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International Compressor Engineering Conference
School of Mechanical Engineering
1986
An Approach for a High-Speed Double Acting
Compressor Using a Single Elastic Piston Ring to
Reduce the Specific Power
X. Qian
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Qian, X., "An Approach for a High-Speed Double Acting Compressor Using a Single Elastic Piston Ring to Reduce the Specific Power"
(1986). International Compressor Engineering Conference. Paper 584.
http://docs.lib.purdue.edu/icec/584
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AN APPROACH FOR A HIGH SPEED DOUBLE ACTING COMPRESSOR
USING A SINGLE ELASTIC PISTON RING TO REDUCE THE SPECIFIC
POWER
Qian Xinghu a
Chemic al Machin ery Sectio n, Xi'an Jiaoto ng Unive rsity,
The People 's Repub lic of China
ABSTRACT
Tris paper, throug h analy3 is to the specif ic power
of the compre ssor, indica tes that to reduce the power
loss caused by frictio n is an import ant way to reduce
the specif ic power of the compre ssor, invest igates the
realiz abilit y employ ing a single piston ring or a piston
ring with small elasti city in the high speed double acting compre ssor, and raises a standp oint for a high
speed double acting compre ssor to use a single piston
ring with small elasti city to reduce the specif ic power.
The experim ent to verify this standp oint has been done
at the compre ssor of the series 12-10/ 8-I, the effici ent
result , baring reduce d the specif ic power by 3 - 3.5 %,
has b_een shown.
SYMBOLS
b
thickn ess of piston ring
D
piston diamet er
f
area for lear off gas
g
accele r ation of qravet y
K
Cp/Cv
m
polytr opic expone nt of the proces s
989
N
shaft power
indicated power
mechanical power
piston ring frictional power
piston ring frictional power from gas pressure
Piston ring frictional power from elastic force
p
pressure of piston ring to cylinder
Pa
pressure of piston ring inertia
p
gas pressure after piston ring
0
pd
discharge pressure
Pg
gas perssure before piston ring
pi
indicated perssure
pm
frictional pressure
Prg
gas pressure in the piston ring trough
Prs
pressure of elastic to cylinder
Ps
suction pressure
Q
capacity
q
specific power
qi
specific indicated power
(qi)
theroretical specific indicated power
qm
specific mechanical power
R
gas constant
r
crank radius
s
piston strok
T
temperature of lear off gas
T5
suction temper~ture
990
t
width of piston ring
v
piston veloci ty
X
piston displac ement
relativ e cleara nce volume
relativ e discha rge pressu re loss
relativ e suctio n pressu re loss
tetal pressu re ratio
stage pressu re ratio
mecha nical efficie ncy of piston ring
volum etric efficie ncy
coeffi cient of frectio n
runoff coeffi cient
w
angula r veloci ty compre ssor
INTRODUCTION
For the compre ssor to reduce the specif ic power is
very import ant. At presen t, the studie s for reduct the
specif ic power are more coucen trated on the interc ooler,
valves , gasflow pulse, howeve r for this paper, is concentra ted on the reduct ion of frectio n. The compre ssor
power loss caused by frectio n are 5 - 15 %'''of the
compre ssor shaft, it equals to the power loss caused by
the valves~ Among the frictio n power loss, the loss
caused by the piston rings are 43 - 53 %cu. So reduci ng
the number of the piston rings or abatin g the piston
ring elasti city is a way to decrea se the frictio n power
loss. When this way is adopte d, the leakag e increa se,
conseq uently the capaci ty decrea se. To proven t this, two
ways may be employ ed:
a) Turn the harmfu l suspen sion to a benef icial
suspen sion, i. e. during the suspen sion proces s, for a
991
double acting compressor, let the high pressure gas via
the suspension clearance entre the other side cylinder,
being counted in the capacity.
b) Increase the cylinder diameter by a small differem
to make up the leakage. The experiment on the high speed
double acting compressor 12-10/8-I has shown the a tangible result to reduce the specific power by 3 - 3.5 %.
