-
Mpa p
r
e
s
sure
is
applie
d on b
o
th sid
e
s. Th
e co
ntact int
e
rface bet
we
en du
al steel
plate and f
r
i
c
tion linin
gs i
s
defined a
s
t
he frictio
n
p
a
irs
and th
e
friction
coef
ficient is 0.3
.
In order t
o
facilitate the
conve
r
ge
nce
of analy
s
is a
nd
solution, i
t
se
le
cted
a
non-symmet
r
i
c
conta
c
t a
n
d
the
enha
nced
Lagrangi
an al
gorithm.
T
he pre
s
tre
s
sed
wet
mo
dal an
alysis bo
unda
ry co
nditi
on
s are provided as
follows. Base
d on the
static analy
s
is, th
e natural
freq
uen
cy of the entire mo
del
may be affect
ed
by
the stre
ss state.
Stati
c
a
nalysi
s
re
sults a
r
e
extracte
d from
boun
dary
co
ndition
s di
re
ctly.
Becau
s
e of the introd
ucti
on of asym
metric
fri
c
tio
n
conta
c
t, throug
h the co
mmand "mo
dopt,
uns
ym, 30,,, on", the firs
t 30-order modes
were extracted.
4.4. Compari
s
on bet
w
e
e
n
Wet Mod
a
l Resul
t
s and
Dr
y
Modal Results
The re
sult
s of static analy
s
i
s
we
re
sele
ct
ed as
initial
condition
s. After setting the rotation
spe
ed of the friction lining
s
, it performe
d
the m
odal analysi
s
of the effect of oil medium on the
bra
k
ing
sy
ste
m
.
The co
mp
arison analy
s
is results
of
dry
mo
dal brakin
g system
in
ai
r cont
ra
st
and wet bra
k
i
ng syste
m
in oil medium a
r
e sho
w
n in Fi
gure 6.
As
s
h
ow
n in
F
i
g
u
r
e
6
,
the mo
da
l fr
eq
ue
n
c
y
o
f
b
r
a
k
i
ng
system
in
the fluid
me
dium i
s
lowe
r than th
at in the ai
r. The d
e
clin
e
can
be in
te
rpreted i
n
the
followin
g
two aspe
cts. Fi
rst,
before
bra
k
in
g, the spa
c
e
betwe
en du
al
steel di
scs a
nd frictio
n
lini
ngs
are filled
with fluid; wh
en
bra
k
ing
start
s
, the addition
al mass of oi
l leads to
the
mass ch
ang
es of frictio
n
lining an
d du
al
steel plate.
Secon
d
, duri
ng braki
ng, the flui
d med
i
um co
upling
betwee
n
th
e fluid and
solid
affected the
modal cha
r
a
c
teristics of th
e bra
k
ing
system.
Figure 6. The
Contra
st Re
sults of Wet an
d Dry Mod
e
l
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TELKOM
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ISSN:
2302-4
046
Noi
s
e Anal
ysi
s of wet Multi
-
disc Bra
k
e Used Com
p
lex Eigenvalue (Tian-hon
g
Lu
o)
7675
4.5The res
u
lts of finite el
ement an
aly
s
is
Testing
results in
dicate tha
t
wet b
r
a
k
e
syste
m in
stabil
i
ty frequen
cy
is g
ene
rally 1
00-3
0
0
Hz
]
9
[
. Thu
s
, p
r
odu
ce
d n
o
i
s
e
belon
gs
to low-fre
q
u
ency vib
r
atio
n noi
se.
Co
nsid
erin
g th
e
influence of
brake oil
on t
he braki
ng
system stabilit
y, it extracted the first 30-order modal
s, as
sho
w
n in Fi
g
u
re 7. An ima
g
inary p
a
rt a
nd two
m
u
tua
lly opposite
real pa
rts o
c
curred at un
st
able
freque
nci
e
s.
