Purdue University
Purdue e-Pubs
International Compressor Engineering Conference
School of Mechanical Engineering
1998
Design of Phase-Angled Balance Weights for an
Inverter Driven Scroll Compressor
H. J. Kim
University of Inchon
J. K. Lee
LG Electronics Inc.
D. K. Shin
LG Electronics Inc.
Follow this and additional works at: http://docs.lib.purdue.edu/icec
Kim, H. J.; Lee, J. K.; and Shin, D. K., "Design of Phase-Angled Balance Weights for an Inverter Driven Scroll Compressor" (1998).
International Compressor Engineering Conference. Paper 1331.
http://docs.lib.purdue.edu/icec/1331
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Herrick/Events/orderlit.html
DESIGN OF PHASE-ANGLED BALANCE WEIGHTS
FOR AN INVERTER DRIVEN SCROLL COMPRESSOR
Hyun ]. Kim*, ]in K. Lee**, and Dong K. Shin**
*University of Inchon, Dept. of Mechanical Engineering
**LG Electronics Inc., Living System Research Laboratory, Korea
ABSTRACT
This paper presents a new design method of balance weights with phase angles for scroll
compressors. Based on force and moment balances on crankshaft and compressor frame,
mathematical formulation of shaft bearing loads, unbalanced force and moment acting on the
frame has been made in terms of balance weight design parameters such as masses and phase
angles of the upper and lower balance weights. Any two of crankshaft main bearing load, sub
bearing load, unbalanced body force, and overturning moment can be controlled by the balance
weight design parameters.
NOMENCLATURE
F 3, F 4
Fa, Frg, Ftg
Fsody
Fcp
F cpc, F esc, Fore, F osc,
Reactions between oldham ring keys and frame
Gas forces in axial, radial, and tangential directions, respectively.
Unbalanced body force or resultant force acting on the frame
Total resultant force acting on crank pin
F sbc Centrifugal forces of crank pin, crankshaft, oldham ring,
orbiting scroll, and slider bush, respectively
Fdw, Fuw
Centrifugal forces of lower and upper balance weight, respectively.
Fmi, Fsi
Main and sub bearing loads at crankshaft, respectively.
Frs
Radial sealing force between wraps of fixed and orbiting scroll members
lcp, lcs, ldw, lh, lsi. luw Lengths defined in Fig. 2 and Fig. 3
Msody
Overturning moment or resultant moment acting on the frame
mdw, muw
Masses of lower and upper balance weights, respectively
rd, ru
Radii of mass center of lower and upper balance weights, respectively
rep, rs
Eccentricity of crank pin, and orbiting radius, respectively
rx, ry
Radial and tangential reaction positions at thrust surface
131, 13 2
Phase angles of upper and lower balance weights
m, B
Angula velocity of crankshaft and crank angle, respectively
Subscripts
c, n
r, t
Conventional and new, respectively
Radial and tangential components, respectively.
INTRODUCTION
Conventional balance weight design for scroll compressors typically employs two balance
weights: upper one is circumferentially positioned 180 deg. from the crank pin and lower one on
749
of
the same side of the pin. Sizing of the balance weights is made to satisfy the balance
centrifugal forces of moving members and the moment balance due to these forces. Nieter and
lly
DeBlois[!] suggested an optional method of designing balance weights which theoretica
weight,
balance
upper
to
angle
eliminates reaction forces at shaft bearings by giving a phase
keeping lower one 180 deg. out of phase to the upper one. As they pointed out, however, the
difference in the centrifugal force of balance weights defined by their method and those defined
by the conventional method would directly go into increasing the frame vibration.
In the present paper, we aim to show that, while unbalanced body force on the compressor
or
body is being kept minimal, one of shaft bearing loads or overturning moment of the compress
frame can be controlled to desired values by providing the balance weights with individual phase
angles.
ANALYS IS OF FORCE AND MOMEN T BALANC ES ON SHAFT AND FRAME
The
Fig.l shows a schematic of the phase-ang led balance weights considered in this study.
2
cos13I,
w
u
Fuwr=muwr
individual force components of the balance weights are as follows:
2
2
F uwt=muwru w2 sin 13 1 , F dwr=ffidwrd w cos 13 2 , F dwt=mdwrd w sin~ 2 • Axial positions of the balance weights
are fixed as shown in Fig. 2. Hence, the balance weight design is composed of finding four
of
independent variables, muw, mdw, 13 1 , and 13 2 , whose combination would give desired values
shaft bearing loads, unbalanced body force, and overturning moment.
