Optimized Radius of Roller Large End Face in Tapered Roller Bearings

Transcription

1 NTN TECHNICAL REVIEW No Tecnical Paper Optimized Radius of Roller Large End Face in Tapered Roller Bearings Hiroki FUJIWARA Takasi TSUJIMOTO Kazuto YAMAUCHI Tapered roller bearings can support eavy combined radial and trust loads, and are widely used for automobiles, railcars and industrial macines. Te bearings ave an inner ring rib into wic te large ends of rollers are trust, and te contacts are accompanied wit rolling-sliding motions. Te arge ends of rollers and te rib surfaces are sperical and conical in sape, respectively. Te typical lubrication regime of te contact is elastoydrodynamic lubrication (EHL). However, some surface damage may occur if te oil film formation is insufficient due to low-rotational and/or eavy-load operations. Te film tickness sould be tick enoug to prevent damage in a given operating condition. In tis paper, an EHL numerical model is developed in consideration of bot asperity contact and roller skewing. A parameter study sows tat to form ticker oil films te optimum radius of te large end face of a roller is about 85% tat of te rib face conical surface. 1. Preface A basic tapered roller bearing consists of a compliment of tapered rollers tat are arranged between inner and outer rings aving conical raceways. Te inner and outer ring of a tapered roller bearing is commonly referred to as a cone and a cup respectively. Because tapered roller bearings can support bot a relatively ig radial load and a singledirectional axial load, tey are widely used in drive systems in automobiles and railway cars, steel mill macines, and oter industrial applications. Te apex of te inner and outer ring raceways and te roller contact surfaces of a tapered roller bearing converge on te bearing centerline. Te rollers develop pure rolling motion witout sliding on te conical raceway surfaces. However, wen a radial load acts on te bearing, an axial component force occurs on te rollers due to a disparity in angles between te inner and outer ring raceways. As a typical means for bearing tis force, a cone flange is provided. As a result, te large end face of eac roller is guided wile being forced to te cone flange. Toug eac roller undergoes pure rolling motion on te raceway surface, tere remains rolling-sliding contact between te roller large end face and te cone flange. Fig. 1 (a) sows a cross-sectional view of a tapered roller bearing. Te cone flange face usually consists of a part of a conical surface perpendicular to te bearing axis, wile te roller large end face comprises a part of sperical surface. Tis condition results in roller endflange face point contact resulting in te igest pressures. Te cone flange face may possess a concave surface matces te contour of te roller large end face. In tis situation, te pressure between tese two faces will be smallest. However, even small rotations of te roller on te y-axis (see Fig. 1 (a)) in tis condition can cause te edge of te roller large end face to come into contact wit te cone flange face, possibly damaging te roller or te cone flange face. To avoid tis problem, te radius of curvature on te roller large end face is designed to be somewat smaller tan tat of cone flange face. Note tat rotational motion on te y-axis is referred to as skewing wile rotational motion on te x-axis is called tilting. At te roller end-flange contact a sufficiently tick oil film may not be readily formed wen te bearing runs at lower speeds or is insufficiently lubricated. Consequently, frictional torque on te bearing will Elemental Tecnological R&D Center Automotive Sales Headquarters Automotive Engineering Dept. Graduate Scool of Engineering Osaka Univercity Modify te Japan Society of Mecanical Engineers. C. Journal (Vol. 75, 29), pp

2 r B r m l g l r (a) Radial cross-section and legend mean flow model 4). Incidentally, a tapered roller as a tendency to skew even if factors suc as misalignment are not present, as pointed out by Harada et al. 6). However, so far, tere ave been few examples of EHL analysis tat consider roller skewing. Furtermore, tere ave been no examples of experiments to optimize te radius of te roller large end face. We recently performed EHL analysis considering roller skewing. Based on te results obtained from tis work, we now propose an optimal radius for te roller large end face in order to form a reliable lubricating oil film. Tis optimal radius will be verified troug a series of experiments. 