High Efficiency Development of a Reciprocating Compressor by Clarification of Loss Generation in Bearings

Transcription

1 Purdue University Purdue e-pubs Internationa Compressor Engineering Conference Schoo of Mechanica Engineering 2010 High Efficiency Deveopment of a Reciprocating Compressor by Carification of Loss Generation in Bearings Masaru Matsui Panasonic Corporation Yoko Kitsunai Panasonic Corporation Ko Inagaki Panasonic Corporation Foow this and additiona works at: Matsui, Masaru; Kitsunai, Yoko; and Inagaki, Ko, "High Efficiency Deveopment of a Reciprocating Compressor by Carification of Loss Generation in Bearings" (2010). Internationa Compressor Engineering Conference. Paper This document has been made avaiabe through Purdue e-pubs, a service of the Purdue University Libraries. Pease contact epubs@purdue.edu for additiona information. Compete proceedings may be acquired in print and on CD-ROM directy from the Ray W. Herrick Laboratories at Herrick/Events/orderit.htm

2 1425, Page 1 High Efficiency Deveopment of a Reciprocating Compressor by Carification of Loss Generation in Bearings Masaru MATSUI 1 *, Yoko KITSUNAI 2, Ko INAGAKI 1 1 Appiances Deveopment Center, Panasonic Corporation, Noji-higashi, Kusatsu City, Shiga , Japan Phone: , Fax: , E-mai:matsui.masaru@jp.panasonic.com 2 Living Environment Deveopment Center,Panasonic Corporation, Yagumo-naka-machi, Moriguchi City, Osaka, , Japan Phone: , Fax: , E-mai:kitsunai.yoko@jp.panasonic.com * Corresponding Author ABSTRACT An anaytica mode for mixed ubrication in bearings of reciprocating compressors for refrigerators has been deveoped and a new bearing which coud decrease its friction osses by 20% has been designed. Friction osses, which are generated in the journa and thrust bearing of our reciprocating compressor, are estimated to be one-third or more of the a osses, so it is an essentia issue to decrease bearing osses to design more efficient compressors. The deveoped anaytica mode can cacuate the oi fim pressure and soid contact pressure between bearing and shaft in each bearing simutaneousy. And it can aso specify the shaft posture which changes at each time step and cacuate the oss generated by oi viscosity and that by contact pressure. By using this mode, how and how much friction oss is generated in each bearing was carified and specific approach to decrease bearing osses was aso carified. 1. INTRODUCTION A reciprocating compressor instaed in our refrigerator is a machine which compresses working fuid (refrigerant) by reduction of cyinder voume by the reciprocation of a piston and has been produced for 80 years. Figure 1 shows a vertica cross section of a reciprocating compressor. The eccentric rotationa motion of a crank pin, which is set up in the upper part of a shaft, is converted into the reciprocation of a piston through a connecting rod. Bearings are constructed by a journa bearing which supports a horizonta oad from a connecting rod (F C ) and a thrust bearing which supports a vertica oad of shaft weight and so on (F T ). For a journa and thrust bearing in our compressor, a pain bearing where a oad is supported by ubricant pressure is adopted. Friction osses generated in these bearings are estimated to be one-third or more of a osses, so it is an essentia issue to decrease bearing osses to make a reciprocating compressor more efficient. In this study, an anaytica mode for mixed ubrication in bearings was deveoped to reduce bearing osses and how and how much friction oss is generated in each bearing was carified by using the mode. 2. ANALYTICAL MODEL FOR MIXED LUBRICATION IN BEARINGS The ubrication condition in a journa and thrust bearing of our reciprocating compressor is considered to be the mixed ubrication, because oads acting on a shaft are supported by oi fim pressure of ubricant, which fied in cearance between shaft and bearing surface, and by soid contact pressure, which generated by contact of shaft and bearing surface. The deveoped mode anayzes a shaft posture as oads acting on the shaft and support force generated by oi fim pressure and soid contact pressure in each bearing are baanced at each time step, and then cacuates bearing osses.

