TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.6, Jun
e
201
4, pp. 4849 ~ 4
8
5
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i6.584
4
4849
Re
cei
v
ed
Jan
uary 18, 201
4
;
Revi
sed Ma
rch 1
8
, 2014;
Acce
pted Ma
rch 3
0
, 2014
Applying Extenics Theory to Motion Performs
Evaluation of Numerical Machines
Chen Liu
North Ch
ina In
stitute of Scien
c
e
and T
e
chno
log
y
, Ch
ina, 0
6
520
1,
email: li
uch
e
n
@
ncist.ed
u
.cn
A
b
st
r
a
ct
T
he motio
n
pe
rforms ev
alu
a
ti
on in
dex
es of nu
meric
a
l co
nt
rol mach
ine to
ols (NC) ar
e
ma
de o
f
mu
ltipl
e
el
e
m
e
n
ts. In order to evalu
a
te moti
on perfor
m
s of
numeric
al con
t
rol mac
h
i
ne to
ols ob
jective
l
y, w
e
have
a
ppl
ied
t
he
exten
i
cs th
e
o
ry to
estab
lish
the
ma
tter-el
e
me
nt mo
del
for
the motio
n
per
forms eva
l
uati
o
n
of the NC. T
h
e
relati
ona
l d
egr
ee w
a
s calc
ul
a
t
ed by i
n
tr
od
uc
ing th
e rel
a
tio
n
a
l functi
on
in t
he exte
nsi
on s
e
t
theory, a
nd th
e
eval
uati
on i
n
d
e
xes w
e
ig
ht co
efficient of
NC
w
e
re defi
ned
b
y
usin
g the
1-9
scale
law
in
A
H
P
(the a
nalytic
hi
erarchy
proc
es
s). A nu
mer
i
cal
control
mac
h
i
ne to
ol
as a
study
obj
ect, the
motion
p
e
rfor
ms
w
a
s studied by
using the
exte
nics theory.
T
h
e result in
dicat
e
s that the ex
tenics the
o
ry is appr
opri
a
te for th
e
moti
on
perfor
m
s eval
uatio
n .T
he
moti
on p
e
rforms
of t
he ev
alu
a
ted N
C
w
a
s goo
d, the ev
alu
a
tion
meth
o
d
possess
es a certain pr
actica
bility.
Ke
y
w
ords
:
extenics the
o
r
y
, motio
n
perf
o
rms ev
al
uatio
n,
AHP (analy
t
ic hierarc
h
y p
r
ocess), nu
me
rica
l
control mac
h
in
e
tool
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
A numeri
c
al
control ma
chin
e tool (NC) ha
s so
me ch
ara
c
te
ristics, such
as hig
h
pro
c
e
ssi
ng
preci
s
ion, th
e stabilizin
g qu
al
ity, high
prod
uction
efficie
n
cy, better a
daptability to
the
cha
nge
d de
si
gn of p
r
od
uct
s
. A num
eri
c
al co
ntrol
ma
chin
e tool
ca
n proces
s th
e pa
rts that t
he
comm
on ma
chine tool ca
n
’
t do. It is beneficial
to the developm
e
n
t of the compre
hen
sive and
automatic ma
nufactu
re te
chnolo
g
y [1]. Along
with th
e exten
s
ive u
s
e
of num
eri
c
al ma
chin
e to
ols,
the use
r
s
de
mand hig
h
e
r
perfo
rman
ce
s. Becau
s
e nu
meri
cal ma
ch
ine tools h
a
ve a great vari
ety
and the
pe
rforma
nce ind
e
xes a
r
e
ma
de of m
u
ltiple
elem
ents, i
t
is not
goo
d
to evaluate
the
motion pe
rforms qualitative
l
y or quant
itatively with a single metho
d
.
