A region-based tool path generation approach for machining freeform surfaces by applying machining strip width tensor

In freeform surface machining, the cutter should move along the feed directions with maximal machining strip widths (MSW) as much as possible to improve machining efficiency. However, since the optimal feed directions usually vary among different regions over a complex freeform surface, only local optimal machining result could be achieved by most existing tool path generation methods which consider the whole surface as one machining region. This research proposes a tensor-based approach to generate regional tool paths for more globally optimal machining result. A rank-two tensor is first constructed to enable the evaluation of the MSW over the whole feed direction space at the cutter contact point (CCP). To make this MSW tensor usable for generic APT cutters, the concept of effective cutting surface (ECS) is raised. The tensor is then obtained by modeling the geometric approximation between the ECS and the part surface around CCP. A MSW tensor field is then induced over the entire part surface. The regional distribution of the optimal feed directions is associated with the degenerate points within the tensor field. Then, the surface may be divided into several machining regions by constructing inside boundaries starting from the trisector degenerate points. At last, tool paths will be separately calculated in each sub-surface. Since the optimal feed directions in each sub-surface vary continuously, the cutter movements can follow the optimal feed directions closely based on the generated regional tool paths which refer to shorter tool path length and machining time. Two parts with freeform surface are selected from the real industry as test cases and the comparisons to other traditional methods are also provided.