球面渐开线齿面的形成理论及其NURBS精确拟合方法

摘要

Distinguished from the approximate spherical involute tooth profile has been in a dominant position in the research field of spiral bevel gear, and whose design and processing were based on the local conjugate theory, discussing some research outcomes on recent relevant spherical involute, a theory of forming the spherical involute tooth surface was improved, and key part namely the generating line and its equation were detailed by derived. In addition, fast and accurate solutions of the boundary curves and the tooth profile curve families were done by taking advantage of forming principle of spherical involute tooth surface, and based on advantages of modeling techniques of the cubic NURBS curve and surface in CAD/CAM, spherical involute tooth surface precision fitting was completed. At last, related optimization program associated with constructed NURBS tooth surface in the use of the Skinning method was proposed, and the parameterization of tooth surface data and precise fitting surfaces were accomplished, so as to further improve the accuracy of the tooth surface and provide tooth contact analysis for the data of the tooth surfaces and the basic model.%区别于螺旋锥齿轮研究领域一直占据主导地位的局部共轭原理及其所设计和加工出来的近似球面渐开线齿形，基于近些年相关球面渐开线的研究成果的探讨，改进球面渐开线齿面形成理论，并对关键的产形线方程做推导。另外，利用球面渐开线齿面形成理论快速精确地求解边界曲线和齿廓曲线族，并结合三次NURBS曲线曲面造型技术的在CAD/CAM中的优势完成球面渐开线齿面的精确拟合。最后，在利用蒙皮法构造的NURBS齿面基础上提出相关优化方案，完成齿面数据的参数化和曲面的精确拟合，以进一步提高齿面精度，并为齿面接触分析提供齿面数据和基础模型。