Leakage losses with a rolling piston type rotary compressor. I. Radial clearance on the rolling piston
T. Yanagisawa and T. Shimizu
Keywords: compressor, leakage, models
Pertes dues des fuites d'un compresseur piston rotatif. I. Jeu radial sur le piston rotatif
Les pertes dues ~ des fuites sont analys~es pour un compresseur ~ piston rotatif; le premier article concerne le jeu radial autour du piston. Ces compresseurs sont utilisds classiquement avec du R22 en conditionnement d'air, La g~om~trie de base est prdsent&e Fig. 1 et la condition pour laquelle la fuite autour du piston est calcul~e est pr~sent~e Fig. 2, le jeu dtant donnd par rEquation 3. Cette valeur est corrigde pour tenir compte de rinfluence des charges du
palier et de rexcentricitd du piston. La fuite est corrigde pour un entrainement visqueux en utilisant le module prdsentd Fig. 5b. I l se produit un dtranglement de I'c~coulement sur une pattie de la course. Des essais expdrimentaux ont ~td effectu&s en fixant un jeu connu au piston rotatif et en appliquant une chute de pression d'air et de R22. La Fig. 9 montre que la fuite calculc~e, tenant compte de rentrainement visqueux, ~ une pente correcte mais donnant une valeur trop ~lev~e. Les essais sur un compresseur en fonctionnement donnent des rdsultats semblables. L "influence de la modifica- tion des jeux du palier et de rexcentricitd du piston rotatif est ~tudi&e par comparaison avec le moddle. On montre que la combinaison du jeu minimum admissible du piston avec une excentricit~ correcte d'angle permet d'obtenir les fuites minimales.
This Paper is concerned with a rolling piston type rotary compressor for air conditioning use. The leakage through a radial clearance on a rolling piston is analysed theoretically and experimentally. Most of the leakage occurs in the later part of the shaft revolution affected by
the dynamic change of the clearance. To decrease the leakage loss i t is desirable to assemble the compressor with an appropriate eccentricity between centres of a cylinder and a main bearing.
Rolling piston type rotary compressors are widely used as air conditioners. They have many advantages over reciprocating compressors: small size, lightweight, low cost and high performance. However, these advantages are only achieved when the compressors are designed and assembled carefully. The most important factors affecting compressor performance are leakages through clearances.
In a rolling piston type rotary compressor, there are many different clearances. Fundamentally the magnitude of each clearance is decided by design and • practically kept within a tolerance by the selective matching of elemental parts when a compressor is assembled. But in the case of a rolling piston the radial clearance, which is the clearance at the closest point between an outer surface of a rolling piston and an inner surface of a cylinder, cannot be controlled by selective matching only, because it is affected by the concentricity of the assembly and by the dynamic behaviour of the bearings.
Previous investigations to analyse the leakage through the radial clearance of the rolling piston 1-s
The authors are from the Department of Mechanical Engineering, Shizuoka University. 3-5-1 Johoku. Hamatsu 432, Japan. Paper received 20 March 1984.
have assumed that the clearance is constant at the design value and have neglected the effect of the fluid friction on leakage. This Paper attempts to analyse this leakage loss taking account of dynamic behaviour and the frictional loss occurring in a narrow channel. We discuss the effect of eccentricity accompanying the assembly of the compressor.
Theoret ica l analysis
Piston radial clearance
Fig. 1 shows a schematic view of a rolling piston type rotary compressor. A rolling piston mounted on an eccentric of a shaft divides a cylinder cavity into two chambers, a suction chamber and a compression chamber, separated by a vane. As the shaft rotates, the piston revolves in the cylinder, which causes suction in the suction chamber and compression and discharge in the compression chamber.
To ensure that the piston moves smoothly, some clearance is established at the closest point between the cylinde~ inner surface and the piston outer surface, through which the gas in the compression chamber leaks into the suction chamber. We have called this clearance the piston radial clearance. The clearance is
0140-7007/85/030075-1053.00 ~) 1985 Butterworth Et Co (Publishers) Ltd and IIR Volume 8 Num~ro 2 Mars 1985 715
Nomenclature C e F h hc / /, M P Pd,P~ q~ R Ro Ro Re r
s
T V W 5
5o
Radial clearance of bearing Eccentricity of eccentric = R - Rp Load of bearing Clearance of bearing to the direction 0 Height of channel Length of bearing Length of straight channel Mach number Absolute pressure of fluid Absolute discharge and suction pressures Mass flow rate of leakage Radius of cylinder Reynolds number Gas constant Radius of piston Radius of bearing Distance along cylinder circumference= ~#R Temperature of fluid Velocity of fluid Width of cylinder Piston radial clearance Concentric piston radial clearance Eccentricity accompanying assembly
£
)I) 0 0., K
V
Q!
