标题: 以弧长为参数的 NURBS 曲线插值器设计
Design of Arc-Length Parameterized NURBS Curve Interpolator
作者: 赖宣宏
Shiuan-Hung Lai
李安谦
An-Chen Lee
机械工程学系
关键字: 运动控制;插值器;即时NURBS插值;数值加工;Motion control;Interpolator;real-time NURBS interpolation;CNC
公开日期: 2008
摘要: 现今的 CNC 工具机已经可以直接接受参数式曲线进行插补,已解决 CAD/CAM 与 CNC 之间大量资料传输的问题,并可进一步改善其加工品质。然而,由于 NURBS 曲线本身复杂的数学表示式,使得 NURBS 插值器需要以数值方法求得每一个插值点的参数值,这对即时环境下而言是相当大的负担。本论文提出以预处理器在非即时环境下对 NURBS 曲线资讯进行预处理,参数区间依所设定的误差容许值 被分割成许多小区间,以数值方法计算各段弧长值与总长度,建立原参数 与弧长 的函数 ,再利用重参数化的流程步骤产生以弧长为参数的 NURBS 曲线表示式,一方面充分利用了总长计算过程的中介资讯,一方面在即时插补时,可以快速地求得每一个位置命令点,避免了复杂的 NURBS 曲线微分项与叠代计算。
本论文所提出之插值方法与其他既有之插值方法经过模拟测试比较,显示本方法在进给率均方根误差的表现上最小;而平均即时插值计算的时间,本论文之方法也比其他插值方法更有效率,最多有近五倍之快速,且本论文之方法在数值计算上相当地稳定,亦不会有累积误差的问题。
Modern CNC systems are designed with the function of arbitrary parametric curves to save massive data communication between CAD/CAM and CNC systems and improve their machining quality. However, the computation loads of NURBS interpolator by numerical methods are relatively large. In this paper, a real-time NURBS motion command generator is presented; this method efficiently integrates the data processing of a NURBS path in a CNC controller, from pre-processing to real-time interpolation. The key point is to generate the arc-length parameterized NURBS curves, in the real-time NURBS path interpolation, the new setting path points can be calculated fast and directly using the arc-length parameterized NURBS curves without the need for any time-consuming computation of NURBS derivatives and iteration.
The comparative results of different interpolation algorithms show that the mean-square feedrate deviation of the proposed method is the smallest among all algorithms. Furthermore, comparison of the average computing times of different algorithms show the excellent performance of the arc-length parameterized NURBS path interpolation method – using the same CPU clock, the proposed method is approximately five times faster. The proposed method is numerically stable and does not have the problems of error accumulation.
URI: http://140.113.39.130/cdrfb3/record/nctu/#GT009514605
http://hdl.handle.net/11536/38599
显示于类别:Thesis