Sliding vane type rotary compressor

A sliding vane type rotary compressor having a rotor, at least one vane slidably mounted on the rotor, a cylinder accomodating the rotor and the vane, and end plates fixed to both ends of the cylinder so as to close vane chambers defined by the vane, the rotor and the cylinder at both sides of the vane chamber. The improvement comprises that the compressor is constructed to meet the following condition: EQU 0.025<.theta..sub.s a/Vo<0.080 where, a is a value given by the following equation of: ##EQU1## .theta. represents the angle (radian) formed around the center of rotation of the rotor between the end of the vane closer to the cylinder and the cylinder top where the distance between the inner peripheral surface of the cylinder and the outer peripheral surface of the rotor is smallest; PA1 .theta..sub.s represents the rotation angle .theta. (radian) at the instant of completion of the suction stroke; PA1 Vo represents the volume (cc) of the vane chamber when the rotation angle .theta. is .theta..sub.s ; and PA1 a(.theta.) represents the effective area (cm.sup.2) of the suction passage between an evaporator and the vane chamber. The refrigerating power is effectively suppressed in the high-speed operation without being accompanied by substantial reduction of refrigerating power in the low-speed operation.

BACKGROUND OF THE INVENTION 
The present invention relates to a rotary compressor of the sliding vane 
type and, more particularly, to a sliding vane type rotary compressor 
suitable for use as the compressor of a refrigerator incorporated in an 
air conditioning system for vehicles. 
The sliding vane type rotary compressor has a small number of parts and is 
small-sized and of simple construction. Thanks to these advantages, the 
sliding vane type rotary compressor now has a spreading use as the 
refrigerating compressor for automobile air conditioning systems, in place 
of the conventional reciprocating compressors. 
The sliding vane type compressor, however, has the following disadvantage 
as compared with the reciprocating compressors. 
The sliding vane type rotary compressor for an automobile air conditioning 
system is adapted to be driven by the engine of the automobile through a 
belt which goes round a pulley coupled to a clutch connected to the rotary 
shaft of the compressor. Therefore, the refrigerating power of the air 
conditioning system incorporating the sliding vane type rotary compressor 
is increased substantially linearly in proportion to the increase of the 
engine speed. 
In contrast, in the conventional reciprocating compressor, the suction 
valve cannot well follow-up the operation of the compressor when the 
operating speed is increased to a high level, so that the efficiency of 
the suction of refrigerant gas into the compressor is decreased to cause a 
saturation of the refrigerating power. In other words, in the case of the 
reciprocating compressor, the refrigerating power is automatically 
suppressed during high-speed running of the automobile. In the case of the 
rotary type compressor, however, such an automatic suppressing effect 
cannot be obtained so that the efficiency is lowered in accordance with 
the increment of the compression work or a state of overcooling occurs as 
the engine speed is increased. 
In order to obviate the above-described problem of the prior art, it has 
been proposed to provide a control valve in the passage leading to the 
suction port of the rotary compressor adapted to vary the opening area in 
such a manner that the opening area is decreased as the engine speed is 
increased to cause some suction loss to automatically control the 
refrigerating power. This solution, however, is not preferred because the 
construction is complicated and the production cost is raised due to the 
provision of the control valve. 
As another countermeasure for overcoming the problem of excessive 
refrigerating power, it has been proposed to use a fluid clutch, planetary 
gear or the like to drive the rotary compressor in such a manner that the 
speed of the compressor is not increased beyond a predetermined limit 
speed. 
The use of the fluid clutch, however, poses a problem of a large energy 
loss due to generation of heat by friction-loss inherent to the clutch 
itself. Also, the use of the planetary gear mechanism, which is inevitably 
accompanied by an increase of the number of parts and increase of the size 
of the driving unit, is impractical in view of the current demand for 
simple and compact construction to meet the requirement for saving of 
energy. 
SUMMARY OF THE INVENTION 
It is, therefore, a major object of the invention to provide a sliding vane 
type rotary compressor suitable for use as the refrigerating compressor of 
an automobile air conditioning system capable of overcoming the 
above-described problems of the prior art. 
The sliding vane type rotary compressor provided by the present invention 
can provide an optimum refrigerating effect even when the rotation speed 
of the driving side of the compressor is varied over a wide range and, 
accordingly, is suitable for use as the refrigerating compressor of an air 
conditioning system of, for example, automobiles. 
More specifically, an object of the invention is to provide a sliding vane 
type rotary compressor suitable for use as the refrigerating compressor 
for an automobile air conditioning system, capable of meeting the 
following functions. 
(1) Small loss of refrigerating power in low-speed operation and effective 
suppression of refrigerating power only in high-speed operation. 
(2) Small loss of compression work and small driving torque. 
(3) High reliability backed by the elimination of mechanical operating 
parts. 
The present inventor has found out, through a minute study of the transient 
phenomenon of the pressure change in the vane chamber of the rotary 
compressor, that the self-suppressing control function similar to that of 
the conventional reciprocating compressor can be achieved also by the 
rotary compressor, by suitably selecting and combining various factors 
such as area of suction port, delivery rate, number of vanes and so forth. 
Namely, by designing and constructing the rotary compressor in accordance 
with the conditions discovered by the present inventor, it is possible to 
create an effective pressure loss only in the high-speed operation, while 
minimizing the loss of suction pressure in the low-speed operation, even 
in the rotary compressor having no suction valve which is essential in the 
conventional reciprocating compressor. 
Thus, according to the invention, it is possible to achieve an effective 
automatic refrigerating power control in an air conditioning system with 
existing simple rotary compressor, without necessitating any additional 
equipment. 
The invention will be more fully understood from the following description 
of the preferred embodiments taken in conjunction with the accompanying 
drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Before turning to the detailed description of the preferred embodiments, a 
general description will be made as to a typical conventional sliding vane 
type rotary compressor for an automobile air conditioning system. 
