CYLINDRICAL ROLLER BEARINGS CARRYING THRUST LOAD

CYLINDRICAL ROLLER BEARINGS CARRYING THRUST LOAD Gh. PRISACARU, Sp. CRETU, D. N. OLARU "Gh. Asachi Technical University, Department of Machine Design & Tribology, Bvd. D. Mangeron, 6-63, 66 Iasi, ROMANIA; e-mail: gprisaca@diac.mt.tuiasi.ro P. LORENZ Polytechnic University of the Saarland, Department of Mechanical Engineering-Materials, Handling Technology, Göbenstr. 4, D-667 Saarbrűcken, GERMANY; e-mail: lorenz@htw.uni-sb.de SUMMARY The thrust load capacity of a cylindrical roller bearing has been experimentally and theoretically studied. A sphere-cone geometry was considered for the rib-roller end contact. A compromise between a maximum lubricant film thickness at the rib-roller end contact and a minimum friction torque are searched in order to improve the thrust load capacity of the bearing. A quasi-dynamic modelling of cylindrical roller bearing has been developed. The model allows describing the effects of the roller end radius on the film thickness at the rib-roller end contact and on the bearing torque. An optimum range of roller end radius has been theoretically estimated. Two test rigs have been used to measure the bearing friction torque and evaluate the lubrication quality. The use of cylindrical roller bearings with different rib-roller end contact geometries confirmed the optimum geometry that was theoretically predicted. Keywords: cylindrical roller bearing, quasi-dynamic equilibrium, friction torque, lubrication, optimisation INTRODUCTION Cylindrical roller bearings are not usually submitted to thrust loads or misalignments. The bearing s users exigencies establish the task for the bearing s designers to develop typical cylindrical roller bearings with thrust load capacity. This supplementary load is supported by the rib-roller end contact, so different solutions were proposed to characterize this contact geometry. Korenn [] proposed a sphere-sphere geometry, where the cylindrical roller end and the rib have a spherical shape. Kispert [2, 3] has two easy solutions to realize: sphere-cone where the roller end faces are spherical and the rib is simply inclined or plane faces with crown radius - cone. Von Bradow [4] and Warda [5] also have studied the solution crown radius-cone. Li and Wen [6] have been worked on a geometry contact of cone-cone type. These studies analysis seems to indicate that geometry sphere-cone is the most performant from thrust load capacity point view. Krzeminski and Warda [7] performed a theoretical study on this bearing type submitted to a combined radial and thrust load. However, their model developed in order to optimise the rib-roller end contact doesn t consider the inertial effect, the rugosities influence, the cage-rollers contacts and the misalignment. This work presents a theoretical and experimental study on the thrust load capacity for a cylindrical roller bearing. A sphere-cone geometry was considered for the rib-roller end contact. A compromise between a maximum lubricant film thickness at the rib- roller end contact and a minimum friction torque or friction power loss are searched in order to improve the thrust load capacity of the bearing. The dynamic model developed allows establishing both the bearing internal kinematics and the load distribution between the rollers and rings. This model has been included the sphere-cone geometry. Two test rigs have been used to measure the bearing friction torque and to evaluate the lubrication quality. The use of cylindrical roller bearings with different ribroller end contact geometries confirms the optimum geometry that was theoretically predicted. 