1.School of Mechatronic Engineering and Automation,Shanghai University, Shanghai 200072,China;
2.Shanghai Tian An Bearing Co.,Ltd., Shanghai 201108,China;
3.Bearing R & D Center of Shanghai Prime Machinery Co.,Ltd., Shanghai 201108,China
A dynamic wear simulation model for angular contact ball bearings with six-degree-of-freedom ball and cage was established.Taking a certain instrument rotor ball bearing as an example, the cage motion under different load conditions and cage clearance ratios was analyzed.The mechanism of the cage unstable motion was discussed from the aspects of the ball-pocket collision, and the magnitude and frequency of the impact force.It is found that under the pure axial load, the cage will swing along the axial direction due to the ball-pocket collision at different positions.Under the joint of axial and radial loads, the orbital velocity of the ball varies with the contact angle, and the collision force and frequency of the ball and cage increase, resulting in the unstable motion of the cage.Under the axial and rotating radial load, when the ratio of the ball-pocket clearance to the cage-guide land clearance B/R is less than 1, the orbit of the cage mass center whirl is close to a circle.The centrifugal force of the cage acts on the ball, resulting in an increase in the ball-pocket collision.When the clearance ratio is greater than 1, the centroid trajectory of the cage is polygonal or irregular, and the constraint of the guide land on the cage reduces the interaction between the ball and cage, so the wear rate of the cage is lower.The circular centroid trajectory is a state of stable motion of the cage, but from the perspective of cage wear and energy loss, it is unfavorable for the wear life of the cage.
[1] 刘春浩, 顾家铭, 周赤忠, 等. 陀螺仪电动机转子轴承研究现状与展望[J]. 机械工程学报, 2006, 42(11)：17-25.
LIU Chunhao, GU Jiaming, ZHOU Chizhong, et al. Research of present state and prospective on gyro-spin bearings[J]. Journal of Mechanical Engineering, 2006, 42(11)：17-25.
[2] WALTERS C T. The dynamics of ball bearings[J]. Journal of Lubrication Technology, 1971, 93：1-10.
[3] KANNEL J W, BUPARA S S. A simplified model of cage motion in angular contact bearings operating in the EHD lubrication regime[J]. Journal of Lubrication Technology, 1978, 100：395-403.
[4] GUPTA P K. Dynamic of rolling-element bearings-Part 3, 4[J]. Journal of Lubrication Technology, 1979, 101：312-326.
[5] MEEKS C R, NG K O. The dynamics of ball separators in ball bearings-Part 1, 2[J]. ASLE Transaction, 1985, 28(3)：277-295.
[6] GUPTA P K, DILL J F, Bandow H E. Dynamics of rolling element bearings experimental validation of the DREB and RAPIDREB computer programs[J]. Journal of Tribology, 1985, 107：132-137.
[7] GUPTA P K. Frictional instabilities in ball bearings[J]. Tribology Transctions, 1988, 31(2) ：258-268.
[8] GUPTA P K. Dynamic loads and cage wear in high-speed rolling bearings[J].Wear, 1991, 147：119-134.
[9] GUPTA P K. Modeling of instabilities induced by cage clearances in ball bearings[J]. Tribology Transaction, 1991, 34(1)：93-99.
[10] GUPTA P K. Cage Unbalance and Wear in Ball Bearings [J].Wear, 1991, 147：93-104.
[11] ASHTEKAR A, SADEGHI F, STACKE L E. A new approach to modeling surface defects in bearing dynamic simulations[J]. Journal of Tribology, 2008, 130：041103-1-8.
[12] WEINZAPFEL N, SADEGHI F. A discrete element approach for modeling cage flexibility in ball bearing dynamic simulations[J]. Journal of Tribology, 2009, 131：021102-1-11.
[13] GUPTA P K. Current status of and future innovations in rolling bearing modeling[J]. Tribology Transactions, 2011, 54：394-403.
[14] LIU Xiuhai, DENG Sier, TENG Hongfei. Dynamic stability analysis of cage in high-speed oil-lubricated angular contact ball bearings[J]. Transactions of Tianjin University, 2011, 17(1)：20-27.
[15] YE Zhenhuan, WANG Liqin. Cage instabilities in high-speed ball bearings[J]. Applied Mechanics and Materials, 2013, 278：3-6.
[16] 邓四二, 谢鹏飞, 杨海生, 等. 高速角接触球轴承保持架柔体动力学分析[J]. 兵工学报, 2011, 32(5)：625-631.
DENG Sier, XIE Pengfei, YANG Haisheng, et al. Flexible-body dynamic analysis on cage of high-speed angular contact ball bearing[J]. Acta Armamentarii, 2011, 32(5)：625-631.
[17] 崔立, 时大方, 郑建荣, 等. 基于ANSYS/LS-DYNA的保持架动力学分析[J]. 机械传动, 2012, 36(6)：78-81.
CUI Li, SHI Dafang, ZHENG Jianrong, et al. Dynamic analysis of cage based on ANSYS/LS-DYNA[J]. Journal of Mechanical Transmission, 2012, 36(6)：78-81.
[18] 姚廷强, 王立华, 刘孝保,等. 变工况下角接触球轴承保持架稳定性分析[J]. 振动与冲击, 2016, 35(18): 172-180.
YAO Tingqiang, WANG Lihua, LIU Xiaobao, et al. Dynamic stability analysis on the of ball bearing under varying working environment[J]. Journal of Vibration and Shock, 2016, 35(18): 172-180.
[19] KINGSBURY E P. Torque variations in instrument ball bearings[J]. ASLE Transactions. 1965, 8：435-441.
[20] KINGSBURY E P, WALKER R. Motions of an unstable retainer in an instrument ball bearing[J]. Journal of Tribology. 1994, 116：202-208.
[21] GUPTA P K. Advanced dynamic of rolling elements, New York：Springer-Verlag, 1984.
[22] ZHANG Tao, CHEN Xiaoyang, GU Jiaming et al. Influence of preload on the friction and wear properties of high-speed instrument angular contact ball bearings[J]. Chinese Journal of Aeronautics, 2017.
[23] GUPTA P K, FORSTER N H. Modeling of wear in a solid-lubricated ball bearing[J]. Tribology Transactions, 1987, 30(1)：55-62.
[23] HOUPERT L. Ball bearing and tapered roller bearing torque: analytical, numerical and experimental results[J]. Tribology Transactions, 2002, 45(3)：345-353.
[25] TALLIAN T E. Rolling bearing life prediction: Corrections for material and operating conditions-Part 2: The correction factors[J]. Journal of Tribology, 1988, 110：7-12.
