TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 10, Octobe
r 20
14, pp. 7108
~ 711
3
DOI: 10.115
9
1
/telkomni
ka.
v
12i8.560
4
7108
Re
cei
v
ed
Jan
uary 8, 2014;
Re
vised June
20, 2014; Accepte
d
Jul
y
1
5
, 2014
Resear
ch on Static Tension Ratio Characteristic of
Double-Vessel Friction Hoist System Components
Xie Lirong*, Ge Laifu, Ko
ng Jun, Che
ng Jing
Electric
al En
g
i
ne
erin
g Col
l
e
g
e
of Xi
nji
a
n
g
U
n
iversit
y
, Urum
qi, 830
04
7, Chi
n
a
*Corres
p
o
ndi
n
g
author, e-ma
i
l
:
w
z
ywww
xr
@
163.com
A
b
st
r
a
ct
Dou
b
le-v
essel
mu
lti-rop
e
friction ho
ist system, of
w
h
ich the lifting, starti
n
g
, runni
ng, an
d braki
n
g
must
me
et the safety con
d
i
tions
i
n
o
per
ation. N
on-ski
d safety bo
un
dary co
nditi
on
s w
e
re origi
n
all
y
deter
mi
ned
by
Euler
’
s
for
m
u
l
a
.
In or
der to
av
oid
the
co
mp
le
x task of
check
an
d c
heck-a
g
ain
calc
ul
ation
i
n
the friction hois
t system
design. In this res
e
arch, stat
ic tension ratio c, whic
h wa
s clos
ely
bonded with anti-
skid design was directly
brought into
the analysis and res
ear
ch
on the system
. As a result, character
i
stic of
static tensio
n r
a
tio c of c
o
mp
one
nt qu
ality
o
f
friction ho
ist s
ystem
w
a
s fou
nd, w
h
ich
offers a si
mp
le, so
u
n
d
and re
lia
bl
e theoretic
al fou
n
d
a
tion for the a
n
t
i-ski
d an
d opti
m
i
z
at
io
n of syst
em co
nfigur
ati
on.
Ke
y
w
ords
:
dou
ble-v
e
sse
l f
r
iction
ho
ist sy
stem, static
ten
s
io
n
ratio,
no
n-
skid s
a
fety, di
me
nsi
onl
ess re
lative
va
l
ue
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
Multi-ro
pe fri
c
tion h
o
ist is one of the
most
imp
o
rta
n
t equipm
ent
in co
al, black metal,
non-fe
rrou
s
metal and
ch
emical
minin
g
produ
ction.
Frictio
n
hoi
st system
can
be divide
d i
n
to
doubl
e-ve
sse
l
friction
hoi
st and
singl
e-v
e
ssel fri
c
ti
on
hoist
system.
Dou
b
le
-vessel frictio
n
hoi
st
system, i
s
ge
nerally
use
d
for si
ngle l
e
vel (laye
r) lifti
ng only, an
d
a si
ngle
-
vessel fri
c
tion
h
o
ist
system
can b
e
use
d
for mu
ltiple levels (l
ayers) lifting.
Based
on p
r
i
n
cipl
es of fri
c
tional fo
rce mult
i-ro
pe fri
c
tion hoi
st re
quire
s that t
hat the
system can bra
k
e
with n
on-ski
d secu
rity complyin
g with
the g
i
ven torqu
e
of deceleration
wheth
e
r in n
o
rmal o
p
e
r
ati
on or in
eme
r
gen
cy,
and t
hat there i
s
on skid b
e
tween the h
o
ist
i
ng
rope
and the
friction pull
e
y. The probl
e
m
of slip in
friction hoi
st is of great imp
o
rtan
ce relati
ng
the safety of mining p
r
odu
ction.
Until
re
cently
, a lot
of re
sea
r
ch
on th
e p
r
obl
em
o
f
slip
in f
r
icti
on h
o
ist
ha
s bee
n
con
d
u
c
ted b
y
sch
olars
worl
dwi
de. T
he existi
n
g
resea
r
ch are
mainly focuse
d on
act
ual
para
m
eter,
combine
d
with
the safety regulatio
n
in anti-skid ch
e
cki
ng calculat
ion
and anti-ski
d
measures [4
-7] without
con
s
id
erin
g establi
s
hi
ng
the mathem
atical mod
e
l
of friction hoist
comp
one
nt quality using d
i
mensi
onle
s
s relative par
a
m
eters syste
m
atically.
