TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.6, Jun
e
201
4, pp. 4861 ~ 4
8
6
7
DOI: 10.115
9
1
/telkomni
ka.
v
12i6.584
6
4861
Re
cei
v
ed
Jan
uary 23, 201
4
;
Revi
sed Ma
rch 1
9
, 2014;
Acce
pted April 3, 2014
Parameter Analysis of Fluid-Solid Coupling for Wet
Brake Disc
Xunjia Zhen
g
*, Tianhong
Luo, Ce Jia
Coll
eg
e of Mechantro
nics & Automob
ile E
ngi
neer
ing, Ch
on
gqi
ng Jia
o
ton
g
Univers
i
t
y
,
Chon
gqi
ng, P.R.Chin
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: xu
nji
a_zh
e
n
g
@
16
3.com
A
b
st
r
a
ct
Due to
the
p
oor co
nd
itions
of w
e
t brake
c
ool
ing
an
d
the hi
gh te
mp
erature
of the
w
o
rkin
g
character
i
stics, this pap
er inte
nde
d to intro
d
u
c
e the
oi
l fil
m
vados
e betw
e
e
n
the brak
e li
ni
ngs, consi
der
e
d
the var
i
atio
n
of volu
me
of gro
o
ves
on th
e fri
c
tion
plat
e,
an
d the
n
pr
op
ose
s
the thr
ee-d
i
mensi
ona
l tra
n
si
en
t
dyna
mic resp
o
n
se of flu
i
d-so
li
d cou
p
li
ng
mathe
m
atic
al
mo
d
e
l. By par
a
m
et
er an
alysis
of the d
i
sc transi
e
nt
thermal stress
field
distrib
u
tio
n
on th
e frictio
n
pl
ate,
an
d ac
cordi
ng to th
e r
eal
di
me
nsi
on
of the br
ake d
i
sc,
the distri
buti
on
of the te
mp
erat
ure a
nd th
e str
e
ss of the w
e
t
brake
disc
duri
ng the
brak
in
g
are a
n
a
l
y
z
e
d
, t
h
e
variati
on of temp
eratur
e field
and stress fie
l
d in fric
tio
n
pl
ate are obta
i
n
ed.
T
he data
curves show
n
the
temp
eratur
e an
d the stress ar
e cou
p
le
d.
F
i
n
a
lly, the r
e
sults
show
s that th
e
math
e
m
atic
al
mo
de
l is effecti
v
e
and feas
ib
le.
Ke
y
w
ords
: w
e
t brake, fluid-s
o
lid c
oup
lin
g, d
y
na
mic res
pon
se, thermal stress field
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
Becau
s
e
of t
he
cha
r
a
c
teri
stics of th
e strong
ability to re
si
st poll
u
tion, the la
rg
e brake
torque,
wea
r
-resi
s
tan
c
e a
n
d
long lifespa
n and so on,
the wet bra
k
e disc is wi
d
e
ly used in t
h
e
system
of me
cha
n
ical b
r
a
k
ing en
gine
eri
ng [1-2].
Ho
wever, du
ring
the
workin
g p
r
oce
s
s of b
r
a
k
e,
the wet b
r
a
k
e di
sc can
b
ear extrem
ely seve
re
we
ar, ri
sin
g
te
mperature
a
nd the
r
mal
e
l
astic
deform
a
tion,
resulting in
deteriorating the stability
of vehicl
e braki
n
g, impacting
on the
comfort
o
f
passe
nge
rs a
nd red
u
ci
ng its se
rvice life [
3
-5].