The bla
ck d
o
ts rep
r
e
s
e
n
ted
the value
of the real p
a
rt a
t
the unstable
frequen
cie
s
i
n
the uppe
r po
rtion of Figu
re 7. As illustrated in
Figu
re 7, the un
stable mo
de
s belon
g to se
ven
orde
rs, who
s
e freque
nci
e
s are re
spe
c
tively
286.75 Hz, 756.32 Hz,
1056.8 Hz, 5435.4 Hz, 99
51
Hz, 11
126
Hz, and 1122
9 Hz.
Figure 7. The
Complex Eig
envalue
s of Braki
ng Syste
m
4.6. Numeric
a
l Analy
s
is
Resul
t
s
Table 2
sho
w
s the wet bra
k
e stiffne
s
s a
nd dam
pi
ng p
a
ram
e
ters of the stru
ctu
r
e, there i
s
a possibility that the equili
brium p
o
ints
are ap
pea
r when
0
Z
:
00
12
2
2
12
2
1
3
22
2
,0
,
,
0
,
,
0
,0
,0
,
,
0
)
xx
x
pp
pp
p
p
p
kk
k
k
k
k
k
（
+,
0
,
+
,
00
a
v
Bringin
g
the wet bra
k
e p
a
rameter into
Jaco
bi matrix, matrix eigenv
alue
s are
cal
c
ulate
d
,
as sho
w
n in
Table 2:
Table 2. The
Paramete
rs o
f
Wet Brake
Parameter Value
Parameter Value
P 33209N
12
23
kk
13000 N/s
13
mm
0.3Kg
12
23
cc
6N·s/m
2
m
0.5Kg
22
x
y
kk
9600N/s
13
kk
9600N/s
22
x
y
cc
4N·s/m
13
cc
6N·s/m
0
v
2.77m/s
Bring the
pa
rameter i
n
to the Jacobi ma
trix,
obtained the
ch
ara
c
te
ri
stic
valu
es which are
sho
w
n in Ta
b
l
e 3:
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ISSN: 23
02-4
046
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KA
Vol. 12, No. 11, Novem
ber 20
14: 76
68 – 768
0
7676
Table 3. The
Eigenvalue
s
of the Jacobi
Matrix
Number
Eigenvalue
Number
Eigenvalue
1
-7.50 + 180.1
2
i
7
3.98+276.05i
2 -7.50
-
180.12i
8
3.98-276.
05i
3 -3.02+792.0
4
i
9
-9.06+153.7
8
i
4 -3.02-7
92.04i
10
-9.06-1
53.78i
5 -7.86+267.4
5
i
11
-2.64+352.5
8
i
6 -7.86-2
67.45i
12
-2.64-3
52.58i
From the a
b
o
v
e results, it can b
e
seen t
hat
the eigen
values a
r
e di
vided into two
parts, a
real
part
an
d an i
m
agi
n
a
ry pa
rt. Imagina
ry eig
e
n
value
s
ap
p
eare
d
in
pa
irs.
Whe
n
t
h
e
cha
r
a
c
teri
stic value is the real part an
d smalle
r
than
zero, the syst
em is
in a sta
b
le state. Wh
en
the cha
r
a
c
teri
stic value
of the re
al
pa
rt is greater th
a
n
ze
ro, the
system is in a
flux state. Since
there a
r
e t
w
o
cha
r
a
c
teri
sti
c
value
s
of th
e real
pa
rt an
d gre
a
ter th
a
n
ze
ro, which
can
pre
d
ict t
h
e
system i
s
un
stable, the uns
table frequ
en
cy is 276.0
5
Hz.
4.7. The Con
t
ras
t
bet
w
e
e
n
Numerical
Analy
s
is and Finite Element An
aly
s
is
Table 4. The
Contrast Results
numerical
Finite element
Result
[9]
In the air
In the oil
276.05Hz
300.49 Hz
286.75 Hz
100-300
Hz
From th
e re
sult it can
seen that, the
unsta
ble fre
quen
cy resul
t
got from th
e finite
element
anal
ysis i
s
2
86.7
5
Hz
whi
c
h i
s
very
cl
o
s
e
to the expe
ri
mental result that is 2
76.
05
Hz,the
relative error is 4%
,the results in
dicate
d the re
liable of the p
r
opo
se
d meth
od.