A
s
a res
u
lt
,
sy
st
em
optimizatio
n
and resea
r
ch
on stati
c
te
nsio
n rati
o chara
c
te
risti
c
of
friction ho
ist
have
b
een
rest
ricte
d
. Fo
cu
sing
on
do
uble-ve
ssel friction h
o
is
t system,
this p
aper
carried out
the resea
r
ch
on the rel
a
tionshi
p betwee
n
static ten
s
i
on ra
tio
a
nd system comp
onent,
usi
ng dimen
s
ionl
ess
relative parameters
.
Dou
b
le-ve
s
se
l multi-rop
e
fri
c
tion hoi
st is
main
ly con
s
i
s
t of frictional pulley, hoistin
g rope,
hoistin
g vessel and bal
an
ce rope et
c., as sh
own in Figure 1.
Figure 1. The
Mode of Fri
c
tion Hoi
s
t System
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Static Tensi
o
n Ratio Characteri
stic
of
Double
-
Ve
ssel Frictio
n
Hoi
s
t
…
(Xie Liro
ng
)
7109
2. Sy
mbol Definition
2.1. Actu
al Parameter De
finition
Plenty of pa
ramete
rs a
r
e
involved i
n
dou
ble-ve
ssel fri
c
tion
ho
ist sy
stem.
Symbols
involved are
defined a
s
fol
l
ows:
(1)
Dea
d
w
e
ig
ht of v
e
ssel Q
z
(kg
)
;
Rated lo
ad Q
N
(kg
)
;
Static tension
ratio c.
(2)
Hoi
s
ting rope pa
ram
e
ters
Numb
er of ho
isting ro
pe n;
Weight of rope per meter p(k
g
/m);
Ultimate lengt
h of suspen
si
on hoi
sting ro
pe L
o
(m
);
Heig
ht of suspen
sion h
o
isti
ng rop
e
H
o
(m)
.
2.2. Dimensionless Relativ
e
Parameter De
finition
A prope
r value sho
u
ld be
selecte
d
as
the base
d
value first, and
then the dimensi
onle
s
s
relative pa
ra
meters are d
e
fined a
s
:
Vessel dea
d
w
eig
h
t coefficient
Z
z
N
Q
Q
Her
e
, Q
z
wa
s sele
cted a
s
the ba
sed val
ue.
Weig
ht coeffi
cient of su
sp
ensi
on hoi
stin
g rope
0
H
N
npH
Q
.
Heig
ht coefficient of suspe
n
sio
n
hoi
sting
rope
0
0
0
H
h
L
.
3. Sy
stem Componen
t
s
and Sta
t
ic Tension Ratio
c
Static tensi
o
n
ratio
c i
s
the
ratio
betwee
n
the m
a
ximum ten
s
ion
si
de a
nd the
m
i
nimum
tensio
n sid
e
of the friction
whe
e
l, or rath
er.
1
2
T
c
T
.
T
1
stand
s for
the value of the maximum
static ten
s
ion
side, an
d T
2
stand
s for th
e value
of the minim
u
m stati
c
ten
s
ion
sid
e
. While stati
c
ten
s
ion
ratio
c i
s
eq
ual to
or small
e
r tha
n
the
boun
dary m
a
ximum value
[c] pe
rmitted (c
≤
[
c
]), the
safety regul
ation of the
system i
s
m
e
t.
Otherwise, the anti-skid
sa
fety regulatio
n w
ill not be
met, and the system
will be at risk.
3.1. Vessel Dead
w
e
ig
ht Coefficient an
d Susp
ensio
n
Hoisting
Rope Heigh
t
Coe
fficien
t
The maximu
m static tension ratio of double ve
ssel
friction hoi
st is the tensi
on ratio
betwe
en the
full load
maximum ten
s
ion
sid
e
an
d th
e load
-fre
e
minimum te
n
s
ion
sid
e
of
the
friction wheel
[2, 3, 8].
