Hydrodynamic Lubrication Effects of Multiple Circular Bump Pattern for a Thrust Sliding Bearing of a Scroll Compressor

Transcription

1 Tribology Online, 7, 1 (01) ISSN DOI /trol.7.13 Article Hydrodynaic Lubrication Effects of Multiple Circular Bup Pattern for a Trust Sliding Bearing of a Scroll Copressor Saneasa Kawabata 1)*, Sigeki Iwanai ), Tadasi Hotta ), Fuiiro Itoigawa 3) and Takasi Nakaura 3) 1) Materials R&D Division, DENSO CORP. ) Cliate Cooling and Heating Engineering Division, DENSO CORP. 1-1 Sowa, Kariya, Aici , Japan 3) Graduate Scool of Engineering, Nagoya Institute of Tecnology Gokiso, Sowa-ku, Nagoya , Japan *Corresponding autor: saneasa_kawabata@denso.co.jp ( Manuscript received 13 Septeber 011; accepted 6 Deceber 011; publised 31 January 01 ) Te optiu texturing pattern for a trust sliding of a scroll copressor was investigated. As te basis of lubrication analysis for ultiple circular bups pattern, fundaental ydrodynaic lubrication effects of te axisyetric circular geoetry expressed by te power law forula were analyzed using elastoydrodynaic lubrication (EHL) analysis. Te optiu geoetry to iprove te load carrying capacity and reduce frictional force for te odel geoetry was discussed. Frictional properties of te proposed trust s were experientally evaluated and copared wit nuerically predicted properties. In order to clarify te robustness against accidental ig load, seizure liits of a circular bup pattern were experientally evaluated. Tese results sow tat te initial frictional properties are able to control by te crowning profile, te proposed pattern as a sufficiently low friction coefficient and quite a ig seizure liits. Keywords: elastoydrodynaic lubrication, circular bup, texture, trust s, scroll copressor 1. Introduction In scroll copressors, a trust sliding is used to support te orbiting scroll against te trust force fro copressed refrigerant in scroll caber (Fig.1). A ig load carrying capacity and low friction is Crank saft Motor Trust Orbiting scroll Fixed scroll Scroll caber Fig. 1 Cross section of CO scroll copressor required especially for a CO copressor due to its ig refrigerant pressure. In conventional refrigerant systes, a siple flat plate as been used as te trust. Oku et al. [1,] explained te lubrication ecanis by te effect of global wedge resulting fro elastic deforation of te orbiting scroll, and proposed te optiu design criteria. Te geoetrical wedge profile plays a doinant role in oil pressure generation and sufficiently flat surface is required. For ig operating pressure CO systes, a ydrostatic trust is often used to ensure te ig load carrying capacity. One of te disadvantages of te flat plate type trust s was a lack of reproducibility in frictional perforances. Te scroll trust is rater a large scale, and tere are soe difficulties of anufacture to keep te flatness and waviness level in desired range for te necessary frictional properties. Te ai of tis study is to acieve a sufficient lubrication perforance using a textured trust plate witout an extra ydraulic circuit. In order to assure te igly stable operation, teoretical and experiental evaluation for initial friction coefficients, and seizure liits concerning wit te pressure fluctuations due to te waviness and elastic deforation, are required. Copyrigt 01 Japanese Society of Tribologists 13

2 Saneasa Kawabata, Sigeki Iwanai, Tadasi Hotta, Fuiiro Itoigawa and Takasi Nakaura Trust Orbiting scroll Olda ring Fixed scroll Fig. Internal construction of scroll unit Figure sows te internal construction of te scroll unit. Fixed and orbiting scroll ave te involute spiral. An eccentric crank saft drives te upper scroll in an orbital otion, and an Olda ring prevents its rotation. In usual trust sliding s, one of te surfaces rotates on te oter ated surface. Soe types of groove pattern is designed to facilitate ydrodynaic pressure generation and oil supply, concerning te rotational otion of te. On te oter and, in case of te trust for scroll copressor, te oving surface does not rotate but only orbits in circle wit te radius