高速加工技術已成為工業先進國家之金屬加工業設備必備條件，而如何
克服熱效應造成熱誤差量與改善，其軟體補償的技術已成一熱門的研究課
題。目前的工具機廠對於高精度需求的機型，大部分以裝置光學尺來回授位
置訊號，如此一來可以解決滾珠螺桿的熱變形問題，但也增加了工具機的成
本。因此，近年來對於透過溫度來預測工具機熱誤差的研究也越來越多，因
為透過補償熱誤差所帶來的經濟效益會比裝置光學尺還佳，如此一來不僅能
提升產品在市場上的位階，也更能用較少的成本來參與市場競爭。
近年來關於熱補償所做的研究，並未考量工作臺與光學尺的變形。而本
論文提出新的熱誤差補償方法，使用雙雷射量測系統，量測工具機重複定位
誤差，以計算工作臺與光學尺之伸長量，並透過熱影像儀來確認熱源的位置
來裝置溫度感測器，並將傳動零件即時溫度與監測點溫度變量一起作為建立
迴歸模型的輸入變數，同時量測軸向重複定位誤差作為迴歸模型的輸出。為
了選出最佳的預測變數組合，透過變數相關係數計算來排除多元共線的問
題，再以判定係數R2 與均方誤差作為最佳組合索引的指標，找出最佳的預測
變數組合。實測結果得知，三軸的軸向熱誤差最多可得到80.93%的改善，與
其他現行方法比較有極大之改善。

High Speed Machining (HSM) technology has become the most important application in the metal cutting industry. The thermal error is the most important issue in high speed machining. Linear encoders are applied to reduce the ball
screw thermal deformation problem in high precision metal cutting, however, this approach increases the production cost. Most current researches are focused on thermal error prediction using temperature data. Thermal error ompensation
produces better cost ratio compared to the linear encoder and also improves the product quality.
Worktable and linear encoder deformation was not considered in the present thermal compensation research method. A new technique is developed in this work
to compensate for thermal errors. Two laser measurement systems are applied to acquire worktable and linear encoder thermal expansion. The heat sources are identified using thermal cameras and temperature sensors. The temperature sensors are applied to detect the real time temperature. A mathematical model is built using multivariable regression analysis based on the sensed temperature variation
and the thermal expansion. In order to select the best combination of predictive variable data, the multi-collinear problem is obviated by calculating the correlation
coefficient. The coefficient of determination (R2) and Mean Square Error (MSE) are determined as optimal indicators of a composite index that identifies the best combination of predictive variables. The experimental results show that the three axial thermal error can be improved by 80.93%.

中文摘要 i
英文摘要 ii
謝誌 iii
目錄 iv
圖目錄 vi
表目錄 x

第一章 緒論……………………………………………… 1
1.1 研究背景與動機……………………………………………………... 1
1.2 本論文之貢獻………..……………………………………………... 6
1.3 論文架構……………………………………………………………..7
第二章 工具機進給系統熱行為探討與分析…………………………………..9
2.1 工具機熱誤差補償方法之文獻探討…………………………….. 9
2.2 滾珠螺桿熱傳導分析…………………………………………….. 14
2.3 溫度感測器位置選擇……………………………………………… 19
2.4 工具機熱模型建立………………………………………………… 24
2.5 本章結論…………………………………………………………… 27
第三章 軸向補償系統建立…………………………………………………… 28
3.1 系統架構…………………………………………………………… 28
3.2 溫度量測模組設計………………………………………………… 29
3.3 軸向補償系統設計………………………………………………… 32
3.4 雷射量測系統建立………………………………………………… 35
3.5 本章結論…………………………………………………………… 52
第四章 實測結果統計與分析…………………………………………………. 53
4.1 變數相關係數分析結果…………………………………………… 53
4.2 變數組合最佳化分析結果………………………………………… 57
4.3 建模分析結果………………………………………………… 64
4.4 本章結論…………………………………………………………… 80
第五章 補償結果與討論………………………………………………………. 81
5.1 實驗結果與分析..…………………………………………………… 81
5.2 本章結論………..…………………………………………………… 96
第六章 結論與未來研究方向…………………………………………………97
6.1 結論……………..…………………………………………………… 97
6.2 未來研究方向…..………..…………………..……………………… 98