2. Analysis of elastoydrodynamic lubrication (EHL) between roller end and flange faces (b) Mode of contact between roller large end face and cone guide flange, and associated coordinates system Fig. 1 Tapered roller bearing increase and under iger loads sliding will occur at te contact surfaces. Tis will increase te possibility of surface damage or seizure at tese areas. Note tat te situation were mating components ave insufficient lubrication is known as starvation. So far, te mode of contact between te roller large end face and te cone flange face as been reviewed troug experimental metods and teoretical analysis. Te experimental metods include te following examples. Yamada performed a series of experiments to study te effects of surface rougness on oil film formation at lower speeds. Tis resulted in acieving lower torque at tese contact surfaces troug reduction in surface rougness of te roller end face and flange face 1). Okamoto, et al. attempted to reduce te distance from te roller large end-flange face contact point to te cone raceway. Te intent was to reduce te slip ratio of tese components in order to improve teir anti-seizure properties 2). Tere are many examples of applying EHL (Elastoydrodynamic Lubrication) analysis. Jiang, et al. performed termal EHL analysis wit non-newtonian fluids and discussed te relationsip between te sape of te contact area and te oil film tickness 3). Nisida, et al. performed EHL analysis under a mixed lubrication condition 5) by introducing te Patir-Ceng 2.1 Isotermal EHL analysis EHL analysis was conducted for te contact area between te roller large end and cone flange face of tapered roller bearings. Te velocity, bearing load, and lubricating oil viscosity used for tis analysis were selected in order to minimize eat generation at te contact area. Terefore, te temperature condition for tis analysis was assumed to be isotermal. Specifically, te following assumptions were made: Adequate lubrication exists. Heat generation in te lubricating oil due to searing is ignored. Equations involving te following variables are solved simultaneously: Reynolds equation Elastic deformation derived from semi-infinite elastic contact teory Hig-pressure viscosity properties of te lubricating oil Balance between force and moment As sown in Fig. 1 (b), in te entire region of contact, bot roller end face and flange face ave a velocity distribution in te x and y directions. Terefore, te Reynolds equation needs to incorporate considerations about stretc terms ( 3rd and 4t terms in te rigt-and side in expression (1)). Consequently, te Reynolds equation will be expressed as: x p 12 x 3 3 p y 12 y u m x v m u m v m 1 y x y were, stands for clearance, viscosity of lubricating oil, p pressure, density of lubricating oil, um and vm x-direction component and y-direction -97-

3 NTN TECHNICAL REVIEW No component of te mean velocity at te contact area between roller large end face and flange face, respectively. To investigate te ig-pressure viscosity property of te lubricating oil, Houpert converted te formula given by Rolelands into te SI system 7). Tis formula incorporates considerations for temperature cange. However, because our study was intended to determine te isotermal viscosity of te lubricating oil, we ave ignored te terms associated wit temperature and ave adopted te following expression: 2.2 Effects of surface rougness We adopted te mean flow model of Patir-Ceng 4) to be able to determine te effects of surface rougness, and introduced te mixed fluid lubrication teory 1) of Greenwood-Tripp. Incidentally, wit tese two models, surface rougness is andled in a probabilistic manner. In oter words, te abovementioned metods ave a low probability of calculating results for pressure and film tickness distribution tat agree wit results obtained from tose of a fixed contact area. In our study, we only considered isotropic rougness in te Patir-Ceng s mean flow model 4). Wen assuming tat te pressure flow factor is defined as: exp ln l p z 2 were, stands for atmosperic viscosity and is expressed as: z ln 9.67 were, represents te viscosity-pressure coefficient, and is given by te following Wu-Klaus-Duda formula 8) : log 1 v m were, v means te kinematic viscosity (mm 2 /s), and m viscosity slope constant appearing in Walter-ASTM formula 9). x y 1.9exp s A exp.25 5 and tat te roller large end face is a smoot surface; and wen adopting te sear flow factor 11) tat results from tese assumptions and is defined as: s A 2 exp 2 3 wen 5 wen 5 6 provided tat, wen 5 A A ten, te Reynolds