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

这笔资金用于开发变权重非均匀有理B-Splines(VW NURBS)，一种偏置曲面生成方法，以及一种在计算机数控(NC)加工中识别无刨削刀具路径的技术。我们将探索大众NURBS的特性。将VW NURBS的结果应用于逼近等距曲线和曲面，通过构造VW NURBS的权函数和使用细分算法来调整误差。利用用户界面中的偏移面识别数控加工刀具轨迹的过切情况。该方法将确定最佳刀具半径及其倾角，以避免在球头铣刀或平头铣刀加工自由曲面时的任何局部干涉。如果研究成功，将为CAD/CAM的发展带来根本性的进步。VW NURBS是目前商用CAD/CAM软件中最有前途的NURBS模型的系统扩展。它提供了比NURBS更通用的模型，可以提高CAD/CAM系统的灵活性、能力和效率。除数控加工外，等距曲线曲面生成方法还可应用于公差分析、模具制造、快速成型、机器人路径规划和有限元网格生成。提出的过切识别方法可以方便地优化刀具尺寸和方向，从而提高数控加工的生产率和质量。

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.