Investigation of the Load Distribution and Stiffness Characteristic of Ball Bearing under Ball-raceway Separation Condition

doi:10.3901/JME.2020.09.073

Abstract

Abstract: Aiming at the theoretical modelling and characteristic analysis of ball bearing under the ball-raceway separation condition, the new initial position for ball bearing modelling is proposed. Combining with the ball-raceway contact analysis, a general model for ball bearing under different load conditions is presented. Then the proposed model is solved by a nested Newton-Raphson iterative algorithm based on the analytical calculation method for bearing stiffness matrix. On this basis, the load distribution and stiffness characteristic of ball bearing under three different load conditions are analyzed. The results show that the proposed model is more reasonable and applicable than the Jones-Harris model. Moreover, the internal load distribution and stiffness are determined by both the external load and internal contact state of ball bearing, and the number of balls in loaded zone caused by the changes of the radial clearance, external load and speeds can further lead to the sudden change of bearing stiffness. In addition, appropriate increases of axial load can effectively improve the load distribution and increase the numbers of balls in loaded zones of ball bearing.

Key words: ball bearing, contact state analysis, initial position assumption, load distribution, stiffness matrix

CLC Number:

TH133

ZHANG Jinhua, FANG Bin, ZHU Yongsheng, YAN Ke, HONG Jun. Investigation of the Load Distribution and Stiffness Characteristic of Ball Bearing under Ball-raceway Separation Condition[J]. Journal of Mechanical Engineering, 2020, 56(9): 73-83.