formula (1) will be modified as follows: x 3 p 3 p x y 12 x y 12 y u r u i sx u m x 2 x v r v i sy v m y 2 y 7 u m u sx x r u i x 2 v m u sy y r u i y 2 If surface asperities of mating components come into contact ten te resultant contact pressure can be, based on Greenwood-Tripp teory 1), expressed as: c 5 t f c * t dt c N 15 F 2.5 c 6.84 c c p a k c E'F 2.5 F 2.5 k c For function c approximation 12) : F , Patir-Ceng offers te following c wen 4 wen c 4 11 were, c stands for te oil film tickness at te midpoint. For values of N, and, available researc so far as attempted to define tem in te form of Nand /. Greenwood-Tripp ave assumed tat N=.3 to.5 1). We also assume N=.5. Incidentally, Patir-Ceng assumes tat / = 1 12) : owever, troug our experience, we believe tat / = 2 is a reasonable assumption. Bearing engineers believe troug experience tat te boundary friction coefficient a related wit contact surface between roller large end face and flange face falls in a range of.12 to.15. For tis study, we ave assumed a =

4 Optimized Radius of Roller Large End Face in Tapered Roller Bearings 2.3 Boundary conditions In ordinary EHL analysis works, researcers coose an evaluation region wose size is several times larger tan te area of projected Hertzian contact surfaces so tat te projected pressure at te outer fringes in tis region is zero. By contrast, wen studying roller large end-flange contact, te region of generated oil film (atced area in Fig. 1(b)) is not sufficiently large relative to te size of Hertzian contact surfaces. Terefore, we ave introduced te boundary conditions defined below. Te contact pressure occurs only in te region were te roller large end face contacts te flat surface of te cone flange face. Te contact pressure in oter regions is assumed to be zero. rm r B 2.4 Assumptions about motions We developed te following assumptions about te motions of te rollers, inner and outer rings: Angular velocities of te rollers and inner and outer rings occur due to te mecanical relationsip between tem. Centrifugal force and gravitational force can be ignored. Interface between te rolling surfaces of te roller and raceways and between te rollers and te cage do not affect roller skewing. Te rollers do not tilt. Skewing occurs due to te oil film pressure distribution between te roller large end face and cone flange face, traction, and metal-to-metal friction between surface rougness asperities. 3. Skewing on rollers in EHL mode Generally, under an EHL (Elastoydrodynamic Lubrication) condition, te pressure on te oil film gradually increases at te fluid inlet side, and suddenly drops at te outlet of te Hertzian contact area. Consequently, te pressure gradient along te oil film is asymmetric relative to te center of contact. Because of tis, a moment is created between te contacting objects. Tis moment will cause te rollers to skew as sown in illustrated in Fig. 2. Wile slip of approximately 2% is occurring between te roller large end face and cone flange, a moment of force deriving from traction is also occurring. Furtermore, if metal-to-metal contact is present, te resultant frictional force also contributes to te occurrence of a moment. Eac roller turns suc tat balance is acieved among te pressure on te oil film, te tractional force from te oil film, te frictional force from metal-to-metal contact, and te outer force (force acting on te cone flange). Te moments taking part in M xpdxdy Fig. 2 Skewing of roller tis rotational motion of rollers are described below, werein te center of rotation is assumed to be at te center of gravity of te roller. Wen referring to te coordinates system given in Fig. 1, te moment of force M deriving from pressure on te oil film p can be calculated by te expression below: 12 werein, te origin is defined as te intersection point of te x-axis and y-axis in Fig. 1 (b). Te magnitude of te moment caused by te tractional force can be determined in te following manner: from te experiment by Ono et al. 13), te maximum tractional coefficient t, max is determined as follows:.9 t, max p wen p t, max wen p were, stands for te viscosity-pressure coefficient. Since te maximum projected skewing angle is as small as approximately.5 degrees, te slip ratio s can be calculated wit te following expression, ignoring minor variation by skewing: -99-

