TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.7, July 201
4, pp
. 5037 ~ 50
4
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i7.502
8
5037
Re
cei
v
ed
No
vem
ber 2, 20
13; Re
vised
Ma
rch 17, 20
14; Accepted
March 29, 20
14
Dynamic Analysis and Optimization of WEDM Based on
AWE and LMS
Jingxing Qi
1
, Chang
t
ao
Cai*
2
, Zhixing
Mao
3
, Dongd
ong Luo
4
Coll
eg
e of Mechan
ical En
gi
ne
erin
g and
Auto
mation,
Xih
ua
Univers
i
t
y
, Ch
e
ngd
u, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: cct0622@m
a
il.xhu.e
du.cn
*
1
, prcqj
x
@1
26.c
o
m
2
, zhuge0
4
@
16
3.com
3
,
709
54
298
6@q
q
.com
4
A
b
st
r
a
ct
In the oper
a
t
ion proc
ess,the W
i
re Ele
c
trical Disch
a
r
ge Mach
ine
(W
EDM) has certai
n
imperfecti
ons s
u
ch as
vibr
atio
n an
d th
e d
e
sc
ent of
mac
h
i
n
e
precis
ion
w
h
ic
h vibr
atio
n pr
o
duces.T
his
pa
p
e
r
studies th
e dy
na
mic p
a
ra
meter of the
mac
h
in
e tool
and
opti
m
i
z
e
s
the
natura
l
frequ
e
n
cy an
d vibr
ati
on.
T
a
king th
e DK
772
5 tap
e
r
ma
chin
e tool
as a
n
exa
m
ple,
th
e
pap
er esta
blis
hes a
3D
mo
de
l
w
i
th ProEngi
n
eer
5.0. Accord
ing
to the Mas
a
tak
s
Yoshi
m
ura
method, th
e a
u
th
ors cou
l
d
asce
rtain th
e stiffne
ss and
d
a
m
pi
n
g
of joint surf
ace
s
amon
g mach
ine
ma
in p
a
rts and
ascertai
n the e
quiv
a
le
nt dyna
mic mod
e
l
.
In order to ha
v
e
a moda
l an
aly
s
is abo
ut the
mac
h
in
e tool
structur
e, the virtual dy
na
mic ana
lysis
modu
le of ANS
Y
S
W
o
rkbenc
h En
viron
m
e
n
t (AW
E
) is use
d
. T
h
roug
h the
stu
d
y
of dyna
mic p
a
ra
meter, the
authors
opti
m
i
z
e
and i
m
prov
e the nat
ural fre
que
ncy an
d vi
bratio
n of ma
chin
e tools, c
o
mpar
ed w
i
th the finite e
l
e
m
ent
ana
lysis resu
lts and the n
o
-o
ptimi
z
a
t
i
on dat
a.And the fin
a
l
results show
t
hat the chan
ge r
a
tes of each or
der
natura
l
freque
ncies o
p
timi
z
e
d rang
es
from 0%to18.9
%
,a
nd the w
hole
mec
h
i
n
e
’
s o
p
ti
mi
z
a
t
i
o
n
achi
e
v
es
satisfied effect.
Ke
y
w
ords
:
joi
n
t surface, equival
ent mod
e
l
,
ansys w
o
rkbenc
h e
n
viro
n
m
ent (A
WE), modal an
alys
is, LMS
test, optim
i
z
at
ion
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.
Introdu
cti
o
n
With the
rapi
d devel
opme
n
t of in
du
stria
l
tech
nol
o
g
y,the
im
porta
nt role of wire electri
c
al
discha
rge m
a
chin
e is m
o
re
and mo
re p
r
ominent. Hi
g
h
pre
c
i
s
ion,hi
gh efficie
n
cy
and hig
h
qu
al
ity
pro
c
e
ssi
ng
p
e
rform
a
n
c
e
b
e
com
e
the
t
a
rget
of wi
re
-cutting
te
ch
nology. Be
ca
use
of the
cl
ose
relation
shi
p
betwe
en ma
chin
e’s p
r
o
c
essing
perfo
rman
ce
and
the machi
ne’s
dynami
c
cha
r
a
c
teri
stics, the authors nee
d
to have a thoroug
h dynamics a
nal
y
s
i
s
of
machin
e st
ru
ct
u
r
e.