The motio
n
p
e
rform
s
of
NC is a
sig
n
ificant
p
a
rt of the overall fu
nction
s. It sh
ows the
techni
cality of
NC. So, th
e
study of
moti
on p
e
rfo
r
m
s
is
followed
with interes
t, it is
necess
ary t
o
evaluate an
d
analyse the
motion pe
rforms of NC
. The motion pe
rform
s
index
es involve fe
ed
velocity, the rotation rate of
chief axis an
d the adj
u
s
tment rang
e of it, the power of
chief axis, the
torque
of fee
d
axis, the
c
oordi
nate
stroke
s, the
ra
nge of
swing
angle, th
e
cap
a
city of t
ool
maga
zine, th
e tool
cha
ngi
ng time, etc
[2]. From th
e
above a
nalysis an
d d
ue to
more
ind
e
xes of
the motion p
e
rform
s
, extenics theory l
eade
d-in, the
matter-ele
m
ent model of
motion perfo
rms
evaluation
of NC i
s
fou
n
d
ed ab
usi
ng t
he matter-
ele
m
ent theo
ry and exten
s
io
n set the
o
ry,
the
motion pe
rforms level of NC is dete
r
min
ed by
solving
its matter-el
e
ment mod
e
l
[3]. The paper
sele
cts
six indexes to eval
uate the NC, whi
c
h fo
rm th
e motion pe
rform
s
evaluati
ng system, th
ey
are fe
ed vel
o
city (m/min
), the rotation
ra
te of ch
ief axis
(r/min), the
x/y/
z coordin
a
te stroke(m
m),
the rang
e of
swing a
ngle (°), the capa
city of tool
magazine a
nd the tool ch
angin
g
time(s).
2.
Founding th
e Model
2.1
．
Foundin
g
the Ma
tte
r-element Mod
e
l
2.1.1. Identify
ing Classical Matter-ele
ment
The qua
ntity
of motion perf
o
rm
s evaluati
on index is n,
sho
w
n c
1
,c
2
,c
3
，，
…c
n
，
the
quantity of motion perfo
rm
s level of NC
is m [4].
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: 4849 – 4
853
4850
jn
n
j
j
j
ji
i
j
j
x
c
x
c
x
c
N
X
C
N
R
,
,
,
)
(
)
,
,
(
2
2
1
1
jn
jn
n
j
j
j
j
j
b
a
c
b
a
c
b
a
c
N
,
,
,
,
,
,
)
(
2
2
2
1
1
1
(1)
i=1,2…,n
；
j
=
1,2…,m
Whe
r
e
equ
ation
(1) is matt
er-eleme
nt m
odel,
N
j
i
s
sh
own
the
moti
on p
e
rfo
r
m
s
l
e
vel j, C
i
is the motion
perfo
rms eval
uation ind
e
x of N
j
, x
ji
is th
e magnitud
e
limits of C
i
in N
j
[4].
2.1.2. Identify
ing Extensional Matter
-element
Extensional
matter-eleme
n
t is the magnitude lim
its of every evaluation index in all the
motion perfo
rms level. Wh
ere Equatio
n
(2) is
sh
own, p is all th
e evaluation index, X
pi
is
the
magnitud
e
limits of c
i
, X
pi
is
〈
a
pi
,b
pi
〉
.
pn
n
p
p
p
p
x
c
x
c
x
c
p
X
C
P
R
,
,
,
)
,
,
(
2
2
1
1
=
pn
pn
n
p
p
p
p
b
a
c
b
a
c
b
a
c
p
,
,
,
,
,
,
2
2
2
1
1
1
(2)
2.1.3. Matter-element A
w
a
i
ting Ev
aluation
The m
a
chini
ng
cente
r
a
w
aiting evalu
a
tion i
s
sho
w
n
PM, the
co
ncrete valu
e
of every
evaluation i
n
dex is
sh
own
by matter-el
ement. Whe
r
e Wquation
(3) i
s
sho
w
n.
xi is the valu
e of
motion pe
rforms index of ci
.
n
n
M
M
M
x
c
x
c
x
c
p
X
C
P
R
,
,
,
)
,
,
(
2
2
1
1
(3)
2.2. Relation
al Degre
e
of
Ev
er
y
Ev
al
u
a
tion Lev
e
l in NC
A
w
a
i
ti
ng Ev
aluation
The interval
distan
ce of P
M
and N
j
with
rega
rd to the motion pe
rform
s
evaluati
on index
C
i
（
is shown
ρ
x
i
，
x
ji
）
, w
h
ich of PM and Np is shown
（
ρ
x
i
，
x
pi
）
. The rela
tional deg
ree
of
evaluation in
dex C
i
with re
gard to the ev
aluation g
r
ad
e j is sho
w
n i
n
Equation (4
).
