五軸TCP路徑之曲線擬合、預讀與插補

本論文提出一結合預視和曲線擬合功能之進給率調節演算法，用來產生平滑的五軸刀具中心點軌跡命令。此演算法包含了兩個主程式:曲塊程序以及預讀程序。在曲塊程序中，曲塊線段交接處的斷點首先被偵測出來，並將其所對應的進給率設為零。接著，將兩斷點間的刀具中心點命令藉由給定的弦誤差擬合成單一區塊線段或是透過雙弦誤差方法擬合成一條C3連續之B-spline曲線，而每個區塊轉角的轉角進給率則藉由滿足TCP三個線性軸的急衝限制所決定。在TCP線性軸與旋轉軸間產生最大移動量的軸被指定為主動軸，而主動軸移動量與TCP線性軸和旋轉軸間的移動量比值同時被求得。在預讀程序中，利用五軸進給率調節公式來決定主動軸的最大速度，接著進給率命令亦透過TCP線性軸和旋轉軸的急衝及速度上限進一步調整，S型加減速方法則被採用以達到速度平滑化以及防止激發機台結構共振。最後，在一台桌上型五軸雕刻機上進行切削實驗來驗證此方法的效能，實驗結果顯示使用本論文所提出的五軸插補方法，其所產生的輪廓循跡精度可較海德翰控制器的方法提升一倍以上。

關鍵字

五軸插補；預視；曲線擬合；刀具中心點；急衝限制；五軸雕刻機

並列摘要

In this paper, a feedrate scheduling algorithm with look-ahead and curve fitting functions is proposed to generate smooth five-axis tool center point (TCP) trajectory. The developed algorithm consists of two programs: block process and look-ahead process. In block process, break-points at the conjunction of block segments are first detected where the feedrates at the break-points are all set to zero. TCP commands between two break-points are fitted to a single block segment within a given tolerance or a C3 B-spline curve by using bi-chord error method. Corner feedrate respecting jerk continuity of three linear axes on TCP at each block corner are determined. The axis with maximum movement among linear axes on TCP and rotary axes is selected to be a master, and the ratios among the movements of the master and other axes are obtained. In look-ahead process, five-axis feedrate regulation formulation (FFRF) is utilized to evaluate the maximum velocity of master axis. Feedrate command is adjusted with the constraints of jerks and velocities of linear axes on TCP and rotary axes. S-shape acceleration/deceleration (ACC/DEC) method is used to achieve velocity smoothing and avoid the excitation of structure vibration. Finally, cutting experiments are performed to verify the efficiency of the proposed method on a desktop five-axis engraving machine. The experimental results demonstrate the proposed method can reduce contouring errors to half of that using Heidenhain controller.

並列關鍵字

Five-axis interpolation ； look-ahead ； curve fitting ； tool center point ； jerk limit ； five-axis machine tool

參考文獻

[1] N. Shibata and T. Otsuki, Numerical Controller, United States Publication Patent No. 6775586 B2, 2004.

Google Scholar

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