Frictional characteristics induced by ring deformation of thin-wall angular contact ball bearing
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摘要:
针对薄壁轴承在制造、安装过程中套圈变形引起的轴承摩擦力矩变化机理不明的问题,基于滚动轴承动力学理论,构建了计入套圈变形时变表征的薄壁角接触球轴承动力学分析模型与摩擦力矩数学模型,研究了套圈沟曲率半径、变形相位角、半幅值及工况条件对轴承摩擦特性的影响规律。结果表明:沟曲率半径系数对轴承摩擦力矩的影响随转速临界值变化而发生改变,该转速值在计入套圈变形时较理想套圈会出现超前或滞后。优化配置套圈变形相位角可降低变形对摩擦力矩的作用。载荷比会影响形成轴承摩擦力矩最小的套圈变形相位角,其对套圈两瓣波相位角变化的影响小于三瓣波变形。合理控制套圈变形半振幅可降低对轴承摩擦力矩波动性的影响。
Abstract:Targeting the unclear mechanism of the frictional torque variation induced by the ring deformation in the process of manufacturing and installation of the thin-wall angular contact ball bearings, based on the dynamic theory of rolling bearing, the dynamic analysis model and friction torque mathematical model of thin-wall angular contact ball bearing were established considering the time-varying representation of the ring deformation, and the effects of the ring groove curvature radius, the deformation phase angle, the half amplitude, and the working conditions on the frictional characteristics were studied. The results indicated that: the influence of the groove radius of curvature coefficient on the frictional torque changed at different speed critical values, which preacted or lagged compared with the ideal ring when considering the ring deformation. Optimal configuration of deformation phase angle of the ring can reduce the effect of the deformation on the frictional torque. The load ratio affected the deformation phase angle of the ring forming the minimum frictional torque, whose effect on the phase angle of two-lobe wave was less than that of three-lobe wave deformation. A reasonable control of half amplitude of ring deformation can reduce the influence of frictional torque fluctuation.
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表 1 薄壁角接触球轴承尺寸参数
Table 1. Dimensional parameters of thin-wall angular contact ball bearing
参数 数值 内径/mm 212.0 外径/mm 248.0 初始接触角/(°) 40.0 钢球直径/mm 16.333 钢球个数/mm 36 保持架外径/mm 236.0 保持架内径/mm 218.0 -
[1] PATALAS A,REGUS M,PETA K. Studies of thin-walled parts deformation by gripping force during turning process on an example of bearing ring[J]. MATEC Web of Conferences,2018,244: 02010.1-02010.6. [2] PALMGREN A. Ball and roller bearing engineering[M]. Philadelphia, US: Burbank, 1959. [3] 邓四二,李兴林,汪久根,等. 角接触球轴承摩擦力矩波动性分析[J]. 机械工程学报,2011,47(23): 104-112. doi: 10.3901/JME.2011.23.104DENG Sier,LI Xinglin,WANG Jiugen,et al. Analysis on the friction torque fluctuation of angular contact ball bearings[J]. Journal of Mechanical Engineering,2011,47(23): 104-112. (in Chinese) doi: 10.3901/JME.2011.23.104 [4] 邓四二,李兴林,汪久根,等. 角接触球轴承摩擦力矩特性研究[J]. 机械工程学报,2011,47(5): 114-120. doi: 10.3901/JME.2011.05.114DENG Sier,LI Xinglin,WANG Jiugen,et al. Frictional torque characteristic of angular contact ball bearings[J]. Journal of Mechanical Engineering,2011,47(5): 114-120. (in Chinese) doi: 10.3901/JME.2011.05.114 [5] WANG Baomin,GAO Chao,WU Zaixin,et al. Prediction of the friction torque in grease lubricated angular contact ball bearings using grey system theory[J]. Journal of Mechanical Science and Technology,2016,30(5): 2195-2201. doi: 10.1007/s12206-016-0427-8 [6] TONG V C,HONG S W. Study on the running torque of angular contact ball bearings subjected to angular misalignment[J]. Journal of Engineering Tribology,2018,232(7): 890-909. [7] TONG V C,HONG S W. Improved formulation for running torque in angular contact ball bearings[J]. International Journal of Precision Engineering and Manufacturing,2018,19(1): 47-56. doi: 10.1007/s12541-018-0006-2 [8] LIU Jing,LI Xinbin,DING Shizhao,et al. A time-varying friction moment calculation method of an angular contact ball bearing with the waviness error[J]. Mechanism and Machine Theory,2020,148(1): 1-23. [9] ZHANG Xi,XU Hua,CHANG Wei,et al. Torque variations of ball bearings based on dynamic model with geometrical imperfections and operating conditions[J]. Tribology International,2019,133: 193-205. doi: 10.1016/j.triboint.2019.01.002 [10] POPESCU A,HOUPERT L,OLARU D N. Four approaches for calculating power losses in an angular contact ball bearing[J]. Mechanism and Machine Theory,2019,144: 1-20. [11] POPESCU A,OLARU D N. Influence of lubricant on the friction in an angular contact ball bearing under low load conditions[J]. Materials Science and Engineering,2020,724: 012040.1-012040.8. [12] OSTAPSKI W,MUKHA I. Stress state analysis of harmonic drive elements by FEM[J]. Bulletin of the Polish Academy of Sciences, Technical Sciences,2007,55(1): 115-123. [13] 蔡素然,陈原,叶军,等. 