Study on Performance and Dynamics of Inverter Controlled Rotary Compressors

Purdue University Purdue e-pubs International Compressor Engineering Conference School of Mechanical Engineering 2 Study on Performance and Dynamics of Inverter Controlled Rotary Compressors J. Wu Xi an Jiaotong University Follow this and additional works at: http://docs.lib.purdue.edu/icec Wu, J., "Study on Performance and Dynamics of Inverter Controlled Rotary Compressors" (2). International Compressor Engineering Conference. Paper 1426. http://docs.lib.purdue.edu/icec/1426 This document has been made available through Purdue e-pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information. Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/ Herrick/Events/orderlit.html

STUDY ON PERFORMANCE AND DYNAMICS OF INVERTER CONTROLLED ROTARY COMPRESSORS Jianhua WU School of Energy and Power Engineering Xi'an Jiaotong University,Xi'an 7149, P.R.China E-Mail: jhwu@xjtu.edu.cn ABSTRACT An inverter controlled refrigeration system with a variable speed compressor is more efficient. In order to improve its efficiency and reliability in wide range of speed, a comprehensive simulation model for an inverter rotary compressor with single cylinder or dual cylinder is developed. The simulated results are compared with measured data. The variations of cooling capacity, input power, COP, various efficiencies and losses, and closing angle and impacting velocity of reed valve are analyzed. The pressure variations in working chambers at various speeds and their effects are explained. That the fluctuation of rotating speed of a single cylinder compressor operating at low speed produces the great difference between the practical and rated efficiency of motor is shown. INTRODUCTION An inverter air conditioner can achieve higher seasonal energy efficiency ratio (SEER) and provide more comfortable environment. Its capacity is adjusted closely according to actual load by the rotational speed of compressor, which is controlled by the frequency or voltage of electric current output by inverter. So its compressor need operate at a very wide range of speed. The internal mechanism of compressor at low or high speed is different from that at conventional speed. Performance and dynamic of compressor varies with its speed. In order to improve its efficiency and reliability in wide range of speed, a comprehensive simulation model for an inverter rotary compressor with single cylinder or dual cylinder is developed and the variation of its performance and dynamics is analyzed. Sakurai and Hamilton developed a simple mathematical model for predicting frictional losses in a variable-speed rotary compressor l'l. Sato and Shirafuji studied the single cylinder and dual cylinder rotary compressors driven under low electric frequencies and analyzed the reason why the performance of a single cylinder rotary compressor was remarkably decreased as its rotational-speed decreased rz1. Liu and Soedel studied the influence of factors on the volumetric efficiency and cylinder process efficiency of compressor under different speeds with paying special attention to supercharging effect l 3 U 4 1 and the temperature distribution of compressorl 5 1. Park and Min developed a dynamic simulation model to predict the dynamic characteristics of a variable speed compressor l 6 1. In this paper, the control volume, energy equation, valve model and motion equation of crankshaft are described (The relative leakage model and vane and roller dynamics are described in the reference [7] and [8]). Purdue University, West Lafayette, IN, USA- July 25-28, 2 491

