TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.6, Jun
e
201
4, pp. 4876 ~ 4
8
8
1
DOI: 10.115
9
1
/telkomni
ka.
v
12i6.584
8
4876
Re
cei
v
ed
Jan
uary 26, 201
4
;
Revi
sed Ma
rch 2
2
, 2014;
Acce
pted April 6, 2014
Structural Intensity Simulation of Bolt Joints in
Vibration Environment
Yongjuan Zh
ang*, Guo
y
ing Zeng, De
ngfen
g Zhao
Schoo
l of Man
u
facturin
g Scie
nce an
d Eng
i
n
eeri
ng,
South
w
est Univers
i
t
y
of Science a
n
d
T
e
chnol
og
y,
Mian
ya
ng; 6
2
1
010; Ch
in
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: zhang
yo
n
g
ju
anj
uan
@1
63.c
o
m
A
b
st
r
a
ct
T
he pap
er a n
onli
n
e
a
r mod
e
l
of bolt joi
n
ts structur
e in vi
bra
t
ion env
iron
me
nt is built, incl
u
d
in
g the
friction, contac
t and so
on co
mp
lex n
o
n
li
n
e
a
r factors. Structure Intensity
(SI)
of it is cal
c
ulate
d
by F
i
n
i
te
Ele
m
e
n
t Meth
od (F
EM) as
an a
ppr
oach
for the state
id
ent
ificati
on of bolts
j
o
ints
str
u
cture in vibration
envir
on
me
nt. T
he p
l
ots of the
structur
e inte
n
s
ity vector un
d
e
r differe
nt
tigh
tenin
g
torq
ue
w
e
re obtai
ne
d
an
d
show
ed th
e SI chan
ges
of b
o
lt jo
ints struct
ure w
i
th differ
ent tight
eni
ng
torque,
and s
h
ow
ed the
en
er
gy
distrib
u
tion
an
d trans
missi
on
at different tig
h
teni
ng torq
ue.
In order to c
o
mp
are, T
he SI
ma
ps of of ri
gi
d
conn
ected b
e
a
m
at differe
nt tighten
in
g torqu
e
also w
e
re o
b
tain
ed.
Ke
y
w
ords
: structural i
n
tensit
y, bolt join
ts, finite elem
ent, power flow,
vibration e
n
viro
n
m
ent
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
The joints fo
rm of mech
a
n
ical a
s
semb
ly is so various, in
cludin
g
the sectio
n of the
degree
of joi
n
ts, bolt
joint
s
, Pin j
o
ints,
weldi
ng,
cem
entation and
so on.
T
he b
o
lt
joints
is
o
ne
multi-scal
e n
online
a
r p
r
obl
em amon
g all
of the jo
ints
above. The di
scontinu
o
u
s
of the stru
cture's
local
stiffness and d
a
mpi
ng is cau
s
e
d
by the
existen
c
e of joi
n
ts. The rel
a
tive sliding
on
tangential
of the joint
s
an
d
the gap
se
pa
ration a
nd
im
pact o
n
the n
o
rmal m
a
y arise in Vib
r
atio
n
con
d
ition
s
. Friction a
nd
cle
a
ran
c
e
are th
e two typical
nonlin
ear
out
come
s of b
o
lt joints, on
ce i
t
's
in vibration e
n
vironm
ental.
Unde
r the d
o
minat
ion of
these b
ehavi
o
rs, a
bund
an
t and intricat
e
nonlin
ear ph
e
nomen
on
will
occu
r i
n
the
dynamic re
sp
onse of
the
b
o
lt joints [1].
Many
schola
r
s
studie
d
the cha
r
a
c
teri
stics of the bolt
joints
in re
cent years. The definition
and co
nst
r
u
c
tor
method
s of nonline
a
r mod
e
l have been
prop
osed by
Peshe
c
k and
Pierre [2], an
d they also di
d a
prima
r
y study
on the nonlin
ear mod
a
l an
alysis by
the way of The finite element method, and this
method is p
r
omoted to pi
ece
w
i
s
e-li
nea
r system by
Jian
g [3]. In
orde
r to find out the statistic
feature for th
e warning of
the failure of bolt
joints, the method
of combinin
g the nume
r
ical
simulatio
n
a
nd expe
rime
nt is ado
pte
d
by
Den
g
F
eng Zh
ao. T
he effect
s o
f
the nonlin
ear
cha
r
a
c
teri
stics of
bolt joi
n
ts on
the vib
r
ati
on re
sp
on
se paramete
r
s
a
r
e dee
ply
re
sea
r
che
d
by
XueQian
Che
n
and othe
rs.
