Research On NC Programming For Subdivi-sion Surface

NC programming technology plays a vital role in NC machining. It is always the focus of scholars'attention. As a promising alternative approach for geometric design, subdivision surface is a hybrid of polynomial splines and polygon meshes. This property makes subdivision surfaces the most desirable choices as the geometric representation for design and manufacturing. Catmull-Clark subdivision sur-faces which are easy to be blended with NURBS surfaces are considered as the generalizations of uniform B-spline surfaces to joint with CAD/CAM seamlessly. It tries to construct a framework of subdivision surface-based design and manufacturing integration in this paper. NC machining which includes rough and finish machining as the manufacturing applications is mainly considered in this work.By introducing the recurrence equation of the second order norm, a subdivision depth computa-tion method for Catmull-Clark subdivision surface with boundary is proposed. Based on the sec-ond/first order differences of the control points, one can predict the subdivide depth within a specified tolerance without subdivide actually. Based on the distance between the control vertices and corre-sponding limit points, computing formula of subdivision depth has been derived. According to the formula one can easily predict how many subdivision iterations are necessary for a user defined error tolerance without the real process of recursive subdivisions. This is quite useful and important for pre-computing the subdivision depth in many engineering application.To obtain NC rough machining models with uniform machining allowance and reduced shape complexity, an adaptive subdivision algorithm based on surface error is developed. A limit mesh is generated by projecting control mesh to the limit surface. The distance between limit mesh and limit surface is used as the self-adaptive subdivision criterion to adaptively subdivide the areas which were not satisfied with specified error tolerance. Therefore, a roughing model with a coarse shape is ob-tained.A novel method for valid boundary tracing of cutting area based on effective edge is investigated for the Z-constant machining to improve the computational efficiency of tool path generation. Mesh model slicing performance can be increased using topological information. Instead of randomly inter-secting each facet with a slicing plane and constructing the slice contour later, it is possible to march from one effective edge to neighboring effective edge collecting contour information as the marching proceeds. Contrast with conventional methods, the method is obviously easier and the complexity has been reduced.Error control is a major concern for finish machining. In order to ensure the fairness of machin-ing, a tool path planning method with G 1continuity of approximate constant scallop-height is proposed. Based on the limit points and their normal vectors, an offset mesh is generated. The deformation sur-face is generated in accordance with the deformation coefficients, which is computed by slope and the curvature of the offset mesh. The tool path, which is computed by slicing the deformed offset mesh, is inversely deformed by those deformation coefficients to a tool path with a constant scallop-height. Furthermore, this method is used in five-axis machining. The tool orientation in five-axis machining is computed by averaging the value which is obtained by the area times the normal vector.In order to test research work and achievements mentioned above, a NC automatic programming system is successfully developed. The system handles subdivision surface modeling for rough ma-chining and finish machining. Moreover, the tool-paths of rough machining and finish machining for subdivision surface have been successfully generated based on the above methods.