2 THEORETICAL STUDY The model includes two different steps: a) a quasi-static model to obtain the bearing s elements displacements, the normal loads and the elastic deformations on line and point contacts [8]. b) a dynamic model using as initial solution the quasistatic model results. It were solved the equilibrium equations, that include the forces and moments acting on every roller, Figure [9, ]. This dynamic model is then used to predict the friction power loss, friction torque and at the same, the lubricant thickness on the rib-roller end contact for a cylindrical roller bearing, type NUP. It was considered a sphere-cone solution for the rib-roller end contact and different operating conditions (inner ring speed, external loading and lubrication). 2. Numerical results The rib-roller end contact geometry is characterized by a geometrical parameter k that represents the ratio between the rib radius on contact point and roller end one. The relations bellow mentioned were used in order to optimise the contact geometry: the minimum film thickness on point contacts, h; it is a parameter correlated to lubrication efficiency in terms of wear and fatigue life. His optimum reefers to the maximization of the function: max h f (k), f =,2,3,4

the outer ring torque, M f ; it is a energetically parameter whose optimization consists in his minimization: min M f (k); the friction power loss, P f ; it is also an energetically parameter whose optimization consists in his minimization: min P f (k). The Figures 2a to 2d show an optimum global field corresponding to k values from.8 to.56. It is necessary to precise that this optimum has been obtained for the following operating conditions: F a = N, F r = 7 N, n = 3 5 rpm and η =.4 Pa.s. The bearing typical data are presented in Tables and 2. Z w e FTRoj e Qoj e FSoj Q o e FAoj Z w FA oj FS oj FTRoj FA oj FTR oj FS oj FS j FAj FS 2j FA2j la/2 FRj 2 Xw MRj FA2j FA j FP ij FS j FS 2j FPoj FC j Y w 4 FS 4j FA 4j FS 4j FA 4j 3 ML j FR j FS 4j FA4j wj FS 3j FA3j ML j FTR ij FA FS ij ij FA ij FS ij FTR ij e FA ij j e FS ij e Q ij Q i e FTRij Figure : Resistance forces acting on the contact surfaces of cylindrical roller 2,5 h min2, [µm] h min4, [µm],4,3,2, Fr = 5 N, Fa = 5 N Fr = 2 N, Fa = 3 N,,2,3,4,5 Figure 2a: Film thickess h 2 (outer rib-roller end contact) versus geometrical parameter k,4,3,2, Fr = 2 N, Fa = 3 N Fr = 5 N, Fa = 5 N,,2,3,4,5 Figure 2b: Film thickess h 4 (inner rib-roller end contact) versus geometrical parameter k Friction torque, M f [Nm] Power loss, P f [W] 2,5,5 Fr = 2 N, Fa = 3 N Fr = 5 N, Fa = 5 N,,2,3,4,5 Figure 2c: Friction torque on the outer ring versus geometrical parameter k 22 2 8 6 4 2 8 6 4 2 Fr = 2 N, Fa = 3 N Fr = 5 N, Fa = 5 N,,2,3,4,5 Figure 2d: Friction power loss versus geometrical parameter k

3 EXPERIMENTAL STUDY Lubrication and friction bearing torque are experimentally studied. Bearings dimensional parameters and lubricant properties is presented in Tables, 2 and 3. 3. Friction torque measurement To measure the friction torque the experimental rig schematically presented in Figure 3 is used. The experimental rig includes: a variable speed between and 2 rpm driving system; a hydrostatic loading system for radial and axial loads; a strain gauge measurement system for the friction torque. 3.2 Electrical resistance measurement To characterize the lubrication quality the low voltage electrical resistance measurement technique is used. This method allows estimating the film thickness related to the measured electrical resistance value, which increases with the film thickness value. The specified test rig to perform these measurements is presented in Figure 4. 3.3 Experimental results 3.3. Friction torque The experimental values for friction torques measured on outer bearing ring are shown in Figures 5 and 6. 3.3.2 Electrical resistance (film thickness) The electrical resistance distribution related to inner bearing ring speed is presented in Figures 7, 8 and 9. The line contacts geometry for all the studied bearings are the same, so the differences can be only explained through the changes on rib-roller end contacts geometry. 