基于广义延拓逼近法的凸轮轮廓反求设计

Reverse seeking design on cam contour based on generalized extended approximation method

在高精度的凸轮轮廓反求设计中,利用凸轮轮廓非圆曲面的离散测量点,采用一种新的方法———广义延拓逼近法,构造出凸轮非圆曲面的广义延拓逼近模型,来实现高精度凸轮轮廓的反求设计。为验证设计效果,分别运用三次样条插值法和最小二乘拟合法对凸轮非圆曲面数据进行逼近计算。结果对比表明,采用广义延拓逼近法数学模型处理凸轮非圆曲面的离散数据时,如果在延拓域边界点上满足插值条件,可以实现区域内部的最佳拟合。此外,在插值次数相同的条件下,广义延拓逼近法具有更高的设计精度。

Within the reverse seeking design of high precision cam profile, we utilized the discrete measuring points of non-circular curved surface of cam profile and adopted a new kind of generalized extended approximation method to construct the generalized extended approximation model of non-circular cnrved surface of cam, so as to realize the reverse seeking design of high precision cam contour. For the sake of verifying the effect of design, the third ordered spline interpolation method and the least square fitting method were applied respectively to carrying out approximate calculation on the non-circular curved surface data of cam. The contrast of resuits showed that while the generalized extended approximation model had been adopted to deal with the discrete data of non-circular curved surface and if the interpolation condition was satisfied at the boundary points of extended region, the optimal fitting within the region can be realized. Furthermore, under the condition of same number of times of interpolation, the generalized extended approximation method possesses higher designing accuracy.