As for the elo
ngated
stru
cture,
the prop
agation of wa
ve is an impo
rtant form of moveme
nt under ex
citation, and it will bee
n cha
nged by the
n
e
w cra
ck in th
e stru
cture which
carrie
d e
n
e
rgy throu
gh vibration
wave
in dissemin
ation. So
the distribution an
d tran
smi
ssi
on
of vibration e
n
ergy have be
en ch
ang
ed. Therefore, th
e vibration
po
wer flo
w
ch
aracteri
st
ics of
damag
ed st
ru
ctu
re ca
n be stu
d
ied thro
ugh t
he pro
pag
atio
n of vi
bration energy, and then the po
siti
on and
size o
f
damag
ed st
ru
cture
can b
e
diagn
osed. Beca
use of
the advantage
s
of the stru
cture vibration in
p
owe
r
flow me
thod, it is more and mo
re widely us
e
d
in engin
eeri
ng p
r
acti
ce. The p
o
we
r flow me
t
hod is u
s
e
d
a
s
analy
s
is too
l
in vibration contro
l research sin
c
e its the
o
ry wa
s creat
ed by H.G.D.
Goyder
a
nd
R.G.White [4
-6] in 1980. By meas
uri
n
g the transfe
r function i
s
not enough
to
provide
sufficient informati
on to dete
r
m
i
ne the
tran
sf
er path
w
ay
whe
n
a conti
nuou
s st
ru
cture
vibration
tran
smissio
n
fro
m
poi
nt to
p
o
int was
stud
ied. In
ord
e
r
to take
effe
ctive mea
s
u
r
e
s
to
improve the
vibration control, the powe
r
flow we
re st
udied wi
del
y in recen
t
years. Th
e m
a
in advanta
g
e
s of po
wer fl
ow metho
d
are that the force and
the spe
ed in the stru
ct
ure
have
b
e
e
n
con
s
id
ere
d
, so doe
s the
impedan
ce
ch
a
r
a
c
teri
stic in the stru
cture. Power i
s
a
singl
e value
whi
c
h can giv
e
an ab
solute
measu
r
e of vibration tran
smissi
on.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Structu
r
al Intensit
y Sim
u
lation of Bolt Join
ts in Vibrati
on Envi
ronm
ent (Yongj
ua
n Zhang
)
4877
2. Computati
onal Metho
d
s of
S
truc
tur
a
l Intensit
y
[7]
The con
c
ept
of structu
r
al
intensity wa
s in
tro
duced
in 1970 to the structu
r
e
aco
u
sti
c
fiddle [8-9] a
nd Pavic dev
elope
d SI formula [10]. Th
e SI focus o
n
the stru
ctu
r
e internal
stress
and the pa
rti
c
le motio
n
. SI was d
e
fined
as po
we
r
pe
r unit width in
a spe
c
ified d
i
rectio
n of flow.
The SI can
a
s
the
po
we
r flow d
e
n
s
ity, which i
s
a ve
ctor a
nd
sho
w
s the en
ergy’s
magnitud
e
a
n
d
dire
ction of a point on the structu
r
e. The
SI of th
ree-di
mensi
onal
structure is vect
or of time und
er
norm
a
l ci
rcu
m
stan
ce
s, which i
s
e
qual
to the po
we
r
flow pe
r unit
area
of the vi
bration
struct
ure
and its matrix
form is:
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
t
y
t
v
t
v
t
t
t
t
t
t
t
t
t
i
i
i
z
y
x
z
zy
zx
yz
y
yx
xz
xy
x
z
y
x
(1)
、
Whe
r
e
σ
l(t
)
τ
nl(t)a
nd vl(t)are the velo
ci
ty and stre
ss
respe
c
tively at time t.
Variou
s
state
variabl
es a
r
e
the h
a
rm
oni
c vibrat
ion
at t
he
same
fre
q
uen
cy in th
e
analysi
s
of harmoni
c
resp
on
se,
whi
c
h i
s
expre
ssed a
s
a pl
ura
l
form. T
he S
I
in the f
r
equ
ency
domai
n
is
divided into two pa
rts. On
e part is a
consta
nt
value, the se
ctio
n of whi
c
h i
s
un
cha
nge
d
.