)
,
(
)
,
(
)
,
(
)
(
ji
i
pi
i
ji
i
i
j
x
x
x
x
x
x
x
K
(4)
The wei
ght of C
i
is w
i
, so the relatio
nal
degree of NC awaiting eval
uation P
M
with rega
rd
to the evaluation gra
de j is
sho
w
n in Equ
a
tion (5
).
n
i
i
j
i
M
j
)
x
(
K
w
)
p
(
K
1
(5)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Applyin
g
Exte
nics Theo
ry to Motion Perf
orm
s
Evalu
a
tion of Num
e
ri
cal Ma
chin
es
(Ch
en Liu
)
4851
2.3.
Defining
the
Weigh
t
of Ev
er
y
Ev
aluation Index b
y
AHP
The gist of AHP is as follo
ws, the influe
nce of
differe
nt factors o
n
a target is co
mpared,
the peopl
e’s subje
c
tive e
v
aluation
s
is sho
w
n a
n
d
handle
d
by
quantum
sh
ape, thereby
its
prop
ortio
n
i
s
founde
d in
th
e targ
et, final
ly the con
c
lu
sion
of e
s
tim
a
te is defin
ed
. [3]
The mov
e
s
and
sub
s
tan
c
es of AHP
roughly
con
s
i
s
t of the fo
llowin
g
aspe
cts: esta
b
lish
the hierarchi
c
al
stru
cture; b
uild the jud
g
m
ent
matrix
of every layer facto
r
s;
test the co
n
s
iste
ncy of the
judgme
n
t ma
trix and
revi
se it; a
scertain the
seq
uen
ce p
r
efe
r
ence of eve
r
y layer fa
cto
r
s;
ascertai
n
th
e overall
seq
uen
ce p
r
eference; ins
pec
t the totality c
o
ns
is
tenc
y.[2] AHP is
us
ed to
obtain the pro
portion
s of evaluati
on ind
e
x
es in the mo
tion perfo
rms.
3.
An Example
of Sy
nthetically
Analy
s
is
of a Motion
Performs Ev
aluation o
f
NC
As the NC machi
ne tool is
developin
g
a
nd
it
s st
r
u
ct
u
r
e cha
r
a
c
t
e
ri
st
ics i
s
impr
ov
e
d
，
the
function a
nd the quality are
raisin
g su
bst
antially
. The motion pe
rforms evaluatio
n indexe
s
of NC
are feed velo
city (m/min), the rotation
ra
te of ch
ief axis(r/min), the x/y/
z coordinat
e stro
ke
s(mm
),
the rang
e of swing a
ngle (°), the capa
city of
tool magazine a
nd the tool ch
angin
g
time(s).
The feed velo
city affects the pro
c
e
ssi
ng
quality,
produ
ce efficie
n
cy
and the tool life. The
chief axis
of NC i
s
d
r
ived
by t
he dire
ct-curre
nt or alt
e
rnatin
g-
cu
rrent motor to
have wid
e
sp
eed
regul
ation
ra
nge
and
hig
h
rotatio
n
a
c
curacy.
High
rotation
rat
e
of chief axi
s
i
s
b
enefici
a
l to
raisi
n
g
the
proce
s
sing
qu
a
lity of part
s
.
The x/y/
z co
ordin
a
te stro
ke
s
a
r
e
the size of coo
r
di
nate
stro
ke
s, it d
e
termin
es the
pro
c
e
ssi
ng
ra
nge, n
a
mely
the si
ze
of th
e p
r
o
c
e
s
sed
part. Th
e
pap
e
r
sele
ct x coo
r
dinate st
ro
ke
as the evalu
a
tion
index. The ra
nge of
swin
g angl
e
is the co
ntro
lled
rang
e of swin
g angle
co
ordinate
s
, it affects th
e pr
ocessing a
b
ility to the spa
c
e
positio
n of pa
rts.