THE WAY TO REDUCE THE SPECIFIC POWER
The formula for specific power is q = N/Q. The N
consists of the indicated power Ni ard the mechanical
power Nm (mainly friction power). Reforning the-formula
as
N'
Ni
+ m
q
o-
cr
Let
Ni
( 1)
qi:c Q
N
q =
m
m
( 2}
u-
qi' qm represent the specific indicated power and
the specific mechamical power separat.ely so
(3)
The formula of indicated power of multistage comprestzl
sor is derived by considering the material
( with the
1
simplification f.=£ /i, T ./T = 1 )
l.
Ni= 1. 634
Sl.
m
:':'"""':f
m-
1
S1
N{(E.1/i
p 1 Q.£
s -i••
Substitutinf" it tnt0 (1)
992
1
( 1
~
0
_+_j_ds
m-1
)J -iii-
_ 1} i
1+Sd ~!11;1
II{~C:c1/i ( -.1-6
m
1.634p s 1~z.
q.:=
m-r.
l
.c"'l
-1} 1
( 4)
s
From (4) we can sero that for a given ambient the·qi
depents On only the relative re3ictan ce pressure loSS
dd. hat is the current way decreasi ng J s' d" d to reduces
q1 • However it is limited to decrease ds and Od. If tfs=O,
Od= O, the ideal value of the q 1 could be represen ted as
m-1
cE im - 1 ) 1
~~
qi = 1.634p s 1 mr ..,
a,
1
For a two stage compress or with a discharg e pressure
3
9 ata the (q 1 )"' 4.22 KW/m /mln. It is obviousl y when 6 8 ,
is approach ing to zeroes a fangible reductio n of q.l is
5d
.
too difficul t to do.
2
Differe tiate ( 2) and cousider ing Q= rrD vr!A/4 :
Nm
dqm =
dN
<r ( ~
m
dA A.
~ )
( 5)
Based on (5), three approach es are availabl e:
a) Decrease friction power loss Nm. b) Increas.e di<charge coeff5 cientJI. • c) Increase the cylinder diameter
D~ Only dEcreasi ng N will be discusse d in this paper.
m
THE ME'IBDD TO DECREASE THE
FRICTION POWER LOSS OF THE PISTON
The friction power loss is vital importan t for a
high speed compress or. There are two parts of the frichion
the
~ower loss -- the useful and useless. The function of
piston ring is of the dynamic sealing. That is useful.
However because of the chopping of the suction and discharge the sealing is neces,sar y only during the compres993
sidg and discharging processes and the se~ling is no need
for sueking and the compressor starting, stopping, unloadlng .so that is the useless part • To analyses the utility
rate ,.the concept on mechanical efficiency of the piston
ring is introdued bellow
?=
N
rP
r
(6)
Wher, N -- the fri9tion power loss caused by frecrg
tion sealing.
Nr
the total frection power loss of the
piston ring.
The Nr depends on its pV value, V represents (Fig. )
1
velocity relative to the cylinder wall, p represents the
contact pressure by which the piston ring acts on the
cylinder wall. There are two parts within p. One is Prs
caused by the piston ring elastic force, the other is gas
pressure p • p
g
rs gives a pre-pressure agains the cylinder
wall, we name it as the first sealing, the p functions
.g
as sealing also • However it acts after esfablishing the
first sealing, subsequently the first sealing is useless.