Dynami
cs
al
so h
a
ve a cl
ose
relatio
n
with the
surf
ace, a
nd research
sho
w
s that over 6
0
%
dynamic flexi
b
ility of machi
ne tool
s is from the j
o
int
surface [1]. The stiffn
ess and dam
ping of t
h
e
joint surfa
c
e
has a g
r
e
a
t
effect on
the
dynami
c
p
e
rforman
c
e
of
machi
ne to
ol, so
joint
su
rface
can b
e
found
in many mechani
cal struct
ure
s
.
There still ha
ve some pro
b
lems of DK
7725
Ta
per
machi
ne whe
n
it proce
s
se
s taper
parts.
Fo
r ex
ample, th
e m
a
chi
ne to
ol vi
bration
lea
d
s
to obviou
s
m
a
chi
n
ing
tape
r e
r
ror. In
ord
e
r
to make th
e machi
ne h
a
ve a goo
d dyn
a
mic a
nd st
at
ic pe
rform
a
n
c
e un
de
r the
con
d
ition of l
o
w
co
st an
d hi
gh
wo
rking
efficiency,
we
ha
d a
dy
nami
cs analy
s
is of t
he m
a
in
com
pone
nts
and
the
overall
stru
cture of the m
a
chi
ne tool. Takin
g
t
he in
fluence of the joint su
rface paramete
r
s into
con
s
id
eratio
n
,
the a
u
thors
set u
p
an
eq
uival
ent m
o
d
e
l ab
out th
e j
o
int surfa
c
e,
and
analy
z
e
and
test the machine’
s dynam
ic model
by
theoretical cal
c
ulatio
n
and
modal si
mula
tion. Moreov
er,
the autho
rs analyze th
e wea
k
p
a
rt
s of the
m
a
chi
ne tool
stru
cture an
d improve t
hem
corre
s
p
ondin
g
ly to lay a solid foundatio
n
for the future
improveme
n
t of the machi
ne tool.
The autho
rs establi
s
h a d
y
namic eq
uat
ion and math
ematical m
o
d
e
l whi
c
h can
reflect
the structu
r
al
ch
ara
c
te
risti
c
s of ma
chi
n
e tool
and
ca
n influen
ce
the p
e
rfo
r
man
c
e
of the
wh
ole
analysi
s
process. Accordi
n
g to the prin
ciple of
dynam
ics, the auto
r
s ca
n kn
ow t
hat the gene
ral
motion differe
ntial equatio
n
of a system with
N de
gre
e
of freedom
unde
r incenti
v
e is [2-3]:
[
]
{}
[
]
{}
[
]
{}
(
)
.
M
xC
x
K
x
f
t
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5037 – 50
43
5038
Among them,
[]
M
is the mass matrix for the machin
e tool,
[]
C
is the damp
i
ng matrix,
[]
K
is the
stiffness mat
r
ix,
()
f
t
is th
e extern
al in
centives th
e m
a
chi
ne tool
re
ceived. T
h
e
,,
x
xx
is the
vari
ation of th
e m
a
chin
e tool
s vi
bration
a
c
cel
e
ration,
re
spe
c
tively (a
ccel
eration
)
, velo
city
and
displacement vari
ation res
pectivel
y
.If the machine vibratio
n is free vi
bration and
the
dampin
g
and
excitation can
be ignored, then t
he theo
ry equation for modal analy
s
is i
s
:
[
]
{}
[
]
{}
(
)
0
.
Mx
K
x
f
t
This
equation is homogeneous
differential equation.T
he result
will
reflect the automatic
vibration
cha
r
acte
ri
stics of
the machine
tool,and
the
results of th
e ch
ara
c
te
ristic equ
ation
will
reflect the nat
ural cha
r
a
c
teristics of the machi
ne tool.
2. The Finite Element Mo
del of the
Whole Machin
e Tool
The main parts of DK7725 taper machi
ne
incl
udes the base,pos
t,the upper and lower
arm an
d slid
e
r
. Acco
rdin
g to Saint Vena
nt’s Prin
ciple
[4-5], the authors elimin
ate or sim
p
lify the
small
ch
amfe
r, fillet, small
craft hole, t
he e
dge
of small p
r
otru
si
on a
nd
so
o
n
. ProE5.0
a
nd
ANSYS Workbench
are used as tools f
o
r m
odeli
ng
and
anslysi
s
. After fini
shing the
model ,
t
he
authors import it into the AWE platform.