3 1425, Page Anaytica Object Connecting rod Horizonta oad FC Crank pin Piston Cyinder Thrust bearing Upper rubbing part Annuar depression Oi groove Lower rubbing part Journa bearing Figure 1: Longitudina cross section of reciprocating compressor Horizonta force acting on the crank pin FC N Journa bearing and thrust bearing as the anaytica object are expained simpy here. On the shaft surface in a journa bearing, an oi groove to pump ubricant up (its depth is more than 1000 Pm) and annuar depression are formed. The average cearance between journa bearing and upper/ower rubbing part on the shaft surface, which are set facing each other across annuar depression, is set to be about 10 Pm. Loads acting on the shaft are supported by oi fim pressure and soid contact pressure generated in these rubbing parts. Oi groove and annuar depression on the shaft surface make cearance between journa bearing and rubbing parts discontinuous in paces. On the other hand, the shape of a thrust bearing is an amost ring whose center is set at the center of the journa bearing, but a groove to discharge ubricant is formed on its surface party. Surfaces of these bearings are ground smoothy. Figure.2 shows an exampe of horizonta oad (FC) variation acting on the crank pin, taking shaft rotation ange Ts in the horizonta axis. Rotationa direction of Ts is same as shaft rotationa one and Ts becomes zero when the eccentric direction of crank pin agrees with the center ine of cyinder (x axis). Horizonta oad (FC) varies by ten times or more during one rotation of shaft. A shaft receives a oad that changes greaty as shown in Figure 2 and rotates whie titing and coming near to a certain direction to a journa bearing The average of FC Rotation ange of the shaft Tｓ ( ) 360 Figure 2: Horizonta oad variations acting on crank pin 2.2 Oi pressure anaysis In cearance between shaft and bearing surface, ubricant forms oi fim and it fows with the rotation of the shaft. In this study, the ubricant fied in cearance is assumed to be incompressive fuid. When the shaft comes near to a certain direction to a journa bearing, oi pressure on the upstream side of the eccentric direction rises up and then oi pressure distribution is changed (wedge effect). To anayze oi pressure distribution in oi fim, Patir-Cheng s modified Reynods equation (Patir et a., 1978 and Patir et a., 1979), which bases on the average fow mode that considers the infuence of surface roughness of shaft and bearings, is used. w rwt wi wh h 3 wp w h 3 wp U wht I x I z V s T rwt ¹ wt 12K rwt ¹ wz 12K wz ¹ 2 rwt (1) In Equation (1), p is oi pressure, r is radius of shaft, T is ange to the circumference direction of shaft, h is cearance between shaft and bearing, ht is expected vaue of oca cearance, K is oi viscosity, U is shaft rotation speed, and Ix,Iz,Is are correction factors. To sove Equation (1) numericay, divergence formuation (DF) method (Kawabata, 1987) is appied as descretization method. DF method can appy discontinuous oi fim thickness in bearings because it puts computationa grids to fit the discontinuous ine of cearance.