工业机器人专用薄壁密封轴承结构设计分析[J]. 轴承,2007(12): 10-13. doi: 10.3969/j.issn.1000-3762.2007.12.003CAI Suran,CHEN Yuan,YE Jun,et al. Thin-walled and sealed bearing used in industrial robot[J]. Bearing,2007(12): 10-13. (in Chinese) doi: 10.3969/j.issn.1000-3762.2007.12.003 [14] 赵滨海,刘正士,宋春磊,等. 谐波传动薄壁柔性轴承力学分析[J]. 轴承,2002(10): 1-3. doi: 10.3969/j.issn.1000-3762.2002.10.001ZHAO Binhai,LIU Zhengshi,SONG Chunlei,et al. Mechanics analysis on flexible thin wall bearing in harmonic transmission[J]. Bearing,2002(10): 1-3. (in Chinese) doi: 10.3969/j.issn.1000-3762.2002.10.001 [15] LEBLANC A,NELIAS D,DEFAYE C. Nonlinear dynamic analysis of cylindrical roller bearing with flexible rings[J]. Journal of Sound and Vibration,2009,325(1): 145-160. [16] 倪艳光,刘万强,邓四二,等. 计及套圈变形的薄壁角接触球轴承性能分析[J]. 航空动力学报,2010,25(6): 1432-1436.NI Yanguang,LIU Wanqiang,DENG Sier,et al. Performance analysis of thin-wall angular contact ball bearings considering the ferrule deformation[J]. Journal of Aerospace Power,2010,25(6): 1432-1436. (in Chinese) [17] 倪艳光,刘玉,焦育杰,等. 薄壁深沟球轴承负荷分析及寿命研究[J]. 机械传动,2012,36(6): 1-4. doi: 10.3969/j.issn.1004-2539.2012.06.001NI Yanguang,LIU Yu,JIAO Yujie,et al. The research on the load distribution and life in thin-wall deep groove ball bearing[J]. Journal of Mechanical Transmission,2012,36(6): 1-4. (in Chinese) doi: 10.3969/j.issn.1004-2539.2012.06.001 [18] POTOCNIK R,GÖNCZ P,GLODEZ S. Static capacity of a large double row slewing ball bearing with predefined irregular geometry[J]. Mechanism and Machine Theory,2013,64: 67-79. doi: 10.1016/j.mechmachtheory.2013.01.010 [19] 郑昊天,邱明,王东峰,等. 机器人用薄壁角接触球轴承振动特性的试验研究[J]. 轴承,2015(12): 42-45. doi: 10.3969/j.issn.1000-3762.2015.12.012ZHENG Haotian,QIU Ming,WANG Dongfeng,et al. Experimental study on vibration characteristics of thin-walled angular contact ball bearings in Robots[J]. Bearing,2015(12): 42-45. (in Chinese) doi: 10.3969/j.issn.1000-3762.2015.12.012 [20] 张阳阳,邱明,王东峰,等. 基于有限元法的薄壁角接触球轴承接触特性分析[J]. 轴承,2016(9): 21-24. doi: 10.3969/j.issn.1000-3762.2016.09.005ZHANG Yangyang,QIU Ming,WANG Dongfeng,et al. Analysis on contact characteristics of thin-walled angular contact ball bearings based on finite element method[J]. Bearing,2016(9): 21-24. (in Chinese) doi: 10.3969/j.issn.1000-3762.2016.09.005 [21] 邱明,郑昊天,陈龙,等. 机器人用薄壁角接触球轴承动态特性分析[J]. 机械设计与制造,2017(9): 250-253. doi: 10.3969/j.issn.1001-3997.2017.09.066QIU Ming,ZHENG Haotian,CHEN Long,et al. Analysis on dynamic characteristics of thin-section angular contact ball bearings for robots[J]. Machinery Design and Manufacture,2017(9): 250-253. (in Chinese) doi: 10.3969/j.issn.1001-3997.2017.09.066 [22] 姜祎,王亚珍,赵坤,等. 谐波减速器柔性薄壁轴承的力学特性分析[J]. 轴承,2017(1): 10-14.JIANG Yi,WANG Yazhen,ZHAO Kun,et al. Mechanical property analysis of flexible thin bearing in harmonic drive[J]. Bearing,2017(1): 10-14. (in Chinese) [23] 林武文,李振,王娇娇,等. 薄壁轴承性能测试平台设计与实现[J]. 润滑与密封,2017,42(11): 100-105. doi: 10.3969/j.issn.0254-0150.2017.11.019LIN Wuwen,LI Zhen,WANG Jiaojiao,et al. Design and implementation of performance testing rig for thin-wall bearing[J]. Lubrication Engineering,2017,42(11): 100-105. (in Chinese) doi: 10.3969/j.issn.0254-0150.2017.11.019 [24] 王亚珍,汪安明,赵坤,等. 基于薄壁圆环理论的机器人用柔性轴承变形特征快速求解[J]. 农业工程学报,2019,35(3): 60-66. doi: 10.11975/j.issn.1002-6819.2019.03.008WANG Yazhen,WANG Anming,ZHAO Kun,et al. Fast solution for deformation characteristics of flexible bearing of robot based on thin-walled ring theory[J]. Transactions of the Chinese Society of Agricultural Engineering,2019,35(3): 60-66. (in Chinese) doi: 10.11975/j.issn.1002-6819.2019.03.008 [25] 赵斗生,王亚珍,赵坤. 基于动力学的柔性轴承疲劳寿命仿真分析[J]. 轴承,2019(7): 20-23. doi: 10.19533/j.issn1000-3762.2019.07.005ZHAO Dousheng,WANG Yazhen,ZHAO Kun. Simulation analysis on fatigue life of flexible bearings based on dynamics[J]. Bearing,2019(7): 20-23. (in Chinese) doi: 10.19533/j.issn1000-3762.2019.07.005 [26] MENG Dezhang,WANG Yanjun,GAO Pengyuan,et al. Thin-wall bearing contact characteristics analysis and deformation research[J]. Earth and Environmental Science,2020,558(2): 022028.1-022028.8.