齿根过渡曲线优化方法研究

Study of Optimization of the Fillet Curve

对以获得齿根最小弯曲应力为目标的齿根过渡曲线的形状优化问题,提出了一种有效的描述齿根过渡曲线形状的参数化方法,该方法采用双指数"超椭圆"曲线方程来描述齿根过渡曲线。由于设计变量少,可以方便地利用内嵌于一般通用有限元分析软件中的优化设计模块描述和求解过渡曲线的形状。通过有限元分析软件ANSYS建立齿轮模型,并运用其内嵌的一阶优化方法对齿根最大VonMises应力进行优化,与已有的优化结果比较表明,利用文中提出的方法可以取得很好的优化结果。

The goal is to obtain optimal fillet curve for minimum bending stress using parameterized geometry models. The boundary shape for fillet curve is described by generalized elliptic function. Thus it becomes very easy to describe and obtain optimal fillet curve just making use of the optimization module provided in a commercial finite ele- ment package due to the less number of design variables. The gear model is founded by ANSYS, and adopting first step optimization in ANSYS optimize the maximum Von Mises stress of tooth root. As compared to the known solutions in the literature, it was shown that extremely good results could be obtained while using the proposed parmneterized equations.