Mechanical behaviors of cross roller bearings with raceway roundness error

Abstract

Taking the raceway roundness error into account, mechanical characteristics of cross roller bearings (CRBs) were investigated. A static analysis model of CRBs considering the raceway roundness error was established. Based on this model, the rotational accuracy and load distribution of CRBs under constraints of geometry and external loads were derived. The fatigue life of CRBs with roundness error was calculated by applying Palmgren-Miner linear cumulative damage theory. The influence of inner and outer raceway roundness error on the performance of the CRBs, such as rotational accuracy, load distribution, and fatigue life, was studied through the analysis of examples. The results indicate that the influence of roundness error on the rotating inner raceway is more significant than that of roundness error on the nonrotating outer raceway. The roundness error on the rotating inner raceway always degrades the performance of CRBs. However, a proper roundness error on the nonrotating outer raceway can reduce the loads acting on the rollers and thus improve the fatigue life of CRBs. The effect of the roundness error amplitude on the bearing performance is ordinal, whereas the effect of the roundness order on the bearing performance is not in order.

Keywords

cross roller bearings / roundness error / load distribution / rotational accuracy / fatigue life

References

[1] TongV C, HongS W. Characteristics of tapered roller bearing with geometric error. International Journal of Precision Engineering and Manufacturing, 2015, 16(13): 2709-2716

[2] TongV C, HongS W. Study on the stiffness and fatigue life of tapered roller bearings with roller diameter error. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2016, 231(2): 176-188

[3] HarshaS P, SandeepK, PrakashR. Non-linear dynamic behaviors of rolling element bearings due to surface waviness. Journal of Sound and Vibration, 2004, 272(3–5): 557-580

[4] ShahD S, PatelV N. Theoretical and experimental vibration studies of lubricated deep groove ball bearings having surface waviness on its races. Measurement, 2018, 129: 405-423

[5] HalminenO, AceitunoJ F, EscalonaJ L, SopanenJ, MikkolaA. A touchdown bearing with surface waviness: Friction loss analysis. Mechanism and Machine Theory, 2017, 110: 73-84

[6] WangX-K, XuQ, WangB-R, ZhangL-X, YangH, PengZ-K. Effect of surface waviness on the static performance of aerostatic journal bearings. Tribology International, 2016, 103: 394-405

[7] ZhangP-H, ChenY-L, LiuX-T. Relationship between roundness errors of shaft and radial error motions of hydrostatic journal bearings under quasi-static condition. Precision Engineering, 2018, 51: 564-576

[8] RafsanjaniA, AbbasionS, FarshidianfarA, MoeenfardH. Nonlinear dynamic modeling of surface defects in rolling element bearing systems. Journal of Sound and Vibration, 2009, 319(3–5): 1150-1174

[9] PatilM S, MathewJ, RajendrakumarP K, DesaiS. A theoretical model to predict the effect of localized defect on vibrations associated with ball bearing. International Journal of Mechanical Sciences, 2010, 52(9): 1193-1201

[10] PetersenD, HowardC, PrimeZ. Varying stiffness and load distributions in defective ball bearings: Analytical formulation and application to defect size estimation. Journal of Sound and Vibration, 2015, 337: 284-300

[11] PetersenD, HowardC, SawalhiN, Moazen AhmadiA, SinghS. Analysis of bearing stiffness variations, contact forces and vibrations in radially loaded double row rolling element bearings with raceway defects. Mechanical Systems and Signal Processing, 2015, 50–51: 139-160

[12] YuY-J, ChenG-D, LiJ-S, XueY-J. Effect of geometric errors of bearing components on motion error of cylindrical roller bearings Part I: Calculation method. Journal of Mechanical Engineering, 2019, 55(1): 62-71

[13] GönczP, PotočnikR, GlodežS. Computational model for determination of static load capacity of three-row roller slewing bearings with arbitrary clearances and predefined raceway deformations. International Journal of Mechanical Sciences, 2013, 73: 82-92

[14] PotočnikR, GönczP, GlodežS. Static capacity of a large double row slewing ball bearing with predefined irregular geometry. Mechanism and Machine Theory, 2013, 64: 67-79

[15] ChenG-C, WangB-K, MaoF-H. Effects of raceway roundness and roller diameter errors on clearance and runout of a cylindrical roller bearing. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2012, 227(3): 275-285

[16] MaF-B, JiP, LiZ-M, WuB-J, AnQ. Influences of off-sized rollers on mechanical performance of spherical roller bearings. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 2015, 229(4): 344-356

[17] ChenS-J, MaF-B, JiP, PengA-Q. Effects of axial preloading displacement and off-sized balls and raceway error on mechanical performance of angular contact ball bearings. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, 2016, 230(4): 293-306

[18] YeZ-H, WangL-Q, GuL, ZhangC-W. Effects of tilted misalignment on loading characteristics of cylindrical roller bearings. Mechanism and Machine Theory, 2013, 69: 153-167

[19] XingY, XuH, PeiS-Y, ZhangX, ChangW. Mechanical analysis of spherical roller bearings due to misalignments between inner and outer rings. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2016, 231(17): 3250-3262

[20] WardaB, ChudzikA. Effect of ring misalignment on the fatigue life of the radial cylindrical roller bearing. International Journal of Mechanical Sciences, 2016, 111–112: 1-11

[21] TongV C, HongS W. The effect of angular misalignment on the running torques of tapered roller bearings. Tribology International, 2016, 95: 76-85

[22] AithalS, SivaP N, ShunmugamM S, ChellapandiP. Effect of manufacturing errors on load distribution in large diameter slewing bearings of fast breeder reactor rotatable plugs. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2015, 230(9): 1449-1460

[23] LiuJ, YanZ-L, ShaoY-M. An investigation for the friction torque of a needle roller bearing with the roundness error. Mechanism and Machine Theory, 2018, 121: 259-272

[24] HARRIS T A, KOTZALAS M N. Essential concepts of bearing technology [M]. CRC Press, 2006.

[25] TeutschR, SauerB. An alternative slicing technique to consider pressure concentrations in non-hertzian line contacts. Journal of Tribology, 2004, 126(3): 436-442

[26] ISO/TS 16281. Rolling bearings—Methods for calculating the modified reference rating life for universally loaded bearings [S]. Geneva, Switzerland, 2008.

[27] HARRIS T A, KOTZALAS M N. Advanced concepts of bearing technology: Rolling bearing analysis [M]. CRC Press, 2006.

[28] LundbergG, PalmgrenA. Dynamic capacity of roller bearing. Acta Polytech. Mechanical Engineering Series, 1952, 2(4): 96-127

[29] ISO 281Rolling bearings-dynamic load ratings and rating life, 2007, Geneva, Switzerland, International Organization for Standardization