Purdue University
Purdue e-Pubs International Compressor Engineering Conference
School of Mechanical Engineering
1986
Computer Modeling of Scroll Compressor with Self Adjusting Back-Pressure Mechanism K. Tojo M. Ikegawa N. Maeda S. Machida M. Shilbayashi See next page for additional authors
Follow this and additional works at: http://docs.lib.purdue.edu/icec Tojo, K.; Ikegawa, M.; Maeda, N.; Machida, S.; Shilbayashi, M.; and Uchikawa, N., "Computer Modeling of Scroll Compressor with Self Adjusting Back-Pressure Mechanism" (1986). International Compressor Engineering Conference. Paper 576. http://docs.lib.purdue.edu/icec/576
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Authors
K. Tojo, M. Ikegawa, N. Maeda, S. Machida, M. Shilbayashi, and N. Uchikawa
This article is available at Purdue e-Pubs: http://docs.lib.purdue.edu/icec/576
COMPUTER MODELING OF SCROLL COMPRESSOR WITH SELF ADJUSTING BACK-PRESSURE MECHANISM
Kenji TOJO, Masato IKEGAWA, Naoki MAEDA, Sigeru MACHIDA, Masao SHIIBAYASHI Mechan ical Enginee ring Researc h Laborat ory, Hitachi Ltd. Tsuchiu ra, Ibaraki , Japan Naoshi Uchikaw a Shimizu Works, Hitachi Ltd. Shimizu , Shizuok a, Japan
ABSTRACT A comput er model for calcula ting the perform amce of a scroll compre ssor with a self-ad justing back-p ressure mechan ism was develop ed. The model gives detaile d geomet rical and thermod ynamic informa tion concern ing the interna l process es. It calcula tes the influen ce of interna l leakage between the neighbo ring gas pockets with its viscous effect. It also calcula tes the contrib ution to adiaba tic ineffic iency from gas flow passing through small apertur es located in positio ns opened to the interme diate compres sion gas pockets . This paper describ es the theory used in the model and then present s some numeric al results of p-v diagram , back-pr essure, and the adiabat ic efficien cy of the machine for several operatin g conditi ons. INTRODUCTION With the popular ization of air-coo led and heat-pum p air conditi oners, the energy efficien cy ratio and high compres sor efficien cy over a wide range of operati ng conditi ons must be improv ed. Likewis e, to improve the annual perform ance factor of heat-pum p air conditi oners, capacit y control by means of motor rotatio nal speed control is becomin g widespr ead. Low noise/ vibratio n level at all rotatio nal speeds is another importa nt conside ration for compre ssors. With this in mind, a new type of col'!pres sor with scroll wraps was develop ed and put into commer cial product ionS). The concept of a scroll fluid machine is very old. It was first describ ed in a u.s. patent in the early 1900s1 l, but was not fully develop ed in the practic al applica tion until recentl y2, 3). This was primar ily because of the lack of precise produc tion techniq ues and the compone nt wear resultin g from the large axial
872
To solve these problems, Hitachi developed a precise gas force. machining technique for mass production, and also developed a controlled thrust force mechanism to support the orbiting scroll in the axial direction with the lowest frictional force and In the controlled thrust force mechanism, so-called a wear4). back-pressure chamber is provided behind the orbiting scroll. The back-pressure chamber is pressurized automatically at a level between the suction pressure and the discharge pressure by means of gas introduced through the small apertures (back-pressure port) open to the intermediate compression gas pockets, and provide pneumatic force against the back of the orbiting scroll. While a calculative method to find the proper range of the backpressure on the back of the orbiting scroll has been reported6), it is necessary to investigate the dynamic characteristics involved as well. Thus, this paper outlines a computer simulation model for analyzing the performance of a scroll compressor with a The model gives detailed self adjusting back-pressure mechanism. geometrical and thermodynamic information to the compression gas pockets and to the back pressure chamber. Application of this is 'demonstrated by an actual example of the scroll wraps.