4 1425, Page Soid contact pressure anaysis To cacuate soid contact pressure, Greenwood s mode (Greenwood et a., 1970 and Patir et a., 1978) is adopted. This mode assumes that soid contact pressure is generated by eastic deformation caused by contact of asperities on shaft and bearing surfaces h P k' E' 4.0 ( h 4 ') (2) c ' In Equation (2), P c is soid contact pressure, k is a coefficient decided by the shape of surface roughness, E is combined Young s moduus of shaft and bearing, is combined surface roughness of shaft and bearing. E is shown in Equation (3) and = ( ) 0.5. E is Young s moduus, is Poisson s ratio, and is surface roughness. Subscript 1 and 2 represent bearing s or shaft s property respectivey E' (3) 2 E1 E2 2.4 Shaft posture anaysis Shaft posture anaysis in the deveoped mode makes it possibe to carify shaft rotationa behavior. It anayzes shaft posture at each rotation ange s as oads acting on the shaft (horizonta oad F C and vertica oad F T ) and pressure fied in journa and thrust bearing obtained by the oi pressure anaysis and soid contact pressure anaysis are baanced. Figure 3 shows a shaft posture at a certain rotation ange s. The initia position of the center of gravity of the shaft is set as the origin, x axis is taken in the same direction as the center ine of cyinder, y axis is taken in the direction that rotated by 90 degree from x axis, and z axis is taken in vertica upper direction. Variabes of shaft posture are represented as foows: e x and e y are x and y components of eccentricity of the center of gravity of the shaft e, x and y are titing ange around x and y axis of the shaft, and d t is distance between the center of the ring of thrust bearing and that on the shaft, respectivey. Cearance distribution between shaft and bearing surface is decided by these shaft posture parameters (e x, e y, x, y, d t ) and pressure distribution in oi fim can be cacuated when it is inputted to the Equation (1) and (2). Then support forces of bearings F B and moment around the center of gravity of the shaft M B can be cacuated by integrating pressure distribution on the shaft surface. When x, y, and z components of F B are represented by F Bx, F By, F Bz and x and y components of M B are represented by M Bx, M By respectivey, shaft posture parameters (e x, e y, x, y, d t ) z shoud be decided to meet Equation (4) and (5) simutaneousy. F Bx F, F F, F F (4) x By y Bz z F C M Bx M, M M (5) x By y x The direction of the tit of shaft In these equations, F x and F y represent x and y components of horizonta oad F c, M x and M y represent x and y components of moment around the center of gravity of the shaft M B, respectivey. Shaft posture parameters (e x, e y, x, y, d t ) cannot be decided directy by giving oad condition (F x, F y, F T, M x, M yt ). In this study, amounts of change of F Bx, F By, F Bz, M Bx and M By when shaft posture parameters change sighty are assumed to contribute to sight change of shaft posture parameters ineary. Shaft posture at each rotation ange s can be decided by changing shaft posture parameters itte by itte to meet Equation (4) and (5) approximatey. y e y e x y x d t Figure 3: Shaft posture parameters

5 1425, Page Bearing oss anaysis When shaft posture is obtained, the distribution of cearance h between shaft and bearing surface is aso decided. Then the distributions of oi fim pressure and soid contact pressure are aso anayzed. To cacuate osses in journa and thrust bearings, oss generated by shear stress of oi viscosity and the one generated by friction force by soid contact are cacuated separatey in each bearing. To cacuate shear stress by oi viscosity, Patir-Cheng s equation derived from the average fow mode is used. U h 2V 1 p 1 hv V h (6) r 2 fs r 2 fp r T 2 r s f 2 In Equation (6), is viscous shear stress per unit area on shaft surface, f fs are shear stress factors in average fow mode, and V r2 = ( 2 / ) 2 is contribution ratio of shaft surface roughness. Friction force by soid contact pressure is assumed to be generated based on Couomb s friction ow. When the coefficient of friction is represented by, friction stress by soid contact per unit area can be cacuated as foows. ( ) P (7) c s c Viscous friction oss W J, W T and soid contact friction oss W Jc, W Tc are cacuated as foows. At first, by integrating ( s ) and c ( s ) on whoe shaft surface, friction force acting on the shaft surface at rotation ange s can be cacuated. Then, by integrating the vaue which mutipy the friction force by the shaft radius at a rotation ange s, W J, W T, W Jc and W Tc, can be obtained. In characters W J, W T, W Jc and W Tc, the first subscript represents journa (J) or thrust (T) bearing and the second one represents viscous () or soid contact (c) friction oss, respectivey. 