If
dampin
g
i
s
zero, the
n
tha
t
part i
s
al
so
ze
ro. An
oth
e
r p
a
rt i
s
th
e
amou
nt of
chang
es with
two
times of harm
onic fre
que
ncies and di
re
ction.
The SI in
the frequen
cy domain can
be defined a
s
follows
:
z
y
x
z
zy
zx
yz
y
yx
xz
xy
x
z
y
x
y
v
v
I
I
I
Re
2
1
(2)
*
*
*
Re
2
1
z
y
x
z
zy
zx
yz
y
yx
xz
xy
x
z
y
x
y
v
v
I
I
I
(3)
Whe
r
e th
e E
quation
(2
) i
s
ch
angin
g
p
a
r
t, Equation
(3) i
s
a
con
s
tant value
po
rtion,
σ
l,
τ
nl i
s
multiplexing
stre
ss as fre
quen
cy dom
a
i
n, vl* is
the conj
ugate of
the spe
ed an
d Re rep
r
e
s
e
n
ts
the sele
ction
of the real pa
rt of complex
numbe
rs.
3. Finite Element Model
3.1. Model Introdu
ction.
The sim
p
lification and
me
sh
mod
e
l
is a
n
importa
nt
step in finite element mod
e
ling,
will
dire
ctly affect the
accura
cy and the computation
a
l
scale
re
sult
s. In the pape
r, the model
is
comp
osed of
a pair
of be
ams a
nd two
bolts of M6
×25. The b
o
lt scre
w an
d st
ructu
r
al
ch
a
m
fer
are ig
nored, the nut an
d b
o
lt as an o
r
g
anic
whol
e,
a
nd sh
own in
Figure 1. In o
r
de
r to refle
c
t
th
e
nonlin
ear b
e
havior of bolt
joints structu
r
e of t
he co
n
t
act and fri
c
tion, use the
contact mo
del
of
finite elemen
t analysis b
y
establishi
n
g
cont
a
c
t pairs b
e
twe
e
n
conn
ecte
d pieces, nut and
con
n
e
c
ted. T
he fri
c
tion
be
tween
the
co
ntact
su
rface
s
m
u
st
be
ta
ken
into
a
c
co
unt. At la
st, the
Coul
omb fri
c
tion model of simple and a
p
p
lica
b
le is
ta
ken. The mod
e
l mesh i
s
sh
own in Fig
u
re
2.
In orde
r to study com
parin
g with
lap joint
structu
r
e
with bolts,
this p
aper h
a
s
establi
s
h
ed the
finite
ele
m
ent model
of rigi
d co
nne
cted be
am. And
the
diffe
ren
c
e
with b
o
lt
con
n
e
c
tion
structu
r
e
finite
element
mo
del is
that
there i
s
n
o
friction
b
e
twee
n a p
a
ir
of beam, inst
ead of usi
ng the adh
esive (that
is, a pair
of form the combinatio
n).
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: 4876 – 4
881
4878
Figure 1. The
Model of the Bolt Joints St
ructu
r
e
Figure 2. The
Finite Element Model
3.2. Model Material and
Boundary
Conditions.
The
releva
nt
material
con
s
tants a
r
e
sh
o
w
n i
n
Ta
ble
1
, and
bolt
s
a
r
e M
6
× 2
5
standa
rd
steel
bolts. E
x
ternal lo
ad i
s
: lap
bea
m fi
xed at on
e e
n
d
, and
the ot
her
end
of th
e ap
plied fo
rce of
10N a
nd 50
0
H
z
sine ex
citation, whi
c
h the po
sition is
point 1 in Fig
u
re 6.
Table 1. The
Material
Con
s
tants
materia
Y
oun
g’s modulus (Gpa
)
Poisson’s ratio
Densit
y
(kg/
3
m
)
Damping
steel 210
0.23
7850
0.0002
3.3. The Bolt Tightening
Torque Simulated b
y
Pr
estr
a
in
Bolt tightening torque is tightene
d the bolt oc
curs d
u
ring the
stre
tching force g
enerated
by the deformation. In ge
neral u
s
e of f
i
nite
element
softwa
r
e p
e
rl
oad elem
ent method, cooli
n
g
method,
pen
etration
co
ntact m
e
thod
to si
mulate
b
o
lt tightenin
g
torq
ue. In t
h
is
pap
er fin
i
te
element
cacu
lations, the b
o
lt tightening
torque to d
e
scrib
e
the u
s
e
of prestrain,
the cal
c
ulatio
n
requi
re
d for the torqu
e
co
n
v
erter bolt
s
prestrai
n appli
e
d to the bolt.