The fluid-stru
cture i
n
tera
cti
on of bra
k
e i
s
analy
z
ed b
y
the virtual simulatio
n
, which h
a
s
been
wid
e
ly
use
d
. Xing Y
u
tao ma
de
a
resea
r
ch on
the p
r
e
s
sure
field of the
co
ntact
surfa
c
e
on
the fully enclo
sed
wet multi
p
le disk b
r
a
k
e, the tr
ansi
e
nt temperatu
r
e field of fricti
on plate a
nd the
stre
ss field [6
]. Payvar P introdu
ce
s the
moving fluid
and
solid
wal
l
flowing b
o
u
ndary laye
r a
nd
thermal b
oun
dary layer the
o
ry into distri
bution of
the nume
r
ical cal
c
ulatio
n of the squ
a
re g
r
o
o
ve
fluid velocity field and temperature fi
eld [7
]. Zagrodzki R
carried out the experim
ent a
n
d
resea
r
ch on the distri
butio
n of temperat
ure field
an
d stre
ss field of the friction p
a
ir on the
we
t
multiple disk
brake [8].
This pa
per e
s
tabli
s
he
d th
e fluid
-
soli
d
coup
lin
g math
ematical
mo
d
e
l of
wet-typ
e
b
r
a
k
e
friction pl
ate, throug
h the
example to
analyze of
the wet mult
iple di
sk
bra
k
e of fluid
-
solid
cou
p
ling dyn
a
mic re
spo
n
s
e,
aim
ed at
improvin
g
th
e a
c
cura
cy o
f
the mathe
m
atical
mod
e
l of
dynamic
re
sp
onse of the brakin
g system,
and then del
ved into wet bra
k
e fri
c
tion
mech
ani
sm.
With the
cont
inuou
s d
e
vel
opment
and
prog
re
ss of
scien
c
e
and
te
chn
o
logy, the
run
n
ing
spe
ed of ma
chin
ery and
equipm
ent is con
s
tantly
improve
d
, wh
ile the wet b
r
ake ope
ratio
n
con
d
ition i
s
getting
wo
rse an
d
wo
rse
and
the
stu
d
y of the
th
eory
of the
wet b
r
a
k
e
fri
c
tion
mech
ani
sm i
s
not
clea
r. Th
erefo
r
e,
it i
s
i
m
perative to
con
d
u
c
t the
t
heoretical
research
of the t
he
wet bra
k
e flui
d-st
ru
cture int
e
ra
ction.
2. Structu
r
e
and Sy
stematic Principle of We
t Br
a
ke Disc
Wet multiple
brake di
sk is
mainly com
p
osed of
brake sh
ell, bra
k
e
piston, fri
c
tio
n
plate,
oil se
al an
d
end pl
ate, etc. Several
fixed and
rotating braki
n
g
friction
plates a
r
e m
u
tu
ally
staggered
and installed in
the br
ake
casing filled with
cooli
ng the
oi
l seal;
while the fixed fricti
on
plates a
r
e
col
l
ected to the
bra
k
e
shell b
y
the spli
ne,
and the rotating frictio
n
sli
c
e
s
rotatin
g
with
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4861 – 4
867
4862
the hu
b, a
r
e l
i
nke
d
with th
e hu
b by th
e
internal
splin
e. Wh
en th
e
oil liqui
d fro
m
the b
r
a
k
e
va
lve
flows into th
e bra
k
e, the bra
k
e pi
ston pre
s
ses t
he
bra
k
ing fri
c
tio
n
plates in
stalled crisscro
ss,
whi
c
h m
a
kes the rotating
friction
plate
s
moves slo
w
l
y
till stop, th
us a
c
hi
eving
the goal
of t
h
e
bra
k
e. The
structu
r
e di
agram of
wet bra
k
e is
sho
w
n i
n
Figure 1.
2
3
4
5
6
7
8
9
1
0
1
1
1
2
1
3
1
4
1
Figure 1. Structure
Diag
ra
m of Wet Bra
k
e
Nome
ncla
ture
ij
total stress of bra
k
es
q
brake fluid velocit
y
ij
Kronecker s
y
mb
ol
1
h
,
2
h
friction linings a
nd stat
ic friction piece sub-
volume ratio of th
e total
p
excess pore pr
essure of oil
Poisson's ratio of oil
a
pore
fluid thermal expansion coeff
i
cient
c
a
coefficient of frict
i
on pair thermal
expansion
K
bulk modulus
K
bulk modulus of the brake vice
l
k
fr
iction coefficien
t of per
meability
G
Lame constant of
friction pair.