~p
Attitude of bearing Viscosity of lubricating oil Leakage rate Angle of shaft revolution Direction of eccentric assembly Adiabatic exponent Friction factor Viscosity of fluid Kinematic viscosity of fluid Angle along cylinder circumference Angular velocity of shaft Angular velocity of piston
Subscripts 1,2 Points on cylinder circumference b,c Suction and compression chambers e,t e and t sections m,p Main and piston bearings * Critical
Superscripts
Time differential - Average
decided statically by the combination of a cylinder radius, a piston radius and an eccentricity of the eccentric. However, in an operating compressor it changes due to the dynamic behaviour of the journal bearings.
If there are eccentricities at the piston bearing and the main bearing as shown in Fig. 1, the bearing clearances of hp and hr, in the direction of the rotational angle, 0, are expressed as follows:
hp=Cp{1 + ~p COS (e - e l - ~p)} (1)
hr,= Cr,{1 -- ~ COS (e - o f - ~m)} (2)
The piston radial clearance. &, is given by Equation (3):
(~ =(~0"F (Cp-hp) + (hm-Cm)
=&0- c.~0 cos (e-e,-~.)-cm~mcos (e-e,-~m) (3)
whereto is the concentric piston radial clearance which is the piston radial clearance when the cylinder centre and the main bearing centre are concentric and each bearing has no eccentricity. 0f is the direction of the bearing load, F.
Equation (3) is valid when the cylinder centre and the main bearing centre are concentric. When they are assembled with eccentricity &r, tO the direction 0m as shown in Fig. 2, ~ is evaluated by substituting 5~ expressed by Equation (4) for 50 in Equation (3).
~8=5o-5m cos ( 0 - 0.,) (4)
The bearing At the piston bearing the load, which mainly consists of the gas compression force, changes its magnitude and direction. The characteristics of the bearing are analysed approximately using the theory of finite length bearing under dynamic loading 6. Then, the
attitude, cp, and the attitude angle, ~p, are expressed as follows:
F(B1 cos ~p- B3 sin (~p) 8P- 2A (B1 B, - B2B3) (5)
• 1 • F(B4sin~p-B2coS#~p) ~p=~((1)~" (Op-- 2ef) (6)
2A (B1B 4 -- B2B3)
where A =~lrJp(rplcp)21= and B1-B 4 are functions of 8~, ~p and 1~/(2rp) as shown in Reference 6. The bearing load, F, is calculated as the combined effect of the gas compression force, the vane contact force and the piston centrifugal force. Angular velocity, (Op, of the rotating piston is found by solving the dynamic equation of the rolling piston.
As shown in Fig. 1 the shaft is supported by two main bearings, one is the frame bearing and the other is the cylinder head bearing. Usually the two bearings are different in length, namely/mf and/me and their centres are not always concentric to each other. Practically each bearing is loaded by different forces of Fmf and Fr, c as shown in Fig. 3a and behaves in a different manner. However, it is difficult and complicated to analyse the characteristics of such a system. In this Paper, to simplify the analysis, it is assumed that the two bearings are concentric and have the same length,/m, equal to the average of the two. Then, they are loaded by half of the piston bearing load, F, as shown in Fig. 3b and the two bearings behave in the same manner. Their characteristics are expressed as follows 6 similar to Equations (5) and (6):
F ( B ~ cos ¢m- B~ sin @m) ~-- (7)
4A'(B~B'4-B'2B'3)
76 International Journal of Refrigeration
Frame ~ ~ _ ~ ~ / S h a f t
Main ~ , - - ~ " ~ Pis ton
Cylinder \ l"'ql 1 I"4 /
Cytinder head
A
f
Fig. 1 Schematic view of a rolling piston type rotary compressor
Fig. I Schema d'un compresseur ~ piston rotatif
in the practical path: S2
- I f r (:Is (9)
81
where the friction factor. ,t.. of the two-dimensional channel is given by Equation (10) as a function of Reynolds number. Re. which is expressed by Equation (11 ):
{'96/Re (Re~<3560) / (1 0) =10.3164~Re °.25 (Re> 3560) J
F(B'4 sin ~n~-- B~ cos 4.,) (8) ~m = ((o- 219,) 4A'(B;B'4- B'2B'3)
where A'=iTrm/m(rm/Cm)2/lt and B~-B'4 are functions of sin. ~,. and Im/(2rm).
