Spiral tool path generation method in a NURBS parameter space for the ultra-precision diamond turning of freeform surfaces

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.