臺灣博碩士論文加值系統

NURBS為Non-Uniform Rational B-Spline的簡稱，已廣泛使用於CAD系統中，做工件幾何外型的表示，特別是自由型曲線及曲面部分的表示。而傳統的CNC控制器只提供直線及圓弧插值器，無法直接接受自由曲線及曲面所設計的模具資料。解決方式為透過CAM系統將刀具路徑，以微小圓弧或直線做逼近，其近似方法會產生較大輪廓誤差、加工程式過長、傳輸負荷量過大、速度不連續、及機台振動等問題，故不易達成高速精密加工要求。
為了解決上述問題，本論文發展出一新型的即時NURBS曲線及曲面插值器，使CNC控制器具有直接進行NURBS曲線及曲面加工的功能，所提之方法含有：(1) 簡單且有效率計算NURBS曲線(曲面)及其微分的即時運算法則；(2) 預測—修正插值器來加工NURBS曲線，可以控制進給速率在一定精度內，並針對此插值器作數學分析及收斂條件的證明；(3) 基於即時變速度NURBS曲線插值器，發展前加減速的演算法則。由於是在插值前作加減速規劃，可以有效克服傳統後加減速所產生的命令誤差；(4) 新型的即時NURBS曲面插值器，針對球刀加工時，可以即時產生刀具路徑命令並維持固定的刀具接觸點速度，並提高加工的效率及品質。這些方法都在以DSP為控制器的多軸機台上作實測驗證，實驗結果顯示本文所提出的方法可以有效降低輪廓誤差、減少加工程式長度、降低傳輸負荷量、進給速率較易達到給定值，故可達成高速、高精度之加工目的。

NURBS (Non-Uniform Rational B-Spline) has been widely used in commercial CAD systems for geometric representation of part shapes, especially for free-form curves and surfaces. However, traditional CNC controllers only provide line and circular interpolators, that is, only motion along straight line and circular paths are supported. In order to perform mold machining, the tool paths are approximated to many short linear or circular segments by CAM systems before being downloaded to the CNC controllers. Such approximation may result in several problems such as large contouring error, increase of NC program sizes and data transfer load, velocity discontinuity, shocks or variations in mechanical systems and low machining efficiency.
To overcome these drawbacks, novel real-time NURBS curve and surface interpolators are developed in this dissertation. The proposed methods include: (1) a simple method to efficiently compute the NURBS curve (surface) with its derivatives in real-time; (2) a predictor-corrector interpolator (PCI) for the machining of parts with NURBS curves, whereby it can be ensured that the feedrate command errors will fall within the specified feedrate command tolerances. In addition, the mathematical analysis and convergence condition of the corrector are also presented; (3) algorithms for the “ACC/DEC before feedrate interpolation” based on the real-time variable feedrate NURBS curve interpolator. The ACC/DEC (acceleration/deceleration) planning on the feedrate command executes before the interpolation takes place, so that the path command errors caused by conventional ACC/DEC planning using the after federate interpolation can be eliminated; and (4) a novel real-time NURBS surface interpolator that is capable of real-time generation of cutter location (CL) motion command for ball-end milling of NURBS surfaces and maintaining a constant cutter contact (CC) velocity along the CC path and its intervals. The efficiency and quality of machining can be improved significantly since the CC velocity along the surface is kept constant. These methods are evaluated on a multi-axis servomechanism with a DSP-based motion control system. Experimental results have indicated that these techniques are effective to significantly reduce the contouring error, decrease the data transfer load, and improve the machining efficiency and quality.

Abstract (Chinese)I
Abstract (English)II
AcknowledgementsV
Table of ContentsVI
List of TablesIX
List of FiguresX
NomenclatureXIV
Chapter 1Introduction1
1.1Motivation …………………………………………………………………1
1.2Research Review …………………………………………………………2
1.2.1CNC Machining Method ……………………………………………………2
1.2.2NURBS in CAD/CAM Systems ………………………………………………4
1.2.3Parametric Curve Interpolators ………………………………………6
1.2.4Parametric Surface Interpolators ……………………………………8
1.3Organization of the Dissertation ……………………………………9
Chapter 2NURBS Curves and Surfaces11
2.1NURBS Curve Representation ……………………………………………11
2.2NURBS Curve Implementation ……………………………………………13
2.2.1Conventional Method ……………………………………………………15
2.2.2Proposed Method …………………………………………………………16
2.3NURBS Surface Representation …………………………………………18
2.4NURBS Surface Implementation …………………………………………21
Chapter 3Real-Time NURBS Curve Interpolator23
3.1Taylor’s Expansion Interpolators for NURBS Curve …………… 24
3.2Proposed Real-Time Predictor-Corrector Interpolator for NURBS Curve27
3.2.1The Predictor …………………………………………………………28
3.2.2The Corrector …………………………………………………………28
3.3Convergence Analysis of the Predictor-Corrector Interpolator 30
3.4Simulation and Experimental Results ………………………………35
3.4.1Simulation Results ……………………………………………………37
3.4.2Experimental Results …………………………………………………46
3.5Summary ……………………………………………………………………55
Chapter 4ACC/DEC Before Feedrate Interpolation56
4.1Feedrate Command Profiles ………………………………………………56
4.2Computing procedures for “ACC/DEC Before Feedrate Interpolation”58
4.3Experimental Results ……………………………………………………60
4.3.1Single Block of NURBS Curve: A Circle ……………………………64
4.3.2Multiple Blocks of NURBS Curves: A Cam …………………………68
4.4Summary ……………………………………………………………………70
Chapter 5Real-Time NURBS Surface Interpolator71
5.1CC (CL) Paths and Velocities …………………………………………72
5.2Proposed Real-Time NURBS Surface Interpolator …………………73
5.2.1CC Path Planning for NURBS Surface ………………………………75
5.2.2Real-Time NURBS Surface Interpolator ………………………………77
5.2.3Computer Implementation Procedure …………………………………79
5.3Experimental Results …………………………………………………82
5.4Summary ……………………………………………………………………95
Chapter 6Conclusions and Recommendations96
6.1Conclusions ………………………………………………………………96
6.2Suggestions for Future Research ……………………………………98
References99
Appendix A106
Vita107

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