Modelling of leakage path At thepiston radial clearance the compressed gas leaks into the suction chamber as shown in Fig. 4. In the past, the leakage has been analysed as a flow through a convergent-divergent nozzle 1-3. However, as the leakage path is narrow and long compared with its height, it is necessary to analyse the leakage taking viscous effects into account.
In this Paper the leakage path developed along the cylinder inner surface, as shown in Fig. 5a, is modelled by the flow channel, as shown in Fig. 5t), which consists of the compression chamber, a convergent nozzle, a straight channel including the viscous drag and the suction chamber. The straight channel has a constant rectangular cross section, height, 5, and width, w. If the length /t satisfies Equation (9), the frictional loss in the model channel is equivalent to that
Fig. 2 Explanation of the eccentric assembly
Fig. 2 Explication de/'assemblage excentrique
I
L /,,.a / , , ,
,4
F _J ~ F _
"" Fmc E
/
(a) Fig. 3 Modelling of the main bearing
Fig. 3 ModMisation du palier principal
II
I 777" F
Votume 8 Number 2 March 1985 77
SMC
ch( ress ion
~amber
P i s t o n
Leakage path in the cylinder
Cheminement des fuites clans le cylindre
centr ic
y l inder
I Piston
/ r - . . . . . " " " q ' " " ~ " . . . . ~ , " " " t ~ ' " " / I -" -~ ~,~ ~,=z ~'2 / ~
/ I-=- s=~R sl sz ICY [ inder
Compression ( a ) chamber
Nozzte , ,Channel
pc . . . . =;,? "T'r"'{'"
"7 / / / / / / / / / ~ ~
( t ) Mt,Pt
( b ) Fig. 5 Modelling of the leakage path
F/g, 5 ¸
Suction chamber
/ / / / / / 1 / / / / / /
: = Pb
/ / / / / / / / / / /
e) Me~)e .re ,Te
Mod~lisation du cheminement des fuites
Re =2hcV=2qm (11) v /~W
As the viscosity, #, of refrigerant 22 used as a working fluid does not change much in the range of pressures and temperatures used in air conditioning, we can use an average viscosity, #, in Equation (11). Correspondingly, Re expressed by Equation (11 ) and 2 expressed by Equation (10) are assumed to be constant everywhere in the flow channel. In Equation (9) if ;t is always equal to the average value ~,, /f is expressed as follows:
S2
$1
The channel height, h c, is expressed by Equation (1 3) Referring to Fig. 4:
hc=AC-AB =R+ (e-6) cos (p- (R 2- (e-&) 2 sin 2 (p)~/2 (1 3)
Usually, as the piston radius, Rp, is much greater than the eccentricity, (e-6), hc is approximated as follows:
h~=e(1 + Z cos (p) (14)
where X= 1 -6/e. Using Equation (14),/f expressed by Equation (12) is represented by Equation (15) by executing substitutional integration of Sommerfelds:
~02
" Rd(p _~R (~'2- "c~ ) /f=6 e( l+zcos(p) e(1 --Z2) 1/2 (15)
Fig. 4
~ . 4
where !=sin-l{(1 -z2)l /2sin(p/( l+zcos(p)}. The channel length, If, changes according to the integration limits. Fig. 6 shows an example of changes of/f and circumferential length, (s2-sl), versus integration range, (q)2- qh). (s2-sl) increases proportionally with increase of (~2-~P~) but/ f saturates immediately. In practice we can represent If as the value at (¢P2- qh) =2~z not paying attention to the selection of the frictional range. The result is expressed as follows: / f= 2~R/{e(1 - Z2) 1/2} (16)
Calculation of mass f low rate
Mass flow rate in the channel shown in Fig. 5b is calculated as the adiabatic flow with fluid friction (fanno flow) 7 If the fluid velocity at the channel exit, e, is equal to the velocity of sound, Mach number, Mr, at
150
~1 O0
_T 50 / /if (5= 40,urn) ~ ~ _ ~ _ . j / l f ( 6 = 2 O p m ) t¢ (6= 20prn)
O ! I ! 0 m 2~
Fig. 6 Relationship between channel length and integration range. R=27 mm. e=3.2 mm
Fig. 6 Relation entre la Iongueur du canal et le domaine d'int~gration. R= 27 mm; e= 3.2 rnm
78 Revue Internationale du Froid
Pressure
R e g u l a t ~ ~- --. ~ J / / ~ r e gaug e~.,~ Regulator
~ - - ' ~ ~ C y l i n d e r
Fig. 7 Experimental apparatus for leakage test
Fig. 7 Appareil experimental pour I'essai de fuite
channel inlet, t, satisfies Equation (17):
-I t 1 - M ~ K+ I (~:+I)M~ - +- --~---K log 2 ~ KM~ 2+ (K-- 1 )M~
(17)
Then, the pressure ratios of Pt/Pe at the channel and PJPt at the convergent nozzle are given as follows:
1 ( ~:+ 1 ~/2 P ' - / t4 , \2+ (K- 1 )e~ / (18) Pe
K
K - 1 . 2\ ~-1 (19) P--~=Pt 1 + ---~M, )
If the total pressure ratio, ~{-pc/p. = (Pc/Pt)(Pt/Pe)}, is less than the given pressure ratio, Pc/Pb, between upper and lower chambers, the flow chokes.