The pressures in compression, suction and clearance chambers, the behavior of reed valve at various speeds are explained. The variations ofthe valve closing angle and velocity of real valve impacting on valve seat and the frictional losses related vane and bearing are shown. The variations of volumetric, indicated, mechanical, motor and overall efficiencies and COP of a single cylinder and a dual cylinder rotary compressor is discussed. The effects of rotational speed fluctuation on motor efficiency and hence overall efficiency and COP are analyzed. The comparison of simulated results with measured data is given. MATHEMATICAL MODEL Control volume The first step to conduct a compressor simulation is to analyze the working process inside the compressor, to define control volume and to determine the mass exchange between the control volume and its surroundings. A rolling piston (roller) and a vane divides the space between cylinder wall and roller outer surface into two chambers: suction chamber (trailing chamber) and compression chamber (leading chamber). The notch on cylinder edge and the discharge port constitute the clearance chamber of a rotary compressor. When the crankshaft rotates in the neighborhood of the discharge port, the pressure in the clearance chamber is significantly different from that in another chamber since the effective flow areas between clearance chamber and compression chamber and between clearance chamber and suction chamber are very small. Therefore, in this time, the clearance chamber is selected as a control volume. But after the pressure in clearance chamber is balanced with that in compression chamber, the clearance chamber and compression chamber are taken as a single control volume during the compression process. After the discharge process of the compression chamber begins, the pressure in clearance chamber is below that in the compression chamber due to the throttle at the entrance of discharge hole and notch. The compression chamber is separated from the clearance chamber and is taken as a control volume alone. The clearance chamber is treated as a throttling element instead of a control volume as Reference [9] because the flow velocity through the discharge port is so large that the refrigerant kinetic energy is not negligible. And the mass flow rate discharged from the compressor chamber and the gas force acting on the valve are calculated directly by the pressure difference between the compression chamber and discharge plenum. The pressure and gas mass in the clearance chamber are estimated by throttling at the entrance of discharge hole. The estimating accuracy has a little effect on the calculated results of cooling capacity and input power. As the crankshaft rotates, the three dimensional gap area formed by the radial gap between the cylinder wall and roller outer surface around the notch edge becomes much smaller than the effective entrance area of discharge port. So the throttle occurs at the notch edge and the pressure difference between the compression chamber and the clearance chamber becomes large. In addition, the flow velocity inside discharge port becomes so small that the kinetic energy could be neglected. At this moment, the clearance chamber is taken as a control volume. So the gas force on the valve is evaluated by the pressure difference between the clearance chamber and discharge plenum and the mass flow rate discharged from the compression chamber is calculated from the pressure difference between the compression and clearance chamber. For the above control volume, when the energy balance is studied, the internal energy of oil within the control volume is considered and the mass equation of oil is formulated correspondingly in order to accurately. Purdue University, West Lafayette, IN, USA- July 25-28, 2 492

evaluate the heating effect of refrigerant and oil leaked on the refrigerant. However, the volume of oil is negligible. The mass equations and the energy equation in terms of the derivative of temperature with respect to angular displacement of crankshaft are expressed as follows: dt db ---{- 1 (LQ; + Lh;riz; +c 1 L7[;mu)-[h-v(az)r +v 2 ( 7 P )r] dm cvm+c 1 m 1 m 5 ; ; Ov in db dm 1 az IJP dv -c1t db -[( 11 )r.,..vc 171 )rl db} When the discharge valve of a rotary compressor opens the reed valve wraps about its curved backer plate. The free length of reed valve varies with the valve displacement and thus the valve stiffness and effective mass always varies too. In this paper the valve system is treated as a one freedom degree vibration system with variable stiffness and mass and its differential equation of motion is expressed as follows: As mentioned above, the discharge process is divided into two phases in this paper. During the first phase, the mass flow rate of refrigerant discharged from the compression chamber and the gas force acting on the reed valve are evaluated from the pressure difference between the compression chamber and discharge plenum. The flow condition at the entrance of the model device by which the available valve flow coefficient and the valve gas force coefficient were measured is different from the real flow condition at the entrance of discharge port of a rotary compressor. The flow and gas force coefficients are improved by the effective entrance area of discharge port, which is relative to the size and position of discharge port and notch and the roller end wall interference. After the radial gap area at the notch edge is less than the effective entrance area, the mass flow rate through the valve and the gas force on reed valve are evaluated by the pressures in the clearance chamber and discharge plenum and both the flow coefficient and the gas force coefficient are taken asl. Dynamic equation of crankshaft For a single cylinder compressor, the resistance moment by compression mechanism is: M z = efen sin(b -17eb) + mnebs (B)+ mmsb (B)+ mtb + mw in which mebs, mmsb and m 1 b are the frictional moment acting on the crankshaft by the eccentric, main and thrust bearings respectively, mw is the wind drag on balance weight and Fen and 1leb are the total force on eccentric bearing and its direction angle respectively. For a dual cylinder compressor, the resistance moment is expressed by: M z = efen (B) sin[() -77eb (B)]+ efen (B + n-) sin[b + 7r -77mb (B + n-)] + mebs (B)+ mebs (() + 7r) + mmsb (B)+ mtb + mw The motor torque could be expressed a function of current frequency and instantaneous slip ratio or Purdue University, West Lafayette, IN, USA- July 25-28, 2 493