2.6 Procedure of ubrication anaysis Figure 4 shows a fow chart of deveoped ubrication anaysis. At first, bearing specifications, horizonta oad F C, etc are inputted, and shaft posture parameters (e x, e y, x, y, d t ) are decided at each rotation ange s, then osses in journa and thrust bearing are cacuated. After rotation ange reaches 2 shaft posture parameters are compared with these cacuated at s - 2 at every cacuation step. If both parameter sets agree with each other approximatey, the anaysis wi finish. START Read Data S = 0 Cacuate F x, F y, M x, M y Cacuate distribution of h Oi fim pressure anaysis Soid contact pressure anaysis Cacuate F Bx, F By, F Bz, M Bx, M By Modify shaft posture parameters (e x, e y, x, y ) Judge of convergence F Bx =F x, F By =F y, F Bz =F Bz, No M Bx =M x, M By M By =M y Yes Bearing oss anaysis S = 2? Judge of convergence Yes e x ( S )=e x ( S -2),. No x ( S )= x ( S -2),. Yes No END -Specification -Load F C, F T Figure 4: Fow chart of anaytica mode for mixed ubrication 3. ANEXAMPLE OF ANALYSIS RESULT The deveoped mode makes it possibe to carify the shaft rotationa behavior and quantify bearing osses. An exampe of anaysis resut for our current reciprocating compressor is shown as foows. In the cacuation, the vaue of shaft radius r, rotation speed, oi viscosity, the coefficient of friction, and the vertica oad F T were set as 8 mm, 50 Hz, 2.7 mpa s, 0.1, 14 N (constant), respectivey. The data of horizonta oad F C were given by that shown in Figure Locus of center of shaft rotationa axis Figure 5 shows oci of center of shaft rotationa axis. In the figure, the thick ine shows the ocus at the top of bearing and the thin ine shows that at the bottom of bearing. In Figure 5, the center and radius of the circe represent the center of journa bearing and average cearance (8m), respectivey. Each number which is written near a circed

6 mark on the ocus shows shaft rotation ange s. The ocus is very compicated and eccentric direction at the top and bottom of bearing at each rotation ange s is amost opposite across the center of the circe. This indicates that the shaft whirs in journa bearing. At the top of bearing, shaft rotationa axis approaches the journa bearing most to the third quadrant at around s = 330. This suggests that the surface of shaft and moment coud come in contact with each other at this direction. This direction is amost same as that of rubbing traces in the journa bearing which can be observed after operating. Thus it can be considered that the ocus obtained by the deveoped mode has vaidity. 1425, Page Bearing osses 0 In Tabe 1, viscous friction oss W J and soid contact friction oss W Jc in journa bearing, and viscous friction oss W T and soid contact friction oss W Tc in thrust bearing, are shown. Each vaue is normaized by tota bearing oss. From this tabe, it can be seen that soid Figure 5: Locus of center of shaft rotationa axis contact friction oss W Tc in thrust bearing cannot be ignored and oss generated in thrust bearing is more than that in journa bearing. The amount of vertica oad F T (=14 N) is ony about one third of the average of horizonta oad F C (=41 N). This suggests that design of the thrust bearing in our compressor shoud be improved. Tabe 1: Friction oss in bearings of reciprocating compressor y Shaft rotation direction x At the top of bearing At the bottom of bearing W J W Jc W T W T Tota LOAD SUPPORT MECHANIZM IN BEARINGS 4.1 Journa Bearing Reation between whir and the baance of forces and moments acting on the shaft: In sub-section 3.1, it is shown that the shaft whirs in journa bearing, and the shaft behavior can be aso expained macroscopicay. When the average pressure generated in upper and ower rubbing part are represented by P u and P respectivey, the force and moment acting on the shaft are baanced ony when the condition of the force baance becomes that shown in Figure 6. If the contribution of support force for F C in thrust bearing is ignored, the baance can be expressed by the foowing two equations simpy. C u P u F C L u 2 rl P 2rL P F (8) u u C P L rlu Pu u 2rL P FC C 2 (9) In Equations (8) and (9), L u, L represent the ength of upper and ower rubbing part, u and represent the distance between the center of upper and ower bearing and the center of gravity of the shaft, and C represents the distance between the acting point of oad F C and the Figure 6: The baance between forces and moments on the shaft

