螺旋曲面加工刀位轨迹数值算法研究与应用

为了提高复杂螺旋面的加工精度，对其刀位轨迹算法进行研究，提出了基于最小有向距离的刀位轨迹数值计算方法。建立了刀具与工件曲面的三维数值几何模型，并通过坐标变换矩阵来建立与实际加工情况一致的数值计算模型。采用空间离散化思想将刀具与工件两空间曲面的最小有向距离的求解问题简化为一个二维求解问题，保证了求解效率和精度。根据阿基米德插补曲线原理，建立了刀位轨迹的数值计算方法。实例加工结果证明，基于该方法得到的刀位轨迹编制的数控加工程序能够加工出满足精度要求的螺旋面。

Study and Applications of Tool Path Numerical Algorithm of Complex Helical Surface Manufacture

In order to improve the machining accuracy of complex helical surface, this paper studied algorithm about the tool path, put forward a numerical algorithm of tool path based on the minimal directed distance. The three-dimensional numerical geometric models of tool and workpiece surface were built, and a numerical calculation model consistent with the real operation was set-up through the coordinate-transformation matrix. To ensure the accuracy and efficiency, the minimal directed distance between tool and workpiece was samplified into a two-dimensional problem by spatial discretization thought. The numerical algorithm of tool path was set-up according to the theory of Archimedean spiral interpolation curve. The results show that it can produce the helical surface meeting precision requirements with NC programming through the method.