多自由度球轴承与轴的刚度耦合分析与计算

Stiffness coupling analysis and calculation of multi-degree of freedom ball bearing and shaft

单一条件下球轴承的载荷变形分析结果在理论和实际上存在偏差,同时分析球轴承时未考虑轴的受载变形影响,为此,将球轴承与轴的变形分析相结合,在考虑轴受载变形的轴承轴刚度模型的基础上,提出了一种球轴承轴的刚度计算方法。首先,基于赫兹接触理论以及变形协调与力平衡原则,构建了轴承刚度计算模型;基于欧拉梁模型,构建了轴刚度计算模型;基于材料力学与结构力学理论,构建了轴承轴刚度耦合模型;然后,根据材料力学理论,通过刚度矩阵的耦合,实现了对轴与轴承的耦合分析;最后,将软件计算结果与文献对照数据进行了对比,以验证所提出的计算方法能够对球轴承轴的刚度进行计算。研究结果表明:采用球轴承轴的刚度计算方法得出的最终数据与文献数据的对比结果误差在7%左右,在可接受的误差范围内,验证了所提出的计算方法能够精确、快速地对球轴承轴模型的刚度进行计算;该研究工作可为传动系统的力学分析提供一些理论和计算方面的参考。

The load-deformation analysis results of the ball bearing under a single condition had deviations between theory and practice.At the same time,the load deformation of the shaft was not considered when the ball bearing was analyzed.Therefore,the ball bearing and shaft deformation analysis were combined.Based on the bearing-shaft stiffness model under load deformation,a calculation method for ball bearing-shaft stiffness was proposed.Firstly,based on the Hertzian contact theory and the principle of deformation coordination and force balance,the bearing stiffness calculation model was constructed;based on the Euler beam model,the shaft stiffness calculation model was constructed;based on the material mechanics and structural mechanics theory,the bearing-shaft stiffness coupling model was constructed.Then,according to the theory of material mechanics,the coupling analysis of the shaft and the bearing is realized through the coupling of the stiffness matrix.Finally,the software calculation results were compared with the literature control data to verify that the proposed calculation method can calculate the stiffness of the ball bearing-shaft.The results show that the error of the final data obtained by the calculation method using the stiffness of the ball bearing-shaft and the literature data is about 7%,which is within the acceptable error range.The proposed calculation method can accurately and quickly calculate the stiffness of ball bearing shaft model.The research work provides a theoretical and computational basis for the dynamic analysis of transmission system.