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研究生:許維中
研究生(外文):Hsu, Wei-Chung
論文名稱:六維運動量測裝置量測五軸工具機之誤差
論文名稱(外文):Measurement of Errors of Five-Axis Machine Tools using 6D-MMD
指導教授:雷衛台
指導教授(外文):Lei, Wei-Tai
學位類別:碩士
校院名稱:國立清華大學
系所名稱:動力機械工程學系
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:2009
畢業學年度:97
語文別:中文
論文頁數:88
中文關鍵詞:六維運動量測裝置史都華平台最小平方法體積誤差誤差建模
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六維運動量測裝置(Six Degree of Freedom Motion - Measurement Device,6D-MMD)為史都華平台機構之一應用,將六隻連接伸縮桿改成被動式精密量測球桿,當上下平台因CNC工具機驅動定位而產生相對運動,可從量測得六隻雙球桿桿長值的變化,計算出上下平台間6D相對運動的關係,即得出CNC工具機驅動定位之位置及轉動角。
本論文首先藉由誤差建模,說明六維運動量測裝置的量測值與誤差項之間的關係;接著,以最小平方法擬合計算出CNC工具機的運動軸線。隨後,建立標準量測程序,以取得必要的量測值;最後,根據理想量具與特定機構參數,以6D-MMD量測值推算出五軸CNC工具機中的各項聯結誤差項。
如此,便可以量測出CNC工具機每個線性軸與轉動軸之定位誤差。以三線性軸的CNC工具機為例,每軸六個定位誤差,再加上三軸彼此間的三個垂直度誤差,總共有21個誤差項可被量測。而在五軸同動工具機上,則增加轉動軸每軸6個定位誤差項,和5個軸線偏心與偏轉誤差項,以及床台誤差項等,經整併計算,六維運動量測裝置共可在一次架設量測中求得43項體積誤差,實為量具系統發展之創舉。
本論文最後以模擬五軸工具機各項誤差與運動的方式,以設定的各項誤差參數,實際製造出與六維運動量測系統量測值具有一樣意義的數據;隨後將數據代入數據處理程式中,直接算得各項聯結誤差與運動位置誤差,以驗證數據處理的理論與可行性,模擬結果證實能確實計算出各項設定的誤差項。
摘要 I
目錄 II
圖目錄 IV
表目錄 VII
1. 簡介 1
2. 文獻回顧 2
2.1. 五軸工具機之誤差建模 2
2.2. 史都華平台機構公式 3
2.3. CNC工具機量測裝置回顧 4
2.4. 研究目的 7
3. 六維運動量測系統量測值與誤差模型之關係 8
3.1. 五軸工具機誤差建模 9
4. 數據處理使用之數學方法簡介 17
4.1. 最小平方法(Least-square)簡介 18
4.2. 以最小平方法擬合空間中直線 19
4.2.1. 以特定變數做為相關變量進行最小平方法擬合 19
4.2.2. 以點至擬合線之距離進行最小平方法擬合 20
4.3. 實現以奇異值分解法擬合最小平方問題:空間中直線 22
4.4. 以最小平方法擬合空間中圓 23
5. 六維運動量測裝置之量測方法 25
5.1. 線性軸量測方法 26
5.2. 轉動軸量測方法 31
6. 量測資料數據處理之誤差項計算 32
6.1. 三軸工具機誤差項數據處理流程 32
6.1.1. 計算垂直度誤差與理想軸線 32
6.1.2. 建立理想機器座標系 34
6.1.3. 計算線性軸各項誤差 35
6.2. 五軸工具機誤差項數據處理流程 37
6.2.1. 建立簡化模型整併誤差項 38
6.2.2. 計算轉動軸誤差項 39
6.2.3. 計算床台轉動誤差項 41
6.2.4. 計算聯結偏移誤差項 42
6.2.5. 計算各項運動誤差項 46
7. 量測系統 47
7.1. 系統軟體模組 47
7.3. 程式畫面 50
8. 系統模擬 52
8.1. 系統模擬方法 52
8.2. 模擬結果 53
8.2.1. 模擬設計(1):聯結誤差項驗證 53
8.2.2. 模擬設計(2):運動位移誤差項驗證 58
8.3. 模擬結果討論 84
9. 結論 85
10. 參考文獻 86
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