Variable Weight Non-Uniform Rational B-Splines, Offset Surfaces, and Gouging-Free Computer Numerical Control Tool Path Generation

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This grant provides funding for the development of variable weight non-uniform rational B-splines (VW NURBS), a method for offset surface generation, and a technique for gouging-free tool path identification in computer numerically controlled (CNC) machining. The properties of VW NURBS will be explored. The results from VW NURBS will be applied to approximate offset curves and surfaces, in which the error can be adjusted by constructing weight functions of VW NURBS and by using a subdivision algorithm. The gouging condition of a CNC machining tool path will be identified by using the offset surface in user interface. The proposed method will determine the optimal cutter radius and its inclination angle to avoid any local interference in manufacturing free-form surfaces with a ball-end mill or a flat-end mill. If successful, this research will lead to a fundamental advancement in CAD/CAM development. VW NURBS is a systematic extension of NURBS, the most promising model used in the current commercial CAD/CAM software. It offers a more general model than NURBS and can enhance the flexibility, capability, and efficiency of CAD/CAM systems. In addition to CNC machining, the method of offset curve and surface generation can also be applied to tolerance analysis, mold and die making, rapid prototyping, robot path planning, and finite element mesh generation. The proposed gouging identification method will allow one to optimize the cutter size and orientation easily, and hence, enhance the productivity and quality of CNC machining.