4. Result
The SI maps of bolt joints stru
cture
at 500
Hz
whe
n
the tightening
torque i
s
0Nm, 1Nm
and
2Nm a
r
e respe
c
tively sho
w
e
d
in
Figu
re
3, F
i
gure
4,
Figu
re
5. Th
e SI
value
is large
influen
ced by
tightening torque at bolt joints.
So the both end
s of lap beam are studied and th
e
con
n
e
c
tion
s are ign
o
red.
In Figu
re 3, t
he
sou
r
ce of
excitation a
n
d
the
flow
of
energy in th
e
bolt joint
s
structure i
s
sho
w
n
clea
rly
and the SI value i
s
very li
ttle. So
the energy tran
smi
tted to
the other e
nd by bl
ots
joints is
so small. The reason why can
cle
a
rl
y sh
ow the flow
of energy an
d
the excitatio
n
sou
r
ce, acco
rding to the wave theory is
reflectin
g
ene
rgy at incenti
v
e points.
The Fi
gu
re
4
sh
owed th
at the di
stri
buti
on a
nd
si
ze
of po
wer flo
w
tran
smitting at la
p
beam
when ti
ghtenin
g
torq
ue is 1
N
m. The ene
rgy tra
n
smitted to th
e other e
nd b
y
blots joints i
s
large
r
th
an t
hat at tighte
n
i
ng torque
is 0Nm.An
d th
e SI value
at bolts joint
s
i
s
la
rge
r
fo
r t
he
tightening to
rque. Accordi
ng to wave t
heory i
s
due
to t the energy transmi
ssi
on and
refle
c
tio
n
sup
e
rp
ositio
n
at co
upling
boun
dary. In
pra
c
tical
en
ginee
ring
structure, by ex
ternal
elasto
mer
won't
like
ide
a
l state
imme
diately produ
ce
deformati
o
n
an
d
stre
ss i
n
the
wh
ole
structu
r
e, b
u
t i
n
the form of
volatility carry energy tra
n
sfer to
th
e distan
ce fro
m
the part o
f
motivated. Carry
energy an
d e
l
astic
wave
i
n
clu
d
ing: lo
n
g
itudinal
wav
e
, torsi
onal
wave and
flexural
wave, th
ese
wave
s a
r
e
pl
ane
wave. A
c
cordi
ng to
wave th
eory,
the
wave
wi
ll en
cou
n
ter i
n
the
pro
c
e
s
s of
compl
e
x stru
cture
of relay
discontin
uou
s pla
c
e,
su
ch
as
materi
al, geomet
ry sh
ape o
r
stru
ct
ure
cha
nge, in thi
s
case, ca
n p
r
odu
ce
reflex
wave a
nd transmi
ssion
wave. And in some cases
with
incid
ent wave
s of different types of wave
is pro
d
u
c
ed.
Whe
n
the tig
h
tening to
rq
u
e
is
2Nm,
sh
o
w
n in
Figu
re
5, the en
ergy
tran
sferred
the whole
lap bea
m sig
n
ificantly enh
anced, and
more e
n
e
r
gy
transfe
rred to
the other en
d by bolts joi
n
ts.
The
SI of
bolt
con
n
e
c
tion
stru
cture is also larg
er, sho
w
in
g
the energy
reflection
and
sup
e
rp
ositio
n
at the bolt jo
ints is st
rong
er.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Structu
r
al Intensit
y Sim
u
lation of Bolt Join
ts in Vibrati
on Envi
ronm
ent (Yongj
ua
n Zhang
)
4879
Figure 3. The
SI Map of Bo
lt Joints Stru
cture
at Tightening
Torq
ue =0Nm
Figure 4. The
SI Map of Bo
lt Joints Stru
cture
at Tightening
Torq
ue =1Nm
Figure 5. The
SI Map of Bo
lt Joints
Stru
cture at Tighte
n
ing To
rqu
e
=2
Nm
The 6 poi
nts sele
cted o
n
the lap be
a
m
, and the p
o
sition a
s
sh
own in
Figu
re 6 (the
excitation p
o
sition is p
o
int
1). The
SI value of ea
ch
po
int are
sh
own
in Figu
re
7, and it in
crea
sed
quickly wh
en
the tightening
torque chan
ging form 0
N
m to 2Nm.