At first, when the flow chokes, Mach number, Me, at the channel exit is equal to unity and the exit pressure, Pe, is equal to Pc/~. Then the temperature, ;re, the velocity. V e, and the mass flow rate, qr,. at the channel exit is expressed as follows:
Te = Tel{1 + (~:- 1 )Me2/2} (20)
Ve=Me(KR~Te) 1/2 (21)
qm=5 wpeVe/ (RQTe) (22)
However, when the flow does not choke, we start the calculation by assuming Mach number. Mr, at the channel inlet. Using the assumed value of Mr, the imaginary critical channel length, If., is calculated corresponding to/f in Equation (17). Also. the critical pressure ratio, p/p. , and the nozzle pressure ratio, pJp,, can be calculated by Equations (18) and (19), respectively. The Mach number, M e, at the channel exit is obtained by reverse calculation of Equation (23):
j h ~ M 2 K+ 1 (K,+ 1 )M~ ~ . , . - _ 1 t- log (23) 2& ~ t4~ ~ 2+ (K- 1)M~
Substituting M e for Mt in Equation (18). the critical pressure ratio, pJp., can be calculated. The final
pressure ratio Pc/P, is obtained from the following equation:
Pc/Pe ={o Jp,) (pJp .) / (p Jp .) (24)
If pc/Pe is equal to the given pressure ratio Pc/Pb, the values of M, and Me are valid and Te, Ve and qn, can be calculated from Equations (20)-(22), respectively.
In this analysis we assume that the steady state equations can be applied approximately, because the changing speed of the state in the practical compressor is fairly slow as compared with the velocity of sound.
Experiments Leakage test Fig. 7 shows the experimental apparatus used to measure the leakage flow rate through the radial clearance. In a cylinder a rolling piston is fixed to maintain the piston radial clearance, (~. (~ is set by the clearance gauge. Both faces of the cylinder are blocked by the cylinder head surfaces using sheet packings. The cylinder cavity is divided by a vane. The fluid supplied to one chamber in the cylinder leaks through the piston radial clearance into the other chamber and the leakage flow rate is measured by the method of water displacement. The pressure of each chamber is controlled by pressure regulators. Refrigerant 22 and air are used as working fluid.
Performance test It is difficult to measure the leakage through the piston radial clearance while the compressor operates. But we can estimate it by the change of the compressor performance when the specified dimension of the compressor which affects the piston radial clearance is changed. The experimental compressor is linked to a refrigeration cycle where R22 is used as working fluid and operated under given steady operating condition. The rate of flow of the liquid refrigerant is measured with a rotameter. Specific dimensions changed in a series of experiment are the piston outer radius, the bearing clearance and the eccentricity of the assembly. Table I shows main dimensions and operating conditions for the experimental compressor.
Results and discussions Comparison of leakage mass flOw rate Fig. 8 shows theoretical and experimental results in leakage tests. They agree well in both regions, a subcritical region where leakage mass flow rate, qm, increases with decrease of the lower to upper pressure ratio, Pb/Po, and a critical region where qm is constant regardless of the change of PJPc. The agreement is good for different fluids and different clearances. This means that the theoretical modelling and calculations are valid for the estimation of the leakage through the piston radial clearance. The jump on the theoretical line corresponds to the change of the friction factor at Re= 3560 in Equation (10).