As will be seen from FIG. 1, a conventional sliding vane type rotary 
compressor has a cylinder 1 provided therein with a cylindrical space, end 
plates (omitted from FIG. 1) fixed to both ends of the cylinder 1 to close 
the vane chamber 2 defined in the cylinder 1, a rotor 3 disposed in the 
cylinder 1 at an eccentricity from the latter and vanes 5 slidably 
received by the grooves 4 formed in the rotor 3. Reference numerals 6 and 
7 denote a suction port and a delivery port formed in the end plate and in 
the cylinder 7, respectively. As the rotor 3 rotates, the vanes 5 are 
projected radially outwardly by the centrifugal force to make a sliding 
contact at their ends with the inner peripheral surface of the cylinder 1 
to prevent the leakage of the gas during operation of the compressor. 
The embodiment of the invention will be described hereinunder on the 
following two cases: 
[I] The case where the effective suction area is varied during suction 
stroke of the gas. 
The case where the effective suction area is regarded as being constant 
during suction stroke will be described hereinunder as the first 
embodiment of the invention. 
FIGS. 2 and 3 are a front elevational sectional view and a side elevational 
view of a compressor constructed in accordance with the present invention. 
Reference numeral 11 denotes a cylinder, 12 denotes a vane chamber of the 
low-pressure side, 13 denotes a vane chamber of the high-pressure side, 14 
denotes vanes, 15 denotes vane grooves slidingly receiving the vanes, 16 
denotes a rotor, 17 denotes a suction port, 18 denotes a suction groove 
formed in the inner peripheral surface of the cylinder 11, and 19 denotes 
a delivery port. 
In FIG. 3, a reference numeral 20 denotes a front panel as the end plate, 
21 denotes a rear panel, 22 denotes a rotary shaft, 23 denotes a rear 
case, 24 denotes a disc of the clutch fixed to the rotary shaft 22 and 25 
denotes a pulley. The compressor of the first embodiment is constructed in 
accordance with the following condition. 
TABLE 1 
______________________________________ 
Parameters Symbol Embodiment 
______________________________________ 
Number of vanes n 2 
Effective suction area 
a 0.450 cm.sup.2 
Theoretical displacement 
Vth 86 cc/rev 
Sliding angle of vane 
.theta..sub.s 
270.degree. 
end for completing 
suction stroke 
Cylinder width b 40 mm 
Cylinder inside dia. 
Rc 33 mm.sup.R 
Rotor dia. Rr 26 mm.sup.R 
______________________________________ 
The sliding angle .theta..sub.s of vane end for completing suction stroke 
as appearing in Table 1 above is defined as follows. 
Referring to FIGS. 4A and 4B, a reference numeral 26-1 designates a first 
vane chamber, 26-2 denotes a second vane chamber, 27 denotes the top 
portion of the cylinder 11, 28-1 denotes a first vane, 28-2 denotes a 
second vane and 29 denotes the end of the suction groove. The position of 
the vane just passing the top portion 27 of the cylinder where the outer 
peripheral surface of the rotor 16 substantially contacts with the inner 
peripheral surface of the cylinder 1 is represented by .theta.=0, and the 
position of the end of the vane when the latter takes any angular position 
is represented by angle .theta. from the starting point .theta.=0 formed 
around the center of rotation of the rotor 16. Referring specifically to 
the first vane chamber 26-1, FIG. 4A shows the state in which the first 
vane 28-1 has just passed the suction port 17, i.e. the state immediately 
after the commencement of the suction stroke. In this state, the first 
vane chamber 26-1 receives the refrigerant directly through the suction 
port 17, while the second vane chamber 26-2 receives the refrigerant 
indirectly through the suction groove 18 as illustrated by arrows. 
FIG. 4B shows the state in which the first vane chamber 26-1 has just 
completed the suction stroke, while the end of the second vane 28-2 is 
located on the end portion 29 of the suction groove. In this state, the 
first vane chamber 26-1 defined between the first and second vanes 28-1, 
28-2 take the maximum volume. 
In the described embodiment, the suction grooves 18 are formed in the inner 
peripheral surface of the cylinder 11 in a manner as shown in FIGS. 5A and 
5B. Each suction groove and each suction port are formed such that, when 
the end of the first vane 28-1 passes on the suction groove 18, the area 
of the suction port 17 is smaller than the cross-sectional area of any 
other part of the fluid passage between the suction port 17 and the second 
vane chamber 26-2. 
Namely, referring to FIG. 5B, representing the area S.sub.1 of suction 
groove by S.sub.1 =2.times.e.times.f, the suction groove is formed in the 
wall of the cylinder to have a depth large enough to satisfy the condition 
of S.sub.1 &gt;a, refer to Table 1. 
FIG. 6 shows the result of measurement of the refrigerating power in 
relation to speed of the compressor of the first embodiment constructed in 
accordance with the foregoing parameters. The measurement was conducted in 
accordance with the following condition, using a secondary refrigerant 
type calorimeter. 
TABLE 2 
______________________________________ 
Parameter Symbol Embodiment 
______________________________________ 
refrigerant press. 
Ps 3.18 Kg/cm.sup.2 abs 
at suction side 
refrigerant temp. 
T.sub.A 283.degree. K. 
at suction side 
refrigerant press. 
Pd 15.51 Kg/cm.sup.2 abs 
at delivery side 
speed .omega. 600 to 5000 rpm 
______________________________________ 
The characteristic curve a shows the refrigerating power determined by the 
theoretical displacement when there is no loss of refrigerating power, 
while the characteristic curve b shows the refrigerating power 
characteristic of an example of a conventional rotary compressor. The 
characteristic curves c and d show, respectively, the characteristic of an 
example of a conventional reciprocating compressor and the characteristic 
of the compressor constructed in accordance with the first embodiment of 
the invention. 
