不同轴承配置下双列角接触球轴承动态特性分析

doi:10.3901/JME.2025.01.220

摘要/Abstract

摘要： 为探究双列角接触球轴承在复杂外载荷工况下的动态特性，基于非线性弹性赫兹接触理论和弹性流体动力润滑理论，建立了五自由度双列角接触球轴承拟静力学数值分析模型，采用改进牛顿拉夫逊交叉迭代算法对其进行求解，该模型综合考虑了离心力、摩擦力、陀螺力矩、轴承间隙、油膜厚度和轴承等因素的影响，最长迭代求解时间不超过2 s。通过对比，背对背配置下位移和刚度最大偏差不超过3.3%，不同配置下轴承对角刚度最大偏差不超过8.6%，验证了模型的有效性。研究结果表明不同轴承配置下内外圈接触角均在方位角180°位置处取得极值，左右侧轴承内外圈接触力随方位角同步变化且存在为接触力为零的现象；与其他轴承配置相比，串联配置轴承刚度随轴向力增加而增加，随径向力和力矩增加处于较低水平，随转速增加出现明显弱化现象，其径向和转矩承载能力不足且不适合高转速工况；面对面配置轴承角刚度随外随外载荷增加处于较低水平，其转矩承载能力不足。

关键词: 双列角接触球轴承, 轴承配置, 接触角, 接触力, 轴承刚度

Abstract: In order to investigate the dynamic characteristics of double row angular contact ball bearings under complex external load conditions, a 5-DOF pseudo-static numerical analysis modelling of double row angular contact ball bearings is established based on the nonlinear elastic Hertzian contact theory and elastic hydrodynamic lubrication theory, the improved Newton-Raphson cross iterative algorithm is used to solve the above numerical analysis modelling. The proposed modelling takes into account the influences of centrifugal force, friction force, gyro moment, bearing clearance, oil film thickness and bearing configuration comprehensively, the longest iteration solution time is less than 2 s. By comparison, the maximum deviation of displacement and stiffness under back-to-back configuration is no more than 3.3% and the maximum deviation of diagonal stiffness under different configurations is no more than 8.6%, which verify the validity of the presented modelling. The research results show that under different bearing configuration, the contact angles of inside and outside ring have extremum at 180°position azimuth, the contact forces of inner and outer ring are the same and exist a phenomenon that the contact forces are zero; Compared with other bearing configurations, the bearing stiffness with tandem con-figuration increases with axial force increased, is at lower level with radial force and torque increased and weakens significantly with speed increased, it can conclude that the capacity of radial and torque of bearing with series configuration is insufficient and not suitable for high speed working conditions; The angular stiffness of bearing with face to face configuration is at a low level with external load increased, it can conclude that the capacity of torque is insufficient.

Key words: double row angular contact ball bearing, bearing configuration, contact angle, contact force, bearing stiffness

中图分类号:

TH133

李震, 王青山, 王瑞华, 秦斌. 不同轴承配置下双列角接触球轴承动态特性分析[J]. 机械工程学报, 2025, 61(1): 220-231.

LI Zhen, WANG Qingshan, WANG Ruihua, QIN Bin. Dynamic Characteristics Analysis of Double Row Angular Contact Ball Bearings with Different Bearing Configurations[J]. Journal of Mechanical Engineering, 2025, 61(1): 220-231.