. rotating speed. So the dynamic equation of crankshaft is given by: wsus +Ncmre 2 ) d;; =Mm(ws(B), fe)-mz(b) in which Is is the moment of inertia of motor rotor and crankshaft, Nc is the number of cylinder. Besides the model menti.oned above, the comprehensive model developed includes the other model such as leakage, heat transfer, mass exchange, gas flow pulsation, vane dynamics, roller dynamics, shaft center loci of bearings, friction loss and lubrication system. The numerical simulation is performed by coupling the models in the energy and mass equations. RESULTS AND DISCUSSIONS Table 1 shows the comparison of the values of cooling capacity, input power, COP and average rotational speed calculated by the above model with the data measured for a single cylinder inverter rotary compressor whose cylinder diameter is 44mm. Table 2 shows that for a dual cylinder inverter rotary compressor whose cylinder diameter is 54mm. The simulated results are very consistent with the measured data. Most deviations are less than 3%. The clearance on roller end face of the above tested compressors is too large. In the following simulation analyses the clearance is taken as 1211 m. Figure 1, figure 2 and figure 3 show the variations of pressures in the compression, suction and clearance chambers with rational angle of crankshaft when the frequencies of current output by inverter are 3Hz, 6Hz and 12Hz respectively. The variations of pressures in suction chamber and in compression chamber during discharging with rotational speed are obvious. The pressure drop in the suction chamber at rotational angle of about 2 o is attributed to the throttling at the edge of suction port. The angle included between notch and cylinder is 45 o The secondary pressure pulse in compression chamber, which increased with the rotational speed, is not so great as that in the reference [9] since a large chamber at the edge of discharge side of vane slot is connected with the notch. In addition, the angle range taken by the reexpansion of compressed refrigerant from the clearance chamber back into the suction chamber and compression chamber increases with the rotational speed. This may decelerate the increase of the velocity of the reed valve impacting on valve seat with the rotational speed. Figure 4 shows the behavior of the reed valve. As shown in Figure 5, the closing angle of valve becomes bigger at the high rotational speed and the velocity of valve impacting on valve seat increases quickly with the rotational speed. Figure 6 shows the main frictional loss in the inverter rotary compressor. The frictional loss at vane sides is directly proportional to the rotational speed basically. As the rotational speed is low, the loss at vane tip is near zero because the sliding velocity between vane tip and roller is very small at the low speed. The loss at main bearing is about proportional to the square of rotational speed when the current frequency is higher than 6Hz. Because it is in boundary friction condition during very big angle range, the frictional loss of the eccentric bearing is greater at the low rotational speed. Figure 7 shows the variations total frictional loss and discharge and suction loss. Figure 8 shows the changes of the various efficiencies of the single cylinder inverter compressor with the rotational speed. The mechanical efficiency does not change basically. The indicated efficiency falls at the high rotational speed due to the discharge loss shown in Figure 7. The motor Purdue University, West Lafayette, IN, USA- July 25-28, 2 494