5. Effect of
Wet Brake Para
meters on S
y
stem Stabilit
y
Wet bra
k
e n
o
ise is influ
e
n
ce
d by man
y
param
eters, tak
e
fric
tion
c
oeffic
i
ent,
brak
ing
spe
ed, bra
k
i
ng pressu
re,
friction linin
g and do
ubl
e plate stiffness for exam
ple. If the quality,
elasti
c an
d d
a
mping
prope
rties of the
sy
stem a
r
e the
same. Simul
a
tion paramete
r
s a
r
e
sh
own
in
Table 5.
Table 5. Simulation Para
meters
Effects of param
eters
Test paramet
er v
a
lues
Friction coefficie
n
t
0.15
0.3
0.45
0.6
Brake speed
（
ra
d/s
）
1
3 5 8
Brake pressure
（
Mpa
）
2
4 6 8
Friction lining stif
fness(EC)
0.8
1
1.2
1.4
Dual steel plate
stiffness(
EO
)
0.8 1
1.2
1.4
EC——F
riction material
Y
o
u
ng’s modulus,EC=1500MPa
EO——
Dual stee
l plate
Y
oung’s m
odulus, EO=175
000MPa
5.1. Effec
t
of Friction Coe
fficien
t on Brake Noise
Instability of Braki
ng sy
ste
m
, due to fri
c
tion,
re
sultin
g in bra
k
in
g
noise, thus
changi
ng
the trend of the friction coefficient on
the infl
uence
of system instabilit
y. Study the stabi
lity
impact of the
system, frictio
n
coeffici
ent wa
s incr
ea
se
d from 0.15 to 0.6, as sh
o
w
n in Figu
re
8.
From the Figure 8 it can be seen that, it
will continue
to the emer
gence of new
unstable
modes as increase
of the f
r
iction
coeffici
ent, causing i
n
stability orig
i
nal value of the real part of
compl
e
x eig
envalue freq
uen
cy increa
sing, ma
ki
n
g
the system
more u
n
sta
b
le. Therefore,
approp
riate to redu
ce the
friction coefficient betwe
e
n
friction linin
gs and the
steel plates
without
affecting the
bra
k
ing p
e
rfo
r
man
c
e
can redu
ce the bra
k
ing n
o
ise.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Noi
s
e Anal
ysi
s of wet Multi
-
disc Bra
k
e Used Com
p
lex Eigenvalue (Tian-hon
g
Lu
o)
7677
Figure 8. Effect of Friction
Coeffi
ci
ent on the Brake Sy
stem Stability
5.2. Effec
t
of Braking Spe
e
d on Bra
ke
Noise
Brake noi
se i
s
affected by
the spe
ed of the
bra
k
e. An
alyze the effe
cts on b
r
a
k
e
noise o
f
spe
ed. Figu
re 9 rep
r
e
s
ent
s the chan
ge
of brak
i
ng speed from 1rad/s to
8 rad/
s have a
n
effect
on the bra
k
e
noise.
Figure 9. Effect of Brakin
g S
peed on the
Brake Syste
m
Stability
The spee
d increa
se
s, wi
th the frequ
ency in
st
abili
ty of the real part of th
e com
p
lex
eigenvalu
e
d
e
crea
se
s, wh
ile the
syste
m
tends to
b
e
more stabl
e, but there i
s
no
signifi
ca
nt
redu
ction
of the re
al pa
rt of each
rotatio
n
sp
e
ed
corresp
ondi
ng to
the value. Th
at is, the sp
e
e
d
cha
nge
s of little effect on the bra
k
e n
o
ise.
5.3. Effec
t
of Braking Pre
ssure on
the
Brake
Noise
Brake pisto
n
is su
bje
c
ted t
o
bra
k
e fluid
pr
e
s
sure du
ri
ng braki
ng, which m
a
kes t
he dual
steel plate a
nd bra
k
e lini
ng friction d
e
cel
e
rate
a
n
d
eventually stop.
Figu
re
10 sh
ows brake
pre
s
sure ch
a
nge
s from 2M
Pa to 8Mpa, the bra
k
e
syst
em gene
rate
s the bra
k
ing n
o
ise.
Evaluation Warning : The document was created with Spire.PDF for Python.