And
element type will be chosen and m
e
sh level
will
be
graded. T
he
grid division
on the whole
will be
ca
rried on before the loca
l
fine division, because
this can redu
ce
comp
utation. In all,184
707 n
ode
s a
nd11
3059
so
lid eleme
n
ts
are divid
ed,
as
sho
w
e
d
in the Figure1.
Figure 1. The
Finite Element Model of
Machi
n
e
Figure 2. The
Sketch of Joi
n
t Surface
3.
The Equiv
a
lent Mod
e
l and Parame
ter Identific
a
tion of Joint
Surfac
es
The dyn
a
mi
cs a
nalysi
s
d
e
pend
on th
e
accuracy
of the ove
r
all
structure m
odel
of the
machi
ne,
whi
c
h
sho
u
ld ta
ke the joint
su
rface
char
act
e
risti
c
s into
consi
deration.
The fixed joi
n
t
surfa
c
e
s
whi
c
h i
s
u
s
ed
wi
dely in t
h
is p
aper in
cl
ud
es the
co
nne
cti
on of
the
ba
se with
the
po
st,
the conn
ectio
n
of th
e p
o
st
with
the
upp
er
and
lo
wer arm and
the
con
n
e
c
tion of
the uppe
r arm
with the
slid
e
r
. And the
sli
der
and
upp
er a
r
m
co
nn
ection
belo
n
g
s
to the
unfix
ed joint
su
rfa
c
e
con
n
e
c
tion. Paramete
r id
entification re
fers to
a pro
c
e
ss
whi
c
h d
e
termin
es a
n
o
ther sy
stem
to
make
su
re t
hat
sy
st
em i
s
nea
rly equ
ivalent with the real
sy
st
em. The an
other sy
stem
is
determi
ned
b
y
the given a
m
ount of in
p
u
t and
output
in the
kno
w
n structu
r
al v
i
bration
sy
ste
m
and th
e obj
e
c
tive fun
c
tion
of minim
u
m
prin
cipl
e [6]
.
One
of the
difficultie
s o
f
machi
ne to
ol
dynamics
re
search
at h
o
m
e
an
d a
b
ro
ad
is
ho
w to
a
c
curately ide
n
tify and o
p
timi
ze th
e dyn
a
m
i
c
para
m
eters o
f
machine joi
n
t surfa
c
e [7].
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Dynam
ic Ana
l
ysi
s an
d Opti
m
i
zation of WEDM Base
d on AWE and
LMS (Jin
gxi
n
g Qi)
5039
By resea
r
chi
ng on the joi
n
t surfa
c
e, Masata
ks Yosh
imura cl
aim
s
that the stiffness and
dampin
g
of the joint surfa
c
e ca
n be acquire
d thro
u
g
h
integral on
the sit
uation that the positi
v
e
pre
s
sure of
units
and
eq
uivalent stiffn
ess a
nd d
a
m
p
ing figu
re
s
unde
r differe
nt co
ndition
s are
kno
w
n [6]. From the dyna
mic pe
rspe
cti
v
e, the join
t surface mu
st h
a
ve normal st
atic force, wh
ich
can
produ
ce
norm
a
l st
re
ss which in tu
rn p
r
od
uc
es
dampin
g
an
d
stiffness. Be
cau
s
e th
e joi
n
t
surfa
c
e
ha
s such
cha
r
a
c
teristics a
s
ela
s
ticity
, damping
, the stora
ge
and con
s
umi
ng of ene
rgy,
so
the authors
con
s
tru
c
t the
dynamic mo
del by spri
ng
and damp
e
r [8].