equal to te eccentric distance of te cranksaft. As te orbiting surface slides toward all directions, an axisyetric local pattern is better for te orbital situation tan rectilinear groove patterns. Soe of te autors [3,4] proposed an ebossed etal seet for sort stroke oscillatory slider, and naed it tribo-seet. Experiental and teoretical results sow tat te geoetrical wedge effect provides consistent and stable lubrication perforance. Tis pattern is axisyetric and suitable for te trust of scroll copressors. Hailton et al. [5] first proposed te lubrication ecanis of circular flat disk pattern and discussed on te role of outlet cavity foration. Tey treat te pattern as a step and applied Reynolds equation to bot of te top surface and groove area. Figure 3 sows te proposed trust sceatically. Te lower flat plate is fixed to te orbiting scroll and slides on te upper patterned plate. Lubrication oil is supplied fro inner circuference of te plate and daed up by te outer seal ring. Filling oil fully into inter-bups lubricate te top of te circular bups. As te ydrodynaic pressure and friction are ainly generated in te tin fil area, te geoetrical design of te top of te bup sould be essential to control te frictional properties of te trust. Fig. 3 Sceatic view of trust sliding Many of researcers ave been reported te lubrication properties of pattered surfaces. Effects of te location and size of surface patterns are often discussed, but te qualitative effects of round off edge geoetry of te flat base plane are erely considered. We reported tat te round off wedge profile generated by wear during initial running-in periods plays a doinant role of te lubrication perforance of parallel sliders [6]. Looking at te industrial side of te production, it would be desired tat an optiu round off profile to deonstrate te axiu lubrication perforance can be designed and elaborated witout running-in process. Tis study focused on te lubrication effects of a round off edge for axisyetric circular patterns for trust plate s. Elastoydrodynaic lubrication states of te idealized soot surface odel for te geoetry of polised single pattern were exained by nuerical EHL analysis. Te practical frictional properties of te trust plate wit proposed lubricating pattern was exained experientally. Te seizure liits under extreely ig loading conditions were also evaluated experientally in consideration of unevenly distributed load due to te effects of initial waviness and elastic deforation of te orbiting scroll. Tese results sow tat te proposed pattern as sufficiently low friction over a wide range of operating conditions, and robustness against te accidental ig loading.. Teoretical analysis and experiental.1. Nuerical analysis Figure 4 sows a typical odel profile expressed by te power law forula, r c r R z, r x y, (1) were c is te crowning eigt, R is te radius of te bup, r, x, y are radial and Cartesian coordinates, and is te sape exponent wic express te flatness or c R Fig. 4 Single bup odel 0 R Japanese Society of Tribologists (ttp:// Tribology Online, Vol. 7, No. 1 (01) / 14

3 Hydrodynaic Lubrication Effects of Multiple Circular Bup Pattern for a Trust Sliding Bearing of a Scroll Copressor bup orbit y u y axisyetric profiles. Governing equations are briefly suarized. Te fil equation, Reynolds equation, and te load balance equation are given as x 0 z r E' ' p x dx', () x x' x Fig. 5 Orbiting otion and coordinate syste te areal ratio of te corner wedge. Tis expression is often used to approxiate te round off edge profile of polised surfaces and tat after running-in. Sperical profiles are involved as te case, tat enables us to copare te results directly wit well-known results of sperical EHL. Te orbiting otion of te flat slider can be decoposed into te translational velocity u and te rotational angular velocity as sown in Fig. 5. All of governing equations in tis paper are defined on te local coordinates x, y. Except for te extra wedge effect due to te elastic deforation, te angular velocity ter doesn t affect te lubrication state of te current