So:
0
00
1
Nz
z
zz
Q
Q
npH
c
Q
npH
h
(1)
Equation (1
)
sho
w
s that the va
lue of static tensi
on ratio
c is co
m
p
letely determined by
the
value of
vessel dead
weight coeffici
ent
z
and hei
gh
t coeffici
ent o
f
su
spe
n
sio
n
hoistin
g rope
0
h
, and will de
cre
a
se a
s
z
or
0
h
increa
se
s. The maximum
static ten
s
io
n ratio
c of doubl
e-
vessel fri
c
tion
hoist
syste
m
is e
quivale
nt to t
he
summ
ation of 1
and
the recip
r
o
c
a
l
of su
sp
en
si
on
hoistin
g rop
e
weig
ht coefficient of load-free sid
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 710
8
– 7113
7110
0
1
1
c
(2)
It is reveal
ed by equation (2) that the va
lue
of c will
decrease
as the value of
0
increa
se
s. So, only by changing the val
ue of
0
, the value of c ca
n b
e
adju
s
ted.
2.2. Minimu
m Permitting Height o
f
Suspend
Hois
ting Rop
e
By changi
ng
the form of
e
quation
(1
) th
e ultimate
su
spe
n
si
on h
e
i
ght co
efficien
t
0
h
can
be expre
s
sed
as a functio
n
of c and
z
.
0
1(
1
)
z
c
h
c
(3)
Equation
(3
)
sho
w
s that
while
c e
qual
s to the
maxi
mum valu
e p
e
rmitted
co
n
s
ide
r
ing
anti-skid safe
ty,
and
z
is co
nstant,
0
h
will b
e
the minimu
m value of susp
end hoi
sti
ng rope
height coeffici
ent, and will d
e
crea
se a
s
z
in
cre
a
s
e
s.
If the suspen
sion
hoi
sting
rope
heig
h
t coeffici
ent is
smalle
r tha
n
the minimum
height
coeffici
ent
0m
i
n
h
,
the
value of c
will be greater
than
the maximum v
a
lue permitted, whi
c
h
violates the
anti-skid
safe
ty condition
s.
So the valu
e of
0
h
figured
out by Equ
a
tion (3) i
s
th
e
minimum
value of
susp
e
n
sio
n
h
o
istin
g
rope
hei
gh
t coeffici
ent
of dou
ble-ve
ssel fri
c
tion
hoist
system, nam
ely the minimum value of
0
h
permitted withi
n
the safety bound
ary co
nd
ition.
2.3. Minimu
m Vessel De
ad
w
e
igh
t
Vessel dea
d
w
eig
h
t coefficient can b
e
figure
d
out by cha
ngin
g
the form of Equat
ion (3
).
0
1
1
z
ch
c
(4)
Equation (4
) sho
w
s that while c equ
als to the maximum permitti
ng value co
n
s
ide
r
ing
anti-skid
safe
ty, and
0
h
stan
d
s
for
a
certai
n value, then
the value
of
z
figured
out b
y
Equation
(4) i
s
the mini
mum value of
dead
weight
of vessel a
n
d
will decrea
s
e
as
0
h
incr
eas
e
s.
If the vessel
dead
weig
ht coeffici
ent i
s
sm
alle
r th
an the mini
mum value
of vessel
dead
weig
ht
coefficient , th
e value
of
c
will b
e
g
r
eate
r
than
the
ma
ximum pe
rmit
ting value,
which
violate the anti-skid safety regulation.
Therefo
r
e, the value of vessel dead
weig
ht coeffi
cient
figured o
u
t by Equation (4
) is the minimu
m one.
3. Dimensio
nless Rela
tiv
e
Value of Sy
stem
Component Par
a
m
e
ter
s
and Static Ten
s
ion
Ratio
The dim
e
n
s
io
nless relative
value of sy
st
em compo
n
e
n
t para
m
eters can b
e
obt
ained
by
repla
c
in
g
z
involved in ea
ch
equation [9
~13] by Equation (4
).
Weig
ht coeffi
cient of ultimate height of su
spe
n
si
on h
o
isting rope.
0
0
1
11
z
L
N
npL
c
Qh
c
(5)
Weig
ht coeffi
cient pe
r met
e
r of hoistin
g rope.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Static Tensi
o
n Ratio Characteri
stic
of
Double
-
Ve
ssel Frictio
n
Hoi
s
t
…
(Xie Liro
ng
)
7111
00
1
*
/1
1
z
N
pc
p
Qn
L
h
c
(6)
Weig
ht coeffi
cient of actu
a
l
height of su
spe
n
si
on hoi
sting rope.