In Fig. 8, the leakage mass flow rate theoretically calculated not taking account of viscous drag is illustrated as a reference (& = 23/Jm, working fluid: air).
Volume 8 Num6ro 2 Mars 1985 7-9
Table 1. Main dimensions and operating conditions Tableau 1. Principales dimensions et conditions de fonctionnement
Cylinder radius R 27.0 mm Cylinder width w 23.8 mm Piston radius Rp 23.8 mm
Piston bearing radius r n 14.8 mm length /p 14.0 mm
radial clearance Cp 0.013 mm
Main bearing radius r m 9.6 mm length /mr 40.0 mm length /mc 18.0 mm
radial clearance c m 0.013 mm
Concentric piston radial clearance &0 0.020 mm
Absolute discharge pressure Pd 2.03 MPa Absolute suction pressure Ps 0.583 MPa Shaft angular velocity (o 358 rad s -~
2.0
o
1.5 o o ~ ~ x ~
S=46um _X without Fr ic t ion T "-/'=- o \
, o o o 13"
O I I I I 0 03 0.4 0.6 0.8 1.0
Phi Pc Fig. 8 Results of the leakage test. O: R22, experimental;--: R22, theory; 0: air experimental; ---: air, theory, Pc=0.79 MPa; Tc= 300 K
Fig. 8 R~sultats de I'essai de fuite. ©: R22, experimental; : R22, th~orique; 0 : air, exl~rimenta#---." air, th~orique. Pc=0.79 MPa; T c =300 K
It is almost three times as much as the broken line (B=23/~m. air) calculated with fluid friction. This indicates that the consideration of the viscous drag is indispensable for the calculation of .the leakage through the piston radial clearance and its effect on the leakage may be evaluated as a flow coefficient of~ 1/3.
Leakage in a practical compressor
Here we investigate the leakage through the radial clearance in a practically operating compressor. Fig. 9 shows the relationship between the leakage rate, ~/=, and the concentric radial clearance, ~0, when the outer radius of the rolling piston is changed (where, T/~ is the ratio of the leakage mass flow rate to the ideal suction
mass flow rate and corresponds to the drop of the volumetric efficiency of the compressor due to the leakage through the piston radial clearance). Two types of theoretical lines are illustrated, one (solid line) calculated including the fluid friction and the clearance changing and the other (broken line) calculated excluding both. Also, experimental results are plotted in Fig. 9 as the leakage rate relative to the leakage rate at &0=20/~m by assuming that the change of the measured mass flow rate of the compressor is equal to the change of the leakage mass flow rate through the radial clearance when the outer diameter of the rolling piston is reduced by grinding. It is clear that we cannot discuss absolute values of the experimental results but only the slope of the curves. The slope of the experiment agrees well with that of the solid line. This means that the theoretical treatment derived in this Paper including the fluid friction and the clearance change is generally appropriate for the calculation of the leakage in the practical compressor. In the ordinally selected clearance range, &o = 10-20/~m, the theoretical leakage rate shown by the solid line is 5-10%, but is ~2 /3o f the calculated leakage rate shown by the broken line.
Fig. 10 shows the change of the instantaneous leakage mass flow rate, q=, during one revolution of the compressor. The broken line expresses theoretical leakage mass flow rate calculated without viscous drag at the constant channel height, &o. It changes similarly with the change of the compression chamber pressure, po, in the compressor. The solid line shows the theoretical mass flow rate calculated taking account of the fluid friction and the changing clearance. In the later part of the revolution, it increases remarkably though the upstream pressure, Pc, does not increase.
50
40
~ 3 0
20
f f f
f f
f f
f f
J f
I / / / I I /
~ o
°1o zo 30 2o so So ~m
Fig. 9 Leakage rate in the pract ical compressor . - - , - - - Theory: - - - O - - - : exper imenta l . - - : Channel height , 6, w i t h f r ic t ion; - - - : channel height, &o, w i t h o u t f r ic t ion
Fig. 9 Taux de fuite clans le compresseur utilis~ clans la pratique. . . . . : Th~orique; - - - 0 - - - : expMimentel. - - : Hauteur du canal, ~, avec frottement; - - - : hauteur du canal, 5~ sans frottement
80 International Journal of Refrigeration
6
4 /T
. / / /
°0 e rod
Fig. 10 Instantaneous leakage mass flow rate. Key as in Fig. 9
Fig. 10 D~bit instantan~ de fuite. Mbrne I~gende que pour Fig. 9
60
~ 2 0
0 _Z.%/" %. . . . . . . . .
