Direct Torque Measurement of Hermetic Rotary Compressors Using Strain Gauge

Purdue University Purdue e-pubs International Compressor Engineering Conference School of Mechanical Engineering 2 Direct Torque Measurement of Hermetic Rotary Compressors Using Strain Gauge M. Matsushima Osaka City University T. Nomura Osaka City University N. Nishimura Osaka City University H. Iyota Osaka City University K. Inaba Hitachi Tochigi Technology Co. Follow this and additional works at: https://docs.lib.purdue.edu/icec Matsushima, M.; Nomura, T.; Nishimura, N.; Iyota, H.; and Inaba, K., "Direct Torque Measurement of Hermetic Rotary Compressors Using Strain Gauge" (2). International Compressor Engineering Conference. Paper 1427. https://docs.lib.purdue.edu/icec/1427 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

DIRECT TORQUE MEASUREMENT OF HERMETIC ROTARY COMPRESSORS USING STRAIN GAUGE M. Matsushima 1, T. Nomura 2, N. Nishimura 2, H. lyota 2, K. Inaba 3 1. Graduate School of Engineering, Osaka City University 3-3 13 Sugimoto, Sumiyoshi-ku, Osaka, 55-55 Japan 2. Mechanical Eng. Dept. Faculty of Engineering, Osaka City University 3-3-13 Sugimoto, Sumiyoshi-ku, Osaka, 55-55 Japan 3. Compressor Design and Manufacturing Dept. Hitachi Tochigi Technology Co., Ltd. Tomita, Ohira machi, Simotsuga gun, Tochigi-Ken, 329-444 Japan ABSTRACT This research was conducted in order to better identify the torque loss of a hermetic rotary compressor for one revolution, and to directly obtain the actual shaft power of the compressor. Torque of the compressor was measured for one revolution by attaching a strain gauge to the part of the rotary compressor crank shaft where the compressor was connected with the motor. The torque loss was obtained from the difference between this torque and the effective compressive torque required to compress a discharge of refrigerant gas. Loss due to over-compression was identified from this torque loss. Moreover, the actual shaft power gained by the compressor and motor output were compared. NOMENCLATURE F P : Piston compressive force F v : Vane contact force F c1 : Vane differential pressure force F k : Spring force acting on vane F m : Vane reciprocating inertia force V c : Volume of compression space V" : Theoretical displacement volume R P : Radius of piston R c : Radius of cylinder a : Angle of eccentricity at piston center : Rotation angle of shaft k :Adiabatic exponent INTRODUCTION Hermetic rotary compressors are widely used in room air conditioners, refrigerators, and so on. They consume a great deal of power, so their efficiency enhancement is strongly desired. They are hermetically sealed and can be compactly stored in a pressurized vessel with high-temperature and high-pressure refrigerant gas. Since the motor and compressor are directly connected by a crankshaft, it is difficult to measure only the torque of the compressor. If the torque of compressors for the crank angle for one revolution is directly measured, loss of compressors of one revolution can be more cleared, parts and quantity need improvement of the efficiency can be gained precisely and exactly. Also actual shaft power is directly obtained. Then various kind of methods about torque measurement have been considered. Measurements of compressor torque with a strain gauge were carried out in 1963 by Matsushima and Yokoyamall using a reciprocating compressor with low-temperature, Purdue University, West Lafayette, IN, USA- July 25-2, 2 499

