内啮合曲线构型齿轮传动基本原理及接触分析

Basic Principle and Contact Analysis of Internal Meshing Gear Drive with Curve Configuration

在齿轮传动共轭曲线理论研究的基础上,以内啮合曲线构型齿轮传动为对象,推导了沿给定接触角方向的空间共轭曲线副啮合方程,建立内啮合条件下空间共轭曲线副表达式,根据空间等距包络方法构建继承内啮合共轭曲线副特性的啮合齿面,通过改变成型曲面的相对运动位置及等距半径,提出凸齿廓-凸齿廓、凸齿廓-平面和凸齿廓-凹齿廓3种接触型式;以空间圆柱螺旋曲线为例,结合理论分析结果及主要设计参数,建立凸齿廓-凹齿廓内啮合曲线构型齿轮副三维实体模型;定义齿面接触点压力角,给出基于空间共轭曲线的齿面滑动率计算算法,完成内啮合齿面接触迹线计算及分析,后续将对齿面啮合性能、接触力学特性及制造方法进行研究。

Based on gear transmission conjugate-curve theory research,taking the internal meshing gear transmission with curve element as the object,general meshing equation of spatial conjugate curves along the designated contact angle position is derived and general expressions of space conjugate curves under internal contact conditions are also obtained.According to space equidistant-enveloping method,conjugate surfaces which inherit the meshing characteristics of spatial conjugate curves are generated and three contact types including convex-to-convex,convex-to-plane and convex-to-concave forms are proposed if changing the relative motion position and equidistant radius.Taking the spatial cylindrical spiral curve as an example,combined with the theoretical analysis results and given design parameters,three-dimensional solid models of internal meshing gear pair with convex-to-concave contact are established.The pressure angle on the tooth surface contact point is defined and calculation method of sliding ratio for the mated tooth surfaces is also put forward in terms of space conjugate curves.Calculation and analysis of the contact locus of conjugated internal meshing tooth surfaces are conducted.Further studies on meshing characteristics,contact mechanics and manufacturing method of tooth profiles will be carried out.