关键词: 齿廓曲线, 纯滚动, 非圆齿轮, 共轭齿条, 啮合方程, 图形仿真, 坐标变换

Abstract: For the pitch-line of a non-circular involute gear being given，its tooth profile is modeled mathematically by using of a conjugate rack．According to the generation mechanism of involute gear tooth profile，if the pitch-line of the conjugate rack is made to roll slidelessly on the pitch-line of the non-circular gear，profile of the conjugate rack will generate the profile of the gear．The geometry model of the conjugate rack and the pure-rolling model of pitch-lines are set up separately，and then joined together with the so-called equation of mash，to obtain the mathematical model of tooth profile in the coordinate system of the non-circular gear．Based on this model，the teeth profiles of non-circular gears are described by graphic simulation to verify its correctness and effectiveness．This model can be used to design the profile of cutter for the non-circular gear，to find the locus of cutter during machining，and to analyze the teeth strength of non-circular gears，etc．

Key words: Equation of mesh, Conjugate rack, Coordinate transformation, Graphic simulation, Non-circular gear, Profile of tooth, Pure rolling