内齿轮剐齿刀具设计及齿形优化

Tool design and profile optimization of internal gear skiving

为突破内齿轮加工受限于插齿等工艺,实现内齿轮的高精高效加工,提出内齿轮剐齿刀具设计及修形优化方法.根据渐开线齿面展成原理求解内齿轮齿面方程;建立剐齿刀具前刀面坐标系和加工运动坐标系,根据啮合原理求解剐齿刀具前刀面和共轭面模型,并用双三次NURBS曲面拟合;利用牛顿迭代法求解共轭面与前刀面交点并拟合获取切削刃数据,导入CAD软件建立剐齿刀具三维模型.分析剐齿刀具齿廓误差来源并利用抛物线齿条对剐齿刀具两侧齿廓分别进行修正,结果表明:剐齿刀具两侧齿廓误差从齿顶到齿根逐渐增大,根据齿条法修形后的刀具齿廓误差明显降低.

In order to break through the process of internal gear processing limited by gear shaping and other processes,and achieve high-precision and high-efficiency machining of internal gear,a design and modification optimization method for internal gear skiving cutter was proposed.According to the principle of involute tooth surface generation,the tooth surface equation of internal gear was solved. The coordinate system of cutting tool rake face and machining motion coordinate system were established. The models of cutting tool rake face and conjugate face were solved according to the meshing principle,and fitted with NURBS surface.The intersection of conjugate surface and rake surface was solved by Newton iterative method,and the cutting edge data was obtained by fitting. The three-dimensional model of skiving cutter was established by importing the data to CAD software. The source of tooth profile error of cutting tool was analyzed,and the tooth profiles on both sides of the skiving cutter were corrected by parabola rack.The results show that the tooth profile error on both sides of the skiving cutter increases gradually from the tooth top to the tooth root,and the tooth profile error of the tool modified according to the rack method decreases obviously.