CNC三維圓弧插補器

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姓名

黃偉峰(Wei-Feng Huang) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

CNC三維圓弧插補器
(Three Dimensional Circular Interpolator in CNC)

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至系統瀏覽論文 ( 永不開放)

摘要(中)

工具機發展已數十年。在自動化當道的今日，CNC工具機普遍運用G-Code作為刀具路徑產生的表示方法，藉由G-Code描述，工具機得以在每次中斷插補得到刀具所要前進的三軸距離。一般常用的G-Code多為直線及圓弧插補，優點是用的廣且技術單純，缺點為資料筆數過多，造成記憶體消耗，且G-Code兩兩加減速不連續導致加工時間增長。目前已知有工具機廠商將NURBS曲線運用於插補器上，可以做到1.減化資料點數，2.縮減加工時間，以解決上述問題。
本論文主要著力在於使用另一種改良型的插補器(interpolator)，運用空間圓弧的堆砌(arc spline)去擬合(approximation)曲線，以利用圓弧G２連續的特性。之後並模擬一工具機上新增一三維圓弧插補的NC指令(以下簡稱3DArc)，以便下達切削及移動工具機的動作，使所擬合出的曲線更易實現於工具機上。以期達到如NURBS插補器的加速效果及切削任何方向空間圓弧。

摘要(英)

The control of CNC machine tools developed by G-Code and M-Code produce cutting route. According to the description of G-Code, three axes of a CNC machine tools can be moved within a desired small distance in each interpolation interrupt. In this thesis, the G-Code commands, like G01 (linear interpolation) and G02 (circular interpolation), are changed to 3D circular interpolation to reduce huge data amount and memory waste. Furthermore, the discontinuity between two G-Codes will be reduced and manufacturing time will be shortened. The purpose of the developed 3D circular interpolation compete NURBS interpolation in performance in manufacture industry.
Besides, the 3D circular arcs approximation has been developed to combine 3D circular interpolation to fit curves and can promise G1 and near G2 continuity between two 3D circular arcs.
All that we do is to approximate a curve by 3D circular arcs and simulate the CNC machine core, thus we can cut any curve or circular arc in any plane.

關鍵字(中)

★ 圓弧擬合
★ 三維圓弧插補器
★ 工具機

關鍵字(英)

★ CNC machine tools
★ circular approximation
★ 3D circular interpolator

論文目次

CHAPTER 1 INTRODUCTION 1
1.1 BACKGROUND AND MOTIVATIONS FOR RESEARCH 1
1.2 THESIS ARRANGEMENT 1
1.3 FRAMEWORK 6
1.4 THESIS ARRANGEMENT 7
CHAPTER 2 PIECEWISE-CIRCULAR CURVES APPROXIMATION 8
2.1 INTRODUCTION 8
2.2 PIECEWISE-CIRCULAR CURVES APPROXIMATION 9
2.2.1 Construction and Representation of single PCCs 10
2.3 REMARK 15
CHAPTER 3 APPROXIMATION ERROR ANALYSIS AND SEARCH METHODS 16
3.1 INTRODUCTION 16
3.2 APPROXIMATION OF TANGENT FROM DATA 18
3.3 ERROR DETECTING METHOD 19
3.3.1 Plane Least Square Error 19
3.3.2 Error Method In Piecewise-Circular Curves 22
3.4 BINARY SEARCH 23
3.5 SIMULATION 24
3.6.1 Small Curvature 28
3.6.2 Long Line 28
3.6.3 Angle 28
3.6.4 Semi-Sphere Approximation 28
3.7 REMARK 31
CHAPTER 4 THREE-DIMENSIONAL CIRCULAR ARC INTERPOLATION 32
4.1 INTRODUCTION 32
4.2 CONTROL POINTS TO CIRCULAR ARC INFORMATION 33
4.3 COORDINATE TRANSFORM 34
4.3.1 Translation 35
4.3.2 Mapping 35
4.4 THREE-DIMENSIONAL CIRCULAR ARC INTERPOLATION 36
4.5 SIMULATION 38
4.6 SIMULATION WITH COUNTING REMAINDER 42
4.7 REMARK 47
CHAPTER 5 CONCLUSION AND FUTURE WORK 48
REFERENCES 49

參考文獻

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指導教授

董必正(Pi-Cheng Tung)

審核日期

2003-7-9

推文