FIG. 7 shows the data concerning the volumetric efficiency .eta..sub.v as 
measured with the compressor of the first embodiment of the invention. 
The compressor of this embodiment exhibits an ideal refrigerating power 
characteristic as shown in FIG. 6d. This goes quite contrary to the common 
sense that the rotary type compressor provides an excessive refrigerating 
power when operated at a high speed. 
Namely, the following features (i) to (iii) were confirmed. 
(i) The reduction of refrigerating power in low-speed operation was 
sufficiently small. 
The characteristic curve in FIG. 7 shows a slight reduction of volumetric 
efficiency at a range of speed below 1400 rpm. This, however, is 
attributable to the leak of refrigerant at the sliding portion. 
The reciprocating compressor having a function of self-controlling of the 
refrigerating power has a characteristic feature that the suction loss in 
the low-speed operation is small. The rotary compressor of the first 
embodiment of the invention showed a characteristic which well compares 
with that of the reciprocating compressor in the low-speed operation. It 
will be seen that the curves b and c well conforms with each other. 
(ii) In the high-speed operation, the rotary compressor of the first 
embodiment showed an effect of suppression of refrigerating power which is 
equivalent to or higher than that achieved in the conventional 
reciprocating compressor. 
(iii) The above-mentioned effect of suppressing the refrigerating power is 
obtained when the operation speed is increased above 1800 to 2000 rpm. 
Thus, the rotary compressor of the fist embodiment presents an ideal 
energy saving refrigeration cycle of good feeling suitable for use in the 
automobile air conditioning system. 
The features (i) to (iii) mentioned above are ideal and quite advantageous 
when the compressor is used in the automobile air conditioning system. 
It is remarkable that the first embodiment of the invention provides a 
sliding vane type rotary compressor having a satisfactory performance 
without necessitating any specific auxiliary equipment which is essential 
in the conventional rotary compressor. 
Namely, according to the invention, it is possible to obtain a rotary 
compressor having a function of self-control of the refrigerating power, 
without deteriorating the advantages of the rotary compressor such as 
small size, light weight and simple construction. 
Generally speaking, in the polytropic change in the suction stroke of the 
compressor, the total weight of the refrigerant in the vane chamber and, 
accordingly, the compression work are reduced as the suction pressure and, 
hence, the specific weight of the refrigerant are small. Therefore, in the 
compressor of the first embodiment in which the total weight of the 
refrigerant is reduced automatically before starting the compression 
stroke, the driving torque is naturally lowered in the high-speed 
operation. 
Hitherto, in the case of the refrigerant cycle for a room air conditioner, 
such a power controlling system has been used as having a control valve 
connected between the high-pressure side and the low-pressure side of the 
compressor to relieve the compressed refrigerant from the high-pressure 
side to the low-pressure side to avoid excessive cooling. In such a 
system, however, the irreversible re-expansion of the refrigerant in the 
low pressure side causes compression loss which in turn results in a low 
efficiency of the compressor. 
In the rotary compressor of the invention, however, it is possible to 
effect the control of the refrigerating power without requiring useless 
mechanical work which corresponds to the above-mentioned pressure loss, so 
as to obtain an energy-saving refrigeration cycle of high efficiency. As 
will be explained later, the invention is distinguishable in making an 
efficient use of the transient phenomenon of a pressure change in the vane 
chamber by a suitable combination of various parameters of the compressor, 
while eliminating any specific moving part such as the control valve. 
Therefore, the compressor of this invention can operate at a high 
efficiency. 
In addition, since the refrigerating power changes gently in a stepless 
manner, the abrupt discontinuous change of the refrigerating 
characteristic as in the conventional refrigerating unit using a control 
valve, can be avoided so that a power control with a natural feeling is 
ensured. 
Hereinafter, an explanation will be made as to the analysis of 
characteristics which have been made to minutely grasp the transient 
phenomenon of pressure change which is an essential factor of the 
invention. 
The transient characteristic of the pressure change in the vane chamber can 
be expressed by the following energy equation (1). 
##EQU2## 
In the equation (1) above, as well as in the following equations (2) to 
(4), the symbols represent the following factors: 
G: weight flow rate of refrigerant, Va: volume of the vane chamber A: heat 
equivalent of work, Cp: specific heat at constant volume, Ta: suction side 
refrigerant temperature, .kappa.: specific heat ratio, R: gas constant, 
Cv: specific heat at constant volume, Pa: pressure in vane chamber, Q: 
calorie, .gamma..sub.a : specific weight of refrigerant in vane chamber, 
Ta: refrigerant temperature in vane chamber, a: effective area of suction 
port, g: gravity, .gamma..sub.A : specific weight of refrigerant at 
suction side, P.sub.s : refrigerant pressure at suction side. 
In equation (1) above, the first term on the left side represents the 
thermal energy brought into the vane chamber through the suction port per 
unit time, while the second term represents the work done by the 
refrigerant per unit time. Also, the third term represents the thermal 
energy delivered per unit time from the outside through the wall of the 
compressor. The right member of the equation represents the increment of 
the internal energy of the whole system per unit time. 
Assuming here that the refrigerant follows the Law of Perfect Gas, and that 
the suction stroke which is completed in a short time causes an adiabatic 
change of the gas, the following equation (2) is derived due to the 
conditions of .gamma..sub.a =Pa/RT.sub.a, dQ/dt=0 
##EQU3## 
Also, using the relationship expressed by 
##EQU4## 
the following equation (3) is derived. 
##EQU5## 
The theory of nozzle is adaptable to the flow rate (weight) of the 
refrigerant passing through the suction port. 
##EQU6## 
The transient characteristic of the pressure Pa in the vane chamber is 
determined by solving the equations (3) and (4) in combination. 