efficiency becomes very low as the operating speed decreases. Figure 9 shows the variations of the total resistance moment by compression mechanism, the resistance moment only by gas pressure and motor torque with the rotating angle of crankshaft for the single cylinder compressor operating at 5Hz. The difference between the resistance moment and the motor torque produces the fluctuation of rotating speed of crankshaft. Figure 1 shows the variations of the instantaneous rotating speed of crankshaft and the instantaneous efficiency of motor during a revolution. The motor efficiency is always below its maximum or rated efficiency except at two instants. So the average efficiency of motor during a revolution is less than its rated efficiency and the difference increases with the fluctuation amplitude of the rotational speed. Figure 11 shows the relative fluctuation of the rotational speed of a single cylinder compressor and a dual cylinder compressor. Figure 12shows the rated efficiencies and the practical efficiencies at various frequencies of the motors of the single cylinder compressor and the dual cylinder compressor. It is seen that the difference between rated efficiency and real efficiency of the single cylinder compressor operating at 3Hz is as great as 15% since the relative fluctuation of rotational speed is near 4%. Therefore, the practical motor efficiency of the single cylinder compressor is much less than that of the dual cylinder compressor at the low rotational speed even though the difference between their rated motor efficiencies is not large. That is to say, for the single cylinder compressor operating at the low rotational speed, the great difference between the practical efficiency and the rated efficiency of motor besides the lower rated efficiency of motor is the cause of that its motor efficiency and hence overall efficiency and COP are very low. For a conventional constant speed compressor with single cylinder, the difference between the practical efficiency and the rated efficiency of motor is also significant, which is about 1-4%. Figure 13 and Figure 14 show the variations of the cooling capacity, input power, COP and volumetric efficiency with the frequency output by inverter. The volumetric efficiency at the high rotational speed is greater due to the suction supercharging effect and is smaller at the low speed leakage. The input power at the high and low speed is relatively large due to the discharge loss at the high speed or due to the motor Joss at the low speed. The COP at 6Hz is greatest. Figure 15 and Figure 16 show the variations of the efficiencies and COP of the dual cylinder compressor with the rotational speed. The drop of indicated efficiency of the dual cylinder compressor with the increase of its operating speed is Jess than that of the single cylinder compressor since the rise of its discharge loss with the speed is smaller. The motor efficiency at the low operating frequency is obviously higher that of the single cylinder compressor since the fluctuation of the rotational speed is very smaller. So, for the dual cylinder compressor, the drop of overall efficiency and COP as the operating frequency increases or decrease is smaller, that is, the range of frequency at which the COP is higher is larger, and the maximum of COP shifts to the low frequency, at which the inverter compressor operates for a long time. CONCLUSIONS A comprehensive simulation model of a rotary compressor is developed. The simulated results agree well with the measured data for a single cylinder inverter rotary compressor and a dual cylinder inverter rotary compressor. The variation of the pressures in three working chambers and the valve behavior with the rotational speed are discussed. The velocity of valve impacting valve seat rises quickly with the rotational Purdue University, West Lafayette, IN, USA- July 25-28, 2 495

speed. The volumetric efficiency at the low speed is lower due to leakage. The indicated efficiency drops with the increase of the speed due to discharge loss. The mechanical efficiency does not vary with the speed basically. For a single cylinder compressor, the practical motor efficiency is much lower than the rated motor efficiency at the low speed because the speed fluctuation is great and thus the motor efficiency, overall efficiency and COP of a single cylinder compressor operating at low the rotational speed are very low. The variations of overall efficiency and COP of a dual cylinder with the rotational speed is smaller. REFERENCES I. Sakurai E, Hamilton J F, The Prediction of Frictional Losses in Variable-speed Rotary Compressors, 1984ICECP 2. Sato Y, Shirafuji Y, The Study of Rotary Compressor Driven under Low Electric Frequencies, 199ICECP 3. Liu Z, Soedel W, Performance Study of Variable Speed Compressor with Special Attention to Supercharging Effect, 1994 ICECP 4. Liu Z, Soedel W, Using Gas Dynamic Model to Predict the Supercharging Phenomenon in a Variable Speed Compressor, 1994ICECP 5. Liu Z, Soedel W, Modeling Temperatures in High Speed Compressors for the Purpose of Gas Pulsation and Valve Loss Modeling, 1992ICECP 6. Park Y C, Min M K, Analysis ofthe Dynamic Characteristics of a Variable Speed Compressor, 1998ICECP 7. Wu J, A Mathematical Model for Internal Leakage in a Rotary Compressor, 2 ICECP 8. Wu J, Dynamic Analysis ofroller and Vane of Inverter Controlled Rotary Compressor, 2 ICECP 9. Nieter J, et al, Analysis of clearance volume equalization and secondary pressure pulse in rolling piston compressors, 94ICECP Table 1 Comparison of results calculated with data measured of a single cylinder compressor fe capacity (w) Power(w) COP average speed (r/m) measured Calculated measured calculated measured calculated measured calculated 5 28 217 762 761 2.73 2.77 2798 2783 6 2597 2599 921 97 2.82 2.87 3382 3355 75 337 3337 1226 1182 2.75 2.82 4217 426 9 4132 4122 1521 1497 2.72 2.75 593 598 12 5556 5529 2256 2194 2.46 2.52 6683 6683 Table 2 Comparison of results calculated with data measured of a dual cylinder compressor fe capacity (w) Power (w) measured calculated measured calculated 3 1884 1834 717 71 5 3342 3372 1142 1131 6 4185 4142 1414 145 9 674 6478 237 2332 15 7667 7485 2928 2867 COP average speed (r/m) measured Calculated measured calculated 2.63 2.58 1625 1661 2.93 2.98 279 2844 2.96 2.95 3377 3425 2.83 2.78 59 5168 2.62 2.61 5835 5952 Purdue University, West Lafayette, IN, USA- July 25-28, 2 496