The
capa
city
of tool mag
a
zine an
d the t
ool chan
ging
time strai
ghtl
y
infl
uence th
e produ
ctivity of
NC. The
cap
a
city of tool maga
zine i
s
the qua
ntit
y o
f
tools that can be checked in it. The tool
cha
ngin
g
tim
e
is th
e time
that the tool
used in
chie
f axis is cha
nged
by the
tool u
s
ed i
n
next
prod
uctio
n
proce
s
se
s in the tool maga
zi
ne.
In evaluation
model, n equ
als 4. The mo
tion perfo
rms
grad
es of NC are A, B, C and D.
3.1. Foundin
g
the Ma
tte
r-element Mod
e
l
Identifying cla
ssi
cal matte
r- elem
ent is shown in Equa
tion (6)
5
,
1
100
,
80
260
,
240
1200
,
1000
10000
,
8000
30
,
20
)
(
6
5
4
3
2
1
c
c
c
c
c
c
N
R
A
a
12
,
5
80
,
60
240
,
220
1000
,
800
8000
,
6000
20
,
15
)
(
6
5
4
3
2
1
c
c
c
c
c
c
N
R
B
B
18
,
12
60
,
30
220
,
200
800
,
600
6000
,
5000
15
,
10
)
(
6
5
4
3
2
1
c
c
c
c
c
c
N
R
C
C
25
,
18
30
,
16
200
,
180
600
,
400
5000
,
3000
10
,
8
)
(
6
5
4
3
2
1
c
c
c
c
c
c
N
R
D
D
(6)
Identifying extensio
nal mat
t
er-el
e
ment is sho
w
n in Eq
uation (7
)
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: 4849 – 4
853
4852
25
,
1
100
,
16
260
,
180
1200
,
400
10000
,
3000
30
,
8
)
(
6
5
4
3
2
1
c
c
c
c
c
c
N
R
P
P
(7)
Identifying the matter-ele
m
ent awaitin
g
evaluation i
s
sh
own in Equation (8).
12
24
210
650
8100
18
)
(
6
5
4
3
2
1
c
c
c
c
c
c
P
R
M
M
(8)
3.2. Calculati
ng the Relati
onal Degr
ee
The rel
a
tional
degre
e
of the NC i
s
sh
own in Equation
(9).
353
.
0
3
25
.
0
167
.
0
47
.
0
4
0
429
.
0
5
.
0
25
.
0
42
.
0
231
.
0
0
818
.
0
25
.
0
5
.
0
033
.
0
25
.
0
75
.
1
875
.
0
5
.
0
583
.
0
036
.
0
5455
.
0
M
K
(9)
3.3. Defining
the Weig
ht
of ev
er
y
Ev
a
l
uation Inde
x b
y
AHP
Acco
rdi
ng to
six eval
uatio
n ind
e
xes de
fined,
qu
antifying the
de
ci
sion
an
alysi
s
, 1 to
9
and their recipro
c
al u
s
ed,
the matrix
S about relat
i
ve importan
c
e two each other ind
e
xe
s is
founde
d. As shown in Equa
tion (10
)
1
2
1
1
1
2
1
2
1
1
2
1
4
1
3
1
5
1
1
2
1
1
2
1
4
1
1
4
1
1
1
3
1
1
3
2
1
1
2
1
2
5
4
3
2
1
S
(10)
Approximate
method of
so
lvi
ng is
used,
feature
vect
ors
w
an
d maxi
mal characte
ristic
ma
x
are gotten [5
], and sho
w
n
in Equation (11).
T
w
142
.
0
058
.
0
128
.
0
152
.
0
169
.
0
351
.
0
132
.
6
max
(11
)
Becau
s
e
of obje
c
tive things’
compl
e
xity
and the un
derstandi
ng
variety of pe
ople, the
con
c
lu
sio
n
s p
r
oba
bly are n
o
t same
whe
n
a great qu
a
n
tity factors a
r
e co
mpa
r
ed
with ea
ch oth
e
r.
So examinin
g the
con
s
i
s
tency of
matri
x
S is ne
ce
ssary. T
he
co
nsi
s
ten
c
y target is
sh
own
in
Equation (12) [6].
0264
.
0
5
6
132
.
6
1
max
n
n
CI
(12
)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Applyin
g
Exte
nics Theo
ry to Motion Perf
orm
s
Evalu
a
tion of Num
e
ri
cal Ma
chin
es
(Ch
en Liu
)
4853
The ave
r
a
g
e
ran
dom
ness target i
s
sh
own
26
.