The Fig. 2a illustrates the ideal relation between an
ideal uiston ring elaEtic p
rs and '-"• i.e. when necessary
to establish the first sealing the p
rs has a certain
value, when unnecessary the Prsis nulled, ccnseqently
only p is left, its average is ~p/2= (p- ~ )/2. Bat
g
g ·o
we ha1e no way to aporoach that, the only way we can do
is to reduce p
rs to the minimum -- the installating
stress (PrJ• the curve of contat pressure p and e is
shown in Fig. Zb, it is piled from CP )and AP/2. The
rs
friction power loss caused by piston ring elastic force
is calculeted throngh
(7)
and that caused by p
g
994
Nrg= (D-2t)(pg1 + Pg2+. • .+ Pgi)bVJ.i.~ Db~#4p
(e)
The total
Nr = Nrs + Nrg = DbV..U.(ip rs+Ap/2),·
(9)
Substitut ing (8), (9) into (6)
1
1 +
The
raise
'I
(10)
Z1prs
-
~p
ap in formula ( 10) is given, so the Rnly way to
is to necreB.se i or Prs • From formulas (7), (9}.
( t1)
Form (11) we can see that if the number of the piston rings is subtracted by .:.i, the compresso r shaft power
will decrease by DbV .M.prs~i;· if reduce tl-JP elastiC force
by 4Prs , the shaft Dower will decrease by DbVA-i.:. prs ;
the third point is that th~ reduction of the shaft power
is propotion al to its rotating valocity. So it is an im•
portant way to decrease the elasticity of the piston
rings or th<=: number of the piston rings ~or reduce
friction Dower loss of the piston rings.
the
ANALYSIS OF Ti-:!E POSSIBILIT Y
Usually there two piston rings in the high speed
dou~le acting compresso r.
1. The possibili ty to employ a single piston ring:
a) The leakage is small; in a high speed compresso r
(2.]
.
see F1g. 3.
b) The leakage is small in a double acting compresso r,
the leakage is expressed as
r------------------~k~+~1---
G
c
j
rD.f~ ~((~) 2 /k_ (~) k
7
,)HT-
K-'1
~
Pg
995
]
( 12)
The maximum of the leakage appearces when
k
P1J :e.;: (
2
p--=
:K+'1
g
)K-l
( 13)
During compressin g process the pressure ratio
( «s + s)k
~s+s-x
"'[1-
~
]k
(1+a)s
Psi
Substitut ing them into (13), the displacim ent
which the maximum leakage speed will cceur
at
1
x;;;a-:(1+or.)
(1 - <k:i)K-1'Js
( 14)
For an ordinary compresso r X~0.4s (stroke). For a
single acting compresso r it occurs all the way except
the first stage.
c) There are counter-fl ow during compressin g, the
leakage
360°
w
=}co
From G-e curve, the leakage is represente d by the
area under the curve, the positive represent s gas leakage
and the negative represent s the counter-fl ow. For' a single acting compresso r 1 its leakage is represente d by the
area abcde in Fig. 4c. Fig. 5a,b,c show the p -e, 6p-e,
1
G-~ of the double acting compresso r. There are three
situations: AP>C, Ap=O, Ap<:O. The leakage oceur when~p>O,
no leakage when ~p=O, the counter-fl ow when .4P < 0, The
area cdeg represent s the leakage during compressin g and
dischargin g at the cover side, the area efg represent s
leakage during the clearance expanding at the cover side,
the area abc represents the
counter flow
from the shaft side to the cover side during clearence
expanding at the shaft side.
996
Generally considerin g the clearance volumes equel,
so the aree. abc end efg are counterac ted, L e. the total
leakage is cdeg during a cirele. Comparing with Fig. 4c,
the leakage of a double acting compres::;o r is much smaller
than that cf a single acting one.
The ana_tysis above shows it is useful to employ a
single piston ring in an high speed double acting compressor.
2. The possibilit y to employ a piston ring with
small elasticity :
a) For a high speed compresso r the average pressure
in the piston ring groove is higher than that in the
. d
cy 1 ln
'())
er. Fig. ~ .
b) For a double acting compresso r, in the piston
ring groove, the pressure exsists during running. See
Fig.7. And singlro e~ctinf different to rlnublP, Fig. 8.
c) For a d mble acting compresso r the labricatin g
oil is supplied by oil pump, and is adjustable , so it. is
unnecessa ry t9 scrape the oil.
