The dynamic characteristics of thin-walled four-point contact ball bearing with crown-type cage are important to the dynamic performance and motion accuracy of an industrial robot. Considering multi-clearances, dynamic contact and impact relationships of the ball, ring raceway and crown-type cage, a general methodology for dynamic simulation analysis of the bearing is investigated in the proposed work. In accordance with the geometry of torus, the geometric equation of accurate ring raceway is derived and integrated into the three-dimensional ring raceway using user’s subroutines. The parameterized and assembled three-dimensional model of the bearing is established using ADAMS’s macro-programs. Applying a penalty formulation and a unilateral nonlinear spring–damper model to the bearing, the internal contact interaction is represented as the compliant contact force model using IMPACT function. The multibody contact dynamic models of the bearing are solved by HHT algorithm with ADAMS/Solver. The dynamic results of the contact force, impact force and motion stability of the bearing are discussed under the condition of different loads. The static load distribution and cage’s angular velocity of simulation model are verified by the theoretical values. The motion trajectory of outer ring’s center is circular with a whirling motion. The sphere-to-partial torus surface contacts (ball–racetrack contact) are always four contact points in the load zone of the bearing. Applying pure radial load or rotating radial load, the impact force of ball-to-cage small pocket contact is much larger than that of radial and axial load combination in the non-load zone of the bearing. As a result of the large impact force of ball-to-cage small pocket contact, the angular velocities of the ball and cage are varying greatly in the non-load zone. The impact force of ball-to-cage big pocket contact is very small. The angular velocity of the ball is always that of pure rolling in the load zone and varying slightly in the non-load zone. The new method can be applied to investigate dynamic analysis and design of high-precision industrial robots with multi-clearances, multi-ball bearings under complex, time-varying working conditions.

中文翻译：

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球，环滚道和冠型保持架相互作用的薄壁四点接触球轴承的多体动力学模拟

带冠型保持架的薄壁四点接触球轴承的动态特性对于工业机器人的动态性能和运动精度至关重要。考虑到球，环滚道和冠形保持架的多个间隙，动态接触和冲击关系，在本文中研究了一种用于轴承动态仿真分析的通用方法。根据圆环的几何形状，得出精确的环形滚道的几何方程，并使用用户的子程序将其集成到三维环形滚道中。使用ADAMS的宏程序可以建立轴承的参数化和装配三维模型。将惩罚公式和单边非线性弹簧-阻尼器模型应用于轴承，内部接触相互作用使用IMPACT功能表示为顺应接触力模型。通过ADAMS / Solver的HHT算法求解轴承的多体接触动力学模型。讨论了在不同载荷条件下轴承的接触力，冲击力和运动稳定性的动力学结果。理论值验证了仿真模型的静载荷分布和保持架的角速度。外圈中心的运动轨迹是带有回旋运动的圆形。球面到局部圆环的表面接触（滚珠与跑道的接触）始终是轴承负载区域中的四个接触点。施加纯径向载荷或旋转径向载荷，球笼式小腔接触的冲击力远大于轴承非载荷区域的径向和轴向载荷组合的冲击力。由于球与保持架之间的小口袋接触具有较大的冲击力，因此在非负载区域，球与保持架的角速度会发生很大变化。球笼式大口袋接触的冲击力很小。球的角速度始终是在负载区域中纯滚动的角速度，而在非负载区域中则略有变化。该新方法可用于研究复杂，时变工作条件下具有多个间隙，多个滚珠轴承的高精度工业机器人的动力学分析和设计。球和保持架的角速度在非负载区变化很大。球笼式大口袋接触的冲击力很小。球的角速度始终是在负载区域中纯滚动的角速度，而在非负载区域中则略有变化。该新方法可用于研究复杂，时变工作条件下具有多个间隙，多个滚珠轴承的高精度工业机器人的动力学分析和设计。球和保持架的角速度在非负载区变化很大。球笼式大口袋接触的冲击力很小。球的角速度始终是在负载区域中纯滚动的角速度，而在非负载区域中则略有变化。该新方法可用于研究复杂，时变工作条件下具有多个间隙，多个滚珠轴承的高精度工业机器人的动力学分析和设计。