low-pressure refrigerant in a hermetically sealed vessel. Later, concerning a rotary compressor with high-temperature, high-pressure refrigerant in a pressurized vessel, the measurement of torque of a rotary compressor was studied in 196 by Sakitani, Koiwa, Maekawa 2 >, using a torque meter. However, measurements of the torque of rotary compressors with strain gauges attached had not been made until now. Accordingly, for these experiments, an experimental compressor was manufactured with a rotary compressor used in a room air conditioner with cooling power of 2.5kW. The experimental compressor had a strain gauge attached to the connection between the motor shaft and the compressor. A lead wire passed through the middle of the crankshaft and, lead upward. Using mechanical sealing, an extension shaft of the crankshaft protruded from just above the pressure vessel and, through a slip ring, compressor torque signals were picked up. In addition, spur gears were attached to the upper part of the crankshaft and, using the gap sensor, changes in the position of the top dead center of the shaft and revolution speed were measured. Under three conditions of Light, Medium and Heavy, the torque of a compressor was measured. Adding the torque by vane contact force to the torque by compressive force of a piston, a new theoretical torque was made and it was multiplied by volumetric efficiency in order to obtain the compressive torque, which effectively compresses refrigerant gas. The difference between measured compressor torque and compressive torque becomes loss torque due to losses such as mechanical friction, heating, suction, over-compression, etc., but of these, over-compression loss was clarified. When the measured mean torque of compressors is multiplied by the rotation speed of compressors, the actual shaft power is obtained. This actual shaft torque is compared with the motor output which is gained by being multiplied the dissipation power and motor efficiency together. TORQUE The measured compressor torque for one revolution Tc can be separated into effective compressive torque Te, which compresses refrigerant flow rate Qv, and loss torque 1L Tc= Te+1I 3 ) (1) Effective compression torque Te can be determined by multiplying volumetric efficiency YJv to theoretical torque Tth Te= 1/v Tth (2) Theoretical torque Tth means the theoretical torque to compress the refrigerant gas at the theoretical refrigerant gas flow rate (/th due to theoretical displacement volume Vo. That is, the torque of an ideal compressor with a volumetric efficiency of 1% and a total adiabatic efficiency of 1%. Moreover, theoretical torque Tth was conventionally considered to be comprised of the torque of piston compression force 1'p only. Yet considering the shape of the measured compressor torque for one revolution, since a big dip in the to 12 degree range can be seen. As the result of the Consideration of the reasons for this dip, it was found that the point where the vane contacted with piston had the differential pressure force by refrigerant gas pressure and that the negative torque was produced. Therefore, with considering that the addition of the torque Tv might be more favorable, the expression was modified as follows. Tth=Tp+Tv 4 > (3) Substituting crank angle() d degree for rotation angle Bradians used in theoretical expressions, the change in torque for one revolution is expressed as a graph like Fig.l. Solving for the adiabatic compression at suction pressure Ps =.626Mpa (5.35kgf/cm2g) and delivery pressure Pd = 2.14Mpa (2.6kgf/cm 2 g), the pressure of compression the space Pc is Purdue University, West Lafayette, IN, USA- July 25-2, 2 5

calculated in expression (4). When this value is used for the calculation of expression (5), torque by piston compression force J'p is obtained. Also, when expression (6) is calculated, torque by vane contact force Tv is obtained. Moreover, a graph of theoretical torque T th can be obtained from expression (3) R=P (Vo)k c,. v c (4) (5) (6) Fv= Fd +Fk +Fm cos a (7) MEASUREMENT PROCESSES Shown in Table 1 are the specifications for rotary compressor of the 2.5 kw room air conditioner used in this experiment. The structures of experimental compressors had flanges, allowing the attachment of various sensors. A sectional drawing is shown in Fig.2. In order to measure the torque applied on the shaft between the compressor and the motor, the strain gauge of 35 4 gauge type was employed. The electric signals from the strain gauge were sent to and amplified by the connected dynamic strain gauge and then collected by a personal computer. The data were displayed on the personal computer screen and saved in a hard disk. Due to temperature changes, the strain gauge changes the zero point of the output signals, so the shift of the zero point was corrected. The expression for the temperature characteristics of the specimen crankshaft had been obtained earlier so it was used. Prior to the experiment, the temperature of the compressor was measured and the zero point of the strain gauge was adjusted. Also, under prescribed experimental conditions, the gas temperature in the compressor was measured, which was considered to be the strain gauge temperature. Defining the temperature measured prior to the experiment as t1, and the gas temperature in the compressor when the data were collected as t2, the amount of the zero point shift caused by temperature fluctuation can be obtained by the following expression: L1 E = E Ct2)- E Ct1). Since this is the shifted amount of the strain gauge output, a test result chart was used for calculations to convert output into torque. RESULTS AND DISCUSSION Experimental conditions were defined as shown in Table.2: light (light load and power-saving), medium (standard), and heavy (overload). The gas cycle experimental apparatus could measure with good precision the refrigerating capacity, power consumption, adiabatic power, refrigerant flow rate, volumetric efficiency, etc. of both commercial rotary compressors and the experimental compressor. Purdue University, West Lafayette, IN, USA- July 25-2, 2 51