Acco
rdi
ng to Masat
a
ks
Yoshim
ura m
e
thod, one jo
int surfa
c
e h
a
s six dynam
ic
forces with
different forms, inclu
d
ing
the
s
h
ea
r
i
ng
fo
rc
e
x
f
in
,
x
z
dire
ction,
the normal
force
y
f
in the
y
dire
ction, a
nd the bend
ing
moment
,,
M
xM
y
M
z
arou
nd the
,,
x
yz
dire
ctio
ns. T
he
actu
a
l
su
rface
can
be a
combin
a
t
ion
of one or mo
re [9]. The cal
c
ulatio
n form
ula
of the equ
ivalent stiffness a
nd dam
pi
ng is:
dxdz
P
k
K
n
i
i
)
(
(1)
dxdz
P
c
C
n
i
i
)
(
(2)
Among th
em, the
()
in
KP
is the
stiffness
on p
e
r
unit area, the
()
in
CP
is th
e da
mpi
ng o
n
per u
n
it area
, the
i
K
is the e
quivalent stiffness
of the
joint su
rface, the
i
C
is the e
quivalent
damping of t
he joint
surface. Assuming t
hat other constant
s
w
ill not influence t
h
e
()
()
kp
c
p
、
,
the auth
o
rs
will get th
e
stiffness
and
da
mping
of
the
j
o
int surfa
c
e
b
y
simplifying
the e
quatio
n
(1)
and (2
):
A
k
K
i
,
A
c
C
i
(3)
The joi
n
t su
rf
ace
of the m
a
chin
e tool m
a
inly
has four
parts: th
e
co
mbination
of t
he ba
se
and the po
st,
the post an
d
the uppe
r an
d lowe
r
arms,
t
he uppe
r arm and the sli
der. The fo
rm
er
three a
r
e fixe
d joint su
rface con
n
e
c
tion,
and the la
st one is th
e sli
d
ing joint con
nectio
n
. The j
o
int
surfa
c
e of
DK7725
sho
w
s in Figure 2.
Figure 3. The
Equivalent Mode of Base
and Post
The ba
se is
conne
cted
with the post by
four
bolts, which b
e
long
s
to fixed joint
surfa
c
e.
As for HT
200
base mate
ri
al, the elastic modulu
s
is 1
.
48×1
0
11
N/m
2
, and Poisso
n's ratio is 0.
31,
and de
nsity i
s
7.2
×
10
3
kg/
m
3
. The four bolts have
certain infl
u
e
n
c
e on th
e joi
n
t stiffness. The
radial
stiffne
s
s of
bolt is e
quivalent to
spring
-d
ampin
g
unit, while the
axial stiffness of
bolt
s
is
equivalent to
the norm
a
l sti
ffness
of join
t. The prete
n
si
on of bolt is a
bout 2.8×10
4
N mea
s
u
r
ed
by
torque
wren
chesth
e. Acco
rding to th
e Masata
ks
Yo
shimu
r
a m
e
thod an
d the
dampin
g
of u
n
it
joint su
rfa
c
e
and
stiffness nu
mbe
r
ta
ble [10], th
e
ratio of
per unit joint
su
rface
stiffne
s
s to
dampin
g
is c
1
/k
1
=0.
5
5
×
10
-1
4
,c
2
/k
2
=0.
5
×
1
0
-3
. From the formula (3
), the authors can kn
ow t
he
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02-4
046
TELKOM
NI
KA
Vol. 12, No. 7, July 201
4: 5037 – 50
43
5040
stiffness of th
e ba
se
an
d p
o
st a
nd th
e d
a
mping
in
ve
rtical. Th
e
stiffness
of joint
surfa
c
e
bet
ween
the ba
se
an
d po
st i
s
la
rgely affecte
d
by thei
r o
w
n gravity an
d the
co
ntact stre
ss is e
v
en
-
distrib
u
ted. So equivalent
dynamic
cha
r
acteri
stic
s of the joint surf
ace
can be
simulated by the
four sets da
m
p
ing unit
s
. Th
e equivale
nt model is
sh
o
w
ed a
s
Fig
u
re 3. Model u
n
its of joint set in
the connecti
on position
between post and base.
And point
s
1,2....8 correspond to
points
1’,2’....8’, res
pec
tively.
The
po
st an
d
the
upp
er a
nd the
lo
we
r
arm
s
a
r
e
con
necte
d
with f
our bolt
s
. All
of them
belon
g to the
fixed joints.