g
acceleration due to gravit
y
j
b
force in spatial coordinate directio
n
T
D
temperatu
r
e gr
ad
ient effecting on seepage
i
displacement in
spatial coordinate direction
2
p
V
heat flo
w
rate
of f
l
uid
j
relative displacement in spati
a
l coordinate
direction
1
p
k
,
2
p
k
,
k
friction linings, the stat
ic friction piece and
brake fluid of hea
t
transfer coefficient
1
density
of the f
r
iction linings,
C
specific heat cap
a
city
of t
he br
ake oil
2
density
of the f
r
iction plate
0
T
initial temperatur
e
density
of the flui
d
T
temperatu
r
e vari
ation
Hamiltonian oper
ator
0
initial brake fluid
density
V
assuming friction
pair volume
0
l
initial porosity
of
the brake friction
1
p
V
volume of the fr
iction lining
c
V
volume of the gr
oove
2
p
V
volume of the static friction piece
represents the
o
v
erall response
1
s
a
thermal expansion coeffici
ent of friction linings
l
friction porosit
y
2
s
a
static friction piece coefficient
effective stress vector of therm
a
l expansion
3. D
y
namic
Resp
onse o
f
Fluid-Solid Coupling Ma
thema
t
ical M
odel
Becau
s
e
of e
x
isting a l
a
rg
e num
ber of
groove
s
i
n
wet bra
k
e
di
scs, con
s
ide
r
in
g that the
friction b
r
a
k
in
g syste
m
exi
s
ts in th
e two
-
pha
se
m
edi
u
m
as th
e form of fluid-structure inte
ra
ction
term, assumi
ng that the friction pai
rs
a
r
e of isot
ropy
linear ela
s
ti
c material, wh
en brakin
g, two
pha
se flow of
the liquid an
d the solid
are in
a heat b
a
lan
c
e, and t
he brake linin
gs suffer sm
all
deform
a
tion d
u
ring b
r
a
k
ing,
and its co
nsti
tutive relation
can be exp
r
e
s
sed a
s
follo
w:
1 annular
gea
r
2
static friction plat
e
3
d
y
namic friction plate
4.6.7.12
obturating
ring
5 return
s
p
ri
ng
8 cy
linder
bod
y
9 piston
10 oil-
in
11 terminal
pad
13 gear
ring
14 w
h
eel
hub
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Param
e
ter Analysi
s
of Fluid-Solid
Coupl
ing for Wet Brake
Disc (Xu
n
jia Zhen
g)
4863
,1
1
2
2
,,
2
0.
5
2
ij
ij
kk
ij
c
i
j
ij
ij
ij
ij
j
j
i
i
r
i
ij
i
j
j
i
vG
GK
a
T
v
p
b
(1)
The brake fluid-he
at cou
p
li
ng equ
ation o
f
motion
：
2
,,
,
1
1
2
2
12
ij
j
i
i
c
i
i
i
i
G
Gp
K
a
T
v
(2)
Assu
ming th
e
volume of f
r
i
c
tion p
a
ir i
s
V
，
inclu
d
ing th
e volume
of the fri
c
tion lini
ng
1
p
V
,
the static frict
i
on piece volume
2
p
V
and the
volume of the groove
c
V
，
The relation
shi
p
among the
four ca
n be e
x
presse
d as:
12
11
1
1
pp
c
VV
V
V
Vt
V
t
V
t
V
t
t
(3)
So the volume cha
nge of friction pai
r ca
n be written i
n
the follow form
：
12
11
2
2
12
1
2
11
1
(1
)
(
1
)
3
pp
pp
pp
p
p
VV
Tl
l
P
lh
a
h
a
l
Vt
t
t
K
K
t
K
K
t
m
(4)
Whe
r
e,
1
1
1
000
m
，
According
to
t
he solid mo
del
1
0.
25
h
、
2
0.
75
h
。
Fricti
on
pair’
s volume will
change ac
cordi
ngly
when the temperature, oil
pressure and eff
e
ctive stress of
groove cha
n
g
ed.