Compressor torque The experimental compressor was operated under the 3 test conditions. Fig.3 shows the torque of light, medium and heavy conditions. Under the respective conditions of them, the mountain shape of the compressor torque Tc measured for one revolution becomes higher as the load becomes progressively heavier and the delivery pressure becomes higher. The mean torque of them were 2.215N m under light condition,2.645n m under medium condition and 2.99N m under heavy condition. The crank angle peaks for compressor torque Tc measured for one revolution were: 211degree for the light condition, 222degree for the medium condition, and 229degree for the heavy condition. Compression begins from crank angle 3degree, but the torque begins to reduce a bit, reaching its lowest at 6degree. From there, the torque increases along with rising pressure of the compression space of the cylinder. This decrease phenomenon can be considered to be due to the torque of vane contact force Tv, as shown in the graph of theoretical torque Tth in Fig.LAlso can be explain by using expression (3). Since expression ( 1) becomes 1i = Tc - Te, torque loss 1i can be found by subtracting the effective compressive torque Te, for compressing the measured discharge of refrigerant Qv, from Tc, the measured torque of one revolution of the compressor. There upon, Fig.3 shows a comparison of the measured torque of one revolution of the compressor Tc, the effective compressive torque Te derived from expression (2), and torque loss 1i found by calculating the difference between Tc and 1i. Loss due to over-compression Fig.4 shows that there is a section where Torque loss 1i is relatively :flat and a section with great swelling. The :flat section can be seen as losses such as loss from mechanical friction, heating, and suction, which occur throughout one revolution. The swollen part occurs just at the crank angle where the delivery valve begins to open and can be considered as loss due to for the most part over-compression. By integrating the area of the section where loss is only due to over-compression, the results derived for loss due to over-compression Wo are shown in Fig.5. We can see from Fig.5 that when delivery pressure rises and load increases, loss due to over-compression Wo also increases accordingly. By using expressions (4) and (5) and an expression to obtain pressure of compression space Pc from the torque due to piston compressive force J'p, pressure changes in the compression space were found from the torque loss due to over-compression in Fig.4. The results solved for are shown in Fig.6. From measurements of the torque of the compressor, loss from over-compression of the compressor was identified, but in order to identify the other losses, whenever torque of the compressor is measured it seems necessary to measure pressures such as that of the compression space by attaching pressure sensors to the cylinder. Compressor revolution speed In Fig.7, the ordinate is the output of the gap sensor. At the abscissa is the time for slightly over one revolution of the compressor t. Attempts were made to measure the widths between mountains or between valleys from this figure, but since width differences couldn't be seen, the revolution speed of one revolution of the compressor was taken to be constant5l_ Purdue University, West Lafayette, IN, USA- July 25-2, 2 52

In addition, as shown in Fig., at the ordinate is output voltage and at the abscissa is time t., the revolution speed ofthe compressor was calculated using the results of concurrent measurements of compressor torque and the power voltage, which dropped down to 6V due to Slidac. From the calculated result, the revolution speeds of the compressor under respective conditions could be obtained. They were found to be: 342min 1 for the light condition, 335 min- 1 for medium, and 324 min- 1 for heavy. Actual shaft power of compressors The actual compressor shaft power WAX can be obtained by multiplying the measured torque of the compressor Tc by the measured revolution speed of the compressor Nand by TC/3. WAX=TcXNX TC/3 () Conventionally, on the other hand, applying a break load to the motor alone, and obtaining the motor efficiency for the power load, compressor shaft power are found with the following: Motor output Wout = Compressor power consumption livt X Motor efficiency TJ mo ( 9) Solving for the respective values occurring under the three test conditions, the actual shaft power WAX of the compressor this time calculated with expression () and conventional motor output Wout calculated with expression (9) were compared and shown in Fig.9 shows this as a graph. Comparing the actual shaft power WAX of the compressor this time and conventional motor output, the shaft power this time was lower by 12W (1.5%) for the light condition, 14W (1.5%) for medium, and 51W (5%) for heavy. The difference is considered that the motor circumference temperature when measured actual shaft power was more higher than the motor circumference when measured motor efficiency. The circumference temperatures were of latter case were 93.5degree Celsius under light condition, 16.9degree Celsius under medium and 121.2degree Celsius under heavy, the former case was 2degree Celsius. CONCLUSIONS Torque of the compressor was directly measured by attaching a strain gauge to the part of the rotary compressor crankshaft where the compressor was connected with the motor. (1) According to the load conditions, torque of the compressor for one revolution could be accurately measured. (2) Studies were conducted to make a more realistic theoretical expression to obtain the effective compressive torque required to compress a discharge of refrigerant gas. (3) By subtracting the effective compressive torque from the measured torque of the compressor, torque loss of the compressor for one revolution was obtained. Loss due to over-compression of the compressor could be identified from this torque loss. (4) Multiplying the measured mean torque of the compressor by the measured revolution speed of the compressor, actual shaft power of the compressor could be directly obtained. When this was compared with motor output, the former was smaller by 1.5% to 5.%. Purdue University, West Lafayette, IN, USA- July 25-2, 2 53