A
ll together,
8 sp
rin
g
-d
am
p units are u
s
ed. T
he
con
nectio
n
bet
ween
the uppe
r a
r
m and the
sli
der a
r
e
slip conne
ction. Th
e motion di
re
ction of the in
terface i
s
e
a
sy to
be re
cog
n
ize
d
, so the auth
o
rs
coul
d set
up sp
ring
-
d
a
m
p units by chara
c
te
risti
c
para
m
eter of
the
singl
e de
gre
e
of freed
om
system. The
e
quivalent
dyn
a
mic m
odel
o
f
the colu
mn,
the upp
er
and
lowe
r arm
s
a
nd the slid
es
are sho
w
ed a
s
follows:
Table 1. The
Stiffness and
Dampi
ng Val
ues of Joints
Joints Names
Bonded
Area
cm
2
Shear
Stif
fness
N/m
3
Shear
Damping
Ns/m
3
Normal
Stif
fness
N/m
3
Normal
Damping
Ns/m
3
A
v
erage
Str
e
ss
pa
Joint sur
f
ace
bet
w
een
base and post
338.8
3.39E16
1.86E2
3.39E6
1.69E3
3.34E6
Joint sur
f
ace
bet
w
een
post and uppe
r
arm
183.4
2.25E16
124
2.25E6
1.13E3
3.2E6
Joint sur
f
ace
bet
w
een
post and lo
w
e
r
arm
152.6
8.4E10
8.4E-4
1.53E6
1.53E2
2.8E6
Joint sur
f
ace
bet
w
een
upper and
slider
139.1
5.5E10
5.5E-2
5.5E3
2
9.9E5
4. The D
y
namic Analy
s
is
and LMS Te
st of the Wh
ole Machine
Tool
4.1. Modal Analy
s
is of the Whole Ma
c
h
ine Tool
ANSYS, which can optimi
z
e the analysi
s
for the st
ructure indirectl
y
, is
also the basi
s
of
dynamic a
nal
ysis such as
harm
oni
c ana
lysis, tr
an
sien
t dynamic an
alysis a
nd sp
ectru
m
analy
s
is
[11]. The ba
sic ide
a
of mo
dal an
alysis is to
an
alyze t
he dynami
c
p
e
rform
a
n
c
e o
f
mecha
n
ism
of
the matrix eq
uation, whi
c
h
can
sho
w
th
e dynami
c
ch
ara
c
teri
stics
of muti-deg
re
e of freedom
with
singl
e degre
e
of freedom
system and
identify t
he
natural fre
q
u
ency and vib
r
ation mod
e
of
st
ru
ct
ur
al dy
n
a
mic c
h
a
r
a
c
t
e
rist
i
cs [
12]
.
Natural fre
q
u
ency a
nd vib
r
ation m
ode,
who
s
e
stabili
ty and relia
bi
lity can imp
r
ove the
stru
cture’s p
e
rform
a
n
c
e a
nd avoid un
n
e
ce
ssary
lo
sse
s
,are im
po
rtant paramet
ers of dyna
mic
properties.Introducing
the 3Dmodel int
o
the ANSYS Workbe
nch,the authors apply the finite
element
con
s
traints o
n
the
model to limit the
degre
e
of freedom in
X, Y and Z
dire
ction of the
base
so
as to
identifying th
e stiffne
s
s a
n
d
da
mpin
g
of
the inte
rface.
Afte
r co
mputi
ng, the
auth
o
r
s
extract the n
a
t
ural fre
quen
cy and vib
r
ation type of
the first 6
steps mode
s. The
modal
cha
ngi
ng
is
as
follows
:
Figure 4. The
First Three
Mode
s of the Whol
e Machi
ne Tool
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Dynam
ic Ana
l
ysi
s an
d Opti
m
i
zation of WEDM Base
d on AWE and
LMS (Jin
gxi
n
g Qi)
5041
Figure 5. The
Second T
h
re
e Mode
s of the Whol
e Machine Tool
In summa
ry, the fluctuating
range of ea
ch fr
eque
ncy o
r
de
r the machine tool is n
o
t wide.
The d
e
form
a
t
ion of the f
i
rst-ord
e
r i
s
not obviou
s
while th
e se
con
d
ha
s o
b
vious b
endi
ng
deform
a
tion.
Both the third-o
r
de
r a
nd f
ourth
-o
rde
r
h
a
ve se
rio
u
s
bendi
ng a
n
d
disto
r
tion. T
he
vibration m
o
de of the
fifth-o
rde
r
sho
w
s that th
e ba
se vib
r
ation
mode
ch
ang
e is
bigg
er.
The
bottom of the base o
c
currs the
bulgin
g
deform
a
ti
o
n
in +y direction. If we improve the
base
stru
cture, the deformatio
n
may
decrea
s
e. Seen from
the vibratio
n
mode of the sixth-order, t
he
uppe
r ma
chi
ne occu
rrs b
endin
g
def
ormation, se
rio
u
sly. And distortion is a
c
compani
ed. T
he
deform
a
tion
of the p
o
st
is a bit
serio
u
s. Obviou
sly, it affects the
perfo
rman
ce
of the m
a
chi
n
e
tool.