Representing m by m=Rr/Rc, the volume Va(.theta.) of the vane chamber is 
given by the following equation (5) 
##EQU7## 
wherein, on condition of 0&lt;.theta.&lt;.pi., Va(.theta.)=V(.theta.) and on 
condition of .pi.&lt;.theta.&lt;.theta..sub.s, 
Va(.theta.)=V(.theta.)-v(.pi.-.theta.). 
The .DELTA.V(.theta.) is a compensation term for compensating for the 
eccentric arrangement of the vanes with respect to the center of the 
rotor, and is usually of an order of 1 to 2%. FIG. 8 shows the case where 
the compensation term .DELTA.V(.theta.) is zero. 
FIG. 9 shows the transient characteristic of the pressure in the vane 
chamber as obtained using the conditions shown in Tables 1 and 2, with an 
initial condition of t=0 and Pa=Ps, with a parameter of the rotation 
speed. 
Usually, R-12 is used as the refrigerant in the refrigeration cycle of 
automobile air conditioning system. The analysis is made on condition of 
.kappa.=1.13, R=668 Kg.cm/.degree.K. Kg, .gamma..sub.A 
=16.8.times.10.sup.-6 Kg/cm.sup.3 and T.sub.A =283.degree. K. 
Referring to FIG. 9, the pressure Pa in the vane chamber has reached the 
suction pressure Ps=3.18 Kg/cm.sup.2 abs, before the suction stroke is 
completed, i.e. at a position of .theta.=260.degree., when the rotation 
speed is low (.omega.=1000 rpm). Therefore, no loss of pressure in the 
vane chamber takes place when the suction stroke is completed. 
As the rotation speed is increased, the supply of the refrigerant does not 
follow up the change of volume of the vane chamber, so that the pressure 
loss at the time of completion of the suction stroke (.theta.=270.degree.) 
is gradually increased. For instance, at the rotation speed of 
.omega.=4000 rpm, the pressure loss .DELTA.P in relation to the suction 
pressure Ps is 1.37 Kg/cm.sup.2 to reduce the total weight of the sucked 
refrigerant, resulting in a remarkable reduction of the refrigerating 
power. 
Instead of using the equation (5) from which the volume Va of the vane 
chamber can be obtained, we now propose the method of obtaining the 
correlation between the parameters and the efficiency of the performance 
capacity control by introducing the following approximation to the 
equations (3) and (4). Supposing that Vo is the maximum suction volume and 
using .PSI.=.OMEGA.t=(.pi..omega./.theta..sub.s)t, the angle .theta. is 
transformed into .PSI., where .PSI. varies from 0 to .pi.. 
In consideration with the conditions, Va(.theta.)=0 and Va'(.theta.)=0 when 
t=0, and Va(.pi.)=Vo and Va'(.pi.)=0 when t=.theta..sub.s /.omega. at 
which the suction stroke has been completed, the approximate function (6) 
is selected as for example: 
##EQU8## 
Representing .eta. by .eta.=Pa/Ps, the following equation (7) is derived. 
##EQU9## 
The equation (4) can be transformed into the following equation (8). 
##EQU10## 
From the above equations (7) and (8), the following equation (9) is 
derived. 
##EQU11## 
In the equation (9) above, K.sub.1 is a dimensionless amount expressed by 
the following equation (10). 
##EQU12## 
In the case of the sliding vane type rotary compressor, the theoretical 
displacement Vth is given by Vth=n.times.Vo, where n represents the number 
of vanes, so that the equation (10) can be transformed into the following 
equation (11). 
##EQU13## 
In the equation (9) above, .kappa. is a constant which is determined by the 
kind of refrigerant. Therefore, under the condition of K.sub.1 being 
constant, the solution of the equation (9), i.e. .eta.=.eta.(.PSI.) can be 
determined always directly. 
This means that the loss of pressure in the vane chamber at the instant of 
completion of the suction stroke is equal for all compressors which are 
constructed to have an equal value of K.sub.1, and the control of 
refrigerating power is effected at an equal rate with respect to a given 
refrigerating power Q Kcal which is obtained when no refrigerating power 
control is effected. 
Representing the pressure in the vane chamber at the completion of suction 
stroke by Pa=Pas, the rate of reduction of pressure .eta..sub.p is defined 
as follows. 
##EQU14## 
Now, a parameter K.sub.2 which depends on the dimensions of the compressor, 
is introduced to evaluate the effect on the refrigerating power control of 
the compressor, and is defined by the following equation: 
##EQU15## 
FIG. 10 shows a result which is obtained by the resolution to the equations 
(3) and (4) in combination under the condition of T.sub.A =283, giving 
.DELTA.T=10 deg as a superheat, with using K.sub.2 as a parameter. 
As will be seen from FIG. 10, it is possible to effectively obtain a 
pressure loss only in the high-speed operation, while minimizing the 
pressure loss in the low-speed operation, by suitably selecting the 
parameters of the compressor. The pressure reduction characteristic in 
relation to the speed has a region which may be referred to as an 
"insensitive region". The presence of this insensitive region is the most 
important feature which permits a more efficient refrigerating power 
control in the rotary compressor of the invention. 
The above-mentioned parameter K.sub.2 is calculated in the embodiment shown 
in Table 1 as follows. 
##EQU16## 
From FIG. 10, the rate of pressure reduction at the rotation speed of 
.omega.=3000 rpm, when the parameter K.sub.2 takes the above-specified 
value, is determined to be .eta..sub.p =15%. As will be explained later, 
the rate of pressure reduction can be considered as being materially 
identical to the rate of reduction of the refrigerating power. In the test 
result shown in FIG. 6, the rate of reduction of the refrigerating power 
is 16.0%. This well corresponds to the above-mentioned calculated value. 