5 NTN TECHNICAL REVIEW No u r u i s x, y u r u i 2 14 were, u r and u i represent te velocity at te roller large end face and te velocity at te cone flange face respectively. If te slip ratio leading to te maximum tractional coefficient is taken as s max, ten te tractional coefficient t can be determined, by adopting te circular-model of Lee-Hamrock 14), wit te following expression: 4. Calculation results 4.1 One detailed example of calculations Calculations were performed under te analysis conditions summarized in Table 1, and te results are sown in Fig. 3. Te R ratio of roller large end face given in Table 1 can be defined as r m /r B, using te associated codes in Fig. 1. Te analysis conditions in Table 1 correspond to a situation were lubricating oil t s / s max 1s / s max 2 t, max 15 Table 1 Analysis condition Terefore, te tractional force F t is defined as: F t t pdxdy 16 Ten, wen assuming tat te distance between te ontact point to te center of gravity of te roller is l g, te tractional moment M t can be expressed as: M t l g F t 17 Te frictional force resulting from metal-to-metal contact can be investigated using te Greenwood-Tripp teory 1). Wen assuming te boundary frictional coefficient as a and te apparent contact area as A, ten te frictional force F a on te asperity contact surface can be expressed as: F a a A p a 18 Cup tapered angle Roller tapered angle R ratio of roller large end face Roller lengt Young's modulus Poisson ratio Oil kinematic viscosity at 4 C Oil kinematic viscosity at 1 C Oil density Viscosity - pressure coefficient Rotating speed Rib load Oil temperature Root mean square rougness of roller large end face Root mean square rougness of cone back face rib deg. deg. mm GPa mm 2 /s mm 2 /s kg/m 3 Pa -1 min -1 N C Te moment M a deriving from F a is: M a l g F a 19 Wen a roller begins skewing, te contact point between te roller large end face and cone flange sifts, and te vector of te contact force no longer intersects te center of te roller. As a result, te flange generates moment M r tat elps reduce skewing. Wen te distance in te x-direction between te roller flange contact point and center of te roller (i.e. te distance te contact point sifts), is taken as l sift, Mr can be defined as follows: M r l sift P 2 (a) Oil film pressure distribution were, P is load on rib. Ten, te geometrical relationsip between l sift and te skewing angle can be expressed as: l sift r B r m l g sin r B r m 21 were, r m, r B and l g are lengts sown in Figs. 1 and 2. Finally, skewing angle can be determined by solving te expression below: M M t M a M r 22 m (b) Oil film tickness distribution Fig. 3 Result of EHL analysis between roller large end face and cone flange face -1-

6 Optimized Radius of Roller Large End Face in Tapered Roller Bearings of viscosity grade ISO VG32 is kept at 4 C, pure axial load of 9.8 kn is applied to te tapered roller bearing 336D, and te inner ring is allowed to run at 2, min -1. Fig. 3 (a) provides an oil film pressure distribution diagram. Fig. 3 (b) sows an oil film tickness distribution diagram. Te x and y -axis in tese diagrams are te same as tose in Fig. 1 (b), and te region enclosed wit solid lines is te zone were lubricating oil film formation can occur. Te two faces generally sift in te positive direction along te x-axis. As sown in Fig. 3 (a), a pressure spike indicative of EHL occurs at te location near te exit of te fluid flow. A skewing angle of -.19 of te roller is present, an angle at wic oil film tends to occur due to a wedge film effect. Te point of maximum oil film pressure as sifted by.2 mm in te positive direction along te x- axis due to skewing. As a result, te inlet oil flow area is greater tan if te roller was not skewed. As sown in Fig. 3 (b), te deformed region constitutes an oval aving its long axis in te x-direction, wic is te major flow direction of te lubricating oil. Tere is a orsesoe-saped neck at te oil flow outlet. Unlike a one-way oil flow situation, te oil film profile is not symmetric along te x-axis at y =. 4.2 Experimental verification of skewing angle Harada et al. measured te skewing angle on a running 3231 tapered roller bearing 6). Te resultant report states tat a skewing angle was calculated using te roller large end face/cone flange face contact program. Tis program simulates an isoviscosity-rigid body region but tere was a discrepancy in magnitude. Harada et al. tink tis is because in te experimental study, a ig viscosity-elastic body region was used in contrast to te calculation-based study, wic assumed an isoviscosity-rigid body region. We compared te experimental result of Harada et al. wit te calculation results obtained from our metod described in tis paper. Te results are