Various forces and their acting points on the crankshaf t are shown in Fig. 2. Shaft bearing
loads can be calculated from force and moment balances on the crankshaf t as follows.
(1)
(2)
1
F sjt=y-:[lcp F cpt+luwF uwt-ZJ dwt]
+[
(3)
T[
(4)
SJ
F mir=
(lcp + fsj)(F cpr+ F cpc)- (lsj-la)F esc- (lsj-luw)F uwr+ (lsj-ldw)F dwr]
SJ
F mit=
(lcp+ lsj)F cpt- (lsj-luw)F uwt+ Usr ldw)F dwt]
SJ
Fig. 3 shows reactions from various members to the frame. Frg, Frs, and Ftg are transmitte d
Fa
from orbiting scroll to the frame via fixed scroll which is rigidly attached to the frame, and
is to the thrust surface. Resultant of these forces is the unbalanced force acting on the frame,
Faooy. By using relations of reaction forces of various members[2], radial and tangential
components of FBody are obtained by the equations {5) and (6), respectively.
F rB= F osc + F sbc+ F
cpc- F
esc+ Fore sin
2
8- F uwr+ F dwr
Fts = F orcsin8cos8 + F uwt- F clwt
(5)
(6)
With the moment center at the sub bearing position, components of overturning moment
acting on the frame are obtained by the equations (7) and (8).
M tB=- (lsi+ lcp + lh)(F rs+ F rg)- (r s- r,.)Fa-lsiF mir
M rB=- (lsi+ lcp+ lh)F tg + ryF a+ l # mit
750
(7)
(8)
While we have eight equations (1)-(8), there are only four unknowns: Fuwr, Fuwt, Fdwr, and
Fdwt. This means that not all of the eight items (Frn.it, · Frn.ir, Fsit, Fsir, Fts, Frs, Mts, and Mrs) can
be set to independent arbitrary values. Instead, only four of them can be given independent
values, and the remaining four items should depend on the others.
In the following example calculation, two components of the unbalanced body force, FtB and
F,8 , and two components of the shaft main bearing force, Frn.it and Frn.ir, will he selected as
independent ones. In particular, if Fm and Frs are set to zero, the equations (5) and (6) give the
following relations.
F dwr~ F llWr- (F osc+ F sbc+ F cpc- F esc+ F orc/2)
(9)
Fc~wt~FllJJJt
(10)
Since the terms including 8, however, can not be taken into consideration in the equations
(9) and (10), Fsooy itself can not be made real zero. By substitution of the equations (9) and(lO)
into (5) and (6), minimum of Fsooy can be found as follows: FBody:=tj F;B+F;B =112Forc . Also,
the equations (3) and (4) can be rewritten for Fuwr and Fuwt by using the equations (9) and (10).
(11)
(12)
From these four equations (9)-(12), four unknowns of Fuwr, Fuwt, Fdwr, Fdwt can be
calculated for given Frn.it and Frn.ir· And, in tum, once Fuwr, Fuwt, Fdwr, Fdwt are found, the design
parameters, muw, ffidw, 6 1 , and 6 2 can be determined.
CALCULATION RESULTS AND DISCUSSIONS
The present method of phase-angle d balance weights has been applied to a radially
compliant 3 hp class scroll compressor. Instead of using individual main bearing load components
F rn.it and F rn.ir as independent inputs for the balance weight design, the resultant load F m.i together
with the phase angle of the upper balance weight, 61 are used for practicality. An example of
correlation between these two pairs is shown in Fig. 4(a), where variation of 6 controls the
1
distribution between F mit and F rn.ir for given F rn.i· As 6 1 is varied from 0° to 360° for
predetermined Frn.i and minimal Fsody, the other design parameters, 62 and muw and ffidw vary as
in Fig. 4(b) and (c), respectively. And the corresponding F sj and Msody are calculated as shown
in Fig. 5(a) and (b), respectively. Minima of both Fsi and MBody take place at about the same
13 1 , the locations of which are marked with diamond marks in the figures. Fig. 6 shows that
decrease in F rn.i is accompanied by increase in MBody, and that there is an optimum value of F l11i
for minimum Fsi·
Shaft bearing loads, unbalanced body force, and overturning moment of the present method
and those of the conventional method are compared at various compressor speeds in Fig.