Friction Plate Cross roller Plate spring Friction plate Trust sliding Drive plate Cross roller x Plate spring 3 p u 1 x, (3) w p x dx, (4) wit pressure p x 0 on te boundaries r R. Reynolds outlet boundary conditions for cavitation zone are assued in nuerical analysis and te pressure boundary conditions on r R ainly affects as te inlet boundary condition. As te bup radius is sufficiently large copared wit te fil tickness, te inlet boundary pressure sould be alost zero. Te effects of te inlet boundary condition were described in section Experiental for frictional properties A sceatic view of te experiental setup for te friction test is sown in Fig. 6. Eac of te trust sliding plates is fixed to te friction plate and te orbiting scroll. A set of te friction plate and te orbiting scroll is supported by te pair of trust cross roller s. Te lower trust plate is driven wit te drive plate by te crank saft and te electric otor installed above te friction unit. A pair of plate springs is ounted on bot side of te friction plate, and te translational friction force was easured as te average of te output fro te strain gages on te plate springs. Representing friction values were obtained by te aplitude of easured sinusoidal wavefors. All of te coponents were assebled in te ig pressure vessel and te axial load was supplied by te ydraulic unit. Te gas pressure inside te ig pressure vessel was controlled by te CO refrigerant syste and recirculating oil was supplied fro te upper side of te vessel. Te bups are arrainged on te trust plate in unifor inter-spacing as sown in Fig. 7. Saple geoetry and experiental conditions are suarized in Table 1. Trust Load Fig. 7 Arrangeent of te bups Fig. 6 Experiental setup for friction easureent Japanese Society of Tribologists (ttp:// Tribology Online, Vol. 7, No. 1 (01) / 15

4 Saneasa Kawabata, Sigeki Iwanai, Tadasi Hotta, Fuiiro Itoigawa and Takasi Nakaura Table 1 Friction test saple and experiental condition Trust plate geoetry Material ardened steel Outer diaeter, [] 100 Inner diaeter, [] 58 Tickness, [] Bup geoetry Bup diaeter, [] 4, 5, 5.5 Inter-bup spacing, [] 0.5 Nuber of bups 176, 118, 106 Groove dept, [] 0.5 Crowning eigt, [] 0.5 to 30 Experiental condition CO gas pressure, [MPa] 3.8 Teperature, [ 0 C] 19 Viscosity, [Pa s] 5 to 7 Load, [N] 11 to 94 / bup Sliding velocity, [/s] 0.4 to Experiental for seizure liits Figure 8 sows an experiental setup for te seizure tests. A tri-islands specien (Fig. 9) is eld on te botto of te oil bat, and a flat plate specien rotates on it. Bot of te saples are ade of ardened steel. In order to keep parallelis between te pair of te specien, te oil pressure load is applied troug te ball joint beneat te oil bat. Inside of te caber is filled wit CO gas copressed at te pressure of 1MPa. As te CO gas is absorbed to te lubricant oil and its pressure reduces in te initial period, a sufficient Load Flat plate Oil Tri-islands Specien Caber CO gas Fig. 8 Experiental setup for seizure tests tie to stabilize te gas pressure was taken before starting te tests. In order to andle a ig load and large torque required to evaluate te seizure liits, te applied load was easured by te supplied oil pressure in te ydraulic cylinder and te frictional torque by te torsion bar on te lower saft. Because tese sensing units are ounted outside of te ig pressure caber, only te ig frictional force in ixed lubrication regie was detected. Te seizure liits were evaluated under a constant increent rate of applied load (0 to 8 kn by 600 s) wit constant sliding velocity (0.78 /s). Frictional forces increased wit increasing in applied load, and suddenly rose up after a period of unstable state. Te seizure liit was defined by te applied load wen te friction coefficient exceeds Results and discussion 3.1. Diensional analysis Ordinary, te nuerical and experiental results are suarized in non-diensional for. Traditionally, different kinds of non-diensional expressions ave been used for plain teory, journal teory, and EHL teory. In tis paper, journal type expression was used, wic describes a lubrication state of fixed profiled s for given operating condition. Te crowning eigt c in Eq.(1) was used for te caracteristic lengt of te fil tickness. Te diensionless variables are defined as, H c P u R G, w, pr w X, x R, Y y R, R, (5) c R S G. c Substitution in Reynolds equation Eq.(3), Fig. 9 A tri-islands specien (left) and a flat plate specien(rigt) Japanese Society of Tribologists (ttp:// Tribology Online, Vol. 7, No. 1 (01) / 16

