小線段預讀之插補器設計與動態分析

Design of The Interpolation for The Short Segment and Analysis of The Dynamic Model

陳慶儒(CHING-JU CHEN)

指導教授 ： 蔡孟勳

國立中正大學/工學院/機械工程學系/碩士(2013年)

摘要

目前市面上大部分的中、低階控制器，幾乎沒有提供高速高精的曲線擬合之功能，如NURBS參數擬合。而當中、低階控制器遇到一些不規則的曲線及曲面加工時，就須仰賴CAD/CAM軟體在容許的誤差範圍內，透過外形擬合方式產生許多直線G01小線段來近似這些不規則的加工路徑。因此本篇論文主要目的就是探討小線段之速度規劃以及位置命令的插補方法。
而長線段與短線段最大的差異就是：長線段單節在速度曲線上，在最大加速度限制下，路徑之長度足夠以致速度可上升至等速段；反之，小線段單節因路徑長度不足以加速至等速，即須降速至零或是所設定之轉角速度。因此，透過預讀的原理提升小線段之速度為本論文重點之一。主要分析：速度規劃時預讀buffer數量、最大加速度、瞬時速度差以及路徑曲率變化等參數對加工速度曲線的影響，並使用MATLAB軟體建構出具有這些參數功能的插補器，觀察其結果。
另一個探討的重點是，在位置命令插補的部分，目前參考到的文獻中多數沒有討論到單節經過取樣時間計算，插補得到位置命令後，不滿足取樣倍數的殘餘線段部分該如何處理；以及小線段在透過預讀速度提升後，所需耗費的時間可能短到不足一個取樣時間。針對這兩個部分，本論文提出一方法來解決此情況。最後，從NC碼解譯至插補後經過一模擬機台之伺服建立成一完整程式，對於工具機加工者在加工前，精度與時間的取決上能有一定的幫助。

關鍵字

預讀 ； 小線段 ； 插補

並列摘要

Currently, there is no NURBS curve fitting function which can attain high speed and accuracy for low or medium level controllers. When the user encounters an irregular curve, the usual procedure is to generate many G01 segments to fit the curve depending on the CAD/CAM software to ensure the error is below the setting limitation. The two topics of this dissertation are to discuss the method to plot the velocity curve and the interpolation of short segments.
The biggest difference between the long and short segments of G01 is that the long segment can reach command velocity under limited acceleration. This is opposed to the short segment, which cannot reach command velocity even when acceleration is set to the maximum allowed setting. This dissertation uses a method called "look-ahead" which eliminates the velocity return to zero after a segment and raises the velocity curve, the impact of this method is discussed in terms of the: look-ahead buffer; maximum acceleration; instantaneous velocity difference; and the curvature variation of the contours. Finally, interpolation is constructed with these parameters using a Matlab program, the same program is used to analyze the results.
As stated earlier, the second topic of this dissertation is interpolation. Much of the source material I researched did not describe detailed information about how to process the remaining distance after the final sampling point of the block, or the solution to the problem of the working time of the block being less than the sampling time. This dissertation proposes a method to solve both these problems. Finally, constructing a program which includes the complete servo loop to simulate controller steps from interpreting the NC code to position command interpolation. It will be helpful to analyze the relationship between accuracy and time consumption, in order to find a suitable compromise of these two parameters.

並列關鍵字

Interpolation ； Look Ahead ； Short Segment

參考文獻

[1] Y. Koren, 1976, “Interpolation for a Computer Numerical Control System”, IEEE Transaction on Computers, pp.32-37.

[2] Y. Koren, “Computer Control of Manufacturing Systems”, McGraw-Hill, New York, 1983.

[5] W. Y. Chao, 2011” A look-ahead velocity blending model for high speed CNC machining of small line blocks”, 2011 Fourth International Conference on Intelligent Computation Technology and Automation.

[6] S. H. Suh, “Theory and Design of CNC Systems ”, 2008, Springer Series in Advanced Manufacturing.

[7] Chuan Shi. Peiqing Ye , 2011, “The look-ahead function-based interpolation algorithm for continuous micro-line trajectories”, Int J Adv Manuf Technol Volume 54, Issue 5-8 , pp 649-668. DOI 10.1007/s00170-010-2975-x.