中文摘要：

基于展成加工原理,采用坐标变换法推导出Ⅰ型带凸角磨前滚刀各切削刃在被加工齿轮上生成的共轭曲线;按平面曲线合成方法对共轭曲线进行离散、压缩、连接与合成,得到加工后的准确齿形.基于APDL与MATLAB混合编程技术,精确地实现凸角型磨前滚刀切制的复杂齿形有限元几何建模,进而探讨了齿面摩擦力对齿轮弯曲强度与轮齿变形的影响.研究表明：实际齿轮承载能力精确计算中,摩擦力对轮齿强度的影响一般不应忽略.准确的齿形计算、建模与分析,对于复杂齿轮的强度分析和齿廓优化具有积极的意义.

英文摘要：

Based on the generating principle, the conjugate curves of processed gear, cut by the different tool edges of I protuberance type pre-grinding hob, were derived in terms of coordinate conversion. The conjugate curves were dispersed, compressed, linked and composed numerically according to the method for plane curve composition, and then the tooth profile was calculated. Based on the method for compositely programming with MATLAB and APDL （ANSYS Parametric Design Language）, the finite element geometrical model of complex tooth form machined by pre-grinding hob was accurately established. According to the model, the relations of friction force to bending strength and tooth compliance were studied. The studies have shown that the effect of the friction force on the tooth strength should be included when the supporting capacity of the gear drive can be calculated accurately. The exact calculation, modeling and analysis of the gear shape paves the way for the study of the gear strength and the optimization of tooth profile.