本研究發展新的逆解法，由電蝕損傷來逆向解析暫態熱源。假設電蝕凹孔的輪廓曲線是材料的熔點溫度，然後用內差法計算出格點上最後時間的溫度，計算出的溫度會包含量測誤差。再利用線性最小平方誤差法來逆向反求未知的暫態熱源參數—陽極表面上電弧半徑隨時間變化的關係、電弧功率及電弧作用在陽極接點上的能量效率。因為量測點的溫度包含誤差，待求的未知數的個數較少時，可逆向求得正解。逆解法對於量測誤差非常的靈敏。

An inverse method is developed to analyze the transient heat source from arc erosion. The temperature at the contour of arc erosion is assumed as melting point. And the temperature in grid points at the last time is calculated by interpolation, which include measurement errors. Then, the unknown parameters of transient heat source can be solved by linear least-squares error method. These parameters are plasma radius at the anode surface grows with time, arc power, and plasma flushing efficiency on the anode. Because the temperature in measuring points includes measurement errors, the exact solution can be found when fewer unknowns are considered. The inverse method is sensitivity to measurement errors.

總 目 錄
頁次
中文摘要 i
英文摘要 ii
總目錄 iii
圖目錄 v
表目錄 xi
符號說明 xii
第一章 緒論 1
1-1 研究動機 1
1-2 文獻回顧 1
1-3 研究目的 3
1-4 本文架構 3
第二章 研究方法 4
2-1 簡介 4
2-2 本文的逆解法 5
2-3 本文逆解法在二維暫態熱傳問題之應用 9
2-3-1 統御方程式與起始條件、邊界條件 9
2-3-2 邊界條件為已知時之直接解 10
2-3-3 用本文逆解法求出未知邊界的結果 10
第三章 電氣接點損傷之模擬分析 19
3-1 數學模式 19
3-2 直接解法 21
3-3 逆解法 24
3-3-1 電弧功率的逆解法 24
3-3-2 電弧半徑的逆解法 25
第四章 結果與討論 31
4-1 前言 31
4-2 在固定的電弧半徑條件下，逆解電弧功率之結果分析 31
4-2-1 邊界條件為已知之直接解 31
4-2-2 逆解電弧功率 32
4-3 在電弧半徑為時間函數的條件下，逆解電弧功率之結果分析 55
4-3-1 邊界條件為已知時之直接解 55
4-3-2 逆解電弧功率 55
4-4 在電弧半徑為時間函數的條件下，逆解電弧半徑之結果分析 79
4-4-1 邊界條件為已知時之直接解 79
4-4-2 逆解電弧半徑 79
第五章 結論與建議 88
5-1 結論 88
5-2 未來研究方向之建議 89
參考文獻 90

參考文獻

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