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研究生:顏于鈞
研究生(外文):Yan, Yu-Chun
論文名稱:五軸工具機雙旋轉軸安裝誤差同步量測與驗證
論文名稱(外文):Synchronous Measurement and Verification of the Position-Independent Geometric Errors of Dual Rotary Axes on Five-axis Machine Tools
指導教授:劉建聖
指導教授(外文):Liu, Chien-Sheng
口試委員:陳昱達林昌進蒲宏彥劉建聖
口試日期:2023-06-13
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2023
畢業學年度:111
語文別:中文
論文頁數:119
中文關鍵詞:五軸工具機旋轉軸雙軸同動安裝誤差觸發式測頭
外文關鍵詞:Five-axis machine toolrotary axisinstallation errortouch-trigger probedual-axis synchronized motion.
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本篇論文將針對五軸工具機的兩個旋轉軸提出一套幾何誤差之八項安裝誤差的雙軸同動同步量測系統,此系統以百德機械的MF400U五軸工具機作為實驗載體,該機台為業界常見的中小型搖籃式工具機,並使用觸發式測頭並搭配兩顆標準基準球,利用此基準球之標準特性回推工具機誤差。研究特點為幾何誤差之安裝誤差在雙旋轉軸同動的路徑下將定位誤差同步量測,藉由一次量測實驗路徑直接解析出這兩個軸的誤差項。預期能改善以往研究只能夠一次量測一個轉軸之缺點。
實驗載具為工作檯傾斜型,通過旋轉軸之間的組合,固定在工作檯面上的工件除了底面之外,剩餘的五個面向都可以透過立式主軸進行加工。研究將針對旋轉軸幾何誤差中的安裝誤差。計算過程包括機器誤差的數學建模、正向和反向運動學的推導和誤差分析方程的建立,以及用最小平方法解決線性超定系統,其變數為幾何誤差。在求解誤差值之前,對整個數學算法進行了模擬,以確保計算過程的準確性。模擬結果也證實了這種測量方法的可行性。
實驗過程會進行觸發式測頭的校正程序,校正完畢便可開始量測兩顆標準基準球之機械座標值。將誤差分析的方程式藉由程式撰寫進電腦端,並將實驗量測所取得的基準球數據代入程式計算出八項安裝誤差。量測完成後再透過Heidenhain控制器中的補償表格功能進行安裝誤差的補償,再透過實際量測比較補償前後的差異,將結果用以驗證量測的結果以及討論補償的優劣。
This paper proposes a dual-axis synchronized measurement system for eight assembly errors of two rotating axes in a five-axis machine tool. The system is based on the MF400U five-axis machine tool from Bede Machinery and uses a touch-trigger probe with two standard calibration spheres to measure the standard characteristics of the calibration spheres and infer the machine tool errors. The research focuses on the assembly errors in the geometric errors of the rotating axes, and measures the positioning errors synchronously in the path of the dual rotating axes. By analyzing the errors from a single experimental path, the error terms of both axes can be obtained, which improves the limitation of previous research that could only measure one axis at a time.

The study focuses on the assembly errors in the geometric errors of the rotating axes. The calculation process includes mathematical modeling of machine errors, derivation of forward and inverse kinematics, establishment of error analysis equations, and solution of linear overdetermined systems using the least squares method with geometric errors as variables.

During the experimental process, the calibration procedure of the trigger-type probe is performed, and the data of the reference spheres obtained from the experimental measurement are input into the program. After the measurement is completed, the compensation table of Heidenhain is used to compensate for the assembly errors, and the difference before and after compensation is compared through actual measurements to verify the measurement results and discuss the advantages and disadvantages of the compensation.
摘要 I
ABSTRACT II
誌謝 VII
目錄 VIII
圖目錄 X
表目錄 XIII
符號說明 XIV
第一章 緒論 1
1-1 研究背景 1
1-2 研究動機與目的 3
1-3 論文架構 4
第二章 文獻回顧 5
2-1 機台構型分類 5
2-2 幾何誤差來源與定義 7
2-3 線性軸幾何誤差量測方法 17
2-4 旋轉軸幾何誤差量測方法 20
2-5 工具機數學模型建立 26
第三章 系統架構與量測原理 40
3-1 實驗載具介紹 40
3-2 量測設備介紹 43
3-3 量測系統構建 47
3-4 量測目標及原理說明 49
第四章 量測幾何誤差模型之建立 54
4-1 系統架構 54
4-2 正向運動學數學模型建立 59
4-3 逆向運動學 69
第五章 實驗結果與討論 74
5-1 實驗方法與流程 74
5-2 實驗誤差計算與量測結果 79
5-3 量測誤差分析與討論 84
5-4 小結 96
第六章 誤差補償與驗證 97
6-1 常見的誤差補償方法 97
6-2 海德漢控制器補償 98
6-3 海德漢Option52功能補償 101
第七章 結論與未來規劃 104
7-1 結論 104
7-2 未來規劃 106
參考文獻 107
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