关键词: 数控系统, 样条曲线, 高精度, 样条插补, 代数三角样条基

Abstract: The Hermite spline curve was commonly used in interpolation algorithm of Computer Numerical Control(CNC), however, its application in real-time CNC was limited due to its low recursion-rate and poor approximation accuracy. After studying the associations between the construction of spline curve on CNC and CAD/CAM system, a new kind of high-accuracy splines generated over the space spanned by {1 cos t, sin t,…, cos nt, sin nt},and optimized together with least square approximation, amplitude, phase and perturbation method were proposed, which were called algebraic-trigonometric Quasi-Hermite splines. Experimental results demonstrated that the recursion-rate improved by 14.5%, and at the same time, approximation precision was promoted by 10-4 magnitude order. The result indicated that the interpolation-algorithm based on new curve not only promoted the machining precision of profile, but also improved the working efficiency simultaneously. As a result, the new curve could satisfy construction requirements of spline curve on middle and top grade CNC.

Key words: computer numerical control, spline curve, high accuracy, spline interpolation, triangular-orthogonal basis