A bisection method for the milling of NURBS mapping projection curves by CNC machines |
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| Authors: | Xiao-Rong Wang Zhao-Qin Wang Yu-Sen Wang Tie-Song Lin Peng He |
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| Affiliation: | 1.State Key Laboratory of Advanced Welding and Joining,Harbin Institute of Technology,Harbin,China;2.School of Mechatronic Engineering,Lanzhou Jiaotong University,Lanzhou,China;3.State Key Laboratory of Advanced Processing and Recycling of Nonferrous Metals,Lanzhou University of Technology,Lanzhou,China;4.School of Railway Technology,Lanzhou Jiaotong University,Lanzhou,China |
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| Abstract: | The concept of non-uniform rational B-spline (NURBS) mapping projection curves (NURBS-MPCs) is proposed in this work. A NURBS-MPC is a projection curve on a NURBS surface of a NURBS curve. The bisection method is used to interpolate NURBS-MPCs. Using an assigned chord, the interpolation of a NURBS-MPC can be obtained easily, and the milling precision of the NURBS-MPC can be controlled effectively. Based on the NURBS theory, the bisection method, and the parametric programming method, an online NURBS software package (NURBS-SP) for FANUC 0i-MB/MC/MD CNC system and an offline NURBS toolbox (NURBS-T) for Matlab have been developed. Using an example of a planar NURBS curve, a NURBS-MPC is created on a NURBS surface. The simulation and milling of the NURBS-MPC show that the bisection method is feasible and effective. The online NURBS-SP endows the NURBS interpolation function for those CNC systems only equipped with linear interpolation (G01) and circular interpolation (G02/G03) and extends the interpolation functions and machining capability of low-middle level three-axis milling machines. The interactive application of the NURBS-T and NURBS-SP can accomplish the design, simulation, and milling for NURBS-MPCs. This feature makes them to have broad application prospects in CNC machining industry. |
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