1
RI
thoug
h
table loo
k
-up
,
so th
e
rand
omn
e
ss
con
s
i
s
ten
c
y ratio is sh
own in Equation (13).
1
.
0
021
.
0
26
.
1
0264
.
0
RI
CI
CR
(13)
The matrix S meets the ne
eds of con
s
ist
ency. The fea
t
ure vecto
r
s
w
sho
w
s the we
ights
of evaluation
indexe
s
.
3.4. Motion Performs Ev
aluation Gr
a
d
e
The feature vectors
w
and equation (9) a
r
e sub
s
tituted
in
Equation (5), the synthe
tical
relation
al deg
ree of motion
perfo
rms eval
uati
on grade
of the NC is
shown in Equa
tion (14
)
.
T
K
391
.
1
279
.
0
073
.
0
140
.
0
(14
)
Based o
n
the
large
s
t deg
re
e of membership,
the motion perfo
rms g
r
ade of this NC is B.
4. Conclusio
n
(1) In thi
s
pa
per, th
e
rea
s
onabl
e motio
n
pe
rf
orms e
v
aluation i
n
d
e
xes
are
sele
cted, a
n
d
the motion performs
ev
aluation s
y
s
t
em of NC is
founded. Re
lational degree is
c
a
lc
ulated though
relation
al fun
c
tion, the wei
ghs a
r
e calcu
l
ated by
AHP. Therefo
r
e, the motion pe
rform
s
evaluati
on
is more rea
s
o
nable.
(2) T
he moti
on pe
rform
s
evaluation of
NC b
a
sed o
n
extenics th
eory a
c
cord
s with the
reality of it, th
e evaluation
con
c
lu
sio
n
is
depe
ndabl
e.
(3) Th
e pap
e
r
con
s
id
ered
the pra
c
tice
usa
ge
of the motion pe
rforms
evaluatio
n of NC,
the evaluatio
n con
c
lu
sio
n
is feasibl
e
. It suppli
ed t
he ma
chine
r
y choice wit
h
an overall
and
reliabl
e meth
od.
Referen
ces
[1]
Zhao Yug
a
n
g
, Song
xia
n
ch
un. T
e
chnolo
g
y
of Num
e
ric
a
l Co
ntrol. Be
ijin
g: Engi
ne
er
ing Ind
u
str
y
Publ
ishi
ng H
o
u
s
e. 2003: 1-
13.
[2]
Che
n
Liu,
Xu
ming W
a
n
g
.
Quality Eval
ua
tion of Belt C
onv
ey
or Base
d on Extenics
T
heory.
4
th
Internatio
na
l
C
onfere
n
ce on Manufactur
i
ng
Scienc
e a
nd E
ngi
neer
in
g (IC
M
SE). Dali
an,
Chin
a. 2
013
;
694-
697: 2
960-
296
3
.
[3] Z
hang
Gen
bao
,
Pang Jihon
g.
A
comprehen
sive eval
uati
o
n
method of fuzz
y
matter elem
ent for CN
C
equ
ipme
nt qua
lit
y
.
Jour
nal
of Cho
ngq
in
g Uni
v
ersity
.
201
1; 3
4
: 36-41.
[4]
Cai W
en. Mat
t
er-elem
ent modl
e an
d ap
pl
icatio
n. Beiji
ng
: Literature of
Science a
n
d
T
e
chnolo
g
y
Publ
ishi
ng H
o
u
s
e. 2008: 3
8
-6
9.
[5]
Y
e
Y
a
oju
n
, W
a
ng sh
ouj
un, W
e
i le
i.
Appro
x
i
m
ate
comp
utation o
n
the ma
ximum ei
ge
nval
ue of matri
x
s
.
Journ
a
l of He
n
an
Agr
i
cult
ural
Univers
i
ty
.
200
1; 35: 69-7
1
.
[6]
W
ang
Y
i
n
g
l
uo. S
y
stem En
gin
e
e
rin
g
. Beiji
ng: Engi
neer
in
g Industr
y
P
ubl
ishi
ng Ho
use. 20
0
3
: 1
12-1
34.
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