5 Hydrodynaic Lubrication Effects of Multiple Circular Bup Pattern for a Trust Sliding Bearing of a Scroll Copressor H X 3 P X H Y 3 P H 1S. (6) Y X Tis expression as te sae for to tat of journal s. Tese expressions can be transfored to te expressions in pad s teory as follows, K K K w w w H in S 0uR R R H in G S in in, (7) ere, K w denotes te load carrying capacity paraeter, K and K w denotes te friction coefficient paraeters. Ordinary, tese non-diensional paraeter is expressed as te function of te ratio between te inlet fil tickness in and te outlet fil tickness out. If te elastic deforation was sufficiently sall, te relations out in, in c in, and tus ( in / out) (1/ Hin) 1 are siply derived. Hereafter te factor H in was also used as te control paraeter for te non-diensional paraeters in Eq.(7). 3.. Inlet boundary conditions Figure 10 defines te boundary position of a single bup odel. In ost of te pysical odel, te pressure on te outer boundary is able to fix at zero. If te groove dept was tin against te orizontal size, Reynolds equation is applicable over wole area of analysis doain. Hailton used tis forulation. Te groove of te scroll application is relatively deep and te Stokes flow analysis is required to deterine te pressure profile in te groove area. Reynolds outlet boundary conditions are assued in nuerical calculation, and te outlet boundary in Fig. 10 is placed inside te cavity area. In tis case, te ost iportant is te odeling of te inlet boundary. One of te possible odeling is te cobined analysis wit Stokes flow analysis in te groove area, and te oter is Inlet boundary Inlet boundary Outlet boundary Outlet boundary Groove Outer boundary Fig. 10 Analysis doain and boundary conditions te Reynolds equation based analysis for te bup geoetry wit sarp step profile. Soe of approxiated forula for te inlet pressure are known in literature. Te full-flooded condition of EHL is derived fro Tipei s [9] potential flow analysis. Te inlet pressure gradient is given by, p u Ci x i, (8) were i is te fil tickness at te inlet cavity boundary, Ci 3/ 3 for pure rolling and Ci 4 for pure sliding. Equating tis result wit Reynolds equation, full-flooded condition is given as, pure rolling : pure sliding : i / b 9 / 1. 5 i b. (9) Lakawatana [10] also analyzed te inlet pressure rise on a sarp corner edge. Te pressure gradient is alost te sae as Tipei s results for pure sliding and te inlet pressure rise is given by, p inlet were Assuing u 3.9, (10) b b is te fil tickness on te sliding surface. b was te order of in, Eq. (10) and Eq. (7) gives te inlet pressure against te average lubricant pressure on te bup as, p inlet R 3.9 in. (11) w K R w As a result, if te bup size was large enoug in relation to te iniu fil tickness, te inlet pressure will never affect te total load support unless te load carrying capacity paraeter was extreely sall. In suc a case, te inlet boundary pressure is able to fix at zero. Te inlet pressure is restricted by te reverse flow and consequent reduction of inlet flow due to te steeply expanded geoetry. It can be called geoetrical starvation. Wide range calculation is desired to express te results in design carts. As discussed later, te effects of inlet boundary conditions only appear in ig S regie. S factor is expressed by bot of te operating condition G and aspect ratio ( c / R). If te ig speed or low load condition was supposed for large S regie, te fil tickness will becoe tick and a step geoetry odeling or full coupling wit Stokes flow analysis is necessary. If te sall ( c / R) ratio of noinally flat bup profile was supposed, te zero inlet pressure approxiation still olds. Tis study ainly considered te later situation. Japanese Society of Tribologists (ttp:// Tribology Online, Vol. 7, No. 1 (01) / 17