I I I 0 ~: 2 ~
e rad Fig. 11 Changes of piston radial clearance and bearing clearance
Fig. I I Modifications du jeu radial du piston et du jeu du palier
This may be because of the dynamic change of clearance described later. Total leakage mass in one revolution of the compressor is evaluated as the area under the solid or broken line. As mentioned before, the leakage mass expected with the fluid friction and the change of the channel height is about 60% of that expected without both.
Piston radial clearance Fig. 11 shows theoretical changes of the piston radial clearance, &, and bearing clearances, hp and hm, when the cylinder centre and the main bearing centre coincide. The curves were obtained by the calculation of Equations (1)-(3) with numerically solving Equations (5)-(8) of characteristic equations of bearings. In this case, & records a maximum value of about twice the concentric clearance, (~0, in the neighbourhood of 0=0 and records a minimum value <&0 in the neighbourhood of 0== rad. Therefore, as shown in Fig. 10, the leakage is restricted in the middle part of the revolution and is intensified in the later part. But in the earlier part, the effect of the clearance increase on the leakage is not serious because the pressure difference across the clearance is small.
The change of ~ is caused by changes of the bearing clearances of h, and hm shown in Fig. 11. Referring to Fig. 1 and Equation (3), at the piston bearing, if the clearance hp is smaller than the average radial clearance, c o. ~ increases by the difference (cp-hp). However, at the main bearing, if the clearance hr, is
larger than the average radial clearance, Cm, & increases by the difference (hm-Cm).
In Fig. 11, both h o and hm change leading to an increase in & in the neighbourhood of 0=0 or 2~ rad and a decrease in & in the neighbourhood of 0=~ rad. Therefore, & changes largely around the concentric piston radial clearance, &0, in one revolution of the compressor.
To understand changes of hp and hm, the bearing load, F, and loci, ~p, ~ , of journal centres are shown in Fig. 12 in a fixed polar coordinate system B located on the cylinder. The change of the magnitude and direction of the load, F, characterizes behaviour of journal centres.
For example, at the main bearing, in the region of 0 =0-~ rad, attitude 8m decreases because F is not so large though F increases. But after that, ~ increases because F becomes larger. Even after F has reached its maximum, 8m increases further. This is because the direction of F changes at nearly half the speed of the angular velocity of the shaft and the pressure of the oil film in the bearing cannot be expected. For the behaviour of the journal centre the clearance hr~ changes as shown in Fig. 11. In Fig. 12 a similar change can be seen in the change of attitude, 8p, at the piston bearing though the phase shifts about ~ rad. ~v~/e have to keep in mind during the design of the rotary compressor that the bearing load changes its direction by half the speed of the shaft revolution and the capacity of the bearing decreases.
e=O rod a=o
1 kN=102 kgf ,~.
Fig. 12 Changes of bearing load and loci of journal centres
Fig. 12 Modifications de la charge du pa/ier et des Iieux g~6om#triques des centres des touri//ons
Volume 8 Number 2 March 1985 8"1
30
20
..,.4
10
O0 vlO 20 30 40 cp ,Cm/urn
Fig. 13 Effect of bearing radial clearance on leakage rate. - - . - - - Theory; - - - O - - - : experimental, Cp constant, c m changing. - - : Cp constant, c m changing; - - - : c D changing, Cm constant
Fig. 13 Influence du jeu radial du palier sur le taux de fuite. - - - , - - - : ThcSorique," - - - 0 - - - - - : exp@rimental, cp constant, Cm variable. - - : cp constant, Cm variable: - - - : c~ variable, Crn constant
4 0 1 ~ . - _ \ / / -...
~. \ / "
20 \ ~ % ~ - ~ ~ /
O I ! I
0 ~: 2~:
e rad
Fig. 14 Effect of bearing radial clearance on piston radial clearance. - - : Cp, Cm=8/~m; .: Cp=8#m, cm=18#m; : Cp = 18/~m: Crn=8 #m; - - - : Cp, cm=18#m
Fig. 14 Influence du jeu radial du palier sur le jeu radial du piston. - - . " cp, cm=81~m: : cp=8/~n, cm=181~n: . . . . : cp = 181~n; Cm=8pfn: - - - : cp, Cm = 181~n
Effect of bearing clearance
Concerning behaviour of the bearings, the effect of the bearing radial clearance on the leakage is examined. Fig. 13 shows theoretical change of the leakage rate, tt~, when the radial clearance, cp of the rolling piston bearing or the radial clearance, c= of the main bearing is changed. In each case, ~/~ decreases with decrease of the clearance. Also in Fig. 13 an experimental result obtained from the compressor performance test under the different main bearing clearance, 5 m, is illustrated at a value relative to the value at 5m=8/~m. The slopes of experimental and theoretical results are almost the same, which indicates the validity of the bearing analyses.