grapically plotted in Fig. 4. In tis cart, Exp. are Skewing angle deg Rib load Exp.1 min -1 Exp.2 min -1 Exp.3 min -1 EHL1 min -1 EHL2 min -1 EHL3 min -1 HL1 min -1 HL2 min -1 HL3 min -1 Fig. 4 Comparison between experimental and calculated of skewing angle experimental results of Harada et al., EHL stands for calculation results obtained from our EHL analysis tecnique previously described in tis paper, and HL indicates a results of fluid lubrication analysis on roller large end flange performed by Harada et al. assuming an isoviscosity-rigid body region. Compared wit values associated wit HL, te values obtained from EHL are more similar to te experimental results. Tis is because wit HL results, te force as an integral of pressure is significantly sifted toward te fluid inlet pat since elastic deformation is not considered. In contrast, wit EHL results, te oil film pressure is approximately te same as te Hertz pressure; tereby, te force (i.e. integral of pressure) acts on a point situated near te contact center. Te calculated effects of te rotational speed qualitatively differ from te experimental results. In te calculated results, a greater rotating speed leads to a greater magnitude of te skewing angle for bot EHL and HL. However, at lower rotational speeds (e.g. 1, min -1 ), te experimental skewing angle closely matces tat obtained from EHL analysis. From tese findings, we believe tat at low rotational speeds, were starvation seems not to be present, te results of our EHL analysis tecnique well represents te experimentally determined lubrication state. Furtermore, we reason tat te experimentally obtained skewing angle is smaller tan tat obtained from te EHL tecnique because experimentally at ig pressure, te pressure at te inlet oil flow pat drops due to starvation causing te moment derived from te oil film pressure to drops. 4.3 Effects of surface rougness Beavior of fluid flow is primarily governed by te pressure gradient across and velocity between two faces. Rougness asperities witin te pressure gradient will result in localized pressure variation. In addition, fluid in te trougs of a roug surface will move along wit te surface: affecting te oil flow rate caused by relative motion between te faces, resulting in a substantial decrease of te oil film tickness. Consequently, te expected flow will vary. By adopting a pressure flow rate coefficient and a sear flow rate coefficient in te Patir-Ceng mean flow model 4), we can quantitatively determine te effects of 2D (twodimensional) surface rougness. Te pressure flow rate coefficient can be defined as te ratio of te mean pressure flow on a roug surface to tat on smoot surface. Te sear flow rate coefficient is similar but wit additional flow caused by a sift of te roug surface. Bot te pressure flow rate coefficient and te flow rate are affected by directional parameters associated wit rougness. For -11-

7 NTN TECHNICAL REVIEW No convenience of discussion, we will deal wit isotropic surface rougness. Taking te values in Table 1 to define surface rougness, we ave determined canges in te oil film tickness caused by te presence/absence of rougness. Fig. 5 plots te resultant cange of te oil film tickness. Using te same conditions, te samples including factors for surface rougness ave exibited somewat larger minimum oil film tickness. In te roller large end-flange contact mode, te cone flange as iger surface rougness and surface velocity. As a result, it seems tat te additional oil flow caused by te sifting of te surface rougness of te rib is greater tan te inward oil flow restricted by te surface rougness of te roller large end face. Also, te amount of oil flowing into te contact area is iger, leading to a ticker oil film. Center oil film tickness Minimum oil film tickness Smoot Roug Rotating speed min -1 (a) Central oil film tickness Smoot Roug Rotating speed min -1 (b) Minimum oil film tickness Bearing: 336D Rib load: 2 N Kinematic viscosity of lubricating oil: 32.2 mm 2 /s Fig. 5 Effect of surface rougness on oil film tickness 5. Optimal end face R ratio resulting from oil film forming capability So far, proposed factors triggering seizure of contacting objects include critical oil film tickness, temperature and frictional loss. Note tat regardless of te underlying cause, metal-to-metal contact must be avoided to prevent seizure. Terefore, a maximum possible oil film is preferred. In order to maximize te oil film tickness in a bearing, we ave attempted to optimize te roller end face R ratio. Because