多层高速旋转过盈配合圆筒的应力分析及径向尺寸优化设计方法研究

为了完善离心力作用下的多层圆筒过盈配合理论以及得到一定约束条件下较优的过盈配合设计方案，该文首先推导了多层旋转圆筒应力和变形分析解析公式以及多层旋转圆筒过盈配合设计公式，然后基于以上理论，以所定义的旋转圆筒最小安全裕度为适应度函数，采用遗传算法优化名义半径使圆筒的最小安全裕度最大化。根据优化并取整后的名义半径，采用有限元软件(ANSYS Workbench)建立磁悬浮轴承转子三维模型模拟了最大过盈条件下装配过程，并且比较了解析方法与有限元的等效应力结果。研究结果表明:所采用的名义尺寸优化方法提高了旋转圆筒的安全系数，增加了转子的安全性；本文模型中的最外层圆筒内壁为最危险环面，此处有限元方法所得最大等效应力比解析方法结果高18.72%，仅采用解析方法预测结果时应适当提高校核安全系数；所给出的解析方法与数值分析方法所得结果总体结果吻合良好，因此所提解析方法可以用于多层旋转圆筒的过盈配合初步设计、分析以及提供理论指导。

STUDY ON STRESS ANALYSIS METHOD AND RADIAL SIZE OPTIMIZATION DESIGN METHOD FOR MULTI-LAYER HIGH SPEED ROTATING SHRINK-FITTED CYLINDERS

To improve the interference fit theory of multilayer cylinders under the centrifugal force and to obtain a better fit design scheme with the specified constraint conditions, the analytical formulas for stress analysis, deformation analysis and interference fit design were derived for a rotor with multi-layer rotating cylinders. Then, based on the above theory, with the minimum safety margin as a fitness function, the genetic algorithm was applied to optimize the nominal radii of the cylinders to maximize the minimum safety margin. According to the optimized and rounded nominal size, the finite element software (ANSYS Workbench) was used to establish a 3D model for the rotor of magnetic bearing to simulate the interference assembly process under the maximum interference, and the equivalent stress results by the finite element method and the analytical method were compared. The results show that the safety coefficient of rotating cylinders is increased by the proposed optimization method, which improves the security of the rotor. Also, the inner wall of the biggest cylinder in the model is the most dangerous torus, where the maximum equivalent stress by the finite element method is 18.72% higher than that by the analytical method, and the safety coefficient should be increased appropriately if only the analytical method is used for the equivalent stress prediction. Additionally, the analytic results are generally in a good agreement with the numerical results, therefore, the proposed analytical method can be used for the preliminary design or for the analysis on the interference fit of multilayer rotating cylinders so as to provide a theoretical guidance.