Abstract: In order to overcome the difficulties in predicting and controlling the rotation accuracy of the four-point contact ball bearings for robots, a numerical method for calculating the rotation errors of the bearings was proposed considering the roundness errors of inner and outer raceways. Firstly, according to the kinematics and geometry relationship of the internal components of the bearings, a numerical calculation model of the rotation errors of the bearings was established. Then, the program for calculating the rotation errors of the bearings was written using MATLAB. the effects of the magnitude and order of the roundness errors of the outer raceway, the magnitude and order of the roundness errors of the inner raceway, the diameter deviation and the number of the steel balls on the rotation accuracy of the bearings were obtained. Finally, experiments on rotation accuracy of the bearings were carried out to verify the correctness of the simulation results. The rotation accuracy of the bearings involves many indicators. The rotation accuracy of four-point contact ball bearings studied herein refers to the radial runout of outer ring of the bearings. The results show that the radial runout of outer ring of the bearings increases smoothly first and then rapidly with the increase of the magnitude of the roundness errors of the inner and outer raceways, changes periodically with the increase of the order of the roundness errors of the inner and outer raceways, decreases linearly with the increase of the diameter deviations of the steel balls and decreases exponentially with the increase of the number of the steel balls. The problem in getting the rotation accuracy of the four-point contact ball bearings theoretically is solved with the model. The rotation accuracy of the bearings may be predicted accurately and a theoretical basis may be provided for the accuracy design of the four-point contact ball bearings.

Key words: four-point contact ball bearing, rotation accuracy, radial runout of outer ring, roundness error

摘要： 针对机器人用四点接触球轴承旋转精度难以预测和控制的问题，提出了同时考虑轴承内圈沟道和外圈沟道圆度误差的轴承旋转精度数值计算方法。根据轴承内部元件运动学和几何学关系建立轴承旋转精度数值计算模型。使用MATLAB编写轴承旋转精度求解程序，得到内圈沟道圆度误差幅值和谐波阶次、外圈沟道圆度误差幅值和谐波阶次、钢球直径偏差及钢球个数对轴承旋转精度的影响规律。进行了轴承旋转精度试验，验证了仿真结果的正确性。轴承旋转精度涉及很多指标，所研究的四点接触球轴承旋转精度衡量指标指轴承外圈径向跳动。结果表明：轴承外圈径向跳动随着内外沟道圆度误差幅值的增大先平稳后快速增大，随着内圈外沟道圆度误差谐波阶次的增大呈现周期性变化，随着钢球直径偏差的增大呈线性减小，随着轴承内部钢球个数的增大呈指数减小。所建模型解决了四点接触球轴承旋转精度难以进行理论求解的问题，能够准确预测轴承的旋转精度，为四点接触球轴承的精度设计提供了理论基础。

关键词: 四点接触球轴承, 旋转精度, 外圈径向跳动, 圆度误差