This paper presents a quasi-static model of high-speed ball bearing, and the analytical expressions of dynamic stiffness are obtained. The action mechanism of centrifugal force and gyroscopic moment and its effect on kinematic and mechanical characteristics of bearing are studied. Results show that with the increase in rotational speed, centrifugal force increases continuously, while gyroscopic moment rapidly first and then slightly. With the increase in inertial force, the inner-ring contact angles and the outer-ring contact force increase, the outer-ring contact angles and inner-ring contact force decrease, and bearing stiffness will increase in all directions, while axial load will reduce the effect of inertial force. Radial force will increase the non-uniformity of load distribution, making the difference of load carried by each ball larger, thus aggravating the instability of the system. Compared with gyroscopic moment, centrifugal force is the main factor, while ignoring both inertial forces, rotational speed no longer affects mechanical characteristics of bearings. This study provides theoretical support for the dynamic analysis of high-speed bearing rotor system.

中文翻译：

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基于离心力和陀螺力矩的无故障轴承力学性能研究

提出了一种高速球轴承的准静态模型，并得到了动刚度的解析表达式。研究了离心力和陀螺力矩的作用机理及其对轴承运动学和力学性能的影响。结果表明，随着转速的增加，离心力不断增加，而陀螺力矩先迅速然后略微增加。随着惯性力的增加，内圈接触角和外圈接触力增加，外圈接触角和内圈接触力减小，轴承刚度将在各个方向上增加，而轴向载荷将减小惯性力的作用。径向力会增加载荷分布的不均匀性，从而使每个球承受的载荷之差变大，因此加剧了系统的不稳定性。与陀螺力矩相比，离心力是主要因素，而忽略了惯性力，转速不再影响轴承的机械性能。该研究为高速轴承转子系统的动力学分析提供理论支持。