The variatio
n of groove vol
u
me be exp
r
e
s
sed a
s
:
1
c
V
Tn
p
qn
a
Vt
t
K
t
(5)
Simultaneo
us Equation
(3), (4) a
nd (5),
the
flow
con
t
inuity equati
on may be
written in
the following form:
11
2
2
12
1
2
(1
)
(
)
11
(1
)
3
pp
pp
p
p
cT
ql
a
l
h
a
h
a
tt
ll
l
p
l
K
KK
t
K
K
t
m
(6)
The heat flux is expre
s
sed
as a friction l
i
near
fun
c
tion
of forces
whi
c
h a
c
t on the brake;
the equatio
n of fluid motion can b
e
expressed a
s
:
l
T
k
qp
w
D
T
gl
(7)
Brake fluid ha
ve a signifi
ca
nt impact to the br
ake thermal co
ndu
ctivity,
the heat flow rate
can b
e
define
d
as:
11
2
2
0
(1
)
(
1
)
(
)
Fp
p
T
qq
C
T
h
l
k
h
l
k
l
k
k
T
T
T
D
p
(8)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4861 – 4
867
4864
Assu
med
the
soli
d-liq
uid
fluid the
r
mal
e
quilibri
um
bet
wee
n
fri
c
tion
and
brake, th
e he
at
balan
ce e
qua
tion can b
e
e
x
presse
d as:
11
1
1
1
1
00
()
()
pp
p
p
p
p
c
F
c
VC
VC
V
C
T
qT
T
a
K
q
T
T
K
a
Vt
t
(9)
The frictio
n
p
a
ir and b
r
a
k
e
fluid are in m
a
ss co
nserva
tion:
11
22
0
0
()
pp
pp
c
V
Vt
V
Vt
V
q
Vt
(10)
Simultaneo
us Equation (8
), (10), the h
e
a
t
balance equ
ation ca
n be
expre
s
sed a
s
:
11
1
2
2
1
0
2
(1
)
(
)
(
)
()
pp
p
p
c
T
lh
C
h
C
l
C
T
T
K
a
a
K
q
tt
CT
q
C
q
T
k
T
k
T
D
p
(11)
Brake fluid eq
uation of stat
e is obtain
ed
as follo
ws:
0
ex
p
(
/
)
aT
p
K
(12)
0
(/
)
aT
p
K
(13)
Acco
rdi
ng to Equation (11), (12), (1
3), a
nother fo
rm can be obtai
ne
d:
2
11
1
2
2
1
0
01
1
2
2
(1
)
(
)
(
)
(/
)
(
)
(
)
pp
p
p
c
pp
T
lh
C
h
C
l
C
T
T
K
a
a
K
q
k
T
tt
CT
q
a
T
p
K
C
qT
k
h
k
h
k
l
T
D
p
(14
)
The ch
ang
es
of groove po
rosity can g
e
t according to
Equation (3), (4):
11
2
2
1
1
22
1
1
22
1
1
22
1
1(
1
)
(
)
c
pp
pp
pp
pp
Ka
lK
T
l
p
lh
a
h
a
th
K
h
K
t
h
K
h
K
t
h
K
h
K
t
(15)
The Equatio
n
(15)
can b
e
simplified as:
0
00
1
1
2
2
11
2
2
1
1
2
2
11
2
2
1
1(
1
)
(
)
c
pp
pp
p
p
pp
Ka
l
K
ll
l
h
a
h
a
T
p
h
K
hK
h
K
hK
h
K
hK
(16)
The po
ro
sity gradi
ent of friction pai
r ca
n
be expre
s
se
d as:
0
01
1
2
2
11
2
2
11
2
2
11
2
2
1
1(
1
)
(
)
c
pp
pp
p
p
pp
Ka
l
K
ll
h
a
h
a
T
p
hK
h
K
hK
h
K
hK
h
K
(17
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Param
e
ter Analysi
s
of Fluid-Solid
Coupl
ing for Wet Brake
Disc (Xu
n
jia Zhen
g)
4865
Simultaneo
us the Equation
(14) a
nd (1
7):
2
11
1
2
2
1
0
00
1
1
2
2
01
1
2
2
11
2
2
11
2
2
(1
)
(
)
(
)
(/
)
(
)
(
)
1(
1
)
(
)
pp
p
p
c
Tp
p
c
pp
pp
pp
Te
lh
C
h
C
l
C
T
T
K
a
a
K
q
k
T
tt
CT
q
a
T
p
K
C
qT
T
T
D
p
k
h
k
h
k
T
Ka
K
lh
a
h
a
T
h
K
hK
h
K
hK
0
11
2
2
1
pp
l
p
hK
h
K
(18)
Overall, the Equation (18
)
is the wet b
r
a
k
e fri
c
tion pai
rs fluid
-
solid couplin
g equat
ion.