圖目錄
圖1.1 X 軸於進給速度10 m/min 進行暖機2 小時的量測結果 3
圖2.1 溫度與位移量測系統 12
圖2.2 微觀固體之一維熱傳導示意圖 14
圖2.3 平板表面熱對流示意圖 15
圖2.4 中空滾珠螺桿熱模型圖 17
圖2.5 後軸承座的熱影像 20
圖2.6 前軸承座的熱影像 20
圖2.7 滑塊與工作臺銜接處的熱影像 21
圖2.8 螺帽座溫度飽和後的熱影像 21
圖2.9 X 軸溫度感測器埋測的位置圖 22
圖2.10 溫度感器安置位置圖 23
圖2.11 變數相關係數意義圖 27
圖3.1 軸向補償的流程圖 29
圖3.2 溫度與電阻的轉換曲線圖 29
圖3.3 PT100 溫度轉換電路 30
圖3.4 儀表放大器電路 31
圖3.5 ADG506A 16 通道A/D 多工器電路圖 33
圖3.6 DAC7614 D/A converter 電路圖 34
圖3.7 DAC7614 輸出的四倍放大電路圖 34
圖3.8 定位與溫度變化之量測平臺 35
圖3.9 X 軸重複定位誤差量測流程圖 37
圖3.10 X 軸重複定位誤差量測示意圖 38
圖3.11 重複定位誤差量測示意圖 39
圖3.12 X 軸的雙雷射系統量測圖 40
圖3.13 雙雷射量測系統於X 軸位置0 mm 的重複定位誤差量測結果 41
圖3.14 雙雷射量測系統於X 軸位置400 mm 的重複定位誤差量測結果 41
圖3.15 雙雷射量測系統於X 軸位置800 mm 的重複定位誤差量測結果 42
圖3.16 雙雷射系統在不同位置的重複定位誤差相減結果 42
圖3.17 工作臺溫度量測結果 43
圖3.18 工作臺與光學尺的變形圖 45
圖3.19 X 軸工作臺與光學尺的變形細部分析圖 46
圖3.20 X 軸雙雷射量測系統的工作臺變形量測結果 47
圖3.21 X 軸雙雷射量測系統的光學尺變形量測結果 48
圖3.22 補償位置示意圖 49
圖3.23 軸向前端透視圖 50
圖3.24 編碼器系統雷射量測示意圖 52
圖4.1 光學尺系統的X 軸溫度量測結果 67
圖4.2 光學尺系統的X 軸單邊工作臺變形預測結果 67
圖4.3 光學尺系統的X 軸單邊光學尺變形預測結果 68
圖4.4 編碼器系統的X 軸溫度量測結果 69
圖4.5 編碼器系統的X 軸單邊工作臺變形預測結果 70
圖4.6 編碼器系統的X 軸位於位置0 mm 的螺桿變形預測結果 70
圖4.7 編碼器系統的X 軸位於位置400 mm 的螺桿變形預測結果 71
圖4.8 編碼器系統的X 軸位於位置800 mm 的螺桿變形預測結果 71
圖4.9 Y 軸光學尺系統的位置0 mm 重複定位誤差預測圖 72
圖4.10 Y 軸光學尺系統的位置250 mm 重複定位誤差預測圖 72
圖4.11 Y 軸光學尺系統的位置500 mm 重複定位誤差預測圖 73
圖4.12 Y 軸編碼器系統的位置0 mm 重複定位誤差預測圖 73
圖4.13 Y 軸編碼器系統的位置250 mm 重複定位誤差預測圖 74
圖4.14 Y 軸編碼器系統的位置500 mm 重複定位誤差預測圖 74
圖4.15 Z 軸光學尺系統的位置0 mm 重複定位誤差預測圖 75
圖4.16 Z 軸光學尺系統的位置250 mm 重複定位誤差預測圖 75
圖4.17 Z 軸光學尺系統的位置500 mm 重複定位誤差預測圖 76
圖4.18 Z 軸編碼器系統的位置0 mm 重複定位誤差預測圖 76
圖4.19 Z 軸編碼器系統的位置250 mm 重複定位誤差預測圖 77
圖4.20 Z 軸編碼器系統的位置500 mm 重複定位誤差預測圖 77
圖5.1 Y 軸的即時補償情形 82
圖5.2 溫度模組的輸出電壓變化量測 83
圖5.3 移動平均濾波器即時補償響應 84
圖5.4 X 軸光學尺系統的位置0 mm 補償結果 86
圖5.5 X 軸光學尺系統的位置800 mm 補償結果 87
圖5.6 X 軸編碼器系統的位置0 mm 補償結果 87
圖5.7 X 軸編碼器系統的位置800 mm 補償結果 88
圖5.8 Y 軸光學尺系統的位置0 mm 補償結果 88
圖5.9 Y 軸光學尺系統的位置250 mm 補償結果 89
圖5.10 Y 軸光學尺系統的位置500 mm 補償結果 90
圖5.11 Y 軸編碼器系統的位置0 mm 補償結果 90
圖5.12 Y 軸編碼器系統的位置250 mm 補償結果 91
圖5.13 Y 軸編碼器系統的位置500 mm 補償結果 91
圖5.14 Z 軸光學尺系統的位置0 mm 補償結果 92
圖5.15 Z 軸光學尺系統的位置250 mm 補償結果 93
圖5.16 Z 軸光學尺系統的位置500 mm 補償結果 93
圖5.17 Z 軸編碼器系統的位置0 mm 補償結果 94
圖5.18 Z 軸編碼器系統的位置250 mm 補償結果 94
圖5.19 Z 軸編碼器系統的位置500 mm 補償結果 95