参考文献

[1] 郝大庆，李鸿亮，郑艳伟，等. 航空飞行器用超高速角接触球轴承的研制与试验验证[J]. 轴承，2022(6)：38-42. HAO Daqing，LI Hongliang，ZHENG Yanwei，et al. Development and test verification of ultra-high speed angular contact ball bearings for aircraft[J]. Bearing，2022(6)：38-42.
[2] 张阗，李雪飞，王玉国，等. 机床主轴用双列圆柱滚子轴承CAD/CAPP软件的开发[J]. 轴承，2023(12)：32-38. ZHANG Tian，LI Xuefei，WANG Yuguo，et al. Development of CAD/CAPP software for double-row cylindrical roller bearings for machine tool spindle[J]. Bearing，2023(12)：32-38.
[3] 高鹏飞. 铁路双列圆锥滚子轴承温度特性的理论与试验研究[D]. 大连：大连交通大学，2023. GAO Pengfei. Theoretical and experimental study on temperature characteristics of railway double row tapered roller bearings [D]. Dalian：Dalian Jiaotong University，2023.
[4] GUNDUZ A，SINGH R. Stiffness matrix formulation for double row angular contact ball bearings: Analytical development and validation[J]. Journal of Sound and Vibration，2013，332(22)：5898-5916.
[5] GUNDUZ A，JASON T，DREYER R S. Effect of bearing preloads on the modal characteristics of a shaft-bearing assembly: Experiments on double row angular contact ball bearings[J]. Mechanical Systems and Signal Processing，2012，31(3)：176-195.
[6] VIVEK P，HUZUR S V，HARSHA S P. Effect of an unbalanced rotor on dynamic characteristics of double- row self-aligning ball bearing[J]. European Journal of Mechanics / A Solids，2020，82(1)：104006.
[7] LIN S L，SUN J L，MA C，et al. A novel dynamic modeling method of defective four-row roller bearings considering the spatial contact correlation be-tween the roller and defect zone[J]. Mechanism and Machine Theory，2023，180(2)：105138.
[8] YANG L H，XU T F，XU H L，et al. Mechanical behavior of double-row tapered roller bearing under combined external loads and angular misalignment[J]. International Journal of Mechanical Sciences，2018，142(1)：561-574.
[9] XU T F，YANG L H，WU W，et al. The stiffness characteristics analysis of the duplex angular contact ball bearings based on a comprehensive multi-degree-of- freedom mathematical model[J]. Applied Mathematical Modelling，2022，106(2)：601-626.
[10] AI S Y，WANG W Z，WANG Y L，et al. Temperature rise of double-row tapered roller bearings analyzed with the thermal network method[J]. Tribology International，2015，87(2)：11-22.
[11] VIEK P，V HUZUR S，SP H. Effect of dynamic misalignment on the vibration response, trajectory followed and defect-depth achieved by the rolling- elements in a double-row spherical rolling-element bearing[J]. Mechanism and Machine Theory，2021，162(2)：104366.
[12] ZHUO Y B，ZHOU X J，YANG C L. Dynamic analysis of double-row self-aligning ball bearings due to applied loads, internal clearance, surface waviness and number of balls[J]. Journal of Sound and Vibration，2014，333(3)：6170-6189.
[13] 邓四二，董晓，崔永存，等. 双列角接触球轴承动刚度特性分析[J]. 兵工学报，2015，36(6)：1140-1146. DENG Sier，DONG Xiao，CUI Yongcun，et al. Analysis of dynamic stiffness characteristics of double row angular contact ball bearings[J]. Journal of China Ordnance, 2015, 36(6)：1140-1146.
[14] 邓四二，胡广存，董晓. 双列圆锥滚子轴承功耗特性研究[J]. 兵工学报，2014，35(11)：1898-1907. DENG Sier，HU Guangcun，DONG Xiao. Study on power consumption characteristics of double row tapered roller bearings[J]. Journal of China Ordnance，2014，35(11)：1898-1907.
