This paper provides the dynamic model of an angular-contact ball bearing–elastic rotor system to study its dynamic characteristics when an asymmetric support mode is used. After defining global and local coordinate systems, necessary vectors (such as position, velocity, force and moment vector) are calculated according to the geometric relationship between each part (ball, cage and ring) of the bearing. The interactive forces between each part are obtained based on lubrication theory and Hertz contact theory. A typical rotor is discretized by finite element method (FEM) and each node of the rotor has 5 degrees of freedom (DOFs). Some constraint equations are built to form a coupled dynamic model of angular-contact ball bearing–elastic rotor system. The validity of this coupled model is verified by comparing the numerical results and experimental data. After analyzing the coupled model, it is found that the vibration spectrum of rotor includes the VC (varying compliance) frequencies of two bearings, the bending resonance frequency of rotor and the rotating frequency when the system has asymmetric ball bearings. Moreover, when the preloading forces of bearings increase, the support stiffness becomes larger and the rotor displacement decreases; moreover, the motions of balls and cage become more stable. Generally, the presented coupled model can be applied to analyze the vibration features of all parts in any ball bearing–rotor system comprehensively.

本文提供了角接触球轴承-弹性转子系统的动力学模型，以研究其在使用非对称支撑模式时的动力学特性。定义全局和局部坐标系后，根据轴承各部分（球、保持架和套圈）之间的几何关系计算必要的矢量（如位置、速度、力和力矩矢量）。基于润滑理论和赫兹接触理论获得各部分之间的相互作用力。典型的转子通过有限元方法 (FEM) 进行离散化，转子的每个节点都有 5 个自由度 (DOF)。建立了一些约束方程来形成角接触球轴承-弹性转子系统的耦合动力学模型。通过数值结果与实验数据的对比验证了该耦合模型的有效性。通过对耦合模型进行分析，发现转子的振动谱包括两个轴承的VC（变柔量）频率、转子的弯曲共振频率和系统具有非对称滚珠轴承时的旋转频率。此外，当轴承预紧力增加时，支撑刚度变大，转子位移减小；此外，球和笼子的运动变得更加稳定。通常，所提出的耦合模型可用于综合分析任何滚珠轴承-转子系统中所有部件的振动特征。发现转子的振动频谱包括两个轴承的VC（变柔量）频率、转子的弯曲共振频率和系统具有非对称滚珠轴承时的旋转频率。此外，当轴承预紧力增加时，支撑刚度变大，转子位移减小；此外，球和笼子的运动变得更加稳定。通常，所提出的耦合模型可用于综合分析任何球轴承-转子系统中所有部件的振动特征。发现转子的振动频谱包括两个轴承的VC（变柔量）频率、转子的弯曲共振频率和系统具有非对称滚珠轴承时的旋转频率。此外，当轴承预紧力增加时，支撑刚度变大，转子位移减小；此外，球和笼子的运动变得更加稳定。通常，所提出的耦合模型可用于综合分析任何球轴承-转子系统中所有部件的振动特征。球和笼子的运动变得更加稳定。通常，所提出的耦合模型可用于综合分析任何球轴承-转子系统中所有部件的振动特征。球和笼子的运动变得更加稳定。通常，所提出的耦合模型可用于综合分析任何球轴承-转子系统中所有部件的振动特征。