00
0
0
1(
)
11
z
H
N
npH
h
c
h
Qh
c
(7)
Weig
ht coeffi
cient of load
-free vessel
sid
e
.
00
0
0
1
11
zz
N
Q
npH
h
Qh
c
(8)
Weig
ht coeffi
cient of full load vessel si
d
e
.
0
0
1
11
Nz
z
m
N
Q
Q
npH
c
Qh
c
(9)
Coeffici
ent of
the
summ
ated
weig
ht of
both
sid
e
s
whe
n
o
ne
si
de i
s
lo
ad-f
r
ee a
n
d
anothe
r is full
load.
0
0
2(
)
1
1
Nz
m
N
Q
Q
npH
c
Qc
(10)
Coeffici
ent of the summ
ate
d
weig
ht of
both side
s whe
n
both sid
e
s
are loa
d
-free.
0
00
2(
)
2
1
z
N
Q
npH
Qc
(11)
Coeffici
ent of the summ
ate
d
weig
ht of
both side
s whe
n
both sid
e
s
are full load.
0
2(
)
2
1
Nz
mm
N
Q
Q
npH
c
Qc
(12)
It is revealed
by equation
(5)~(12
)
that each co
effici
ent is inverse
l
y propo
rtiona
l to c-1,
and the valu
e of
L
,
*
p
,
H
are al
l equal. In addition, each coefficient is a
function of si
ngle
variable
c wit
h
an exce
pt that
z
and
H
are fu
nction
s of c a
nd
0
h
.
4. Parameters in Various Forms
Since th
e stat
ic ten
s
ion
rati
o c i
s
the
rati
o of
stati
c
ten
s
ion
of two
si
des
of frictio
n
whe
e
l,
function
s of c can be
conv
erted into fun
c
tion
s of T
1
and T
2
.
Symbols of
dimensi
onl
ess relative
par
am
eters of system
compo
nent
s and its
relation
shi
p
with actual p
a
rameters, othe
r dimen
s
io
nle
ss
relative pa
ramete
rs,
static tensi
on ratio
c and
static tensi
on T are listed in the ta
ble bello
w.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 10, Octobe
r 2014: 710
8
– 7113
7112
Table 1. Para
meters and Its Vario
u
s Fo
rms of Fri
c
tion
Hoist Compo
nents
No.
S
y
mbol
Actual parameter
s
rela
tive paramet
ers
C function
T function
1
z
N
Z
Q
Q
z
1
1
0
c
ch
2
1
0
1
2
T
T
h
T
T
2
H
N
Q
npH
0
0
0
1
)
1
(
h
h
Z
1
0
c
ch
2
1
0
1
T
T
h
T
3
L
N
Q
npL
0
0
1
1
h
Z
1
c
c
2
1
1
T
T
T
4
*
p
0
nL
Q
p
N
Ditto Ditto
Ditto
5
m
N
Z
N
Q
npH
Q
Q
0
Ditto Ditto
Ditto
6
O
N
Z
Q
npH
Q
0
0
0
1
h
h
Z
1
1
c
2
1
2
T
T
T
7
OO
N
Z
Q
npH
Q
)
(
2
0
0
0
1
)
(
2
h
h
Z
1
2
c
2
1
2
2
T
T
T
8
mm
N
Z
N
Q
npH
Q
Q
)
(
2
0
0
0
1
)
1
(
2
h
h
1
2
c
c
2
1
1
2
T
T
T
9
Om
N
Z
N
Q
npH
Q
Q
)
(
2
0
0
0
1
2
1
h
h
Z
1
1
c
c
2
1
2
1
T
T
T
T
As is sh
own in Table 1, e
a
ch p
a
ra
met
e
r
of system
comp
one
nts
can b
e
expre
s
sed in
four form
s. T
hey are the f
o
rm of
a
c
tual
value, the form of dimen
s
ionle
ss
relative value, funct
i
ons
of static ten
s
i
on ratio
c a
n
d
func
tio
n
s
of static ten
s
io
n of the hoi
sti
ng ro
pe. Ea
ch of the four
has
its uniqu
e fea
t
ure and valu
e.