2.5..,. -- sudioo -- rompression 2. - - - dewance.b E 1!! 1.5 () " U> U> a. 1. '" 2.5 2..2l E.fl 1.5 I () " 1. I a. --rompression --suction - - - dearance.5 9 18 27 36 Jlngl e of shaft (degree) Fig. I Pressures in working chambers at 3Hz. 18 27 36 Jingle of shaft (degree) Fig. 2 Pressures in working chambers at 6Hz. 3. --rompression '" 2.5 --sudion.,. 2. E -6 = 1.5 m 5 1. a..5 - - - clea:wjce 18 27 36 Jlngle of shaft (degree) Fig. 3 Pressures in working chambers at 12Hz. 'E.s c " 6.8 '" c. u Ill 1.6,.-----.-----.------,------...,.4 J--------------" 9 18 27 36 Jingle of shaft (degree) Fig. 4 Behavior of reed valve at various speeds.,. 2.5 36 ;::!il' 2. 3 :2. 355 Cl) /. 3. lil g> Sl // 1.5 lii 35 "iii. 1. u 3 345./- -o- ange in -- \elodty 34 l_.j3=-----6:'::----9:'::-------:12=---:-15=-_j o.o Fig. 5 Closing angle and impacting velocity of valve..5 8 I 6o 9. iii 4 8 u it 2 -o- rren bea-rg ---- ecc. bea-.-g - - vaneside _..,_ varetip /" ----------=-# Q.-----., / 3 6 9 12 15 Fig. 6 Main individual friction losses 8r--r-----r----r-----.-----.--, 1,.--,--------.-------r-------.------r-. 6 -- dscharge&sudion --- fiidion 8 -- - ---- --- ---- E 4!:!.3 2 9 12 15 Fig. 7 Discharge loss and total frictional loss. 4 - - rrechcnical -..--nuta - -overall 3 6 9 12 15 Fig. 8 Various efficiencies for single cylinder comp. Purdue University, West Lafayette, IN, USA- July 25-28, 2 497

If b., ' ' ' ' ----- ' ' {3. ' ' Rotating angle of aankshaft (degree) Fig. 9 Resistance moment and motor torque. '. 1. 3 - -. speed O.!E --Efficiency 29 o.ro / 28 tl' ;o / ii.85 Iii a / 27 g' co..,.. 26 le E.75..7 ' ' -s: 25 2..65 24 9J 1 27 :l6j Pllgle r:i aankshaft (degree) Fig. I Rotating speed and efficiency of motor at 5Hz. 4.--,--------------r---------- 9 6 -sil;)le.rale::l -<>- snge, rml _.,_ wa,rale::l -.6..- dlblfebi 3 6 9 12 Fig. II Relative fluctuation of rotational speed of shaft. 3 6 9 12 Fig. 12 Rated and practical efficiencies of motor 8.-------,-------.-------.------- -o- capacity - - pdner 3 6 I.,. 2 (ll &1 4. m 2 OL--3o-------6LO-------oo, 12o------1Jo Currentfrequiency (Hz) Fig. 13 Capacity and power for single cylinder comp. I :i El.-------------.-------.-------,-,1 3. //<-----' 96 2.75 2.5,/.. 92!I 2.25 ---<>- CCP 88 -A- \.U. eft. 2. Currentfrequency(Hz) Fig. 14 COP and val. efficiency for single cylinder comp. l't c 3 Sll. ::>. Q. g_.e.. 1.----------------.--------.------- 3. 96 ro #. ro ii '6 in -o-ildi::ated 4 - -rredlali:al -u-notor - -overau Fig.l5 Various efficiencies for dual cylinder comp. i [5 2.8!> 926- c 3.. I 88 Q... ::>.Q -o- vol. eff. 84 2.6 9: 2.4 -A- CCP 2.2 L, ---,-------,'-:-------'-----...J 6 9 w Currentfrequency(H2) Fig.I6 COP and vol. efficiency for dual cylinder comp. Purdue University, West Lafayette, IN, USA- July 25-28, 2 498