Fabrication of randomly distributed V grooves on the great circles of a spherical surface using ultra-precision five-axis milling

Abstract

Multi-axis ultra-precision milling is a powerful technology which enables the manufacturing of various complicated curved surfaces. However, in the fabrication of an undetermined and random micro-structured surface, the conventional manufacturing mode from a given geometry model to the final surface machining is no longer applicable. Therefore, this work presents an integrative numerical control (NC) code generation method for fabricating randomly distributed V grooves on the great circles of a spherical surface firstly, in which the tool path generation is integrated into the geometry design process. The randomness of the V grooves refers to the geometric feature that the normal vectors of all the planes of the great circles are randomly generated, which are uniformly distributed towards the corresponding points on a unit sphere. Besides, the singular movements in five-axis milling of the randomly distributed V grooves on the great circles are analyzed. It is revealed that there are two distinct mechanisms of the singularity problem. One is the singular configuration of the machine tool, and the other is the discretization of the generated tool path. Subsequently, a general post-processing algorithm is contributed to solve the singularity problem, which enables the generation of NC code with error control. Furthermore, in five-axis milling of the randomly distributed V grooves on the great circles, the position error of tool virtual center can also significantly influence the machining accuracy. Therefore, a two-point calibration method is proposed to accurately determine the position of tool virtual center. Finally, a high-precision random V groove-structured sphere is machined by using the proposed NC code generation method and the tool virtual center calibration method. The maximum depth error of the V grooves is controlled less than 3.3 μm. The proposed methods in this work enable five-axis milling of high-precision random micro-structures on a spherical surface.