内啮合非圆齿轮加工的数学模型及图形仿真

Investigation on Mathematical Model and Simulation for Machining Noncircular Internal Meshing Gear

根据范成法加工内啮合非圆齿轮时刀具和齿轮节曲线间的位置关系,建立了插齿加工的数学模型,分析了加工非圆齿轮时其节曲线为凸的条件。根据所建模型和节曲线为凸的条件,将加工内啮合非圆齿轮的范成过程用计算机进行了动态图形仿真。根据图形仿真结果,可以分析和判断所加工非圆齿轮的齿形特征,为设计和制造节曲线封闭型内啮合非圆齿轮提供了直观的判断方法。

According to relation-ship of internal meshing between the shaper and the pifch curve of noncircular internal gear based on the generative catting method a concise mathematical model for a shaper cutting noncircular internal gear is set up. At the same time, the limits of bulge for the noncircular internal gear pitch curve are studied. On this basis, by using computer graphics simulation the concise mathematical model is applied to demonstrate the generating cutting process and its result dynamically. The generating feature can be observed the graphics so it provides a convincing basis for correct design and cutting.