A test was conducted with a compressor mounted on an actual automobile. The 
test result showed that the refrigerating power controlling effect which 
provides a practically sufficient performance of the automobile air 
conditioning system is, for example, as follows. (1) The rate of reduction 
of refrigerating power (pressure loss) is less than 5% at speed of 
.omega.=1800 rpm. (2) The rate of reduction of refrigerating power at 
speed of .omega.=3600 rpm is less than 10%. 
The range of the parameter K.sub.2 which meet both of the above conditions 
(1) and (2) is given as follows. 
EQU 0.040&lt;K.sub.2 &lt;0.075 (13) 
Thus, by selecting the parameters a, .theta..sub.s, n and Vth of the 
compressor to meet the above-equation (13), it is possible to obtain a 
compressor having a function of self-controlling of the refrigerating 
power and fulfilling the conditions (1) and (2) stated above. It is to be 
noted, however, the equation (13) is based on the value of K.sub.2 
obtained on the assumption that the refrigerant temperature T.sub.A is 
283.degree. K., so that the range specified by the equation (13) may be 
somewhat changed depending on the selection of the temperature T.sub.A. 
When freon R-12 is used as the refrigerant of the refrigerating cycle of 
automobile air conditioning system, the evaporation temperature T.sub.A of 
the refrigerant is determined taking the following points into account. 
The refrigerant temperature T.sub.A is preferably low, because the rate of 
heat exchange in the evaporator becomes larger as the temperature 
difference between the ambient temperature and the circulated refrigerant 
becomes greater. However, when the refrigerant temperature is lowered down 
below the freezing point of moisture in the air, the moisture is frozen 
around the refrigerant pipes to undesirably lower the heat exchanging 
efficiency. It is, therefore, preferred to construct the refrigeration 
cycle such that the refrigerant temperature is maintained higher than the 
above-mentioned freezing point. In the case where there is a flow of air, 
a refrigerant temperature around T.sub.A =-5.degree. C. is optimum, and 
the practically allowable limit of the refrigerant temperature T.sub.A is 
-10.degree. C. The evaporation temperature of the refrigerant becomes 
higher during low-speed running or the idling of the engine in which the 
condition for heat exchange is not good. The rate of heat exchange may be 
increased by increasing the flow rate of air provided by the blower or by 
increasing the surface area of the evaporator. These solutions, however, 
have a practical limit in mounting the air conditioning system on the 
automobile. 
Therefore, the practical upper limit of the refrigerant temperature is 
T.sub.A =10.degree. C. The refrigerant temperature is maintained, more 
preferably, less than 5.degree. C. 
Therefore, in order to construct a practically acceptable refrigeration 
cycle, it is necessary that the following condition be met. 
EQU -10.degree. C.&lt;T.sub.A &lt;10.degree. C. (14) 
As a point of information, the refrigerant suction pressure in this state 
is given by the following equation (15). 
EQU 2.26 kg/cm.sup.2 abs&lt;Ps&lt;4.26 kg/cm.sup.2 abs (15) 
Taking the superheat .DELTA.T=10 deg. into account, the equation (14) can 
be reformed as follows. 
EQU 0.degree. C.&lt;T.sub.A &lt;20.degree. C. (16) 
Therefore, it is possible to correct the range of the parameter K.sub.2 
determined by the equation (13), using the equation (16). Thus, only a 
1.8% increase of the upper limit value and 1.7% reduction of the lower 
limit value are the necessary correction. 
The "effective suction area" as referred to in the present invention has 
the following meaning. 
If there is any portion of minimum cross-section in the fluid passage 
between the outlet side of the evaporator and the vane chamber of the 
compressor, it is possible to grasp the approximate value of the effective 
suction area a as the product of the minimum cross-section and the flow 
contraction coefficient C which is usually 0.7 to 0.9. In a strict sense, 
however, the value obtained through the following experiment following JIS 
B 8320 or the like rule is defined as the effective suction area a. 
FIG. 11 illustrates an example of such an experiment. In FIG. 11, a 
reference numeral 100 designates a compressor, 101 denotes a pipe 
interconnecting the evaporator and the suction port of the compressor when 
the air conditioning system is actually mounted on an automobile, 102 
denotes a pipe for supplying a pressurized air, 103 denotes a housing for 
providing a communication between the pipes 101 and 102, 104 denotes a 
thermocouple, 105 denotes a flowmeter, 106 denotes a pressure gauge, 107 
denotes a pressure regulating valve and 108 denotes the source of the 
pressurized air. 
In FIG. 11, the compressor to which the present invention pertains is 
encircled by a chain line N. In the testing apparatus shown in FIG. 11, if 
there is any restriction which imposes an innegligibly high resistance in 
the evaporator, it is necessary to provide a restriction corresponding to 
that of the evaporator in the pipe 101. 
For measuring the effective suction area a of the compressor having a 
construction as shown in FIG. 3, the experiment is conducted with the 
front panel 20 demounted from the cylinder 11, after removal of the disc 
and the pulley 24, 25 of the clutch. 
Representing the pressure of the pressurized air by P.sub.1 Kg/cm.sup.2, 
and assuming that the atmospheric pressure P.sub.2, specific heat ratio 
.kappa..sub.1 of air, specific weight of air and gravity g are 1.03 
Kg/cm.sup.2 abs, 1.4 .gamma..sub.1 and 980 cm/sec.sup.2, respectively, 
while representing the flow rate (weight) by G.sub.1, the effective 
suction area a is determined in accordance with the following equation 
(17). 
##EQU17## 
The high pressure P.sub.1 is determined to meet the condition of 
0.528&lt;P.sub.2 /P.sub.1 &lt;0.9. 
The following table 3 shows the result of test conducted with compressors 
having different values of the parameter K.sub.2, mounted on actual 
automobiles. 