表目錄
表2.1 溫升資料表 22
表4.1 X 軸編碼器系統的各溫度間相關係數計算表 54
表4.2 X 軸光學尺系統的各溫度間相關係數計算表 54
表4.3 Y 軸編碼器系統的各溫度間相關係數計算表 54
表4.4 Y 軸光學尺系統的各溫度間相關係數計算表 55
表4.5 Z 軸編碼器系統的各溫度間相關係數計算表 55
表4.6 Z 軸光學尺系統的各溫度間相關係數 55
表4.7 高相關係數之變數統計表 56
表4.8 X 軸光學尺系統的工作臺與光學尺各數量變數之最佳組合分析表 58
表4.9 X 軸編碼器系統的工作臺熱變形之各數量變數最佳組合分析表 59
表4.10 X 軸編碼器系統的滾珠螺桿熱變形之各數量變數最佳組合分析表 59
表4.11 Y 軸光學尺系統的各數量變數之最佳組合分析表 60
表4.12 Y 軸編碼器系統的各數量變數之最佳組合分析表 60
表4.13 Z 軸光學尺系統的各數量變數之最佳組合分析表 61
表4.14 Z 軸編碼器系統的各數量變數之最佳組合分析表 61
表4.15 最佳化變數組合分析結果 63
表4.16 X 軸建模資料分析表 64
表4.17 Y 軸建模資料分析表 65
表4.18 Z 軸建模資料分析表 65
表4.19 各軸光學尺系統熱誤差預測結果 78
表4.20 各軸編碼器系統熱誤差模型預測結果 79
表4.21 各軸光學尺系統與編碼器系統的預測結果比較表 80
表5.1 光學尺系統差補各軸熱誤償結果 85
表5.2 編碼器系統補償各軸熱誤差結果 85
表5.3 各軸光學尺系統與編碼器系統的補償結果比較表 96

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