7(a)(b)(c), respectively. In the figures, 'A' and 'B' represent the conditions specified in Fig. 6,
and 'C' stands for the conventional method. The trend of monotonic increase in all of the items
751
conventional
with increasing speed is general, except Fsi of the condition B. For Fsody, the
variation in
able
consider
method gives a little larger value. Furthermore, as shown in Fig. 8,
for the
Fsooy with the crank angle exists for the conventional method, while no such variation
of the
present method. Fairly steadine ss in Fsody of the present method results from inclusion
frame.
sor
compres
the
on
centrifugal force of oldham ring in the radial force balance
CONCLUSIONS
t scroll
From the application of phase-an gled balance weights to a radially complian
compressor, the following conclusions can be drawn:
two of the
1. By circumferential positioning of balance weights ' in addition to sizing, any
load,
bearing
sub
load,
bearing
following items can be controlled to desired values: shaft main
unbalanced body force, and overturning moment of the body.
can be
2. With minimum unbalanced body force, reduction in the shaft main bearing load
moment
obtained at the expense of increase in the overturning
al
3. The unbalanced body force can not be. totally eliminated, mainly because the centrifug
the
into
value
force of the oldham ring changes with the crank angle. Consideration of its mean
force with
body
ed
unbalanc
the
in
variation
of
radial body force balance results in the removal
the crank angle.
REFERENCES
bearing
[1] Nieter, ]. ]. and DeBlois, R. L., "Counterweighting scroll compressor for minimal
loads," Intern. Compr. Eng. Conf. at Purdue, 1988, pp.l75-181
t scroll
[2] Kim, H. J. and Kim, ]. H., "Balance weight design for a radially complian
39
compressor," Intern. Compr. Tech. Conf., Chengdu, 1997, pp.232-2
Upper Balanc e
Weight
Lower Balanc e Weight
Fuwr
Fdwr
I
I
Fig. 1 Phase-angled balance weights and their force components
752
A
A
~r
t
Fcpt
Fmjt
lu,.
_L
Fuwr
ld.w
1~
1
Fdwt
Fsjt
(a)
Fig. 2
I
(b)
Forces acting on crankshaft. (a) Radial forces; (b) tangential forces
Fmjt-
Fsjt
(a)
Fig. 3
(b)
Forces acting on compressor frame. (a) Radial forces; (b) tangential forces
DDF-----------~--~--~
-----F~
m~
,
.......
.,
6
."'"·.
1000
0
~E-
'E'
u.;
''
''
I
\
I
\
I
\
-1000
·.·.
f:;;,t ..
I
\
\'
.\, ,'
I
'
••••
.....
-:3000
0
ZDr-----------------------------~
I
\
-:20CJO
''
........
90
180
Z70
··- ..F~..
360
f31[deg.]
(31 [c:Eg.]
Fig. 4(a) Effects of upper balance weight phase angle
on main bearing load components.
Fig. 4(b) Effects of upper balance weight phase angle
on lower balance weight phase angle.
753
0.8
7000
0.7
0.6
......
:2
.....
0.5
OA
~
0.3
~
0.00
ZlO
180
90
360
131 [deg.]
Effects of upper balance weight phase angle
on sub bearing load at Fmi=2800N.
p1 [deg.]
Fig. 4(c)
Fig. 5(a)
Effects of upper balance weight phase angle
on masses of balance weights.
2XO,-----------------------------~
1~r-----------------------------~
'E'
Fsj
1500
z
;
~
u_w
180
90
~
Fig. S(b)
4000
.
Fig. 6
IFnt-c
..· B
140
AB
120
~
A
)
~/
100
eo
60
0
20
40
----~·'"·'~:...: ..................................
60
eo
100
120
140
;...--~
0
0
100
20
40
60
60
100
120
140
160
1-2
on balance weight
speed
r
Fig. 7(b) Effects of compresso
performance : unbalanced body force.
1-2
Fig. 7(a)
.
.,.,., "'
20
B
/
//
::,...--/
40
F!!l
!DDO
c
160
1000
0
4500
4000
3500
3JOO
2500
Variations of sub bearing load and overturning
moment with main bearing load.
1eo
F
2lOO
.;_~
0
c
~ -='c.=,::.::::.:::-:.::.::.
u_w
~~c
500
(cleg.]
Effects of upper balance weight phase angle
on overturning moment at Fmi=2800N.
axJO
,.1
Frri[!\1
~r-----------------------------~
6
F9 j-c
'o'-o
ZlOO
360
Z10
A
1000
Effects of compressor speed on balance weight
performance : shaft bearing loads.
500~--------------------------------~
400
'E'300
~
"§'200
':!
100
0
~o~--~--90~--~--1~eo~----~Z7~0~~--~360
Crankangle[deg.]
Fig. 7(c)
Fig. 8 Variation of unbalanced body force with crank
angle.
Effects of compressor speed on balance weight
performance : overturning moment.
754