基于响应面的柔轮应力和刚度分析

针对柔轮的小体积、高刚度、高寿命的设计要求，在理论上建立弹性齿圈受力模型，探究设计时结构间的尺寸搭配与补偿方法. 基于响应面法和中心复合设计（CCD）采样方法，在ANSYS Workbench中进行参数化建模和有限元分析，得出应力和刚度对结构参数的响应曲面（线），分析各结构参数对应力和刚度的影响规律. 分析结果表明，在柔轮的小体积设计中，可以减小径向变形量以抵消半径减小时增加的应力，减小壁厚以抵消筒长减小时内壁产生的应力. 柔轮的小体积设计会使承载能力减弱，加剧齿圈后端的应力集中和疲劳破坏. 应在保证啮合状态和承载能力的情况下，增大厚径比，减小径向变形量，以减轻齿圈后端的应力集中现象. 通过响应面法得出关于柔轮应力和刚度的回归曲线，可以用于设计时获取最优值.

Analysis of stress and stiffness of flexspline based on response surface method

The mechanical model of flexspline gear ring was theoretically established aiming at the design demand of flexspline such as small size, high stiffness and long life. The matching and compensating method of dimension was explored in the design. Then the finite element analysis was conducted in ANSYS Workbench by using response surface method and central composite design (CCD) method, and the response surface of stress and stiffness was analyzed. The influence law of each structural parameter on stress and stiffness were obtained. The analysis results show that radial deformation can be reduced to counteract the increased stress when radius decreases, and thickness can be reduced to counteract the generated stress when length decreases in the design of small volume. The small volume design of the flexspline will weaken the bearing capacity and aggravate the phenomenon of stress concentration and fatigue damage at the ring gear. It is necessary to increase the ratio of thickness to diameter or reduce the radial deformation to reduce the phenomenon of stress concentration at the end of the ring gear under the condition of ensuring the meshing state and the bearing capacity. The regression curves of stress and stiffness were obtained, which can be used to obtain optimal value.