ACKNOWLEDGMENTS The authors would like to thank President Mitsuru Murata of Hitachi Tochigi Technology Co., Ltd. for his valuable advice in carrying out this study. REFERENCES 1 )M. Matsushima, A. Yokoyama : "Studies on Torque Characteristics of Refrigerating Hermetic Compressor", Hitachi Hyoron, VoL 45, No. 5, pp71 76(1963). (in Japanese). 2 )K. Sakitani, L Koiwa, T. Maekawa: "Performance Evaluation of Hermetic Refrigeration Compressor Using Torque Measurement Method", Processing of the 196 Purdue Compressor Technology Conference, Aug. 4 7, pp22-241(196). 3 )M. Matsushima, T. Nomura, M. Murata : "Development of Refrigerating Hermetic Compressors Adapt to Starting Performance", Trance. JSRAE VoL 15, No.4, pp369-3(199). (in Japanese). 4)T. Yanagisawa, M. Mori, T. Shimizu, Y. Ogi: "Studies on Vibration ofrolling Piston Type Rotary Compressor", Trans. Jpn. Soc. Mech. Eng. (Series C), VoL 49, No. 444, pp1346 1353(193). Gn Japanese). 5 )H. Iwata, A. Sakazume, k. Yokoyama : "Loss Analysis of Rolling-Piston Type Speed Controlled Rotary Compressor", Trans. Jpn. Soc. Mech. Eng. (Series B), VoL 51, No. 465, pp1736-1741(195). (in Japanese). Table 1 Specification of the experimental compressor Radius of cylinder Radius of piston Radius of vane nose Vane thickness Half of center angle of nose circle Cylinder hei_ght Theoretical displacement volume Spring constant Maximum deflection of spring Mass of vane Refrigerant Adiabatic exponent He Rp Rv Bv r h Vo kv xo 2L5X 1Q 3m 16.65 X 1Q 3m 3.2X I 3m 3.2X I 3m n/3 rad 27.X 1Q 3m 16.2 X IO Gm3 159N/m 12.3X 1Q 3m mo 14.74X 1Q 3kg HCFC-22 K 1.2 Purdue University, West Lafayette, IN, USA- July 25-2, 2 54

Theoretical torque Tth Torque mplstonr _'o~~~,c~o~ ~ 1.--------------------------------, 1 s 6 z 4 Compressor torque Tc (]) ;::l... " 2 ~ 6 12 1 24 3 36 Crank angle d o (Medium) Fig.l One revolution of theoretical torque -2 6 12 1 Crank angle (Light) 3 36 sor Suction tube 1 s z 6 (]) 4 ;::l... " 2 ~ -2 ~-- 6 12 1 24 Crank angle d (Medium) 3 36 1 Fig.2 Sectional drawing of the experimental Suction compressor Table2 Test conditions Test conditions Light pressure R Delivery pressure Pd Suction gas temperature ts Medi Heavy urn MPa.626.626.626 MPa 1.769 2.14 2.553 "C 35 35 35 Subcool oc Power source loov 6Hz s 6 z 4 (]) ;::l... " 2 ~ -2 Effective compressive tqrque Tc 6 12 1 24 Crank angle d (Heavy) 3 Fig.3 Compressor torque Tc, effective 36 compressive torque Te, and torque loss 'II Purdue University, West Lafayette, IN, USA- July 25-2, 2 55

3 e Loss of over-compression z 2 ::J '1 E-< 6 12 1 24 3 36 Crank angle d o Fig A Fluctuation of torque loss ~6r---------------------- ~o 4... ;... 2 C) i-. ~ L-----L---~~--~----~----~ ~ 1.7 1.9 2_1 2.3 2.5 2.7 Delivery pressure P d MPa j Fig.5 Relation of delivery pressure and loss of over-compression (1j p., ~31""":"':-----::----~------ ~"2_5 g 2 -. r::: 1.5... 1... e p_._5 Pressure of compression space P c pressure Pa ~------~----~--~--~-- J 6 ;... ::J ;... 6 12 1 24 3 36 Crank angle d o (Medium) p., Fig.6 Pressure fluctuation of >- ~4 (1j ~ ::s -fr-4 ::s - llfl compression space Compressor torque -- - l fgl1 =:f~ LT 1\ Lj lf1 ~ ~oltaqe of ele~ ric- oower ('J :,: ~. 25...-< ~ ~ 4 12 16 Time t ms Fig.7 Output of gap sensor ~ 11.------------ ::s 15 -. g 1 ;... 95 ~ ~~ 9 ;::;:: 5 ::-. ~ -. Motor output Wout 'Actual shaft power WAX <!:::': 75 -------------------------...1 (1j 1.7 1.9 2.1 2.3 2.5 2.7 5 1 15 2 ~ Delivery pressure P d MPa Time t ms Fig_ Compressor torque and...-< voltage of electric power ~ B Fig.9 Comparison of actual shaft (1j power and motor output Purdue University, West Lafayette, IN, USA- July 25-2, 2 56