te optimal roller end face R ratio appears to be governed by bearing operating conditions, we ave calculated te oil film tickness using velocity, viscosity and load as parameters. Fig. 6 includes examples of plotting te relationsip between roller large end face R ratio and oil film tickness, wit several sets of operating parameters. Tese carts sow te following trends: (1) Regardless of te combination of operating parameters, tere is a particular R ratio tat leads to a maximum oil film tickness. However, te oil film tickness can suddenly decrease wen te R ratio is increased above te optimum value (toug R ratios smaller tan te optimum value do not lead to as drastic a decrease). (2) Te R ratio tat leads to a minimal oil film tickness appears to be least affected by rotating speed and viscosity (except for cases wit a ig viscosity lubricating oil). Now, let us discuss te relationsips we ave learned so far concerning velocity, viscosity and optimal R ratio wit our tapered roller bearings. 5.1 Effects of velocity As sown in Fig. 6 (a), at a rotational speed of 5 min -1, te minimum oil film tickness is largest wen te R ratio is 93%; wit a iger rotating speed, te optimal R ratio is somewat smaller, standing at 88% at 4, min -1. However, at te lower rotational speed range were te oil film tickness is smaller, te variation in minimum oil film tickness near te optimal R ratio is smaller. Terefore, we tink it is not necessary to seriously consider te effects of rotating speed for optimal R ratio at low rotational speeds. 5.2 Effects of viscosity In Fig. 6 (b), te minimum oil film tickness is largest wen te R ratio is 78% and te kinematic viscosity is 335 mm2/s. Because te magnitude of te oil film tickness is large in tis case, te viscosity of te lubricating oil is not an important factor wen pertaining to oil film formation and R ratio. On te oter and, at lower viscosities were te oil film tickness is small, te -12-

8 Optimized Radius of Roller Large End Face in Tapered Roller Bearings Minimum oil film tickness Minimum oil film tickness Minimum oil film tickness.6 4 min min min min min min R ratio of roller large end face % (a) Effect of rotating speed Rib load: 2 N Kinematic viscosity: 32 mm 2 /s R ratio of roller large end face % (b) Effect of oil kinematic viscosity Bearing speed: 2, min -1 Rib load: 2 N R ratio of roller large end face % (c) Effect of rib load Bearing speed: 2, min -1 Kinematic viscosity: 32 mm 2 /s 335 mm 2 /s 117 mm 2 /s 32 mm 2 /s 11 mm 2 /s 5.5 mm 2 /s 2N 1N 2N 35N 5N Fig. 6 Relationsip between R ratio of roller large end face and minimum oil film tickness to design te R ratio smaller tan te optimal value since te oil film tickness decreases dramatically wen te R ratio exceeds te optimal value, but muc less so wen te R ratio is less tan te optimum value. 5.4 Experimental verification We produced tapered roller bearing samples wit varying roller end face R ratios 97%, 91.7% and 8%. We analyzed te temperature rise of te outer ring wit increasing outer ring rotational speeds. Fig. 7 sows a plot of te measured bearing temperatures. Typically, flange faces are super-finised. However, te flange faces in tese samples were ground so tat te effects of lubrication would be more apparent. Excessive eat buildup occurred in te samples wit 97% R ratios running at 2, min -1 and 91.7% R ratios running at 3, min -1. It was determined tat tese samples were generating an excessive amount of eat, too ig for recommended operation. In contrast, samples wit 8% R ratios proved to be able to run at 5, min -1 witout excessive eat generation. In te previous sections, we demonstrated troug analysis tat oil film tickness is optimized by selecting an R ratio of 85% or smaller. Troug experimental verification, we proved te appropriateness of our analytical results. Bearing temperature C R ratio 97% R ratio 91.7% R ratio 8% effect of te viscosity of te lubricating oil on te optimal R ratio is small. 5.3 Effects of load From Fig. 6 (c), it is apparent tat increasing te load causes te optimal R ratio to be smaller. Furtermore, under iger loads, te minimum oil film tickness resulting from an R ratio greater tan optimal will be smaller. Terefore, wen te oil film tickness is smaller and te rib load is iger, te R ratio needs to be smaller. In summary, based on our results of te optimal R ratio and oil film formation, it is not necessary to give particular considerations to te effects of velocity and/or viscosity, assuming te operating conditions in our study. It is reasonable to set te R ratio to approximately 85% for a ig load situation and to approximately 95% for a low load situation. At te same time, it is desirably Rotating speed min -1 Bearing: 336D Radial load: 19.6 kn Axial load: 6.9 kn Lubricating oil viscosity grade: ISO VG 56 Fig. 7 Results of measured bearing temperature: Effects of R ratio of te roller large end face -13-

