面向制造的弧齿圆柱齿轮建模及强度分析

Modeling and Strength Analysis of Cylindrical Gears with Curvilinear Shape Teeth for Manufacture

在分析弧齿圆柱齿轮加工原理和数学建模的基础上,提出一种面向制造的弧齿圆柱齿轮建模新方法,解决长期以来弧齿圆柱齿轮3维造型和实际加工不一致的问题,保证后续分析、加工等工序的正确性。基于UG的二次开发,采用齿坯滚动进给、刀具旋转切削的方法,实现面向制造的弧齿圆柱齿轮的3维造型和快速原型制造,在此基础上深入分析刀具半径对弧齿圆柱齿轮的接触应力分布的影响,得出不同曲率下齿轮强度的变化规律。有限元分析结果表明同等条件下弧齿圆柱齿轮的接触强度较直齿轮有显著提高,其最大齿根应力仅为直齿圆柱齿轮的27%,弧齿圆柱齿轮齿根应力与弧齿线半径有明显的关系。此方法为弧齿圆柱齿轮在高速重载等工况下的工业应用提供理论依据和工程应用价值。

Based on the analysis of generating mechanism and mathematical model for the cylindrical gears with curvilinear shape teeth,a new way of modeling such gears for manufacture was proposed to solve the long existing inconsistencies between three-dimensional modeling and actual processing and to ensure the correctness of follow-up analysis of finite elements and gear machining.Adopting the secondary development of UG and the approach of gear blank＇s rolling feed and gear cutting tool＇s rotary,the three-dimensional model of such gears was accordingly built and proved to achieve rapid prototyping manufacture.Then,with the analysis of the model＇s strength and finite elements performed,it was confirmed that the contact strength of tooth surface of cylindrical gears with curvilinear shape teeth could be substantially improved,compared with that of spur gears,and that the maximal stress equivalent was only twenty-seven percent of spur gears＇.Meanwhile,the requirements of high speed and heavy duty gear transmission could be satisfied.Therefore,this approach was a good example of the establishment on strength theory and the design of processing,and provided theoretical basis and guidelines for industrial applications of cylindrical gears with curvilinear shape teeth in today＇s China.