本研究主要在建立非球面(Aspheric)光學射出元件表面精度之補正技術，藉由使用不同函數對光學射出元件之輪廓誤差進行曲線擬合，對模仁進行一至多次誤差補正加工，求得最佳輪廓誤差補正方式。實驗中使用表面輪廓儀(Form Talysurf)對射出鏡片表面輪廓進行量測，將光學元件之模仁加工誤差與射出成型產生的變形量匯入自行撰寫之補正程式進行曲線擬合，並產生刀具路徑進行誤差補正加工，且藉由多次補正加工至形狀精度達到最佳為止。曲線擬合所使用的函數分別為多項式、雲線及指數三種，擬合過程則是使用最大陡降法、單形法、Levenberg-Marquardt法及高斯-牛頓法四種演算法進行計算。由實驗結果顯示，利用不同函數的誤差補正技術進行輪廓修整加工，可有效降低其殘留誤差，而改善射出件之輪廓精度，而在使用刀鼻半徑為0.5278mm刀具時，以指數函數搭配高斯-牛頓演算法進行第二次補正可得最佳之輪廓精度，其PV值為0.6679μm，改善率為91.62%，表面粗糙度為Ra0.1059μm。

In this study a surface precision compensation technology was used to perform error compensation machining for aspheric molded optical parts. Different functions were used to implement curve-fitting for the form error of injection molded optical products. Single or multiple error compensation machining iterations were executed to identify the optimized form error compensation practice. A surface profilometer (Form Talysurf) was used to measure the surface contour of the injection molded optical lens. The machining error of the mold insert, together with the warpage for the injection molding product, was imported into an innovative error compensation program to perform curve fitting and to generate tool path for error compensation machining; the machining iterations were implemented until the optimized form precision was achieved. The three types of curve fitting function used are polynomial, spline and exponential functions, and the four algorithms used are the steepest descent, Simplex, Levenberg-Marquardt and Gauss-Newton methods. The result of experiment indicated that modification machining based on the compensation technology effectively reduces residual error and improves form precision of the lens. The optimized form precision was achieved by performing two compensation iterations using tools radius of 0.5278mm with exponential curve-fitting function and the Gauss-Newton algorithm. The form precision of lens after the second compensation iteration was 0.6679μm and the roughness was 0.1059μm; an improvement rate of 91.62% in form precision was achieved compared with the initial form precision of lens.

摘 要
目錄 I
圖目錄 III
表目錄 V
符號索引 VII
第一章 緒論 1
1.1 研究背景與目的 1
1.2問題敘述 2
1.3研究流程 2
1.4論文架構 2
第二章 文獻回顧 4
2.1 誤差補正相關文獻 4
2.2 加工精度相關文獻 6
第三章 理論基礎 8
3.1 非球面定義 8
3.2 射出成型原理與流程 10
3.3 輪廓精度定義 10
3.4表面粗糙度定義 10
3.5曲線擬合過程 12
3.6 最佳化方法 14
3.7迴歸曲線方程式檢測 17
3.8誤差改善率 18
第四章 實驗方法 19
4.1 實驗設備 19
4.2 實驗材料 26
4.3 實驗刀具 29
4.4 最佳射出成型參數 29
4.5 實驗流程 32
第五章 結果與討論 34
5.1 射出成型之實驗 37
5.2 實驗之穩定性 44
5.3 刀鼻半徑之影響 52
5.4 擬合函數與演算法之影響 61
5.5 補正次數 68
5.6最佳補正結果與比較 77
第六章 結論 80
參考文獻 81

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