However, Fig. 14 shows changes of the theoretical piston radial clearance, 5, during one revolution of the compressor. As bearing clearance, cp or cm, decreases, the clearance, 5, decreases in the later part of the revolution where instantaneous leakage velocity is large, which causes the decrease of ~t= as shown in Fig. 13. Incidentally the influence of the increasing clearance in the middle part of the revolution on the leakage is not so serious because the instantaneous leakage velocity in that part is not so large.
Since the effect of the reduction of Cp or c m is independent, both effects are added when both clearances are reduced simultaneously. However, the reduction of the clearance is limited by the bearing performance.
Effect of eccentric assembly
Fig. 15 shows theoretical changes of the piston radial clearance, 5, during one revolution of a compressor which is assembled eccentrically between centres of the cylinder and the main bearing. & is strongly affected by the direction 8= of eccentric assembly even if the eccentricity, 6, is constant (=10#m). Corresponding to Fig. 15, the theoretical relationship between the leakage rate, t h, and the eccentric direction, 8m, is illustrated in Fig. 16. ti~ at 8r,= 3~/2 rad is less than that at the concentric assembly (5~=0). On the contrary, ~/r at 8r~=~/2 rad is larger than that at 6==0. The inclination of changing r h can be explained by the changing pattern of 5, whether& becomes larger or less than the standard value corresponding to 5~=0 in the later part of the revolution as shown in Fig. 15. In Fig. 16, tl~ at 8 m = 0 o r ~ rad is almost equal to that at 5m=0. This is because the increase and the decrease of the leakage due to the change of 5 is averaged in one revolution.
60 t 40
E
20
° o
Fig. 1 5
I I I
e rad
Effect of eccentric assembly on piston radial clearance. --: &m = 0/~m, ~m = 0 rad; - - : •m = 10/~m, 8m = 0 rad; - - - - - : &m = 10 #m. 8m=~/2rad; . . . . : &m=10#m, 8m=~rad; - - - : &m=10#m, em= 33/2 tad
Fig. 15 Influence de I'assemblage de I'excentrique sur le jeu radial du piston. - - : &m=O I~n, 8m=O tad; : &rn = 10 l~n, ~m=O tad, - - - - - . " &m = lOpm, em=~/2rad: - - - - ~ - : &m = 1Olin, Om=~rad:
: &m = 10#m, 9m=3~/2rad
82 Revue Internationale du Froid
E.
30
20
10
I I I
0 ~ 2 z em r a d
Fig. 16 Effect of eccentric assembly on leakage rate. - - : Theory, ~rn=0prn; ~ : theory, 6m=10pm; - - - : theory, ~irn=20pm. O: Experimental, ~m=0pm; O: experimental, ~m = 10pm
Fig. 16 Influence de I'assemb/age de I'excentrique sur le taux de fuite. - - - : Thdorique. &m=OiJm, • ~ : thdorique. ~m = 10pm; :" thdorique, &m=20 IJm. 0 : Expdrimental, &rn=O pin," O.' expdrimental &m = 101~n
,0 1 s
s S
2o % , o ,s
I I I I
0 10 20 3 0 40 So /urn
Fig. 17 Effect of eccentric assembly with reduction ofB o on leakage rate. - - : Without eccentricity, ~m=0; - - - : 5rain= constant (equal to the value at A)
Fig. 17 Influence de/'assemblage de I'excentrique avec r~duction de &o du taux de fuite, m " Sans excentricit~, &re=O; - - - . " &rain =constant (~gale b la valeur au point A)
The experimental change of the leakage rate, T/i, against the change of em is also plotted in Fig. 16 based on the assumption that experimental and theoretical leakage rates are equal when ~==0. Experimental results are in good agreement with the theoretical results. This supports the view that the eccentric assembly in the direction of er~ = 2=/3 rad is favourable for decreasing the leakage.
Moreover, to decrease the leakage, it is useful to increase the eccentricity, &m, to the direction 0m = 3=/2 rad as shown in Fig. 16. But as &m increases, the minimum value of & decreases and the danger that the rolling piston collides with the cylinder inner surface increases.