GEOMETRICAL CHARACTERISTICS The main elements in a scroll compressor are two identical They are assembled- at a involute spiral scrolls shown in Fig.1. relative angle of 180° so that they touch at several points and One of the scroll form a series of crescent-shaped pockets. member is fixed and the other orbits around the center of the The orbiting scroll is driven by a fixed fixed scroll wrap. short-throw crank mechanism. The pair of contact points between the two spiral walls shift along the spiral curves with shaft The relative angle of the two scroll members are rotation. maintained by means of an anti-rotation coupling mechanism located between the back of the orbiting scroll plate and the stationary part. SCROLL
Figure 1 Basic configuration of scroll compressor 873
Volume curve The geometrical relation of scroll wrap is shown in Fig.2, and 3. When the n pairs of pockets are formed, as shown in Fig.3, the roll angles,lpi at the contact points are given as: 1
lpi = (- 8 +
-,.;
= (- 9 +
-'I!;
)+2(i-l)., .;
0 :i! 8:;;
2
1
-,.;
2
1
-n :s;9:s; 2n
) + 2 in
2
(1)
2
The volume of the i-th pocket, Vpi• is obtained from the geometrica l considerat ion of the involute spiral as follows;
Vpi = a .,.; a h" ( 2 ( l pi - ,.; ) + a )
(2)
The displacemen t volume, Vth• and the built in volume-rati o, Vr, are then given as: (3)
2
vr
l
-,.; ) + a
pso
= ----------
(4)
where lpso is the roll angle at th seal-off position of the suction pockets, and lpdo is the roll angle at the contact point when the discharge process commences. The volume of the outermost pocket in the suction process illustrated by the shaded area in Figure 3 is given as:
1
V • = a a• h ( - 8 ( 2 l P~ 2 S
PSO
- 9
S
+a )
(5)
where 9 is the orbiting angle taken from the suction seal off 8 position. The innermost sealed pocket in the discharge process is defined by the dotted area in Fig.3. The volume of the pocket in the the discharge process is given as:
1
V = h (- a"{(.:t +n)"-l }+a 2 (.,.;-2a) pi 6 pl p1
874
1 -2-n;+a)"} -2n)'-(l. +a)"+(A. - a"{(l. +n)'-(l. pdo pl pdo p1 6
-
1 1 1 -2-n;+a)+ r) + --n;a 2 } {- r • ( -n+
BACK-PRESSURE CHAMBER
Figur·e 7 Analytical model of scroll compressor
883
THERMO
F~UID
5CR0~~
ANALYSIS
DYNAMICS
I
I
I
I
L
L ____ _lI
OUTPUT
Figure 8 Flow diagram
5.00
---~----~---------y----~----T----~----~----~-~--~
---+----r----!.----!-----t----t----I----.:.----1----i
:::: ""
----f---. r----[ --~::~:::1 ::::I~:~:: ~:~:t:: :~::::: I - - - - - .
c. 4.00
....
w
"'~
~ 3.00
-
U1 U1
~ !.00~-----------------~--------------~ BACK-PRESSURE PORT OPEN
0. 00 L...____...l__ _ _---~._ _ _ _ _,..1__ _~-------:--' 0. 00 o. 20 0. 40 0.150 0.80 t. 00 VOLUME IN GAS POCKET
Figure 12
Vi/Vth
Influence of effective back-pressure port area on P-V diagram 100
1-
~
\
1'-....r..... Ptl ..
:z.o
m··
Pll - 0.59UI'!1
--
111 • 29l"K
I
0
I
t. 80 ~
....""
/
~ 1. 70
0 ....
~
1. 60
::l
[;i
~ "' :-J
1.50
I
"'
1-
J v
1. 40
10 4
/
-
I Vb/Vth • 1.0
1111 .. 0.0
1-r•O.O
~
I 10 3
EACK-PRESSURE PORT AREA Cab·Afi;b/w•Vr.h (•/II)
Figure 13
Variation of compressor efficiency and back-pressure with effective back-pressure port area 886
