蜗线齿轮及其共轭齿轮的几何分析与仿真

LIMACON GEAR AND CONJUGATED GEAR'S GEOMETRY ANALYSE AND SIMULATION

蜗线齿轮是一种节曲线向径按余弦规律变化的新式齿轮。为了选择合适的切齿方案和切齿刀具,实现齿轮不同的数控加工方法,对该蜗线齿轮及其共轭齿轮进行理论分析和计算模拟。根据新式齿轮的节曲线曲率半径公式,给出节曲线凸凹性的判别式;由齿形法线在节曲线上的分布规律,用解析法建立齿形渐屈线方程;基于齿形上任一点的向径与节曲线向径的几何关系,由节曲线方程推导出了齿形方程。并由所建立的方程进行了蜗线齿轮及其共轭齿轮的渐屈线及齿形的图形仿真,为新式齿轮的开发应用提供了理论依据。应用该理论设计、加工的齿轮已用于生产实际,性能良好。

Limacon gear is a new kind of gear whose pitch-curve varies in cosine rule. In order to select the proper cutting method and cutter and realize different CNC processing methods, theoretical analysis calculation and simulation are done. According to the formula of the new kind of gear＇s radius of pitch-curve cavature, pitch-curve＇s convex and concave discriminants are given; According to the distribution disciplinarian of the gear＇s normal on the pitch-curve, the equations of the gear＇s tooth evolute are set up by analytic method; By the geometry relation between the vector of a point on tooth and the vector of the corresponding point on pitch-curve, the equations of the gear tooth are deduced from the equations of the pitch-curve. Based on above, the graphics simulation of the evolute and tooth are finished, which provides theory basis for this new kind of gears. Gears based on these theories have been used in practice and achieved good results.