Tool path generation for multi-axis freeform surface finishing with the LKH TSP solver

In freeform surface finishing, there are three major types of tool path topologies: the direction-parallel type, the contour-parallel type and the space-filling curve (SFC) type. The SFC topology is capable of covering the whole surface with only one path. In this paper, we present a new way of planning the SFC type tool path by formulating the planning task as a traveling salesman problem (TSP). The optimal path is generated in two steps. Firstly, a set of regular cutter contact (CC) points is generated on the input surface. A cutting simulation method is developed to evaluate the scallop error and determine the position of the next CC point in cross-feed direction. This method is free of local surface curvature assumptions and is therefore accurate for big cutters. Secondly, the obtained CC points are input into an efficient TSP solver LHK for the optimal CC point linking sequences. To stop the CC points from diagonal linking or penetrating linking, the Euclidean distance evaluation function for two CC points is redefined in LHK. The proposed tool path generation method is verified with several freeform surface examples; the results show that the method can automatically find the optimal feed direction and it can generate shorter tool path than the traditional SFC method. The feasibility of the proposed method is also verified by a cutting experiment.