4.2. LMS Test.Lab Experi
ments an
d O
p
timization
This expe
rim
ent use
d
the LMS TEST.Lab noi
se
an
d vibration eq
ui
ment of Gelgi
u
m LMS
Inc. The fun
c
tions of data
pro
c
e
ssi
ng a
nd acqui
si
tio
n
of this devi
c
e is ve
ry strong. Wh
en t
h
e
machi
ne i
s
in
non
workin
g
state,
four
sensors a
r
e resp
ectively fixed on the
b
a
se, p
o
st, lo
wer
arm an
d slid
e
r
. The autho
rs use a ham
mer with a pl
astic
se
ction to hamme
r th
e top of post.
The
trigge
r level
i
s
0.0
25V, a
n
d
p
r
etrig
ger i
s
ze
ro
second.
Wh
en t
he
au
thors
set the
actual
sen
s
itivity
of ch
annel
setup, the in
p
u
t of force i
s
set
as
2.25
mV/N.
The F
R
F
e
s
timato
r
is H1. Different
knocking posi
tion, different
knocki
ng force, sens
ors placem
ent and others factors will influence
the results di
rectly of indirect
ly. After several expe
ri
ments,the
aut
hors got different re
sults,
and
there
some
d
e
viations am
ong th
em. T
h
e follo
wing
d
a
ta is extra
c
t
ed from th
em
, as sho
w
n i
n
the
Table 2.
Table 2. Co
m
pari
s
on of LM
S Experiment
Data and the
Optimization
of Data
Names First-orde
r
Second-orde
r
Third-o
r
der
Forth
-
orde
r
Fifth-ord
er
Sixth-or
der
LMS expe
riment
al
data
69.7 Hz
102.49Hz
130.7Hz
175.37Hz
236.59Hz
285.59Hz
Relative errors
34.3%
9.6%
5.75%
32.5%
2.8%
1.6%
Acco
rdi
ng to
cha
ngin
g
of t
he n
a
tural
fre
quen
cy a
nd v
i
bration
mod
e
,
the up
per p
a
rt an
d
the ba
se
of t
he ma
chi
ne t
ool h
a
ve maj
o
r d
a
ma
ge.
On the
condit
i
on of
app
rop
r
iate
stiffness and
stren
g
th, the
authors coul
d optimize th
e machine
structu
r
e to mi
nimize the
changi
ng rate
of
natural frequ
ency an
d vibration mo
de. The optimi
z
a
t
ion aim is to
decrea
s
e n
a
t
ural freq
uen
cy
and the
be
nd
ing a
s
well a
s
defo
r
matio
n
. Optimizati
on vari
ation i
s
the
stru
ctu
r
al ch
ang
e of
the
machi
ne tool
and the den
sity of each unit. The
authors gra
duall
y
optimiz
ate the stru
cture by
improvin
g ke
y parts si
ze, i
n
crea
sing the
stiffener
and
adju
s
ting the
area
s of the joint surfa
c
e
s
.
The structu
r
e can b
e
improve
d
by the
followi
ng step
s: firstly, set a quad
rate
reinfo
rcement
rib15m
m in
width an
d 5
mm in heig
h
t
under th
e
base. Seco
n
d
ly, chang
e the
sha
pe an
d si
ze of the ba
se an
d thicken the su
ppo
rting plate in
the base. T
h
irdly, adju
s
t the
sha
pe an
d area of the inte
rface
and
strengthe
n the sti
ffness as
well a
s
incre
a
se the
dam
ping
para
m
eter. T
he autho
rs set the variation ra
nge of
optimizatio
n
param
eters in the ANSYS
Wo
rkb
e
n
c
h
e
n
vironm
ent pl
atform. P1-DS_d143
is th
e thickn
ess
o
f
stiffener,
an
d its
ra
nge
is [9,
11]. P2-DS_
d6 is the
po
st height, an
d its ra
nge i
s
[648, 79
2]. P3-DS_
d5 i
s
the wi
dth o
f
the
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02-4
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TELKOM
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Vol. 12, No. 7, July 201
4: 5037 – 50
43
5042
bottom of the
post, and its range is [14
2
.2, 173.8]. The
initial sampl
e
value is10
0
.
By calcul
ation,
the stress
clo
ud of the
st
ru
cture
si
ze
an
d the
n
a
tural freque
ncy of the
whole ma
chin
e
is
sho
w
n
as Figu
re 6.