6 Saneasa Kawabata, Sigeki Iwanai, Tadasi Hotta, Fuiiro Itoigawa and Takasi Nakaura Fig. 1 Fig. 11 Diensionless iniu fil tickness for = [ W 8, 16, 3,..., ] for full-flooded and iso-viscous rigid (IR) regie as reference. Here te relation ( R / c) for full-flooded sperical profile was used. Te starvation effect appears as te reduction of H in at iger S regie, and te inclination point are located at near-by S 1, oterwise 3.3. Nuerical EHL analysis Figure 11 sows te diensionless iniu fil tickness for te case. Here te load conditions are expressed by te non-diensional paraeter H in 1. As sown in te transfored diagra Fig. 1, te load carrying capacity paraeter sows axiu at tis inclination point ( H in 1 ), tat eans te ost effective crowning eigt is nearly equal to te iniu fil tickness. Te well-known optiu point of plain is also placed at H in 1 W w / E' R. Tis case is sperical in sape, but te analysis area is liited to te radius R and te starvation effect is considered. In te lower S regie, iniu fil tickness varies by te applied load due to its elastic deforation (iso-viscous elastic; IE regie). Te lowest S part of te lines are located in te full-flooded regie, and teir values are identical to tat of standard EHL results. Te strait red line sows te Kapitza s [8] analytical solution, H in 6 5 S, P in ur ( in / out ), and tis condition as a coon pysical eaning. Figure 13 sows typical pressure profiles for low, iddle and ig H in regie. As Fig.1 is a plain (8) a) c/r = 0.0 (in/c=0.1) Load carrying capacity paraeter for = b) c/r = 0.00 (in/c=1) c) c/r = (in/c=10) p ( in/r = 0.00 ) Fig. 13 Effects of aspect ratio on pressure profile Japanese Society of Tribologists (ttp:// Tribology Online, Vol. 7, No. 1 (01) / 18

7 Hydrodynaic Lubrication Effects of Multiple Circular Bup Pattern for a Trust Sliding Bearing of a Scroll Copressor type expression, tese pressure was analyzed for a fixed iniu fil tickness in / R 0.00, and copared te results for te aspect ratios c / R. Gray colored area indicates te cavitation or outside area of te bup, were te pressure is fixed at zero. In low S and low H in regie (Fig13 a), te fluid pressure arises only around te center of te bup and te ost of te surface area doesn t contribute to te load support. Tis regie is a full-flooded regie and te inlet boundary condition doesn t affect te pressure profile. On te oter and, large S and H in regie (Fig13 c), te pressure widely spreads over a bup, but te inlet flow is restricted by te starvation effect and te pressure level reduces. Wit increasing iniu fil tickness, te tail of te oil pressure profile approaces te inlet boundary, and after te tail reaced te boundary, te axiu pressure gradually restricted by starvation. Tus te sligtly starved situation (Fig 13 b) gives te axiu load carrying capacity, were te relatively ig oil pressure widely spreads over a bup. In case of te iger load conditions in Fig. 1, te elastic deforation effect enances a load carrying capacity paraeter K w and te axiu K w point oves toward tin fil tickness regie. Tis trend expresses te cooperative effect of starvation and elastic deforation. As well known for plain s, eac of te friction coefficient paraeters K and K w as a iniu near by te axiu K w point. Figure 14 sows te results for te iger sape exponent ( 8 ). Te slope of te H in on S decreases copared to te sperical case, and te effects of elastic deforation is also reduces. Tis trend is explained as follows. By flattening te initial profile, te contact stiffness increases and te inlet fil tickness Fig. 14 Diensionless iniu fil tickness for =8 Japanese Society of Tribologists (ttp:// also reduces. As a result, te load supporting area is enlarged and its load carrying capacity is iproved. Tese flattening effects on te lubrication state are siilar to tat of elastic deforation. As sown in Fig. 15 and 16, te axiu point of te load carrying capacity paraeter and iniu point of friction coefficient paraeter are still located at H in 1. Load support effects of flat top profiles are suitable for tin fil regie at severe operating conditions. If te load was evenly supported by ultiple bups, te noinal applied load of scroll applications is relatively low, and ajority of te bups operate under IR regie. In order to describe te overall perforance of te, later discussion is focused on te starvation effects in IR regie. Fig. 15 Fig. 16 Load carrying capacity paraeter for =8 Friction coefficient paraeter for =8 Tribology Online, Vol. 7, No. 1 (01) / 19