S:o it is possible to employ a piston ring with
small elasticity for a high speed double acting compresso r.
However at present the standard is simuleted according to
the cylinder diameter, it is suitable for low speed, and
high speed either, so it is not reasonable for the high
speed double acting compresso r.
THE U'TILIZATION OF THE CLE.A.RANCE EXPANDING GAS
It is known the clearence volume reduces the volumetric efficiency of the compresso r so it is peruiciou s.
The suspension of the piston ring in the ring groove
distroys the second sealin<; surface and increasing the
~ernicions motion. But it
leakage so it is termed
could be utilized in the double acting compresso r.If it
is controlled to make suspension during one side of the
cylinder is in the initial compressin g stage and the
other side is in the clearance expanding stage, then the
high pressure gas will go throuzh the second sealing
997
surface and entering the compressing snace to make the
capacity increase. To realige this, the following relation
must be satisfied
or
( 15)
Where the e represents the crank shaft. ea, eb represent the crank shaft angles at the points where the pressent on the both sides are e~ual. gee Fig. 9a. According
to the expanding equation and compressing equation there
are
( 16)
p = (
g
O(.S+S
OCs+s-x
)m Ci-1
Considering the niston
x ;,
5
~
(
1-Cose
ea = Cos- 1
Bb""
( 17)
di~n1acemPnt
( 18)
So
{
Ps1
2
(1
(1+'ltHE1/m_1~ J
1+C#.( 1+ e1/m)
(19)
180° + t:l a
There are forces along the shaft on a unit area p ,
g
~· pm' Pa showing on Fig. 10. Take the piston moving
direction us the posifive, when ~p=pb- (p -p -p )
g
m
a
1s
negative, thP nistonring suspBnsion will occur. where
n
=
m
Pa=
(D-2t)bMpb+DbAprs
tr(D-t)t
g;r(D-t)t
998
Considering (16), (17), (18), the relation to occur
the suspension is
(
1
1-CoseJ-mci- 1
-
2C1+olJ
c
mrufCosA + DbMprs
Ps1 + grc(!')-t)t
rr(D-t)t
( 20)
From Fig. 9b, the Z:p is negative during
18/J(~..:. ebo the useful suspension will occur.
-
0
CONCLUDING RElVJARKS
The experiment has been carried out on the two
stage compressor L2-10/8-I ( n = 980 r.p.m, Q = 1oM 3/min,
pd= 9 ata ) •.The methods stated above have been employed
and the specific power reduced by 3 - 3.5 % •
CONSULTING DOCUMENTS
(1)
T. F. Condlajiywa,
U.s.s.R. 1968.
{2)
M. E. Flenker, " Reciprocating Compressor ",
U.s.s.R .. 196o.
OJ
B. Y. Jicibol, 11 The Theory & Calculate of the
Piston Ring 11 , U.. S.S.R.
11
Horizontal Oprosed Compressor",
999
Fig .. 1
b
Pr-----~----~----------~
Fig. 2a
P - e
- 0
Fig. 2b
P -
e
1/J(l
0
w
Fig. 3
_..___.,...__.....____,..~,
o.or._l
o.u· ,,!r
,.J.r
.l,..
V
r
1000
Fig. 4b
e
.o.P -
Fig. L+c
a- e
-~-
1
-I
---r ____ _! __
I
(}
Fig. 5b
AP-
e
Fig .. 5c
G-
1001
e
Fig. 6
Fig. 10
1l/: \/ J
0
/60'
~I/
~ki
0
11a,
Prg- B
.loa•
K
:
Fig. 8
Prg-
~
IM"
0
Fig. 7
.1&:>"'
~
JfJD"
e
Cl"
I
Fig. 9a
pi -
e
.16D"
Ip
Fig. 9b
~P-
1002
e