Mathematical Modeling and Graphics Simulation for Tooth Profile of an Ellipse Involutes Gears

A new modeling method of an ellipse gear's profile was proposed.Firstly,according to the analysis of the forming principle of the involutes profile and the tooth thickness of formula,a mathematical model of involutes profile was established. Secondly,a geometric relationship of pinion cutter and pitch curve of an ellipse gears was established,which made pinion cutter do pure rolling.Then the engaging equations of two models were combined and the mathematical model of tooth profile of ellipse gear was established.Third,in processing,the arc length of cutter on the pitch curve was equal to be the length of cutter rotating around its axis in order to guarantee the generating between the pinion cutter and the blank.Finally,an involutes profile of an ellipse gears was formed using the method of computer graphics simulation.The accuracy and the validity of the mathematical model were confirmed by simulation.