Eccentric assembly with reduction of concentric piston radial clearance
Fig. 17 shows the theoretical change of the leakage rate, r/~, through the piston radial clearance against the change of the concentric piston radial clearance, &o. The solid line expresses the relationship between q~ and &o in the conventional case that the compressor is assembled with concentric cylinder and main bearing. As &o decreases, T/~ decreases almost linearly.
Incidentally, to decrease the leakage rate, it is desirable to reduce the concentric piston radial clearance, ~o. However, taking account of the dynamic behaviour of bearings there is a limit to the reduction of &o to avoid collision of the piston and the cylinder. If the eccentric assembly to the direction er,=0rad is executed, the change of & in one revolution of the compressor is averaged and the minimum value of 6 increases as shown in Fig. 15. Then, we can easily reduce&o until the minimum value of& is equal to that at the concentric assembly. Fig. 18 shows patterns of changing & when the reduction Of&o is combined with the appropriate eccentric assembly to the direction 0m=0 rad while keeping the minimum value, &rain, constant.
The broken line shown in Fig. 17 expresses the relationship between T h and &0 corresponding to Fig. 18. On this line, &r,~, is equal to the value at point A on the solid line. In this case, r/~ at point B is less than half of that at point A. By the eccentric assembly to 8m = 0 with the reduction of the concentric piston radial clearance the leakage can be considerably reduced without decreasing the minimum clearance, &min,.Or increasing the danger of collision. There is an optimum value of &n~ according to the amplitude of 6 which is decided by the dynamic behaviour of bearings. Though that value is affected by operating conditions of the compressor, their influence is not so serious.
60
co
7 f~ min.
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0 ~E 2 ~ e rad
Fig. 18 Effect of eccentric assembly with reduction of (~o on piston radial clearance, m : &0=20, ~m=0/Jm, 0m= 0 rad; - - : &o=l 5, <~rn =5pm, 8m=0rad; .: &o=10, 6m=10prn, 8m=0rad; . . . . : &o=10. &rn=15pm. em=0rad; . . . . . : &o=15, &rn = 20 pm, 8rn = 0 rad
Fig. 18 Influence de I'assemblage de I'excentrique avec r~duction de &o du jeu radial du piston. ~ : &o= 20, &m=O pm, 8m=O rad,'--." & 0 =15, ~m=S pm, Om=Orad,---m. &o=10, 6m=1O pm, em=Orad
Volume 8 Num~ro 2 Mars 1985 83
C o n c l u s i o n s
In this Paper leakage through the piston radial clearance in the roll ing piston type rotary cqmpressor was analysed theoretically and experimentally. The results are summarized as follows. 1. The leakage mass f low rate calculated using the theoretical f low model including the fluid friction is in good correlation wi th the experimental one. 2. The piston radial clearance increases in the later part of the revolution because of the dynamic behaviour of bearings, which increases the leakage through the clearance. 3. The reduction of the bearing clearances controls the change of the piston radial clearance and lessens the leakage. 4. When the centre of the main bearing is assembled eccentrically wi th respect to the cylinder in the direction 8m=3~/2rad , the piston radial clearance decreases in the later part of the revolution and leakage decreases. 5. When the eccentric assembly to the direction
e~=O rad is combined wi th the appropriate reduction of the concentric piston radial clearance, the leakage decreases considerably.
R e f e r e n c e s
1 Pandeya, P., Soedel, W. Rolling piston type rotary compressors with special attention to friction and leakage, Proc Purdue Comp Tech Conf (1978) 209
2 Chu, I. et al. Analysis of the rolling-piston type rotary compressor. Proc Purdue Comp Tech Conf (1978 ) 219
3 Shimizu, T. et al. Volumetric efficiency and experimental errors of rotary compressors. Int J Refrig 3 (1980) 219
4 Tanaka, H. lit al. Noise and efficiency of rolling piston type rotary refrigeration compressor for household refrigerator and freezer, Proc Purdue Comp Tech Conf (1980) 133
5 0 z u , M., Itami, T. Efficiency analysis of power consumption in small hermetic refrigerant rotary compressors, Int J Refrig 4 (1981) 265
6 Nakagawa, E., Aoki, H. A calculation method of characteristic performance of journal bearings under dynamic loading, (in Japanese). Lubrication Japan 16 (7) (1970) 385
7 JSME Data Book Hydraulic losses in pipes and ducts, (in Japanese), JSME Japan (1979) 133
84 International Journal of Refrigeration
