五軸加工效能改進-利用誤差控制與刀具軸向平滑化

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研究生：	何明哲 Ming-Che Ho
論文名稱：	五軸加工效能改進-利用誤差控制與刀具軸向平滑化 Five-axis Machining Improvement via Cutting Error Control and Tool Orientation Smoothing
指導教授：	黃衍任 Yean-Ren Hwang
口試委員:
學位類別：	博士 Doctor
系所名稱：	工學院 - 機械工程學系 Department of Mechanical Engineering
畢業學年度：	92
語文別：	英文
論文頁數：	119
中文關鍵詞：	五軸加工、刀具路徑規劃、加工精度控制、刀具軸向指定
外文關鍵詞：	five-axis machining, tool-path generation, cutting-error control, tool-orientation assignment
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五軸加工機具有加工效率佳與加工品質好之特性，為現代機械工業不可或缺的工具，應用範圍相當廣，從航空、造船、汽車、塑膠、模具或到光學產業，都可利用五軸加工機來執行各式加工任務。但是五軸加工機涉及的各軸運動關係相當複雜，且求解困難，同時機組昂貴，若撞機維修所費不貲。所以刀具路徑必須妥善計算，才能達成預期效能，發揮五軸加工的優勢。
近年來五軸加工研究方法，不是將複雜的問題簡化與系統化，就是針對特定情況進行單獨推導。前者歸納出簡單的數學式子，應用上較具彈性，但由於五軸加工各軸運動關係較三軸加工複雜許多，傳統的簡化觀點顯得不夠周延，常導致預期之外的錯誤；而後者雖歸納出簡單且周延的數學式子，但只適合特定情況，應用上沒有彈性。本研究仔細分析五軸加工各軸運動模式，提出全新的五軸加工觀點，並歸納一套系統化的法則，只需經過簡單的參數設定，就可以產生各種機台的切削碼程式，同時滿足加工精度與加工效率，並達到刀具路徑自動規劃的要求。
本研究內容包括：(一)建構工具機各軸的動態模型，及分析刀具和工件間相對的幾何關係。 (二)研發弦高誤差估算與貝丘高度控制演算法。(三)綜合弦高誤差估算演算法與貝丘高度控制演算法，提出刀具接觸點產生法則。(四)研發無干涉且平滑的刀具軸向指定方法。(五) 綜合刀具接觸點產生法則與刀具軸向指定方法，提出刀具路徑產生程序。

Comparing to three-axis machines, five-axis machines perform more efficient and accurate machining. It has become an important tool for modern engineering industries and is widely used in aerospace, shipbuilding, automobile, plastic, mold, and optical industries. However the kinematic equations of five-axis machines are highly complex, and hard to solve. A careless collision between the parts of the machine will be a disaster, because the maintenance is extremely expensive. Therefore, the tool paths should be computed correctly in order to fully exploit the flexibility of five-axis machines.
These methodologies can be considered only either the simplifications of the machine systems or the applications for some special circumstances. The former methodologies obtain mathematical models by simplifying some factors which can be applied flexibly. However, due to the kinematic complication, it is hardly to fulfill all five-axis machining conditions. Consequently, it results in unexpected errors. The latter methodologies, researchers try to limit the scope of the machining conditions to overcome the problems. However, this will deteriorate the flexibility of the resulted equations seriously. In this dissertation, a systematic methodology is developed to obtain the exact kinematic motions among axes of the machine through simple kinematic parameter assignment. Based on these accurate kinematic equations, efficient tool paths are determined.
This research comprises the following tasks: (1) analyze the kinematic relation between the machine tools, and the geometric relation between the cutter and the part surface; (2) develop generalized formulae for the chordal deviation estimation and the scallop height control, which can be applied to all types of five-axis machines; (3) develop the CCPG method, which combines the CDE algorithm and the SHC algorithm in order to improve the machined surface quality; (4) develop the TOS method, which can be used to assign interference-free and smooth tool orientations; (5) combine the TOS method and the CCPG method to form a new tool-path generation procedure.

摘要								I
Abstract								II
Acknowledgement							III
Contents								IV
Figure List							VI
Table List							IX
Nomenclature							X
Chapter 1 Introduction						1
1 Motivation							1
2 Related Works							3
3 Research Methodology						6
4 Organization of the Dissertation					8
Chapter 2 Kinematic Model for the Five-axis Machine			10
1 Introduction							10
2 Five-axis Machine Tools						10
2.1 Classification of Five-axis Machines				10
2.2 Dimension of the Generalized Cutter				12
3 Coordinate Definition						14
4 Manipulator Kinematics of the Machine				17
5 Postprocessor for a Five-axis Machine				19
5.1 Kinematic Model of a Five-axis Machine				20
5.2 Postprocessor for a Table-tilting Type Five-axis Machine		22
5.3 Machine Rotational Angle Arrangement Method			25
Chapter 3 Computational Geometry for Five-axis Machining		29
1 Introduction							29
2 Effective Surface Curvature					29
3 Effective Cutting Curvature					32
3.1 Generalized Tool Description for Five-axis Machining		33
3.2 Effective Cutting Profile of a Generalized Inclined Cutter	34
3.3 Effective Cutting Curvature of the Effective Cutting Profile	37
4 Parametric Increment Conversion Method				39
4.1 Marching along a Marching Direction				40
4.2 Error Compensation Algorithm					41
4.3 The Parameter Adjusting Algorithm				43
4.4 Procedures for the PIC Method					44
Chapter 4 Cutter Contact Point Generation for Five-axis Machining	46
1 Introduction							46
2 Chordal Deviation Estimation Algorithm				47
2.1 Traditional CDE Algorithm					48
2.2 Modification on Traditional CDE Algorithms			50
2.3 Generalized CDE Algorithm Using D-H Matrix			58
3 Scallop Height Control Algorithm					61
3.1 SHC Algorithm for a Convex Surface				64
3.2 SHC Algorithm for a Concave Surface				68
3.3 SHC Algorithm for a Flat Surface				71
4 CC Point Generation Method					72
Chapter 5 Tool Orientation Smoothing for Five-axis Machining		76
1 Introduction							76
2 Quaternion Interpolation of Tool Orientations			77
3 Interference Avoidance of Tool Orientations			80
3.1 Gouge Avoidance Algorithm					80
3.2 Collision Avoidance Algorithm					82
4 Tool Orientation Smoothing Method				83
Chapter 6 Tool Path Generation for Five-axis Machining			88
1 Introduction							88
2 Tool Path Generation Procedure					88
3 Machining Experiments						92
3.1 Verification of the Performances of the CCPG method		92
3.2 Further Verification of the Tool-path Generation Procedure	97
Chapter 7 Conclusion and Future Trend				111
1 Conclusion							111
2 Future Trend							111
Reference								113

                                

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