8 Saneasa Kawabata, Sigeki Iwanai, Tadasi Hotta, Fuiiro Itoigawa and Takasi Nakaura In Fig. 17 and 18, te diensionless iniu fil tickness and friction coefficient calculated for varied were copared. Te load condition is te iniu of te calculated range in Fig.11, were te elastic effects are negligibly sall. Especially for te low S and tin fil conditions, te iniu fil tickness reduces for lower. Tis tin fil regie is stated at full-flooded condition and its oil pressure is concentrated around te center of te bup. In suc a case, igly arced top causes a tinner fil tickness. On te oter and, friction coefficients increases wit over all area, and tis trend is explained as te effects of spreading frictional surfaces due to te flattening of te bup. In order to avoid te etal contact and reduce friction, iddle range of 10 is optiu Experiental friction coefficients Experiental conditions are expressed by te duty paraeter G and teoretical optiu points are given by te caracteristic paraeter S. Tese two paraeters are cobined wit te aspect ratio (c / R ). In order to validate te geoetrical effects of te circular bups, te friction coefficients of te trust plates finised in various aspect ratios were experientally evaluated. Te surface geoetries of te finised plate were easured by a surface rougness eter and te geoetrical paraeters c, were calculated by te eigt of sapling points. As sown in Fig. 19, tere are te correlation between te crowning eigt c and te sape exponent, were te large round off aount cases iger c and saller. Fig. 19 Geoetry factors of test saples Fig. 17 Effects of on iniu fil tickness [ W ] Fig. 18 Effects of on friction coefficients [ W ] Japanese Society of Tribologists (ttp:// Figure 0 plots te evaluated friction coefficients for te duty paraeter G, wic represents te operating condition. Te lubricant viscosity 5 Pa s was assued as lower estiation. In ig velocity range (rigt and side of Fig. 0), all of te saples sow a trend to increase te friction wit G, and its logaritic slope is approxiately 0.5. Tis trend is a feature of ydrodynaic lubrication regie in full-flooded condition. In low velocity conditions, te friction coefficient arise by reducing G, tat sows te ixed lubrication effects appears. Tese friction coefficients were sufficiently sall copared wit te results for pattern-less flat plate pair. Tese experients were conducted fro lowest sliding speed of 0.4 /s to 1.1/s in 5 steps, and te load was increased under eac constant velocity. Except for te saple c / R , te friction curve traced on a single curve in ixed and ydrodynaic lubrication regie. Tis fact sows tat te surface profile and surface rougness didn t cange during te operation in ixed lubrication regie. Only te ost pointed profile saple of c / R sows te quite a ig friction in te first set of te experients and gradually reduced during later experients. As a Tribology Online, Vol. 7, No. 1 (01) / 0