Figure 6. Th
e Stress Clo
u
d
of Three Va
riable
s
(P2,P
3
and Natural
Frequ
en
cy)
Figure 6
sho
w
s the
rel
a
ta
tionshi
p am
o
ng the
th
ickn
ess of
stiffen
e
r, the
wi
dth
of the
bottom of the post and th
e post hei
ght
, the natural
freque
ny of every st
ep
s. The optimization
results
sho
w
s that there
are some
differen
c
e b
e
twee
n opti
m
ization
and
no-o
p
timizat
i
on.
Whe
n
the thickne
s
s of the stiffener i
s
9
mm,
the
he
ight of th
e
post i
s
648.
72mm
and
the
width of the p
o
st bottom is142.36m
m,
the optimizatio
n effect is better, while si
ze
partly becom
es
small an
d the
stru
cture i
s
simplified. The
optimized d
a
t
a is sho
w
n a
s
Table 3.
Table 3. The
Optimize
d Da
ta of Natural
Freq
uen
cy
Names First-orde
r
Second-orde
r
Third-o
r
der
Forth
-
orde
r
Fifth-ord
er
Sixth-or
der
The optimized da
ta
77.86Hz
91.12Hz
128.62Hz
243.37Hz
243.37Hz
267.3Hz
Relative
errors
16.8%
18.9%
6.9%
4.7%
1%
4.9%
In con
c
lusi
on
, the optimized data is m
o
re
cl
ose to the LMS Test experiment
al data.
Comp
ared
wi
th the n
a
tura
l frequ
en
cy that is
not op
timized ma
ch
ine,
the de
creased ran
g
e
of
optimize
d
nat
ural fre
que
nci
e
s is from 0
%
to20%,
and
the variance
ratio of the first-o
r
de
r and t
h
e
se
con
d
-o
rd
er is big
ger. M
o
st of the n
a
t
ural fr
e
que
n
c
ie
s got
som
e
de
cline
s
, a
nd the vibration
mode
s al
so
h
a
ve some
ch
ange
s.
Ho
we
ver, ther
e a
r
e
still
som
e
g
a
p
s
amon
g the
optimized
da
ta
of ANSYS, th
e result of LMS experiment and the
no-optimi
z
ation.
The
gaps which i
s
probably
cau
s
e
d
by th
e interfe
r
en
ce frequ
en
cy prod
uced
d
u
ring the te
st p
r
ocess, an
d some comp
on
ents
su
ch a
s
ba
se, post affect the measurem
ent
of the dynami
c
perfo
rman
ce,
or inaccu
ra
te
measurement
modeling, im
prop
er
o
peration and oth
e
r reason
s. If t
he autho
rs
want to get better
dynamic pe
rforma
nce, they sh
o
u
ld m
a
ke
f
u
rt
he
r
r
e
se
ar
ch
on
the structu
r
e
of the
who
l
e
machi
ne, an
d
improve the
unde
rsta
ndin
g
of the detai
ls incl
udin
g
the joint pa
ra
rmeter
sele
ction,
cal
c
ulatio
n of stiffness and
dampin
g
and
so on.
5. Conclusio
n
Thro
ugh th
e
finite element
analysi
s
of
DK
772
5 ma
chine b
a
sed o
n
AWE, the
authors
learn
the
effe
cts
on th
e m
a
chin
e p
e
rfo
r
mance
cau
s
e
d
by the
defo
r
mation
an
d t
a
ke
mea
s
u
r
e
s
of
stiffener or chang
ed stru
ct
ure
to red
u
ce
the
defo
r
mat
i
on. Accordin
g to the resul
t
s of the Mo
d
a
l
analysi
s
,the j
o
int surfa
c
e
s
betwe
en th
e
slide
r
a
n
d
up
per arm,and
the
sti
ffness
o
f
post
have
the
greate
s
t influ
ence on
the
whol
e ma
chi
ne pe
rforma
n
c
e, which a
r
e
also
the
we
ake
s
t pa
rt of
the
machi
ne. Th
e optimi
z
ed
natural
freq
u
ency
i
s
d
e
creased by
0%
to 17% by
DOE m
o
dule.
The
authors
sho
u
l
d
co
ntrol th
e
deform
a
tion
of the main
compon
ents
so that the n
a
tural frequ
en
cy is
more
clo
s
e t
o
the re
sult
of LMS expe
rimen
t. The
LMS experim
ent ca
n refle
c
t the ma
chi
ne
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Dynam
ic Ana
l
ysi
s an
d Opti
m
i
zation of WEDM Base
d on AWE and
LMS (Jin
gxi
n
g Qi)
5043
perfo
rman
ce
i
n
the
actu
al
work conditio
n
. The
c
ontra
stive an
alysi
s
of ex
pe
rime
n
t
al data
and
the
optimize
d
dat
a lays th
e fo
undatio
n for f
u
rthe
r st
u
d
y
on the
effect
s of inte
rfere
n
ce f
r
eq
uen
cy o
n
the whol
e ma
chin
e.