7 center of gravity of the shaft. It is suggested the shaft rotation whie titing because pressure P u and P woud generates in opposite direction (see Figure 6). Idea engths of upper and ower rubbing parts: When F C is eiminated from Equation (8) and (9), the ratio of P u and P can be obtained. 1425, Page 6 P P u L L u C u (10) C The theoretica pressure ratio P / P u is equa to 1.0, it is considered that ubrication condition in each rubbing part is same. Actuay, the vaue of right side of Equation (10) when ubrication condition in each rubbing part is same is different from 1.0 because of the infuence of shaft tit. But, it woud be an idea condition when P / P u is equa to 1.0, i.e. upper and ower bearing share horizonta oad F C equay. Athough ony baance between P u and P is considered in Equation (10), each rubbing part (especiay upper rubbing part) needs enough ength to bear horizonta oad F C as shown in Equation (8). If the ength of each upper rubbing part (L u or L ) is not enough, there is no method except raising the pressure on the surface in each rubbing part (P u or P ) to bear F C. As a resut, cearance between surface of shaft and bearing becomes smaer, the possibiity that both surfaces come in contact becomes stronger. In such a situation, much bearing oss woud be generated and soid contact woud exert a bad infuence on operating reiabiity. Therefore, it is considered to be important that theoretica pressure ratio P / P u is kept appropriatey and each rubbing part is designed to have enough ength. 4.2 Thrust Bearing The deveoped mode carified that, in thrust bearing, the tit of the shaft generates oi fim pressure and soid contact pressure to bear the vertica force F T. This phenomenon can be expained by using Figure 7. When the tit of the shaft is arge, the sectiona area aong fowing route of ubricant in the thrust bearing changes greaty. So, on the upstream side of the pace where the surface of the shaft approaches that of the bearing most, more ubricant is dragged into the fowing route and oi fim pressure rises up greaty. As a resut, high oi fim pressure woud be generated to bear F T, even though the shaft does not approach the bearing so much. On the other hand, when the tit of the shaft is sma, the ring on the shaft is neary parae to that on the bearing and the sectiona area aong fowing route of ubricant in the thrust bearing changes sighty. So, on the upstream side of the pace where the surface of the shaft approaches that of the bearing most, oi fim pressure rises up sighty. As a resut, the surface of the shaft must approach that of the bearing more and then reative ow pressure shoud be generated in wider area to bear F T. It is suggested that shaft rotation with appropriate tit is effective to reduce the oss in thrust bearing, because the vertica oad is borne in the condition that the shaft does not approach the bearing so much and soid contact of shaft and bearing is decreased. 5. APPROACH TO REDUCE BEARING LOSSES When ( s ) in Equation (6) is integrated on whoe shaft surface, the term of oi fim pressure gradient (the second term) becomes sma than that of viscosity (the first term) reativey. This is because oi fim pressure in journa and -When the tit is arge -When the tit is sma Shaft Vertica oad F T Minimum oi thickness bering Figure 7: The mechanism for thrust bearing to support oad