References

[1] STRIBECK R. Ball bearings for various loads[J]. Transactions of the ASME, 1907, 29:420-463.
[2] SJOVALL H. The load distribution within ball and roller bearings under given external radial and axial load[J]. Tekniks Tidskrift Mek., 1933, 9.
[3] PALMGREN A. Ball and roller bearing engineering[M]. Burkbank, 1959.
[4] JONES A B. A general theory for elastically constrained ball and radial roller bearings under arbitrary load and speed conditions[J]. Journal of Basic Engineering, 1960, 82(2):309-320.
[5] HARRIS T A. Rolling bearing analysis[M]. New York:John Wiley and Sons, 2001.
[6] 丁长安,周福章,朱均,等. 滚道控制理论与滚动体姿态角的确定[J]. 机械工程学报, 2001, 37(2):58-61. DING Changan, ZHOU Fuzhang, ZHU Jun, et al. Raceway control assumption and the determination of rolling element attitude angle[J]. Chinese Journal of Mechanical Engineering, 2001, 37(2):58-61.
[7] WANG W, HU L, ZHANG S, et al. Modeling angular contact ball bearing without raceway control hypothesis[J]. Mechanism and Machine Theory, 2014, 82:154-172.
[8] HARRIS T A. An analytical method to predict skidding in thrust-loaded, angular-contact ball bearings[J]. Journal of lubrication technology, 1971, 93(1):17-23.
[9] RUMBARGER J H, FILETTI E G, GUBERNICK D. Gas turbine engine mainshaft roller bearing-system analysis[J]. Journal of Lubrication Technology, 1973, 95(4):401-416.
[10] NELIAS D, SEABRA J, FLAMAND L, et al. Power loss prediction in high-speed roller bearings[M]. Amsterdam:Elsevier, 1994.
[11] YAN K, WANG Y, ZHU Y, et al. Investigation on heat dissipation characteristic of ball bearing cage and inside cavity at ultra high rotation speed[J]. Tribology International, 2016, 93:470-481.
[12] YANG Z, YU T, ZHANG Y, et al. Influence of cage clearance on the heating characteristics of high-speed ball bearings[J]. Tribology International, 2017, 105:125-134.
[13] FANG B, ZHANG J, WAN S, et al. Determination of optimum preload considering the skidding and thermal characteristic of high-Speed angular contact ball bearing[J]. Journal of Mechanical Design, 2018, 140(5):053301.
[14] WANG Y, WANG W, ZHAO Z. Effect of race conformities in angular contact ball bearing[J]. Tribology International, 2016, 104:109-120.
[15] SERVAIS C, BOZET J L. New computational method of the ball/race contacts transverse loads of high speed ball bearings without race control hypothesis[J]. Tribology International, 2017, 113:206-215.
[16] WANG Y, WANG W, ZHANG S, et al. Effects of raceway surface roughness in an angular contact ball bearing[J]. Mechanism and Machine Theory, 2018, 121:198-212.
[17] ANTOINE J F,ABBA G,MOLINARI A. A new proposal for explicit angle calculation in angular contact ball bearing[J]. Journal of Mechanical Design, 2006, 128(2):468-478.
[18] TOMOVIĆ R. Calculation of the boundary values of rolling bearing deflection in relation to the number of active rolling elements[J]. Mechanism and Machine Theory, 2012, 47:74-88.
[19] REN X, JIA Z, GE R. Calculation of radial load distribution on ball and roller bearings with positive, negative and zero clearance[J]. International Journal of Mechanical Sciences, 2017, 131:1-7.
[20] ZHANG J, FANG B, HONG J, et al. Effect of preload on ball-raceway contact state and fatigue life of angular contact ball bearing[J]. Tribology International, 2017, 114:365-372.
[21] GARGIULO E P. A simple way to estimate bearing stiffness[J]. Machine Design, 1980, 52(17):107-110.
[22] WARDLE F P, LACEY S J, POON S Y. Dynamic and static characteristics of a wide speed range machine tool spindle[J]. Precision Engineering, 1983, 5(4):175-183.
[23] 方兵,张雷,曲兴田,等. 角接触球轴承刚度理论计算与实验[J]. 吉林大学学报, 2012, 42(4):840-844. FANG Bing,ZHANG Lei,QU Xingtian,et al. Theoretical and experimental research of stiffness of angular contact ball bearing[J]. Journal of Jilin University, 2012, 42(4):840-844.
[24] HERNOT X, SARTOR M, GUILLOT J. Calculation of the stiffness matrix of angular contact ball bearings by using the analytical approach[J]. Journal of Mechanical Design, 2000, 122(1):83-90.
[25] LIM T C, SINGH R. Vibration transmission through rolling element bearings, part I:Bearing stiffness formulation[J]. Journal of Sound and Vibration, 1990, 139(2):179-199.
[26] NOEL D, RITOU M, FURET B, et al. Complete analytical expression of the stiffness matrix of angular contact ball bearings[J]. Journal of Tribology, 2013, 135(4):041101.
[27] SHENG X, LI B, WU Z, et al. Calculation of ball bearing speed-varying stiffness[J]. Mechanism and Machine Theory, 2014, 81:166-180.
[28] ZHANG J, FANG B, HONG J, et al. A general model for preload calculation and stiffness analysis for combined angular contact ball bearings[J]. Journal of Sound and Vibration, 2017, 411:435-449.
[29] FANG B, ZHANG J, YAN K, et al. A comprehensive study on the speed-varying stiffness of ball bearing under different load conditions[J]. Mechanism and Machine Theory, 2019, 136:1-13.
[30] WHILE M F. Rolling element bearing vibration transfer characteristics:effect of stiffness[J]. Journal of Applied Mechanics, 1979, 46(3):677-684.
[31] BOLLINGER J G, GEIGER G. Analysis of the static and dynamic behavior of lathe spindles[J]. International Journal of Machine Tool Design & Research, 1964, 3(4):193-209.
[32] CAO Y, ALTINTAS Y. Modeling of spindle-bearing and machine tool systems for virtual simulation of milling operations[J]. International Journal of Machine Tools & Manufacture, 2007, 47(9):1342-1350.
[33] CAO H, HOLKUP T, ALTINTAS Y. A comparative study on the dynamics of high speed spindles with respect to different preload mechanisms[J]. International Journal of Advanced Manufacturing Technology, 2011, 57(9-12):871-883.
[34] ZHANG J, FANG B, ZHU Y, et al. A comparative study and stiffness analysis of angular contact ball bearings under different preload mechanisms[J]. Mechanism and Machine Theory, 2017, 115:1-17.
[35] OSWALD F B, ZARETSKY E V, POPLAWSKI J V. Effect of internal clearance on load distribution and life of radially loaded ball and roller bearings[J]. Tribology Transactions, 2012, 55(2):245-265.
[36] HAGIU G D, GAFITANU M D. Preload-service life correlation for ball bearings on machine tool main spindles[J]. Wear, 1994, 172(1):79-83.