9 NTN TECHNICAL REVIEW No Conclusion Studying roller large end-flange face contact on tapered roller bearings, we performed isotermal EHL analysis wile considering roller skewing. We discovered te following caracteristics about lubrication at te roller large end-flange face: Assuming isotropic surface rougness, te magnitude of oil film tickness will be greater wen surface rougness is taken into account. If an EHL condition is assumed, te calculated value of te roller skewing angle is smaller tan tat obtained witout considering deformation of te contacting elements; it more closely matces te actual measured value. In addition, we discovered te following design guidelines for end face R ratios to maximize te lubricant oil film tickness: Te optimal end face R ratio tat elps maximize te lubricating oil film tickness can vary depending on te rotational speed, lubricating oil viscosity and load conditions. Basically, it sould be approximately 85% for ig load situation. However, once te end face R ratio exceeds te optimal value, te oil film tickness suddenly decreases. Terefore, te design end face R ratio sould be smaller tan te optimal value. Tapered roller bearings can experience operational problems wen te oil film tickness is very low. If te low oil film tickness is due to low speed or low oil viscosity, ten te optimal end face R ratio as little affect. From tese studies it is desirable to design te roller wit an end face R ratio of approximately 85% at most. Tis will allow te tapered roller bearing to operate properly under eavy loads. In preparing tis tecnical paper, te autors ave revised Transactions of te Japan Society of Mecanical Engineers (Trans. Jpn. Soc. Mec. Eng.), Book C, Vol. 75 (29), pp References 1) T. Yamada, Torque Control and Operational Improvement of Tapered Roller Bearings, SAE Tecnical Paper Series, (1986), ) Y. Okamoto and T. Tsujimoto: ECO-Top Tapered Roller Bearings, NTN Tecnical Review No. 68 (2) ) X. Jiang et al., Termal Non-Newtonian EHL Analysis of Rib- Roller End Contact in Tapered Roller Bearings, Transactions of te ASME, Journal of Tribology, 117 (1995), ) N. Patir and H.S. Ceng, An Average Flow Model for Determining Effects of Tree-Dimensional Rougness on Partial Hydrodynamic Lubrication, Transactions of te ASME, Journal of Lubrication Tecnology, 1 (1978), ) H. Nisida et. al., Analysis of mixed lubrications between te Large End Faces of Tapered Roller Bearings and Ribs, Proceedings of te Fall 21 Tribology Conference in Utsunomiya, (21), (Japanese) 6) K. Harada and T. Sakaguci, Rolling Element Skew in Dynamic Analysis for Tapered roller Bearings, Proceedings of Te Tird Asia International Conference on Tribology, (26), ) L. Houpert, New Results of Traction Force Calculations in Elastoydrodynamic Contacts, Trans. ASME, J. Tribol., 17-2 (1985), ) C.S. Wu, E.E. Klaus and J.L. Duda, Development of a Metod for te Prediction of Pressure-Viscosity Coefficients of Lubricating Oils Based on Free-Volume Teory, Trans. ASME, J. Tribol., (1989), ) ASTM, Annual Book of ASTM Standards, Section 5, Vol.5.1 Petroleum Products, Lubricants, and Fossil Fuels, (1987), ) J.A. Greenwood and J.H. Tripp, Te Contact of Two Nominally Flat Roug Surfaces, Proceedings of IMecE, 185 (197-71), ) N. Patir and H.S. Ceng, Application of Average Flow Model to Lubrication Between Roug Sliding Surfaces, Trans. ASME, J. Lub. Tec., 11 (1979), ) N. Patir and H.S. Ceng, Effect of Surface Rougness Orientation on te Central Film Tickness in E.H.D. Contacts, Proc. of 5TH Leeds-Lyon Symp. on Tribol., (1978), ) N. Ono et al.: Effect of Bulk Modulus of Solidified Oils under Hig Pressure on Tractional Beavior, Journal of Japanese Society of Tribologists, Vol. 38 (1993), (Japanese) 14) R.T. Lee and B.J. Hamrock, A Circular Non-Newtonian Fluid Model: Part I - Used in Elasto-ydrodynamic Lubrication, Transactions of te ASME, Journal of Tribology, 112 (199), Poto of autors Hiroki FUJIWARA Elemental Tecnological R&D Center Takasi TSUJIMOTO Automotive Sales Headquarters Automotive Engineering Dept. Kazut YAMAUCHI Graduate Scool of Engineering Osaka Univercity -14-

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