内啮合双圆弧摆线锥齿轮齿面建模与啮合特性仿真

针对斜航线式双圆弧内啮合锥齿轮副齿面难以高效加工的问题,提出一种端面滚切加工外锥齿轮,进而基于外锥齿轮的平面产形轮产成内锥齿轮的齿面设计方法.首先,以双圆弧齿形作为切削刀刃的基本齿廓,基于端面滚切方法建立双圆弧锥齿轮的平面产形轮.其次,根据平面产形轮与双圆弧内、外锥齿轮的展成运动关系,建立内、外锥齿轮的齿面方程.再次,通过精确求解齿面数据生成齿面"点云",建立双圆弧锥齿轮副三维实体模型.最后,运用ANSYS仿真内啮合双圆弧锥齿轮副的啮合特性.实验结果表明:基于本方法生成的内啮合双圆弧锥齿轮工作齿面接触良好,可以实现正确啮合传动.当前研究可为内啮合双圆弧锥齿轮的高效加工提供理论依据.

Tooth surface modeling and contact analysis of an internal gearing with double circular-arc cycloidal bevel gears

To improve the cutting efficiency of double circular-arc spiral bevel gear, this paper proposes a face hobbing based tooth surface design method for internal bevel gears. Firstly, a plane profile of the double circular-arc bevel gear is established based on the face hobbing method by taking the double circular-arc profile as the basic profile of cutting edge. Secondly, according to the generative motion relationship between the generating gear and the double circular-arc bevel gears, the mathematical equations of tooth surfaces of the internal and the external bevel gears are established. Thirdly,the "point cloud" of the tooth surface is generated by solving the tooth surface equations accurately, based on which a 3D model of the double circular-arc bevel gear pair is established. Finally, the meshing characteristics of the double circular-arc bevel gear pair with internal meshing are simulated with ANSYS. The results show that the contact status of the internal meshing double circular-arc bevel gears generated by the proposed method is physically reasonable and satisfactory, indicating a correct meshing can be realized. The present work provides a theoretical basis for the efficient cutting of internal meshing double circular-arc bevel gears.