延伸外摆线锥齿轮的成形原理及齿面结构研究

用全新的观点诠释了延伸个摆线锥齿轮的齿面成形原理，并由此推导了刀刃在工件上的轨迹曲面（族）的统一表达形式。论述了在Free-form型铣齿机上加工延伸外摆线锥齿轮的实现方式。分析了Free-form型铣齿机上用成形法加工延伸外摆线锥齿轮时的齿面微分几何结构。通过刀刃长度和刀盘转角实现了齿面参数化，并获得了齿面上任意点的全部一至三阶微分几何参数。

Analysis of the Forming Principle and the Differential Str ucture of Extended Epicycloid Bevel Gear Tooth Surface

An entirely new point of view is introduced to explain the forming principle of extended epicycloid bevel gears, with which a general expression of the trajectory surface formed by the cutting edge on work-piece is deduced. The realization method of formatting extended epicycloid gears on Free-form bevel gear milling machines is also presented. The differential structure of extended epicycloid bevel gear tooth surface is analyzed when formatted on free-form bevel gear milling machines. The tooth flanks are parameterized using the length of the blade and the angle of rotation of the cutter, and all the geometric parameters of tooth surfaces from the first to third order are obtained.