臺灣博碩士論文加值系統

本論文提出一具有穩定數值解的數學模型來鑑別工具機之幾何誤差，為求得數學模型需先利用齊次轉換矩陣解出該工具機之運動學及體積誤差模型，五軸工具機整體誤差可分為三線性軸的21項誤差與兩旋轉軸的22項誤差，其中兩旋轉軸誤差又可分為12項元件誤差及10項位置誤差。求解兩旋轉軸22項誤差之前需先利用Renishaw雷射干涉儀量測三線性軸誤差並進行補償，接著經過矩陣分析將旋轉軸的22項誤差與6項量測儀器架設誤差降為9項線性相依誤差與2項線性獨立誤差，接著使用R-test進行量測實驗，將量測資料代入本論文所提出的數學模型，即可求得最多11項的誤差，最後進行實機測試補償8項位置誤差，三個向量的誤差量在補償前最大誤差為Y方向，可在補償後下降98.6 um，驗證此方法之可行性。

This paper proposes a mathematical model with a stable numerical solution to solve the geometric error of any machine tool. In order to obtain the mathematical model, the kinematics equation and volumetric error model of the machine tool must be derived by using the homogeneous transformation matrix.
The overall error of the five-axis machine tool can be divided into 21 errors of the trilinear axis and 22 errors of the two rotation axes. The rotation axis subtracts two rotation errors which are relative to itself, and can be divided into 12 Error motions and 8 Locaion errors. Before deriving the rotation axis error, the Renishaw laser interferometer and Ballbar should be used to measure and compensate the trilinear axis error. Through matrix analysis, the 22 linear independent errors of the rotation axis and the 6 erecting errors of the measuring instruments are reduced to 9 linear dependent errors and 2 linear independent errors, among them, the 8 Location errors of the rotation axis are dispersed in the 9 linear dependent errors. Then, using R-test to carry out the measurement experiment, substituting the measurement data into the mathematical model proposed in this paper, and can get up to 11 errors.
Finally, the real machine test compensates for 8 Location errors. The volume error of the three vectors Y-axis can be reduced by 98.6 um after compensation , which verifies the feasibility of this method.

摘要......i
Abstract......ii
誌謝......iii
目錄......iv
表目錄......vi
圖目錄......vii
符號說明......viii
第一章 緒論......1
1.1 研究動機與目的......1
1.2 文獻探討......1
1.2.1 誤差模型......1
1.2.2 誤差量測......2
1.2.3 誤差分析......2
1.3 研究方法......3
1.4 論文架構......3
第二章 工具機之座標轉換......4
2.1 機械座標系定義......4
2.2 齊次座標轉換矩陣......4
2.3 順逆向運動學......7
第三章 誤差建模與分析......10
3.1 工具機之誤差......10
3.1.1 元件誤差......10
3.1.2 組裝誤差......11
3.2 幾何誤差......12
3.3 工具機之幾何誤差模型推導......17
3.3.1 三軸工具機誤差建模......17
3.3.2 五軸工具機誤差建模......20
3.4 誤差矩陣特性......29
3.5 誤差單位之換算......31
第四章 實驗結果與驗證......32
4.1 實驗架構......32
4.1.2 量測儀器......33
4.1.3 誤差量測......33
4.1.4 誤差鑑別......34
4.2 誤差補償......35
4.3 體積誤差效應......37
第五章 結論與未來展望......40
參考文獻......41
附錄一 雷射干涉儀量測數據......44
附錄二 R-test量測數據......46
Extended Abstract......58

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