光機整合分析應用於620mm反射鏡變形分析與八吋反射鏡彈性膠緊固設計

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游振廷(ZHEN-TING YOU) 查詢紙本館藏

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光機電工程研究所

論文名稱

光機整合分析應用於620mm反射鏡變形分析與八吋反射鏡彈性膠緊固設計
(Applying Integrated optomechanical analysis to the Deformation of a 620mm Collimator Mirror and Elastometric Mount Design of an 8-Inch Mirror)

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摘要(中)

本論文針對兩種反射鏡變形進行光機整合分析，前半部為口徑620mm Zerodur準直儀反射鏡變形分析，旨在探討支撐與調整機構對鏡面變形產生的影響。主鏡的材料種類、減重結構形式、支撐與組裝方式等因素會影響主鏡成像品質，本研究利用有限元素法，通過改變邊界條件與支撐位置貼近真實工作情形，再利用調整螺絲對主鏡自重變形進行改善，最後得到最佳調整結果。第二部分則利用相同光機分析流程，對八吋反射鏡片以RTV(Room temperature culcanizing)膠合固定方式進行模擬，從溫度、膠黏面積與共振頻率等方面進行探討，最後串聯最佳化軟體找出最佳膠合厚度。實驗方面則利用最佳化設計的膠合模型，設計相對應的灌膠輔助治具完成六片式分散式膠合，並且藉由環境溫度的改變，驗證膠合固定對鏡面的影響，同時以干涉儀進行量測。
一般光學分析不易計算鏡面受力變形對光學品質所產生的結果，本研究建立一套光機分析的流程，使用自行撰寫光機轉換程式，整合有限元素法與Zernike多項式曲面擬合，能將鏡面變形之節點資料匯入程式中進行分析，結合模擬在結構變形上的預測，進而觀察對光學層面上的影響，以利後續光學機構設計目的使用。

摘要(英)

This article builds an opto-mechanical analysis process based on finite element analysis and optimization. The deformation and stress of mirror caused by supporting and adhesives were discussed in this study. A 620 mm collimator mirror made of Zerodur was analyzed to obtain the deformation induced by gravity. The lightweighting structure and supporting structure of mirror also affect the optical quality. The best performance of the collimator mirror was investigated through several analysis under different boundary conditions, supporting positions of the inner ring and the adjustment actuators. The data of deformation of the mirror was obtained by using finite element analysis, Zernike polynomial was also adopted to fit the optical surface to calculate the corresponding aberrations by using opto-mechnacal analysis program. On the other hand, selecting the proper thickness of RTV elastomer is critical to minimize the effect of geometry, structure and thermal variation. Eventually, the best thickness of RTV elastomer was found by using optimization algorithm connected to finite element analysis.

關鍵字(中)

★ 光機整合分析
★ 有限元素分析
★ 鏡面變形
★ 彈性膠
★ 絕熱設計
★ 最佳化

關鍵字(英)

★ Optomechancal analysis
★ Finite element analysis
★ Surface deformation
★ Elastomer
★ Athermal design
★ Optimization

論文目次

摘要 i
Abstract ii
致謝 iii
目錄 iv
圖目錄 vi
表目錄 xi
一、緒論 1
1-1 前言 1
1-2 文獻回顧 2
1-2-1 反射鏡支撐與固定方式 2
1-2-2 反射鏡面變形分析 5
1-2-3 RTV膠合固定與絕熱厚度設計分析 7
1-3 研究目的與動機 10
二、基礎理論 11
2-1 初階像差介紹[27] 11
2-1-1 球面像差(Spherical aberration) 12
2-1-2 彗星像差(Coma) 12
2-1-3 像散(Astigmatism) 13
2-1-4 場曲(Field curvature) 13
2-1-5 畸變(Distortion) 14
2-2 實驗用干涉儀介紹 14
2-3 實驗用波前感測器介紹 16
2-4 光機轉換程式 16
2-4-1 光學曲面變形分析 17
2-4-2 Zernike多項式擬合 20
2-4-3 Zernike多項式係數[13] 22
2-4-4 曲面節點誤差分析結果與討論 22
2-5 RTV膠合設計分析 24
三、準直儀反射鏡模擬分析 27
3-1 研究流程與架構 27
3-2 模型幾何外型與材料性質 28
3-3 有限元素模擬 31
3-3-1 邊界條件 31
3-3-2 內環支撐 33
3-3-3 網格設定 34
3-4 自重變形分析結果與討論 36
3-5 調整機構模擬與分析 40
3-5-1 調整螺絲位置分布與前進位移關係 41
3-5-2 反射鏡自重變形模擬與量測結果比較 43
3-5-3 反射鏡自重變形模擬與量測最佳調整分析結果 45
3-6結果與討論 49
四、八吋反射鏡膠合固定分析 50
4-1 研究流程與架構 50
4-2 模型幾何外型與材料性質 51
4-3 有限元素模擬 52
4-3-1 邊界條件與膠黏方式 52
4-3-2 膠黏厚度對鏡面影響模擬分析 54
4-3-2 重力與溫度個別影響 58
4-3-3 最小膠黏面積分析 63
4-4 膠合最佳化設計 65
4-4-1 膠黏面積與厚度最佳化 66
4-4-2 灌膠輔助治具設計 67
4-4-3 灌膠流程 68
4-5 實驗架構 75
4-6 實驗量測結果比較 76
4-6-1 膠合固定方式實驗量測結果 76
4-6-2 彈片(Clip)固定方式實驗量測結果 80
4-7 結果與討論 84
五、結論與未來工作 85
5-1 結論 85
5-2 未來工作 86
參考文獻 87
附錄 91
附錄A 支撐位置與應力變形與像差分布圖 91
附錄B 調整螺絲旋轉度數與應力、像差關係圖 101
附錄C 膠合厚度對鏡面影響分析 106
附錄D 膠合面積對鏡面影響分析 121
附錄E 溫度與重力個別分析-六片式分散式膠合 122
附錄F 灌膠輔助治具與Mount設計 135
附錄G 灌膠過程照片 137
附錄H 實驗架設照片 143
附錄I 膠合溫度實驗量測結果 144
附錄J 光機轉換程式與現行商業軟體比較 148

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指導教授

陳怡呈(YI-CHENG CHEN)

審核日期

2015-8-17

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