4 DISCUSSION The numerical simulations were performed before the experimental study in order to prepare an experimental campaign. Particularly, a compromise between a maximum lubricant film thickness at the rib- roller end contact and minimum friction torque or friction power losses are searched in order to improve the thrust load capacity of the bearing. To characterize the particular contact (rib-roller end) the dimensionless parameter k (the ratio between the rib radius R f in point contact and roller end radius R s ) was included. The experimental study allows comparing the standard bearing versions NUP 26E and NUP 22E with modified bearing versions. The versions with modified geometry lead to a reduced friction torque (Figure 5, 6) and a better lubrication (Figures 7, 8) related to standard version (Figures 7, 8, 9). The experimental results confirm an optimum value for k parameter. This is expressed through the determination of minimum friction torque values and maximum electrical resistance values (Figures 6, 9) at the same time. The best results were obtained for modified geometry with k =.3 (R s =35 mm) for NUP 22E bearing and k =.6 (R s = 76 mm) for NUP 26E bearing (Figures 5, 6, 8, 9). It can be remark the benefice effect of rotational speed that increases the film thickness on rib-roller critical contact (Figure 8) and so the improvement of bearing thrust load capacity. At the last, it can be noticed the characteristic shape for the curves presenting the friction torque related to the rotational speed (Figure 5) where it can be recovered the Stribeck characteristic shape []. NUP 22E standard NUP 22E with modified geometrie Roller diameter, D w [mm] 4 Axial roller length, l w [mm] 4 4.327 4.272 4.33 End roller radius, R s [mm] 76 35 Ring flange angle, γ f [ o ] o 2 42 o 57 54 Geometrical parameter, k.98.22.3 Inner raceway diameter, d I [mm] 72 Outer raceway diameter, d o [mm] Number of rollers, z 6 Radial clearance, [mm].5 Rib surface roughness, R a [µm].32 Raceway surface roughness, R a [µm].6 Table : NUP 22 E test bearing specifications

NUP 26E standard NUP 26E with modified geometrie Roller diameter, D w [mm] 9 Roller diameter, D w [mm].9.3.57 End roller radius, R s [mm] 76 35 Ring flange angle, γ f [ o ] o o 57 o o 42 Geometrical parameter, k.27.6.55 Inner raceway diameter, d i [mm] 37.5 Outer raceway diameter, d o [mm] 55.5 Number of rollers, z 2 Radial clearance, [mm].3 Rib surface roughness, R a [µm].32 Raceway surface roughness, R a [µm].6 Table 2: NUP 26E test bearing specifications Type of lubricant M 3 Density at 5 C, [kg m -3 ],95 Kinematic viscosity at 5 o C, [cst] 68,5 Kinematic viscosity at o C, [cst],7 Viscosity index (IV), 9 Thermal conductivity, [W m - K - ],2 Table 3: Physical properties of the lubricant R a A Shaft Test bearing A Hydrostatic axial journal A-A P a Tensometric gauge F a Termocouple P a Bearing support A F r Pump AC-Driving motor Hydrostatic radial journal P R n C DC-Driving motor Variable speed control Wheatstone bridge Figure 3: Schematic test ring view for the friction torque measurements DC-driving motor axial loading system support bearings termocouple measuring circuit of lubricant film resistance driving shaft test bearing lubricant sealing housing Fr base rubber radial loading system Figure 4: Schematic test ring view for the electrical resistance measurements

Friction torque, M f [Nm] Friction torque, Mf [Nm] 2,2 2,8,6,4,2,8,6,4,2 NUP 22E Fa = 554 N Fr = 43 N T = 35 o C Standard Rs = 35 mm Rs = 76 mm Rs = mm 2 3 4 Bearing speed, n[rpm] Figure 5: Friction torque vs. bearing speed and rib-roller end geometry 2, F r = 43 N n = 345 rpm,9 Lubricant M3 T = 35 o C,8,7,6,5,4 F a = 554N F a = 443N F a = 332N,3,,5,,5,2,25,9,, k = R f/r s Figure 6: The influence of the geometrical parameter k on the friction torque Electrical resistance, [k W ], F r = 43 N n = 6 rpm F a = 665 N F a = 443 N F a = 277 N,,2,4,6,8,2,95, k = R f / R s Figure 9: Electrical resistance vs. geometrical parameter k at different axial loads for NUP26E (T=35 o C) 5 CONCLUSION To describe the NUP bearing running ( with