TABLE 3 
______________________________________ 
rev. effect of 
speed power control 
K.sub.2 
test result 
______________________________________ 
1800 rpm 
22.5% 0.025 Efficiency at low speed 
is somewhat lowered but 
sufficient refrigerating 
power confirmed provided 
that compressor having 
Vth in excess of 95 
cc/rev is used 
9.0 0.035 Slight loss of efficiency 
observed but practically 
usable 
4.5 0.040 Reduction of efficiency 
is very small. It is 
possible to construct 
ideal energy saving 
refrigeration cycle 
having high efficiency 
4600 21.5 0.065 Best control of power at 
high-speed operation and 
best energy-saving 
effect obtained. 
18.0 0.070 Effect equivalent to 
that of conventional 
reciprocating compressor 
obtained. Practically 
sufficient 
12.0 0.080 Power controlling effect 
somewhat insufficient. 
Provided that the engine 
displacement is in 
excess of 2000 cc, a 
practically usable 
refrigeration cycle can 
be designed with the use 
of a condenser having a 
large capacity. 
______________________________________ 
The data shown in FIG. 6 were obtained with constant suction and delivery 
pressures P.sub.s, P.sub.d. In the actual running of the automobile, 
however, the suction pressure is reduced and the delivery temperature is 
raised during high speed operation of the compressor. In consequence, 
assuming that no control of the refrigerating power is effected, the 
compression ratio is increased not only to increase the compression work 
(driving torque) but also an overload of the condenser due to the elevated 
delivery temperature, resulting, in the worst case, a breakdown in the 
cooler. The margin to the overload is increased as the size of the 
condenser becomes large. Therefore, a sufficiently large margin for the 
excessive refrigerating power is preserved as the size of the automobile 
becomes large, because it is possible to mount a condenser having a larger 
size. 
From the test result shown in Table 3, it is derived, taking into account 
the selection of class of the automobile having different engine 
displacements, that the present invention can be practically carried out 
when the parameter K.sub.2 falls within the range specified below. 
EQU 0.025&lt;K.sub.2 &lt;0.080 
A first embodiment has been described hereinbefore on an assumption that 
the effective area of the passage leading to the vane chamber is regarded 
as being constant over the whole part of the suction stroke. The 
theoretical explanation using the parameters K.sub.1 and K.sub.2, however, 
does not apply when the opening of the suction passage to the vane chamber 
has a substantial length in the direction of running of the vane to vary 
the effective area of the opening depending on the position of the vane. 
This is because, in the relationship expressed by the equation (9), the 
parameter K.sub.1 changes as a function of .psi. to vary the value of 
.eta. in accordance with K.sub.1 (.psi.) within the region of 
0&lt;.psi.&lt;.pi.. 
For instance, in the case where the compressor has the suction port 6 in 
the rear end plate as in the case of the compressor shown in FIG. 1, the 
effective area of opening of the suction passage is gradually decreased in 
the final part of the suction stroke in which the vane 5 passes over the 
suction port 6. 
Hereinafter, a description will be made as to the second embodiment of the 
invention which applies to the case where the effective suction area is 
changed during the suction stroke of the compressor. 
Referring to FIG. 12, the compressor has a suction groove 56 and a suction 
port 54 formed in the inner peripheral surface of the cylinder. The 
effective suction area S.sub.1 determined by the width e, depth f and the 
number of the suction grooves is selected to be somewhat smaller than the 
aforementioned suction port 54. In this case, the effective area of the 
suction passage is reduced in the later part of the suction stroke. (As to 
the symbols e and f, refer to FIG. 5) 
Referring to FIG. 12, a reference numeral 50 denotes a rotor, 51 denotes a 
cylinder, 52 denotes vanes, 53 denotes a vane chamber, 54 denotes a 
suction port, 55 denotes a delivery port and 56 denotes a suction groove. 
The shape of the suction groove as illustrated in FIG. 12, if it is 
acceptable in view of the characteristics of the compressor, is 
advantageous from the view point of mass production of the compressor, 
because such a shape affords a curvature of the profile of the groove 
corresponding to the diameter of the tool. 
Thus, in ordinary compressors, the effective suction area is often changed 
largely in the suction stroke, due to the reason in the processing or 
general arrangement. The second embodiment of the invention described 
hereinafter can apply to such a type of compressor. 
(i) In the case where the suction passage is closed in the earlier part of 
the suction stroke: 
A discussion will be made hereinunder as to the influence of the closing of 
suction passage in the earlier half part of the suction stroke, i.e. the 
stop of supply of refrigerant to the vane chamber, on final pressure of 
the refrigerant. 
To investigate this influence, a numerical experiment was conducted as 
follows on an assumption that the rotation speed .omega. is 3600 rpm, with 
the parameters other than the effective suction area a(.theta.) of 
equation (10) set at the same values as those in Tables 1 and 2. 
Representing the region in which the suction passage shown in FIG. 13A is 
closed (region of a(.theta.)=0) by .theta..sub.1, the rate of pressure 
reduction .theta..sub.p was obtained in relation to .theta..sub.1 
/.theta..sub.s, the result of which is shown at FIG. 14. 
From FIG. 14, it will be seen that the presence or absence of the suction 
passage does not affect the final pressure materially, when the ratio 
.theta..sub.1 /.theta..sub.s falls within the range expressed by 
0&lt;.theta..sub.1 /.theta..sub.s &lt;0.5. Namely, the rate of pressure drop 
.eta..sub.p at the instant of completion of the suction stroke is ruled 
solely by the area of the suction port a(.theta.)=0.78 cm.sup.2 which 
opens in the later half part of the suction stroke, and has no relation to 
the state of the suction passage in the earlier half part of the suction 
stroke. 
FIG. 15 shows the transient characteristics which are the practical 
examples of the above-described result. More specifically, the 
characteristic a is obtained when the suction area is maintained constant 
over the whole part of the suction stroke, while the characteristic b is 
obtained when the suction passage is closed over the period of 
0&lt;.theta./.theta..sub.s &lt;0.37. 