9 Hydrodynaic Lubrication Effects of Multiple Circular Bup Pattern for a Trust Sliding Bearing of a Scroll Copressor of exponent of easured saples wit te lower value ( 3 ), respectively, and 64 is arbitrarily-cosen large value. Te predicted friction is sligtly larger tan te experients, but differs only witin a doubling. As te paraeter S corrects te crowning eigt effect by te factor (c / R ), te results of igly arced Fig. 0 Experiental friction coefficient result, te friction coefficients for tis saple plotted in separated 3 curves. Tis is considered tat te top of te bup wore out during te operation under ixed lubrication regie. Figure 1 sows te transfored diagra to te non-diensional paraeter sets, S, ( R / c) wic correct te effects of te crowning eigt. By introducing te easured crowning eigt of eac saple, all of easured data in ydrodynaic lubrication state is able to express in single line. Te strait lines represent te nuerically predicted friction coefficients for selected. In tis experient, 5 and 1 denote te iniu and axiu value Fig. 1 Noralized friction coefficients coparing wit nuerical prediction Japanese Society of Tribologists (ttp:// saples wit large (c / R ) and sall are plotted on te left and side of Fig. 1, and te flat saples wit sall (c / R ) and large on te rigt and size. In te sall and igly arced bups, te central fil tickness is tin and te top te bup will wear out during te sliding in ixed lubrication. Te result of axiu c / R ( ) sees to be separated in tree lines. It is considered to be te effect of running-in wear during te series of experients. Tis effect is one of te possible ecaniss of relatively low friction in low S range. On te oter and, te surface profiles of te large ( 60) saples in ig S range are noinally flat. In suc a situation, unavoidable waviness effects will reduce te friction. Middle range of te geoetry sows a relatively good agreeent wit experients. In coparison wit te friction coefficients, te iniu fil tickness is ore sensitive on te lubrication state, because te friction coefficient is te averaged property over te sliding area, but te iniu fil tickness is a local variable. In order to validate te nuerically predicted iniu fil tickness, te fil paraeter, in /, (9) was calculated using te cobined rougness easured before testing, and te nuerically predicted iniu fil tickness in at te caracteristic nuber S on te iniu friction point in a series of experiental friction coefficients of a saple, upon te assuption tat te iniu point addresses te starting S of ixed lubrication. Figure sows te analyzed fil paraeters. Regardless of te saple geoetry, all of te results is varied around 3, wic is reasonable as te fil paraeter at a starting point of te ixed lubrication state. Despite te siplicity of te single bup odel based on a sapling geoetry, te proposed odel gives a pysically consistent result and expresses te effects of crowning eigt and overall frictional properties Seizure liit Under te noral applied load, relatively flat top profiles ave a suitable load support by ydrodynaic lubrication effects, but if te extreely ig load was applied, te pressure concentration due to te edge load sould be considered. Tribology Online, Vol. 7, No. 1 (01) / 1

10 Saneasa Kawabata, Sigeki Iwanai, Tadasi Hotta, Fuiiro Itoigawa and Takasi Nakaura In order to confir te robustness against te fluctuation of te applied load of eac bup due to te waviness of te trust plates and global elastic deforation of copressor coponents, te seizure liit of a bup was evaluated by tri-island pattern saple sown in Fig. 9. Figure 3 sows te evaluated seizure liits as te supportable axiu average pressure over te bup for te initial sape exponent of te saple. Te lower group of te saples was finised by polising, and te iger group in te rigt-and side of Fig. 3 is non-polised group. Te lowest seizure liit sown in Fig. 3 are still uc iger tan te possible axiu load of te copressor, but te seizure liits tend to reduce by sarp edge profiles. 4. Conclusion Fig. Fil paraeter Fig. 3 Seizure test result A trust sliding wit a ultiple circular bup pattern for a scroll copressor was proposed. Te effects of te round off wedge profile of a bup were analyzed by elastoydrodynaic lubrication analysis. Based on te coparison wit te experiental results, te following conclusions can be drawn: 1. General expressions independent fro te aspect ratio of a bup can be derived by introducing non-diensional paraeters based on te crowning eigt.. Te crowning eigt approxiately equal to a iniu fil tickness gives te axiu load carrying capacity and te iniu friction coefficient, were te caracteristic nuber is te order of 1. Te latter condition gives an optiu aspect ratio of a bup. 3. Te flattened top profile wit large sape exponent assists te load support in tin oil fil conditions, but enlarges te friction and sligtly reduces te seizure liit. 4. Te frictional properties of te proposed trust in ydrodynaic lubrication state are able to predict by te nuerical analysis of a single bup odel wit considerable accuracy. 