环面渐开线齿轮的动态接触分析

Dynamic Contact Analysis of Torus-involute Gear

以环面渐开线齿轮为研究对象,根据齿轮啮合原理及滚齿加工原理,利用产形齿条的齿面方程,分别推导出凸、凹环面渐开线齿轮齿面方程。根据不产生尖化或根切的数学条件,基于MATLAB开发了环面渐开线齿轮几何参数设计的Graphical User Interface。以环面渐开线齿轮齿面上点的三维坐标构建三维实体模型,并将实体模型导入Hypermesh中划分网格。基于非线性接触算法,建立凸—凹环面渐开线齿轮啮合的有限元模型,在ABAQUS中对其进行动态接触分析,结果表明环面渐开线齿轮齿宽受根切及尖化的限制,而在齿面接触应力方面,双齿啮合区齿面接触应力较小,单齿啮合区齿面接触应力较大。

Taking the toms -involute gear as study object, according to the theory of gear meshing and the gear bobbing process, the tooth surface equations of toms - involute gears with convex and concave teeth are derived by using the tooth surface equation of counterpart rack. According to the mathematical conditions of nei- ther undercutting nor tooth pointing, based on MATLAB, the Graphical User Interface which contains geometric parameter designs of torus - involute gear is developed. In the light of the tooth surface equations of toms - in- volute gear, the three - dimensional coordinates of torus - involute gear are calculated which can be used to de- velop the3 - D solid models. The Hypermesh is used to mesh the 3 - D models of toms - involute gear. Based on the nonlinear contact algorithm, the finite element models of convex and concave toms - involute gears mes- hing are established which can be used to implement the dynamic contact analysis in ABAQUS. The results re- veal that the width of toms- involute gears is limited by gear undercutting or tooth pointing and the maximum contact stress will be steady after hobbing for a while. The contact stress is small when just a pair of gear teeth are meshing, while the contact stress is large when two pairs of gear teeth are meshing.