standard geometry and modified geometry, the roller face becoming spherical and the rib inclined) a dynamic model for cylindrical roller bearings was developed. This model was used to estimate the influence of the rib-roller end contact and to define an optimum geometry in order to prepare an experimental campaign. This contact optimisation consists in minimizing the bearing friction torque in the same time with maximizing the contact film thickness. The experimental study on NUP bearings shown that it is possible to obtain a substantially increase of the thrust load capacity if his internal geometry is easy modified. A good agreement between the numerical and experimental results indicates that this proposed model can be used as an optimisation tool for cylindrical roller bearings, particularly for those operating under combined axial and radial load. Figure 7: Electrical resistance vs. bearing speed at different rib-roller end geometries for NUP22E (T=35 o C) Figure 8: Electrical resistance vs. bearing speed at different rib-roller end geometries for NUP26E (T=35 o C) 6 REFERENCES [] Korrenn H.: The Axial Load Carrying Capacity of Radial Cylindrical Roller Bearings, ASME Journal of Lubrication Technology, 92 (97), 29-37. [2] Kispert K.: Das SU-Layer-ein axial hochbelastbares Radial-Zylinderrollenlager, "VDI-Z", 23 (98), /2, 3-34. [3] Kispert K.: Leistungsfahigkeit it moderner Zylinderrollen-layer, Antriebstechnik, 24 (985), 6, 33-39. [4] Von Bradow B.: Auswahl und Berechnung von Zylinderrollenlagern, Antriebstechnik, 26 (987), 2, 322-326. [5] Warda B.: Modelling of the Pressure Distributions Between Roller End Flange Contacts of NJ Type of Cylindrical Roller Bearing, Mechanika, 9 (99), 2, 2-29. [6] Li M. & Wen S.: The Study of Roller End and Guiding Shoulder Construction of Roller Bearings, Proceedings of the 9 th Leeds-Lyon Symposium on Tribology, September 6-9, 989, Lyon (France), 297-3.

[7] Krzeminski-Freda H., Warda B.: The Effect of Roller End-Flange Contact Shape Upon Frictional Losses and Axial Load of the Radial Cylindrical Roller Bearing, Proceedings of the 9th Leeds-Lyon Symposium on Tribology, September 6-9, 989, Lyon (France), 287-295. [8] Prisacaru G., Bercea I., Mitu N., Cretu S.: The Analysis of the Quasi-Dynamic Equilibrium in Cylindrical Roller Bearing", Proceedings of the 6th Nordic Symposium on Tribology NORDTRIB 94, 3 (994), Uppsala (Sweden), 72-73. [9] Prisacaru G., Bercea I., Cretu S., Mitu N.: Non- Newtonian Behaviour of Mineral Oils in Cylindrical Roller Bearing, th International Colloquium on Tribology, January 9-, 996, Esslingen (Germany), 67-623. [] Cretu S., Prisacaru G., Bercea I., Mitu N.: The Effect of Rib-Roller End Contact Geometry on Friction Torque in a Cylindrical Roller Bearings, th International Colloquium on Tribology, January 3-5, 998, Esslingen (Germany), 67-63. [] Brown S.R., Poon S.V.: The Lubrication of the Roller-Rib Contacts of a Radial Cylindrical Roller Bearing Carrying Thrust Load, ASLE Transaction, 26 (982), 3, 37-324. 7 NOTATIONS e position of force application point, [m] Fa external thrust load, [N] FA traction forces due to asperity contacts, [N] FC normal force to roller-cage contact, [N] FP hydrodynamic force, [N] Fr external radial load, [N] FR drag forces, [N] FS sliding traction forces, [N] FTR rolling resistance forces, [N] h min minimum film thickness, [m] J inertial moment, [kgm 2 ] K dimensionless parameter characterizing the ribroller end contact ML friction torque between rollers faces and airlubricant mixture, [Nm] MR friction torque between roller cylindrical surface and air-lubricant mixture, [Nm] Q roller- raceway normal load, [N] R f rib radius of curvature on the rolling direction, [m] R s roller end radius, [m] T lubricant temperature, [ o C] ω skew skewing angular speed, [rad/s] roller angular velocity, [rad/s] ω w 8 SUBSCRIPTS f rib-roller end contact I inner raceway for line contact o outer raceway for line contact vs versus w roller