最小輪廓誤差之參數化插值器

Abstract

隨者產品設計的越來越美觀，使得物品的曲線越來越複雜。電腦輔助設計(Computer Aided Design, CAD)發展出使用參數化曲線來描述這些複雜的曲線和曲面。由於輪廓複雜及電腦的進步，加工路徑已多由CAD直接轉換。早期參數化曲線是被轉換成一條條的近似直線，但如此會造成需要大量的記憶體。因此需要把參數式曲線插值放入電腦數值控制工具機(Computer Numerical Control, CNC)內部作即時的插補。 而針對參數式曲線有許多不同方向的研究，如位置插值、或是進而考慮到速度控制、加減速控制、減少弦長誤差、或考慮曲線弧長。而這些研究似乎無法兼顧等速及弦長誤差，因此本論文提出了一個不同的曲線插值方法，在容許徑向誤差下，使曲線降低弦長誤差且又盡量維持等速。數值模擬與實驗均顯示，這個方法可以有效改善曲線插值的精度。

In modern CAD/CAM systems profiles or curves for parts like dies, vanes, aircraft turbines, shoes, mobile phones, etc., are usually represented in parametric forms. As conventional CNC machines only provide linear and circular interpolators. The parametric curve is approximated by a lot of line segments and sent to CNC systems. It causes a lot of computer memories. Thus, it is necessary to embed the parametric interpolation inside CNC machine to achieve real-time parametric interpolation. There are a lot of researches about parametric curves, like position interpolation, constant speed interpolation, acceleration and deceleration control, reducing the chord error, and or concerning about the arc length of the curves. But these researches didn’t consider the issues of both achieving minimal chord error and maintaining the constant speed. This article proposes a method to decrease the chord errors while maintaining a constant speed under a radial error. The simulation and the experimental results show that the proposed method effectively improves the interpolation accuracy in terms of the contouring position error and maintains speed accuracy at the specified level.