8 thrust bearing is cacuated in periodic boundary condition. Thus viscous friction oss W J and W T is amost proportiona to the vaue which mutipies U/h by area of upper/ower rubbing part A. 1425, Page 7 W, W UA h (11) J T / Ony area A can be changed in variabes in right side of Equation (11) in the design process. In this study, the approach to reduce of bearing oss has been taken, ony by changing the ength of rubbing parts (L u + L ) in the vaue of area of upper/ower rubbing part A=2r(L u + L ). At first, the osses of journa and thrust bearing were cacuated when changing the ength of L u + L by using the deveoped mode. In this cacuation, ength of L u and L were changed respectivey to keep theoretica pressure ratio P / P u amost constant. Figure 8 shows the cacuation resut. The vaue of horizonta axis is normaized by tota bearing oss of current compressor. This figure shows that tota bearing oss takes minimum vaue by 0.77 at around L u + L =16mm, but it shoud be carefu to this ength is proper to be adopted. So the oss generated in each bearing is considered furthermore. When the ength of L u + L is reduced from 26mm of our current compressor, the oss of journa bearing decreases graduay, and takes its minimum vaue at around 17mm, and then increases oppositey. It is suggested that our current compressor has enough rubbing part in journa bearing, and viscous friction oss W J coud be decreased with keeping the situation that soid contact oss W Jc is tiny even if the rubbing part is reduced by 7-8 mm. But If the ength of L u + L is reduced from 18mm furthermore, soid contact oss increases graduay and then the increase W Jc of exceeds the decrease of W J. On the other hand, the oss of thrust bearing decreases monotonousy according as the ength of L u + L decreases. As mentioned in section four, when the ength of L u + L is 26mm of our current compressor, the tit of the shaft is sma and the shaft rotation is stabe. Thus the surface of shaft approaches that of bearing and both W T and W Tc are arge. When the ength of L u + L is shorter, the tit of the shaft woud be arger and the shaft rotation woud become more unstabe. Thus the cearance between the surface of shaft and bearing increases and both W T and W Tc become sma. By deiberating both above mentioned consideration and the reiabiity of journa bearing which receive arge oad, the optima ength of L u + L shoud be taken as 18mm which is the minimum ength that soid contact is enough tiny to be ignored in journa bearing. The deveoped mode estimates that tota bearing oss coud be reduced by 20% when the ength of L u + L is taken as 18mm. Bearing oss (normaized by tota oss) Minimum tota oss Optima ength Current ength 1 W J +W Jc 2 W T +W Tc 3 Tota L u +L (mm) Figure 8: The reation between L u +L and bearing osses

9 1425, Page 8 6. CONCLUSIONS An anaytica mode for mixed ubrication anaysis in bearings of reciprocating compressor has been deveoped. By using this mode, the osses was quantified, mechanism of oss generation was carified, and means of oss reduction was examined in journa and thrust bearing. As a resut, these concusions are obtained. In our current reciprocating compressor, it is shown that the oss at thrust bearing is arger than that at journa bearing and to reduce the oss of thrust bearing is essentia issue for making the compressor more efficient. It aso shown that the optima ength of L u + L exists, which can minimize tota osses of bearings whie keeping theoretica pressure ratio appropriatey. By using the deveoped mode, it is estimated that the optima ength of L u + L woud reduce tota osses of bearings by 20%. The vaidity of the deveoped mode was verified by experiments, because a compressor which was designed to reduce the ength of L u + L decreased its input power and the amount of the decrease is amost same as the oss reduction cacuated by the mode. REFERENCES Patir, N., Cheng, H. S., 1978, Appication of Average Fow Mode for Determining Effects of Three-Dimensiona Roughness on Partia Hydrodynamic Lubrication, Trans.ASME, Journa of Lubrication Technoogy, vo. 100, No. 1: p Patir, N., Cheng, H. S., 1979, Appication of Average Fow Mode to Lubrication between Rough Siding Surfaces, Trans.ASME, Journa of Lubrication Technoogy, vo. 101, No. 4: p Kawabata, N., 1987, A Study on the Numerica Anaysis of Fuid Fim Lubrication by the Boundary-fitted Coordinates System : 1st Report, Fundamenta Equations of DF Method and the Case of Incompressibe Lubrication, Transactions of the Japan Society of Mechanica Engineers. C, vo. 53, No. 494: p Greenwood, J.A., Tripp, J. H., 1970, The Contact of Two Nominay Fat Rough Surfaces, Proceedings of the institution of mechanica engineers, vo. 185, No. 48: p Patir, N., Cheng, H. S., 1978, Effect of Surface Roughness Orientation on the Centra Fim Thickness in E.H.D. Contacts, Proceedings of the fifth Leeds Lyon symposium on Triboogy: p