Spiral tool path generation methods for the ultra-precision diamond turning of freeform surfaces can significantly affect machining efficiency and surface quality. However, effective methods for freeform surfaces with a high slope, especially nonrotation symmetric surfaces and those determined by the recursive formula, are unavailable. Therefore, a new spiral tool path generation method based on a nonuniform rational B-spline (NURBS) parameter space is proposed for the ultra-precision diamond turning of freeform surfaces. The discrete points are used for NURBS global interpolation by discretizing the surface in a radial Cartesian coordinate system, thereby forming a NURBS surface. A more uniform spiral tool path of freeform surfaces with a higher calculation efficiency can be obtained by directly utilizing the parameters on the NURBS surface than by applying existing methods. In addition, a solution is provided for freeform surfaces determined by the recursive formula. Simulation and experiments are conducted to show the effectiveness and adaptability of our method.

用于自由曲面的超精密金刚石车削的螺旋刀具路径生成方法会显着影响加工效率和表面质量。但是，没有有效的方法来处理具有高斜率的自由曲面，尤其是非旋转对称曲面以及由递归公式确定的曲面。因此，针对自由曲面的超精密金刚石车削，提出了一种基于非均匀有理B样条（NURBS）参数空间的螺旋刀具轨迹生成新方法。通过在径向笛卡尔坐标系中离散曲面，从而将离散点用于NURBS全局插值，从而形成NURBS曲面。与直接应用现有方法相比，直接利用NURBS曲面上的参数可以获得具有更高计算效率的更均匀的自由曲面螺旋工具路径。另外，提供了一种针对由递归公式确定的自由曲面的解决方案。仿真和实验表明了该方法的有效性和适应性。