In the case of the characteristic b, the pressure Pa in the vane chamber is 
largely decreased while the suction passage is kept closed, but is 
increased abruptly as the passage is opened. No substantial difference is 
found between the values of characteristic curves a and b at the instant 
.theta..sub.s =270.degree. at which the suction stroke is completed. 
(ii) In the case where the suction passage is closed in the later part of 
the suction stroke: 
FIG. 16 shows how the final refrigerant pressure is affected when the 
suction passage is closed over an angular range .theta..sub.2 in the later 
half part of the suction stroke. It will be seen that the rate of pressure 
reduction .eta..sub.p is increased in proportion to the angular range 
.theta..sub.2. In fact, the rate of pressure reduction .eta..sub.p is 
about 80% or higher when the ratio .theta..sub.2 /.theta..sub.s is 0.5. 
The following fact is derived from the above considerations (i) and (ii). 
The influence of the opening state of the suction passage and the size of 
the opening of the suction passage upon the final refrigerant pressure 
varies largely depending on the angle .theta. of running of the vane in 
the suction stroke. The influence is small in the earlier half part of the 
suction stroke, i.e. in the region of 0&lt;.theta.&lt;.theta.s/2, but is 
gradually increased as the angle .theta. approaches .theta..sub.3. 
The above-described fact tells that, it is possible to obtain an adequate 
mean value a(.theta.) of any desired function a(.theta.), by providing the 
area a(.theta.) of the suction passage with "weight" in accordance with 
the position. 
FIG. 17 shows various weight functions g(.theta.). In the function g.sub.1, 
g(.theta.)=0 on condition 0&lt;.theta./.theta..sub.s &lt;0.5 and 
g(.theta.)=2(.theta./.theta..sub.s)-1 on condition of 
0.5&lt;.theta./.theta..sub.s &lt;1. The function g.sub.2 is 
g(.theta.)=(.theta./.theta..sub.s).sup.2, the function g.sub.3 is 
g(.theta.)=.theta./.theta..sub.s and the function g.sub.4 is g(.theta.)=1. 
The weight mean a is defined here as follows. 
##EQU18## 
The mean value a of a(.theta.) was obtained from the a(.theta.) as the 
function of vane sliding angle .theta. and from various weight functions 
g(.theta.). From the thus obtained mean value a, the transient 
characterisic at an operation speed of 3600 rpm was obtained using the 
equations (3) and (4), as well as conditions specified in Tables 1 and 2 
(except the area a), the result of which is shown at shown in FIG. 17. 
The value of the area a as shown in FIG. 19 is used as the area a(.theta.) 
of the suction passage. The pa(.theta.) shown in this Figure is a strict 
answer as obtained without using the mean value. The term "strict answer" 
used here means the value obtained through a numerical analysis precisely 
taking the suction area a(.theta.) into account but does not mean any 
analytically determined value. 
TABLE 4 
______________________________________ 
weight function 
weight mean -a 
error from strict answer 
______________________________________ 
g.sub.1 0.365 cm.sup.2 
-9.4% 
g.sub.2 0.450 0.3 
g.sub.3 0.530 7.9 
g.sub.4 0.630 17.3 
______________________________________ 
According to the result shown in FIG. 18, the strict answer Pa(.theta.) 
exhibits a pressure loss of .DELTA.P=0.78 Kg/cm.sup.2 abs with respect to 
the suction pressure Ps=3.18 Kg/cm.sup.2 abs, at the instant 
.theta.=270.degree. at which the suction stroke is completed. 
The pressure Pa(.theta.) according to the strict answer starts again to 
decrease at an instant .theta..sub.s1 =200.degree.. This is attributable 
to the fact that the effective area of the suction passage is reduced from 
a(.theta.)=0.78 cm.sup.2 down to 0.31 cm.sup.2. 
The errors of the values obtained with various weight functions from the 
strict answer are shown in Table 4. 
From FIG. 18, it will be seen that, when the weight function g.sub.1 is 
used, the value obtained with the use of the weight mean is somewhat 
smaller than the value of the strict answer. To the contrary, when the 
weight function g.sub.2 is used, the value obtained with the use of weight 
mean is somewhat greater than that of the strict answer. Since there is a 
relation expressed by g.sub.1 &lt;g.sub.2 &lt;g.sub.3, the function 
g(.theta.)=g.sub.2 =(.theta./.theta..sub.s).sup.2 provides the optimum 
effect under the condition explained above. Thus, substituting 
g(.theta.)=g.sub.2 =(.theta./.theta..sub.s).sup.2 into Equation (18) and 
noting that .theta..sub.s is constant, the following equation is obtained: 
##EQU19## 
FIG. 19 shows the relationship between the effective suction area 
a(.theta.) in relation to the rotation angle .theta. of the vane in the 
compressor having the suction groove of the shape shown in FIG. 12, for 
each of the three cases (a), (b) and (c) as shown in Table 5 below. 
TABLE 5 
______________________________________ 
angle at which effective 
effective area -a obtained 
area is changed using weight function g.sub.2 
.theta..sub.s1 
.theta..sub.s2 
-a 
______________________________________ 
a 200.degree. 
250.degree. 
0.450 cm.sup.2 
b 220.degree. 
270.degree. 
0.551 cm.sup.2 
c 240.degree. 
270.degree. 
0.631 cm.sup.2 
______________________________________ 
FIG. 20 shows, for each of the cases (a), (b) and (c), the rate of pressure 
reduction in relation to speed as obtained by the strict answer in 
comparison with that obtained by the use of the weight mean a. 