Figure 6. The
Position of 6 Points Sele
cted
Figure 7. The
SI Value of e
a
ch Point
The SI map
of of rigid
co
nne
cted b
e
a
m
at 500
Hz
whe
n
the tigh
tening to
rque
is 0
N
m,
1Nm an
d 2Nm are resp
ect
i
vely showed
in Figure 8, Figure 9, Fig
u
re 10.
In Figure 8, the so
urce of excitation an
d t
he
flow
of
energy in the rigid co
nne
ct
ed bea
m
is sho
w
n
cle
a
rly an
d the
SI value is v
e
ry little.
So the en
ergy tra
n
smitted to t
he othe
r e
n
d
by
blots joint
s
is so
small. But compa
r
in
g with t
he
Figure 3, it sh
owe
d
t
hat
the energy
loss of
throug
h the b
o
lt joints stru
cture is la
rge
r
than that thro
ugh the rigi
d con
n
e
c
tion b
eam.
The Fig
u
re
9 and Fi
gure 10 sho
w
e
d
that t
he di
stributio
n an
d si
ze of po
wer flo
w
transmitting
at lap be
am
whe
n
tighte
n
ing to
rque
i
s
1
N
m a
nd
2Nm. Th
e S
I
value of ri
gid
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 6, June 20
14: 4876 – 4
881
4880
c
o
nn
ec
te
d
b
e
a
m
is
lar
g
er
w
i
th
th
e p
e
r
f
or
c
e
gr
o
w
ing. And
be
ca
use no
lo
nge
r con
necte
d
by bol
ts,
the ene
rgy transmi
ssion
a
nd refle
c
tion
sup
e
rp
ositi
o
n
is smalle
r at
rigid
con
n
e
c
ted bo
und
ary, the
SI at this place is no that la
rge comp
arin
g with the Fig
u
re 4 an
d Fig
u
re 5.
Figure 8. The
SI Map of Rigid Co
nne
cte
d
Beam at Tigh
tening To
rqu
e
=0
Nm
Figure 9. The
SI Map of Rigid Co
nne
cte
d
Beam at Tigh
tening To
rqu
e
=1
Nm
Figure 10. Th
e SI Map of Rigid Co
nne
ct
e
d
Beam at Tightenin
g
Torque =2Nm
5. Conclusio
n
The lap b
e
a
m
model with
bolts joints i
s
built, inclu
d
i
ng the frictio
n
, conta
c
t an
d so on
compl
e
x nonli
near fa
ctors.
The SI
at different
tighteni
ng to
rqu
e
i
s
calcul
ated, a
n
d
the
SI map
is pl
otted. Th
e sou
r
ce
of excitation t
he
flow
of
en
ergy in th
e bo
lt joints
st
ru
cture i
s
sho
w
n
clea
rly. At different tig
h
teni
ng
torque , the e
nergy di
strib
u
t
ion and tran
smissi
on a
r
e d
i
fferent.
As the energ
y
transmi
ssio
n
and refle
c
ti
on sup
e
rpo
s
ition at coupli
n
g bound
ary, the SI a
t
bolt joints bo
unda
ry is larg
e. And the SI
incr
ea
se
s wit
h
the bolt tightening torq
ue
growi
ng.
The SI val
u
e
of e
a
ch
p
o
i
n
t at lap
b
e
a
m
chan
ged
q
u
ickly when
the tighte
n
ing
torq
ue
cha
ngin
g
, an
d p
r
ovide
the
ba
sis for the
state
identif
ication of bolt
s
joints struct
ure in vibrati
on
environ
ment.
Ackn
o
w
l
e
dg
ements
This work was finan
cially
supp
orted b
y
the NSAF (108
760
34),
Nation
al Scie
nce a
nd
techn
o
logy
major spe
c
ia
l Proje
c
t
(2
011ZX0
400
2-081) an
d P
o
stgradu
ate Innovation F
und
Proje
c
t by Southwe
s
t Univ
ersity of
Scie
nce a
nd Te
ch
nology (1
3ycjj
44).
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ces
[1]
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i
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ijing: S
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ienc
e Press.
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nes
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TELKOM
NIKA
ISSN:
2302-4
046
Structu
r
al Intensit
y Sim
u
lation of Bolt Join
ts in Vibrati
on Envi
ronm
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ua
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