本論文旨在針對反算問題於實際工程問題上之研究，演算法為反算法中的函數預測法又稱急遽遞減法(Steepest Descent Method)，研究主題可區分為三個章節分表如下：第一章為反算法於三維切削刀具熱通量之預測；第二章為反算法於高速主軸馬達冷卻條件之最佳化控制研究；第三章為反算法於高速主軸馬達內部熱通量之預測。
　　第一章旨在利用反算法中的急遽遞減法並結合熱流計算軟體CFX4.4來預測切削刀具於三維熱傳導問題中隨時間變化之未知熱通量。論文主要針對二組切削刀具在不同的幾何形狀、不同形式的未知熱通量函數、不同的量測表面以及不同的量測誤差下，來驗證所預測的準確度。結果顯示透過數值的反覆疊代後可以順利得到吾人所欲求解的未知熱通量函數，故能藉由此參數來控制加入切削油劑(或冷卻劑)之流量，以得到有效率的最佳冷卻方式，並且減少在切削過程中所產生的高熱現象。
　　第二章亦是利用急遽遞減法並結合熱流計算軟體CFX4.4，利用反算法預測三維內藏式主軸馬達冷卻水道中隨時間變化之有效最佳與實際的熱對流係數。本章分別針對在加熱面上二個不同的設計溫度範例，並依此設計溫度，對水道中的冷卻水之熱對流係數進行最佳化控制，結果證明了急遽遞減法在不須事前知道未知函數的形式下，即能成功地預測未知函數的形式，且可順利地求出可靠之控制函數。
　　由於為了避免造成內藏式主軸產生熱變位甚至熱破壞的發生，因此必須瞭解主軸馬達因銅損所產生之熱通量大小，並且結合於上一章中對冷卻水道的熱對流係數進行的預測，即可獲得最佳冷卻方式，進而提高高速切削加工之準確度。故同樣地，第三章仍然是利用相同的演算法來預測內藏式馬達高速主軸於三維熱傳導問題中隨時間變化之未知熱通量函數。本章針對二組不同形式的未知熱通量函數以及不同的量測誤差進行反算分析。最後，由所得的結果驗證了急遽遞減法卓越的數值運算能力，即本章在進行預測未知的熱通量函數之前，我們無須預先知道此函數的形式，即可藉由急遽遞減法以及電腦疊代的運算，便可獲得吾人所欲求解的未知有效熱通量函數，如此便能有效控制冷卻液體的流速，避免主軸因受熱而產生熱變位以及熱破壞。

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