齿轮齿面的分形模拟

Fractal Simulation of Gear Tooth Surface

任何加工精度下的齿轮齿面都不会是绝对光滑的,而是有粗糙度的,对于磨削加工的齿轮齿面而言,表面粗糙度在加工纹理的方向和垂直于加工纹理的方向是异性的。而目前基于W-M函数分形模拟的二维粗糙表面轮廓曲线和三维粗糙表面都是针对于各向同性的表面,因此提出利用两个WM函数叠加来分形模拟各向异性齿轮齿面的方法。模拟结果表明,此方法可以很好地模拟两个方向具有不同分形维数和特征尺度系数的粗糙表面,通过改变分形维数和特征尺度系数可以有效控制齿轮齿面的纹理。

Gear tooth surfaces are not absolutely smooth, but have roughness and waviness pro- duced with all machining techniques. For the grinded gear tooth surface, its surface roughness is ani- sotropic in the direction of machining path and the perpendicular direction of the machining path. However, the available fractal simulation of two dimensional rough surface profile curves and three- dimensional roughsurfaces based on W-M function are used to simulate isotropic rough surfaces. A method of superposition of two W-M functions for the fractal simulation of gear teeth surfaces with anisotropic textures is presented. Simulation results show that, rough surfaces with different fractal dimensions and different feature scaling constants in two directions can be well simulated with this method, and the gear tooth surface textures can be effectively controlled with the changes of the fractal dimension and feature scaling constant.