Technologies Of NC Machining For Subdivision Surface Based On Multi-resolution Mesh Segmentation

The geometry shape used in aerospace, ship-building, automotive, mold and other industry fields are increasingly complex. The requirement for the precision and efficiency of NC machining is getting higher and higher. The flaws of traditional NURBS method in the aspects of geometric design and machining are shown up. Subdivision surface combine smooth spline surfaces and polygonal meshes together, therefore, a smooth design model and discrete machining models may be unified and subdivision surfaces may be used as a common representation for geometric design and machining. At present, Subdivision surface has become a hot spot in the CAD/CG/CAGD field, and It’s also an important development direction of CAD/CAE/CAM integrated system in the future. Now the research on NC machining for subdivision surface is still at an exploratory stage. There are some key problems need to be solved. Therefore, high-performance NC machining technology for subdivision surface is as the research object in this paper.In order to solve the problems in machining model construction, tool path calculation and machining interference, data structure of subdivision surface, geometric properties calculation, surface intersection, offset surface and interference detection are researched based on multi-resolution mesh segmentation. The primary items in this work are as follows:The topological characteristics of the control mesh of Catmull-Clark subdivision surface are analyzed, which are different from the general polygon mesh. With Catmull-Clark subdivision surface patch as data element, a two-level data structure (named CELL structure) is proposed. By analyzing the basic types of new vertices of CELL, some computational formulas of different types of new vertices are deduced. Based on CELL, piecewise representation of subdivision surface is realized.The topological characteristics of the limit mesh of Catmull-Clark subdivision surface are analyzed, which are different from control mesh. Computational formula for multi-resolution representation limit mesh is deduced. And based on that, the method of machining model construction is proposed combining limit mesh and multi-resolution representation. Computational formulas for position and normal of boundary limit vertex are deduced by feature analysis of local subdivision matrix. Combining with curvature computational method of uniform bicubic B-spline surface, computational formula for curvature of inner regular limit vertex is deduced. It is proved that boundary limit mesh of Catmull-Clark subdivision surface converges to limit surface at an exponential rate. Computational formula for subdivision depth calculation of regular Catmull-Clark subdivision surface patch with boundary is deduced.The methods of cutter location surface construction for some cutters are proposed by spatial relationships between and cutter contact point and cutter location point. Aiming at the topological structure of subdivision surface patch, the multi-segmentation method of subdivision surface patch is presented. And the method for computing intersection between line and subdivision surface is presented combining with AABB collision detection technology. Using the topological structure of subdivision surface patch, a method for computing intersection between plane and subdivision surface patch is presented by computing initial, subsequent and terminational intersection point. Based on divide and conquer, a method for computing intersection between plane and subdivision surface is presented. Through analyzing the condition of discrete parameter representation of subdivision surface patch, some methods for parameter line extraction form subdivision surface patch are presented.The inner relationship between global interference of cutter location surface and rear interference is analyzed. With cutter location surface patch as interference detection unit, a method for interference detection of cutter location surface is proposed by piecewise representation and multi-segmentation. The four-dimensional space-time model of AABB of cutter location surface patch is constructed. Combining with the continuous dynamic collision detection, a fast method for estimating collision possibility between cutter location surface patches is presented. Utilizing multi-resolution sampling technology, the method for searching closest point pairs between cutter location surface patches is proposed. And the prediction method for global interference of cutter location surface is proposed. By using results of interference prediction and interference detection between cutter location surface patches, a method for searching the region of global interference of cutter location surface is presented.These key methods presented in this paper are validated through algorithm implementations and machining experiments. The results show that:CELL is not only better than half-edge structure in aspects of computational efficiency, computer memory consumption and other properties for Catmull-Clark subdivision surface representation, but also provides the basis for multi-resolution mesh segmentation; Limit mesh used for machining model construction is better than control mesh in aspects of computer memory consumption and geometric properties calculation of machining model; Tool path of projection, section and parameter line method are generated based on methods of intersection computation between line/plane and subdivision surface and discrete parameter line extraction of subdivision surface patch. The calculated tool path can be applied to actual machining and ensure the accuracy and quality of workpiece; The problems of optimum small cutter calculation and region search of machining interference are solved. And the methods for machining interference treatment can be applied to actual machining and ensure the accuracy and quality of workpiece.