4. The Nume
rical Analy
s
is of Fluid-Structur
e Inter
action
In orde
r to te
st the a
c
cura
cy of the e
s
tab
lishment of
wet he
at flow fluid-soli
d
cou
p
ling
model on the
brake frictio
n
pair, this se
ction will
make
a compa
r
ativ
e analysi
s
of the data of the
wet b
r
ake e
m
erg
e
n
c
y brakin
g mea
s
u
r
ed by the n
u
m
eri
c
al
cal
c
u
l
ation an
d ex
perim
ent of h
eat
flow and
solid
coupli
ng mo
del.
Setting a ce
rt
ain wet bra
k
e actu
al stru
cture
as
an e
x
ample, the related p
a
ram
e
ters
of
cal
c
ulatio
n an
d analysi
s
are sho
w
n in T
able 1 to 3. The total bra
k
i
ng time is 3.5
s
and the o
r
ig
inal
bra
k
ing
spe
e
d
is 50
km/h
Table 1. Wet Brake Ch
ara
c
teristic Pa
ram
e
ters of e
a
ch
Comp
one
nt Material
s
Parameter
3
/(
)
kg
m
/
E
GPa
11
/(
)
Wm
K
1
/(
)
cJ
k
g
K
1
/
aK
D
y
namic friction plate
7900
210
0.3
42
480
1.27e-5
Friction linings
1125
0.3
0.25
0.241
385.2
1.3e-5
Static friction tablets
7900
210
0.3
42
480
1.27e-5
Brake oil
857
—
—
0.126
9.85
3e-4
Note: the b
r
ake viscosity
62
1
20
1
0
(
)
ms
Table
2. Geometrical Dimens
ions
mm
Parts
Inside diameter
Major diameter
Thickness
D
y
namic friction plate
32
155
3
Friction linings
115.3
155
1.56
Static friction tablets
111.4
156
2.5
Table 3. Cal
c
ulation Para
meters
Variable
G
K
1
p
K
2
p
K
0
T
l
T
D
Parameter
1
4.1
0.2
175
293
0.253
1.7e-11
Unit
M
pa
Gp
a
Gp
a
Gp
a
K
—
2
/
ms
℃
Duri
ng
brakin
g, sin
c
e
he
at gen
erate
d
i
s
much
hi
ghe
r than th
e
spe
ed of tran
sfer to the
internal, thi
s
make
s th
e fri
c
tion
su
rface
temperature
is hi
ghe
r tha
n
the inte
rnal
, and the
r
e i
s
a
large
axial te
mperature
gradient. With t
he pa
ssag
e o
f
time, the he
at impa
ct on
the tempe
r
at
ure
field is decreased with the input inte
nsity dec
rea
s
e
s
. Becau
s
e the surfa
c
e of the coo
ling
con
d
ition
s
we
re better,
th
e disc su
rface
t
e
mpe
r
ature d
e
crea
sed
rapi
dly.
Finally, the tem
peratu
r
e
of axial points gradu
ally uni
fied.