5. A transition to te ixed lubrication state is also predictable by coparing te surface rougness and te nuerical iniu fil tickness. Te proposed trust wit ultiple circular bups sows a superior load carrying capacity and its frictional properties are controllable by te round-off wedge profile of crowning eigt and sape exponent. Noenclature r z : un-defored surface profile c : crowning eigt R : outer radius of te bup : sape exponent x, y : Cartesian coordinates, x x, y T r, : cylindrical coordinates E ' : density : viscosity : pressure viscosity index : reduced elastic odulus E' 1 1 E1 1 E : cobined rougness 1, 1, : root ean square rougness u : translational velocity u u, 0 T u : ean velocity u u u x x1 x : ean angular velocity w p : applied load : pressure : fil tickness 1 Japanese Society of Tribologists (ttp:// Tribology Online, Vol. 7, No. 1 (01) /

11 Hydrodynaic Lubrication Effects of Multiple Circular Bup Pattern for a Trust Sliding Bearing of a Scroll Copressor 0 in : rigid displaceent : iniu fil tickness : inlet fil tickness in out : outlet fil tickness : friction coefficient X, Y : diensionless Cartesian coordinates X x / R, Y y / R H : diensionless fil tickness H / c P : diensionless pressure P pr / w W : load paraeter W w /( E' R ) U : velocity paraeter U ( 0 u ) /( E' R) G : duty paraeter (Lebeck[11,1]) G U / W S : caracteristic nuber S G( R / c) K w : load carrying capacity paraeter K w H in / S K : friction coefficient paraeter K R / in K w : friction coefficient paraeter K w / G : fil paraeter in / References [1] Oku, T., Isii, N., Anai, K., Sawai, K., Morioto, T. and Iida, N., An Optial Perforance Design on Lubrication Mecanis at Trust Slide-Bearing of Scroll Copressors, Transactions of te JSRAE, 4, 3, (In Japanese). [] Oku, T., Isii, N., Anai, K., Knisely, C., Sawai, K., Morioto, T. and Hiwata, A., Teoretical Model of Lubrication Mecanis in te Trust Slide-Bearing of Scroll Copressors, HVAC&R Researc, 14,, 008, [3] Nakaura, T., Matsubara, T., Itoigawa, F. and Nakaura, T., Developent of Tribo-Seet Supporting Sort-stroke Oscillatory Slide wit Low Friction: Soft-EHL Analysis, JSME Annual Meeting III(01-1), 001, (in Japanese). [4] Nakaura, T., Matsubara, T., Itoigawa, F., Hayakawa, S. and Yaada, T., Soft-EHL Analyses of Sliding Surface Structure and Developent of Tribo-Seet, Macine Design and Tribology Division Meeting in JSME,, 00, (in Japanese). [5] Hailton, D. B., Walowit, J. A. and Allen, C. M., A Teory of Lubrication by Micro- Irregularities, ASME Journal of Basic Engineering, 88, 1, 1966, [6] Kawabata, S., Yosida, K., Itoigawa, F. and Nakaura, T., Transition of Surface Profile and Hydrodynaic Properties of Parallel Sliders under Running-In, Tribologists, 55,, 010, (In Japanese). [7] Venner, C. H. and Lubrect, A. A., Multilevel Metods in Lubrication, Elsevier Science B.V., Asterda, 000, [8] Kapitza, P. L., Hydrodynaic Teory of Lubrication During Rolling, Zurnal Tekniceskoi Fiziki, 5, 4, 1955, [9] Tipei, N., Boundary Conditions of a Viscous Flow Between Surfaces Wit Rolling and Sliding Motion, ASME Journal of Lubrication Tecnology, 90, 1, 1968, [10] Lakawatana, P., Matsubara T. and Nakaura, T., Mecanis of Hydrodynaic Load Capacity Generation on a Slideway, JSME International Journal, Series C, 41, 1, 1998, [11] Lebeck, A. O., Parallel Sliding Load Support in te Mixed Friction Regie. Part 1 Te Experiental Data, ASME Journal of Tribology, 109, 1987, [1] Lebeck, A. O., Parallel Sliding Load Support in te Mixed Friction Regie. Part Evaluation of te Mecaniss, ASME Journal of Tribology, 109, 1987, Japanese Society of Tribologists (ttp:// Tribology Online, Vol. 7, No. 1 (01) / 3