(1) A
c
tual value paramete
r
s: Intuit
ive, e
a
sy to unde
rstand and ma
ster.
(2)
Dime
nsi
o
nless relative
value: Abstract, it
can
si
mplify the cal
c
ulatio
n; sig
n
ificantly,
truths a
nd rul
e
s in the prob
lem can e
a
sil
y
be revealed
and theori
z
e
d
.
(3) The
c fun
c
tion:
Usi
ng
static ten
s
ion
ratio
c
in cal
c
u
l
ation without the
ne
ed
of a
n
ti-skid
che
c
king
calculation, it
can
ma
ke the
opt
imizatio
n
an
d
dispatch of t
he
system
m
o
re vali
d, sou
nd
and re
asona
b
l
e.
(4) The
stati
c
ten
s
ion
T
function: M
a
i
n
ly
use
d
in
the checkin
g
cal
c
ulatio
n, safety
insp
ectio
n
an
d equipm
ent testing of t
he hoist
sy
stem before
a
ppli
c
ation.
Once the mi
nimum
weig
h
t
of load-free
side
i
s
m
e
a
s
ured, nu
merous
other pa
rameters
are dete
r
min
ed as
well.
5 Conclu
sion
At prese
n
t, in friction hoi
st engine
eri
n
g,
system co
mpone
nts an
d its param
e
t
ers a
r
e
usu
a
lly pre
-
selecte
d
and
then ch
ecked by ca
l
c
u
l
ation wh
eth
e
r o
r
not the pre-sele
cted
comp
one
nts
and its pa
ra
meters co
mpl
y
with the ant
i-skid safety
regul
ation
s
. If not, the related
comp
one
nts
and it
s pa
ra
meters
sho
u
l
d
be
adju
s
te
d an
d
che
c
ked ove
r
a
gai
n by
cal
c
ulat
ion.
Only wh
en a
ll of the anti-ski
d safety regulatio
ns
a
r
e sati
sfied can the pa
ra
meters be fi
nally
determi
ned. This is the
so-called h
euri
s
tic al
go
rithm
,
which can
not be avoid
ed in engin
e
e
ring
usin
g actu
al para
m
eters.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Re
sea
r
ch on
Static Tensi
o
n Ratio Characteri
stic
of
Double
-
Ve
ssel Frictio
n
Hoi
s
t
…
(Xie Liro
ng
)
7113
(1) In order t
o
avoid the
s
hortcoming and facilitate t
he de
si
gn
in friction hoi
st system,
static te
nsi
o
n ratio
c was
dire
ctly b
r
oug
ht into t
he
cal
c
ulatio
n in di
men
s
i
onle
s
s rel
a
tive
para
m
eters. As a result, para
m
eter va
lue figure
d
out by this mean
s fits the anti-skid safety
regul
ation
s
very well.
(2) Fou
r
fo
rm
s of
com
pone
nt paramete
r
s a
r
e
o
ffered
in the p
ape
r t
o
facilitate th
e de
sign
in engin
eer.
Each h
a
s its
uniqu
e feature and value.
They ca
n also be converte
d into ea
ch ot
her,
makin
g
the d
e
sig
n
and
cal
c
ulatio
n more
conveni
ent.
(3) It is reveal
ed by table I that the qualit
y
of system compon
ent increa
se
s as the
height
of su
spe
nd h
o
isting
rop
e
i
n
crea
se
s, de
cre
a
ses
as
st
atic ten
s
ion
ratio increa
se
s, and
de
cre
a
se
s
as the ten
s
io
n margi
n
of two si
de
s of friction wheel in
cre
a
ses.
Ackn
o
w
l
e
dg
ements
This research is sp
on
sored by the “Natio
n
a
l Nat
u
re Sci
e
n
c
e
Found
ation o
f
China”
(num
bered 5
1264
036, an
d
61362
030
).
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ces
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hang
F
u
d
e
.
T
he min
e
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qui
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m
ent
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oal
Industr
y
Pu
bli
s
hin
g
Hous
e. 2
004.
[2]
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a State Administrati
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i
sio
n
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n
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quar
antin
e. Ch
ina Nati
on
a
l
Standar
diz
a
tio
n
Ma
nag
eme
n
t Committe
e. GBl64
23-2
0
0
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n
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eta
l
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ienc
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