As it ca
n be
see
n
from
the cu
rve
s
i
n
Figu
re 2,
dynamic fricti
on pie
c
e
out
er h
a
s
particula
rly tremend
ou
s ch
ange
s in tem
peratu
r
e flu
c
t
uation
s
, due
to the larg
e li
near vel
o
city
at
external
of fri
c
tion di
sk, a
nd the tu
rbul
ence of
b
r
a
k
e oil ha
s
a relatively larg
e impa
ct on
the
temperature;
The oth
e
r h
a
nd, due to
th
e insi
de fri
c
ti
on di
sk
sm
all
linear velo
city, brake oil e
x
ists
only within th
e narro
w g
r
o
o
ve, bra
k
e te
mperature fl
u
c
tuation
s
i
s
smaller. Fin
a
ll
y, and the brake
temperature i
s
stabl
e at about 134
C
wh
en the bra
k
e
time to reach
3.26s, and t
he bra
k
e di
sc
temperature
stabili
zed at b
e
twee
n 122
C
and 134
C
.
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ISSN: 23
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TELKOM
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KA
Vol. 12, No. 6, June 20
14: 4861 – 4
867
4866
Figure 2. Different Point T
e
mpe
r
ature a
t
r
=11
4
.
5
mm
Figure 3. Different Point Radial Stre
ss a
t
r
=11
4
.
5
mm
From the Fi
g
u
re 4, an
othe
r discove
r
y is gai
ned. In th
e conta
c
t are
a
of the disc, due to
the com
b
inati
on effect of th
e bra
k
in
g p
r
e
s
sure,
fri
c
tion
force and th
e
r
mal
stre
ss,
a
t
the begin
n
in
g
of bra
k
ing,
with the tem
peratu
r
e
risi
ng, the
pa
rt
s of the
eq
uivalent st
re
ss val
ue a
n
d
the
maximum
stress ha
s
rea
c
hed o
r
ex
ce
ed the m
a
terial yield limit
stre
ss. Although it
doe
s not
rea
c
h the
strength of the
material limit, the parti
al pl
astic d
e
form
a
t
ion will occu
r, further m
o
re,
with b
r
a
k
ing i
n
crea
sing
an
d the temp
erature
de
cr
e
a
s
ing, the
co
rresp
ondi
ng
circulatio
n of st
ress
add
s and th
e fatigue cra
ck d
a
ma
ge
accumul
a
tion
of plastic d
e
formatio
n will lead to fatigue
cra
c
k. Ho
we
ver, if the brakin
g strengt
h is inten
s
ifi
ed in a
singl
e eme
r
gen
cy
bra
k
e, an
d
the
temperature
gradi
ent is bi
g, which may
result t
hat the hermal
stre
ss of
the fricti
on su
rface may
excee
d
the strength of
the steel
pl
ate m
a
terial limit, a
t
this time, the outer space of the mate
rial
will
suffer gre
a
t dam
age
a
nd the
n
the
i
n
itial cra
c
k h
appe
ns.
Com
pare
d
with Fi
gure
2
an
d 3,
we
can cl
ea
rly see that the circu
m
fere
ntial
stress is
mu
ch larger tha
n
the radial
stre
ss. With the
increasing number of
br
ake, the alternating therm
a
l
stress
will l
e
ad to the
common brake
disc
cra
c
k in a
c
tu
al situation, t
he ra
dial the
r
mal fati
gue
crack. In the ca
se of
the u
n
reasona
ble of
the
bra
k
e, the
stress of the b
r
ake
ca
nnot a
pply t
he force evenly on t
he on fri
c
tion
lining, and t
he
conta
c
t area
of the conta
c
t pressu
re
wi
ll be more
u
n
rea
s
o
nabl
e, seri
ou
sly, which i
s
ea
sy
to
cau
s
e the the
r
moel
asti
c instability pheno
menon.