[15] 邓四二，盛明杰，邓凯文. 双列调心滚子轴承摩擦力矩的特性[J]. 航空动力学报，2017，32(7)：1666-1675. DENG Sier，SHENG Mingjie，DENG Kaiwen. Friction torque characteristics of double row aligning roller bearings[J]. Journal of Aerospace Power，2017，32(7)：1666-1675.
[16] 程超，汪久根. 双列角接触球轴承的载荷分析[J]. 机械科学与技术，2014，33(6)：829-833. CHENG Chao, WANG Jiugen. Load analysis of double row angular contact ball bearings[J]. Mechanical Sci-ence and Technology，2014，33(6)：829-833.
[17] 程超，汪久根. 基于遗传算法的双列角接触球轴承优化设计[J]. 机械设计，2015，32(2)：46-50. CHENG Chao，WANG Jiugen. Optimal design of double row angular contact ball Bearing based on genetic algorithm[J]. Machine Design，2015，32(2)：46-50.
[18] 胡浪，王文中，赵自强. 双列圆锥滚子轴承滚子大端-引导边润滑接触分析[J]. 摩擦学学报，2013，33(1)：22-28. HU Lang, WANG Wenzhong, ZHAO Ziqiang. Lubrication contact analysis of roller large end-guide edge in double row tapered roller bearing[J]. Journal of Tribology，2013，33(1)：22-28.
[19] 刘悦阳，杨海生，苏冰，等. 航空发动机双列角接触球轴承摩擦功耗仿真分析[J]. 机械传动，2021，45(2)：129-135. LIU Yueyang，YANG Haisheng，SU Bing，et al. Simulation analysis of friction power consumption of aero-engine double row angular contact ball bearings[J]. Mechanical Transportation，2021，45(2)：129-135.
[20] 吉博文，景敏卿，刘恒，等. 双列角接触球轴承疲劳寿命分析与研究[J]. 机械设计与制造，2014，10(1)：26-28+31. JI Bowen，JING Minqing，LIU Heng，et al. Fatigue life analysis and research of double row angular contact ball bearings[J]. Machinery Design and Manufacture，2014，10(1)：26-31.
[21] 唐云冰，高德平，罗贵火. 航空发动机滚动轴承的载荷分布研究[J]. 航空学报，2006，27(6)：1117-1121. TANG Yunbing，GAO Deping，LUO Guihuo. Study on load distribution of aeroengine rolling bearings[J]. Chinese Journal of Aeronautics，2006，27(6)：1117-1121.
[22] 王黎钦，崔立，郑德志. 航空发动机高速球轴承动态特性分析[J]. 航空学报，2007，28(6)：1461-1467. WANG Liqin，CUI Li，ZHENG Dezhi. Dynamic characteristics analysis of aeroengine high speed ball bear-ing[J]. Chinese Journal of Aeronautics，2007，28(6)：1461-1467.
[23] 崔立，王黎钦，郑德志. 航空发动机高速滚子轴承动态特性分析[J]. 航空学报，2008，27(2)：492-498. CUI Li，WANG Liqin，ZHENG Dezhi. Dynamic characteristics analysis of aeroengine high speed roller bearings[J]. Chinese Journal of Aeronautics，2008，27(2)：492-498.
[24] 张涛，陈晓阳，顾家铭. 高速角接触球轴承保持架稳定性研究进展[J]. 航空学报，2018，39(7)：32-44. ZHANG Tao，CHEN Xiaoyang，GU Jiaming. Research progress on cage stability of high speed angular contact ball bearings[J]. Chinese Journal of Aeronautics，2018，39(7)：32-44.
[25] JANG G H，JEONG S W. Vibration analysis of a rotating system due to the effect of ball bearing waviness[J]. Journal of Sound and Vibration，2004，269(3)：709-726.
[26] HAN Q K，YANG L H，WU W. Nonlinear dynamic model for skidding behavior of angular contact ball bearings[J]. Journal of Sound and Vibration，2015，354：219-235.
[27] 李震，关先磊，钟锐，等. 联合载荷下角接触球轴承的动态特性分析[J]. 机械工程学报，2020，56(17)：116-125. LI Zhen，GUAN Xianlei，ZHONG Rui，et al. Dynamic characteristics analysis of angular contact ball bearing under combined loads[J]. Chinese Journal of Journal of Mechanical Engineering，2020，56(17)：116-125.
[28] LI Z，WANG Q S，QIN B. Vibration characteristic analysis of flexible rotor-bearing system subjected to external combined loads[J]. European Journal of Mechanics/ A Solids，2022，96(3)：104688.
[29] TONG Z C，HONG S W. Analysis of the stiffness and fatigue life of double-row angular contact ball bearings[J]. Chinese Journal of Mechanical Engineering，2017，34(1)：813-821.