Ackn
o
w
l
e
dg
ements
The a
u
tho
r
s espe
cially a
c
kno
w
led
ge t
he
supp
ort f
r
om th
e ele
c
tric Processi
ng Key
Labo
rato
ry of Sichu
an
Coll
ege.And thi
s
pape
r i
s
fund
ed by G
r
ad
ua
te Innovation
Fund P
r
oje
c
t
of
Xihua Unive
r
sity (No.ycjj2
0133
1).
Referen
ces
[1] Z
M
Levina.
Re
search o
n
the
Static Stiffne
ss of Joints in Machine Tool.
MT
DR Conf. 19
67
; (8): 45-48.
[2]
LI T
ao, MA Ch
un-
xi
ang. T
he
d
y
nam
ic ch
ara
c
terist
ic a
nal
ys
is of th
e MB4
2
50-2
hi
gh-
preci
s
ion
contro
l
vertical h
oni
ng
machi
ne.
Mach
inery D
e
sig
n
a
nd Man
u
factur
e.
2008; (1
1): 163-1
65.
[3] Yafeng L
i
, Yuxiu
Xu.Oper
ation
a
l mod
a
l
anal
ysis of
w
i
nd turbi
n
e spee
d-incr
e
a
se ge
arbo
x.
T
E
LKOMNIKA Indon
esi
an Jou
r
nal of Electric
al Eng
i
ne
eri
n
g
.
2013; 1
1
(11):
669
9-67
05.
[4]
Z
hang
Xi
an
g
y
u
,
Xio
ng Ji, etc.
T
opolo
g
ic
al o
p
timi
zati
on
of slide of
machi
n
in
g center b
a
sed on
ans
ys
.
Manufactur
i
ng T
e
chno
logy an
d
Machi
ne
T
o
o
l
.
2008; (6): 68-
74.
[5]
Z
hang
Jie, T
o
n
g
Z
h
o
ngfan
g.
T
he probl
em of
d
y
nam
ic mo
d
e
lin
g
of bo
lted
joints
in m
a
chi
ne to
ol. 1
9
9
4
;
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[6]
F
ang Z
i
l
i
a
ng. Identific
atio
n of
Comp
le
x M
o
d
a
l Par
a
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Journ
a
l
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njin
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n
iv
ersit
y
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nc
e
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e
ch
no
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y
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[7]
Z
hang
Xu
eli
a
n
g
, Hu
ang
Yu
mei, W
en
Shu
hua. M
ode
lli
ng
Static
b
a
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o
f
Machi
ne T
ool
Joint S
u
rfaces
and
its Ap
plic
a
t
ion.
Ma
nufact
u
rin
g
T
e
ch
nol
o
g
y a
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a
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19
98
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[8] ZHAO
Weilong.
A R
ease
a
r
ch a
bout
Dy
na
mic P
a
ra
meter Ide
n
tificat
i
on
of A M
a
chin
e F
i
xe
d
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mbi
nati
on.
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anzh
ou: La
nzh
ou Un
iversit
y
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f
T
e
chnolo
g
y
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[9]
M Yoshimur
a,
T
Hamada, K Yura.
Des
i
g
n
opti
m
i
z
a
t
io
n
of mac
h
i
ne-t
ool structur
e
w
i
th respect to
dynamic characteristics. De
sign Automation Comm
ittee
. Desi
gn
an
d Prod
uctio
n
Engi
ne
erin
g
T
e
chnical Co
nferenc
e, W
a
sh
i
ngton, DC. 1
9
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5
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[10]
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o
Bo
yu, Z
h
ou
Xinm
in, Yin
Z
h
ihon
g. Mod
e
rn
mech
an
ica
l
d
y
nam
ics an
d
its engi
neer
in
g app
lic
ation
:
Mode
lin
g, ana
l
y
sis, simu
lati
on
, control, optim
i
z
ation. Bei
jin
g: Chin
a Mach
in
e
Press. 2004.
[11]
Xi
ao
pen
g L
i
, H
ao Gu
o, Jin
gni
an L
i
u, Y
a
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