A unified method of generating tool path based on multiple vector fields for CNC machining of compound NURBS surfaces.

The vector field based tool path method can conveniently generate the desired tool paths according to the preferred feed directions which reflect the machining intent of the designers at CC (cutter contact) points, thus recently, it has become the focus of interests. But, the current methods are still limited to the single surface machining. When machining the compound surface patch by patch, it has to plan additional tool path to machine the blending areas of the adjacent patches, and more importantly, the solutions of the key issue, i.e. tool path construction over the vector field, are still heuristic due to the high computational complexity. To solve the problems, this paper develops a unified method of generating tool paths based on multiple vector fields for CNC machining of the compound NURBS surfaces. In this method, the preferred feed directions on the surfaces are mapped into the corresponding parameter domains, and for the vector field on each parameter domain, a stream function which is a polynomial with B-spline basis is reconstructed to represent the vector field and is used to produce the streamlines along these preferred feed directions. A novel algorithm is subsequently proposed to blend the vector fields in the adjacent parameter domains with G1 continuity. Meanwhile, to guarantee the tool path, obtained by reversely mapping the streamline onto the surface, be smooth, continuous and no unappealing visual artifact left at the blending area of two adjacent patches, the condition maintaining G1 continuity of the vector fields between the adjacent patches is also given, avoiding planning additional tool paths to machine the blending areas. Further, to make our method be implemented easily in CAD/CAM systems, a specific implementation process is also briefly presented. Finally, three examples are given to demonstrate the validity of the proposed method.