Figure 4. Different Point Ci
rcu
m
fere
ntial Stress at r =1
14.5mm
In the Figure
2~4, we ca
n find that the brak
e disc tem
peratu
r
e field
and stress field are
cou
p
led. At th
e begi
nning
o
f
the bra
k
e, t
he di
sc te
mp
eratu
r
e
rise
s f
a
st, and
at th
e sa
me time t
h
e
stre
ss also
ch
ange
s fast. When the temp
eratu
r
e of th
e
disc tre
n
d
s
to uniformity, the stre
ss of the
plate on the same axial se
ction al
so ha
s the t
enden
cy to be more con
s
i
s
tent. While more
clo
s
er
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TELKOM
NIKA
ISSN:
2302-4
046
Param
e
ter Analysi
s
of Fluid-Solid
Coupl
ing for Wet Brake
Disc (Xu
n
jia Zhen
g)
4867
to the surfa
c
e of the friction, more p
r
omi
nently th
e temperature
cu
rve beh
aves, and th
ese
fluctuation
s
a
r
e d
ue to
the
excha
nge
effect b
e
tw
e
en t
he h
eat
stro
ke of movin
g
h
eat source
a
nd
the heat con
v
ection. With
the time extensi
on an
d the de
crea
sin
g
stre
ngt
h
of the
inputting heat
flow, the tendency of the freque
ncy of the fluctuatio
n
is sho
w
ed from fast to slow. This ki
nd
of
heat stro
ke
and uneve
n
temperatur
e
distrib
u
tion
o
f
the corre
s
p
ondin
g
the
r
m
a
l st
re
ss led
to
fluctuation
s
, whi
c
h will
cau
s
e thermal sh
ock and the
r
mal fatigue.
5. Conclusi
on
(1) Thi
s
p
a
p
e
r
sets up
th
e wet brake
fricti
on
pair o
f
fluid-solid
couplin
g math
ematical
model, taki
n
g
the a
c
tual
size, materi
al
s, oil gr
oove
form an
d th
e influen
ce
o
f
fluid-structu
r
e
cou
p
ling
effe
ct into
co
nsi
deratio
n, whi
c
h
ca
n
b
e
tter respon
se
the dyn
a
mic
prop
erty of t
he
temperature f
i
eld, stre
ss fie
l
d and seep
a
ge fiel
d in the
braki
ng p
r
o
c
ess of the we
t brake.
(
2
) In
th
e pr
oc
es
s o
f
br
ak
in
g
,
th
e
fr
ic
tion
p
a
i
r
e
x
is
ts
s
t
r
o
ng
the
r
ma
l sh
oc
k
,
a
n
d
th
e
br
ak
e
disc tem
perature
field,
stre
ss an
d
see
p
a
ge fiel
d
have
the coupli
ng
relation
ship, v
a
rying f
r
om
the
time c
o
ns
tant
ly.
(3) Th
e theoretical cal
c
ul
ation data cu
rves is in
acco
rd with the cla
ssi
c tren
d data, thus it
sho
w
s that
th
e e
s
tabli
s
hm
ent of th
e
we
t bra
k
e
fl
uid
solid
coupli
n
g math
ematical mo
del
of t
h
is
pape
r is a
c
cu
rate in ce
rtain
degre
e
.
(4)
This
re
se
arch con
s
ide
r
s th
e oil film
betwe
en the
bra
k
e lini
n
g
s
state
of m
o
tion a
s
see
pag
e, and
gives a
n
exa
m
ple of fluid
-
solid
co
upling
for wet brake disc. Th
rou
gh an
alysi
s
a
n
d
validation, thi
s
m
a
y con
c
lu
de that
the
propo
se
d
meth
od m
a
kes go
od u
s
e
of th
e
advanta
g
e
s
of
the wet bra
k
e
disc fo
r heav
y truck, an
d g
e
ts an efficie
n
cy and a
c
cu
racy math
em
atical mod
e
l.
Ackn
o
w
l
e
dg
ements
This
work was finan
cially
supp
orted
b
y
a Grant from the Nati
onal Natural
Scien
c
e
Found
ation o
f
China
(5
13
7551
9), an
d
Cho
ngqin
g
Ji
aotong Unive
r
sity
po
stgra
duate
e
d
u
c
at
ion
Innovation Fu
nd proj
ect.
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GUAN Di-hu
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An Over
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