In each case, both characteristics well match to each other at a speed 
range of between .omega.=3000 rpm and .omega.=4000 rpm. The gradient of 
rate of pressure reduction in relation to rotation speed is more gentle in 
the case of the strict answer than in the case of the weight mean. 
Therefore, in the region of a comparatively high rotation speed, a larger 
rate of pressure reduction is obtained when the weight mean a is used, 
whereas, in the region of comparatively low speed, a greater rate of 
pressure reduction is obtained by the use of the strict answer. 
From these results, it will be seen that, within the range in which the 
parameter K.sub.2 can be selected suitably, the effective suction area is 
preferably maintained constant rather than being decreased gradually 
during the suction stroke, in order to achieve an ideal refrigerating 
power controlling characteristic. 
The above-described method using the weight mean can provide an 
approximation of a practically sufficient accuracy, so that it is possible 
to evaluate the characteristic employing the parameter K.sub.2 as in the 
case of the [I] stated before. 
To sum up, the present invention can be applied in the following manner to 
an ordinary compressor in which the effective suction area of the suction 
passage is changed during the suction stroke. 
(1) To obtain the effective area a(.theta.) of the passage between the 
evaporator and the vane chamber of the compressor within the range of 
0&lt;.theta.&lt;.theta..sub.s. 
(2) To determine the weight mean a using the effective area a(.theta.) as 
determined above, making use of the following equation. 
##EQU20## 
(3) To determine the parameter K.sub.2 =a..theta..sub.s.n/Vth, making use 
of the weight mean a obtained in the preceding step (2). 
(4) To make the evaluation of the characteristic from the value of the 
parameter K.sub.2, making use of, for example, the data in Table 3. 
In the foregoing description of the first and second embodiments of the 
invention, the rate of reduction of the pressure .eta..sub.p is used as 
the index of the effect of the refrigerating power control. This is 
because the use of this index makes it possible to evaluate the effect of 
the refrigerating power control solely by the ratio .DELTA.P/Ps of the 
suction pressure Ps to the pressure reduction .DELTA.P. 
However, more strictly, the rate of reduction of the refrigerating power 
can be obtained from the specific weight of the refrigerant at the suction 
side and that in the vane chamber. Namely, representing the specific 
weight of the refrigerant at the suction side by .gamma..sub.A and that of 
the refrigerant in the vane chamber by .gamma..sub.a, while expressing the 
specific weight of the refrigerant in the vane chamber at the instant of 
completion of the suction stroke by .gamma..sub.a =.gamma..sub.as, the 
rate .eta..sub.j of reduction of the refrigerating power can be defined as 
expressed by the following equation (19). 
##EQU21## 
Assuming here that the refrigerant temperature at the instant of completion 
of the suction stroke is given by Ta=Tas, the equation (19) can be 
transformed into the following equation (20), because there is a relation 
expressed by .gamma.=P/RT. 
##EQU22## 
The refrigerant temperature Ta in the vane chamber can be determined as 
follows. 
In the energy equation (1) mentioned before, representing the total weight 
G.sub.o of refrigerant in the vane chamber by G.sub.o =.gamma..sub.a.Va, 
and assuming that the conditions of Ta=T.sub.A and dQ/dt=0 are obtained at 
the instant t=0, the following equation (21) is derived. 
##EQU23## 
The equation (21) was solved under the conditions given in Tables 1 and 2, 
on the assumption of A=1/42700 Kcal/Kg.cm, Cp=0.147 Kcal/Kg.degree.K. and 
Cv=0.130 Kcal/Kg.degree.K., to determine the transient characteristic of 
the refrigerant temperature Ta in the vane chamber. 
The change of the refrigerant temperature Ta is gentle as compared with the 
change of the pressure in the vane chamber (See FIG. 9) obtained under the 
same condition, and the offset of the refrigerant temperature from that of 
the suction side T.sub.A is rather small. The difference of the final 
refrigerant temperature caused by the difference of the rotation speed is 
within an order of 5.degree. C. to 12.degree. C. at the greatest, and the 
rate of change of temperature T.sub.A /Tas is as small as 1.09 to 1.14. It 
will be understood that the rate .eta..sub.j of reduction of refrigerating 
power is determined almost completely by the ratio P.sub.as /P.sub.s of 
refrigerant pressure or by the rate of pressure reduction, .eta..sub.p 
=1-P.sub.as /P.sub.s. From the above consideration, it will be understood 
that the effect on the refrigerating power control can be evaluated solely 
from the rate .eta..sub.p of pressure reduction. 
Preferred embodiments of the invention applied sliding vane type compressor 
having two vanes have been described. It is to be understood, however, 
that the invention can be applied to various types of compressors 
irrespective of the displacement, number of vanes and other factors. 
Although a larger displacement can be obtained by mounting the vanes at an 
eccentricity from the center of the rotor, such an eccentric arrangement 
is not essential and the invention can be applied to sliding vane type 
compressors having vane mounted without any eccentricity from the center 
of the rotor. 
Also, the constant angular pitch of the disposal of vanes as employed in 
the described embodiments is not essential, and the invention can be 
equally applied to sliding vane type compressor having an irregular pitch 
of the vanes. In such a case, the refrigerating power control of the 
invention is effected on the vane chamber having the greater value of the 
maximum suction volume Vo. 
The cylinder which has a cylindrical form in the described embodiments can 
have an oval cross-section. The invention can be applied even to a 
single-vane type compressor in which a single vane is slidably mounted 
radially across the rotor. However, this single vane substantially acts as 
two disposed in the compressor. 
As has been described, by constructing the compressor under the condition 
specified by the present invention, it is possible to effectively suppress 
the refrigerating power only in the high-speed operation while avoiding 
substantial reduction of the refrigerating power in the low-speed 
operation. Thus, the present invention offers an advantage of the 
refrigerating power control with ordinary rotary compressor having a 
simple construction, without necessitating addition of any specific 
auxiliary equipment.