射出成型精密光學鏡片之幾何精度是一重要的品質需求，然而即使幾何尺寸符合標準，也有可能其光學性質評估仍不合格，這是因為成型產品有雙折射的存在；若雙折射過大則會造成光學系統之光程差，不易透過組合透鏡等方法做像差矯正。所以，為使塑膠射出光學鏡片良率提高，對於成型過程所可能產生之雙折射研究就顯得非常重要。本研究運用流變學實驗，結合流變學理論，取得光學材料之流變參數與彈性參數，並運用Moldex3D模流軟體，對光學凸透鏡進行模流分析，並將目標鎖定於雙折射之分析探討。本研究分別採用三個流變模式(White-Metzner、Phan-Thien Tanner、Giesekus Models)，針對COP(Zeonex 480R)與PMMA(Kurary GH-1000S)兩種光學材料，以Moldex3D軟體作模流分析。從模擬計算之雙折射與光彈條紋的分布來看，是以流動所造成之殘留應力為主要影響因素，而且在澆口附近的雙折射最為嚴重。再與實射成品之光彈條紋實驗值比較，發現以PTT模式所得模擬結果最為接近。
本研究另針對PMMA材料，進行蠕變/回復實驗，輔以Burger模式之參數迴歸分析，探討材料之彈性效應。在PMMA這支材料上，可以發現當溫度升高時，材料彈性效應會越衰減；此外，當蠕變時間越長時，材料之彈性效應會減弱。

For the injected optical lens, the geometric precision is really an important quality requirement. But, even standard geometry, the optical properties are probably assessed to be unsatisfactory, because of the existence of the part birefringence. Severe birefringence in the optical part could cause the optical path difference in the optical system, which is not easy to be overcome through the optical aberration correction or other methods. Therefore, in order to improve the yield of the injected optical lenses, the investigation of the induced birefringence generated during the molding process is very important. In this study, the rheological measurements along with the theoretical models were firstly used to obtain the material parameters, and then the commercial Moldex3D software was applied to numerically simulate the injection molding process of the concave lens, focusing on the analysis of the birefringence inside the molded part. Three kinds of rheological models ( White-Metzner, Phan-Thien Tanner and Giesekus Models) and one kind of creep equation ( Burger Model ) were employed in the software with the COP (Zeonex 480R) and PMMA(Kurary GH-1000S) material. The creep/recovery experiment were conducted to discuss the factors which impact the elastic effect. It resulted that elastic effects of PMMA would be more obvious with the rise of the temperature; however, increasing the creep time would weak the elastic effect. From the simulated birefringence and the photoelastic fringes, it was found that the flow-induced, rather than the thermal-induced, residual stress is the major factor to bring about the birefringence, and it was the most serious near the gate. It was also found that the simulated photoelastic fringes by using the PTT model can show the most agreements with the experimental results among the three models in this study.

本文目錄	                                            I
表目錄	                                                   IV
圖目錄	                                                    V
符號說明	                                           IX
第一章	緒論	                                            1
1.1 前言	                                            1
1.2 文獻回顧	                                            3
1.3 研究動機與目的	                                    6
第二章	理論介紹                                            8
2.1 射出成型製程	                                    8
2.2 流變學理論	                                            9
2.2.1 蠕變實驗	                                           10
2.2.2 WLF方程式	                                           11
2.2.3 Cross 模式	                                   12
2.2.4 Cox-Merz & Laun's 關係式	                           13
2.2.5 Maxwell(Multi-Mode)模式	                           15
2.3 流變學模式	                                           15
2.3.1 White-Metzner流變模式	                           16
2.3.2 Phan-Thien-Tanner流變模式	                           17
2.3.3 Giesekus流變模式	                                   19
2.4 CAE應用於射出成型光學鏡片	                           20
2.4.1 殘留應力	                                           21
2.4.2 光學性質分析	                                   22
第三章	研究方法	                                   24
3.1 實驗材料	                                           24
3.1.1 PMMA(聚甲基丙烯酸甲酯)	                           24
3.1.2 COP(環烯烴聚合物)	                                   24
3.2 實驗流程	                                           26
3.3 實驗設備與操作條件	                                   27
3.3.1 振幅掃描	                                           28
3.3.2 頻率掃描	                                           29
3.3.3 穩態剪切黏度	                                   30
3.3.4 N1正向應力差	                                   30
3.3.5 蠕變實驗	                                           31
3.4 CAE射出成型模流分析介紹與設定	                   31
3.5 流變儀實驗-穩態溫度掃描	                           35
3.5.1 流變儀實驗-穩態黏度測試	                           37
3.5.2 流變儀實驗-動態頻率測試	                           39
3.5.3 流變儀實驗-N1測試	                                   42
3.5.4 蠕變回復(Creep/Recovery)實驗	                   43
3.6 動態力學分析(DMA)實驗-溫度掃描測試	                   45
3.6.1 動態力學分析(DMA)實驗-頻率掃描測試	           48
第四章	結果與討論	                                   49
4.1 蠕變/回復 實驗	                                   49
4.1.1 蠕變/回復(Burger Model)驗證	                   54
4.2 Cross模式黏度參數擬合	                           57
4.3 Modified White-Metzner流變模式參數擬合	           62
4.4 WLF方程式參數整合	                                   67
4.4.1 WLF方程式參數驗證	                                   70
4.5 Maxwell (Multi-Mode) 參數擬合	                   72
4.6 Phan-Thien-Tanner流變模式	                           76
4.7 Giesekus流變模式參數應用	                           80
4.8 黏彈模型比較	                                   82
4.9 材料參數改變的影響	                                   84
4.9.1 黏度改變	                                           84
4.9.2 黏彈參數改變	                                   86
第五章	結論	                                           88
第六章	未來研究方向	                                   90
第七章	參考文獻	                                   91
附錄(A) PTT.Giesekus 參數求解	                          101
附錄(B) W-M流變模式推導	                                  106
附錄(C) PTT流變模式推導	                                  111
附錄(D) Giesekus流變模式推導	                          117
附錄(E) Burger Model推導	                          120
附錄(E) Moldex3D 內建材料特性	                          123

表目錄
表 3.1.1實驗材料性質表	                                   25
表 3.4.1模型網格資訊	                                   33
表 3.4.2成型條件表	                                   34
表 4.1.1 PMMA在不同溫度之黏彈係數表	                   53
表 4.1.2 PMMA在不同條件下之回復比(%)	                   57
表 4.2.1 Cross模式參數整理	                           62
表 4.3.1黏彈性模式之參數	                           67
表 4.4.1 WLF方程式參數整理	                           70
表 4.5.1 Maxwell (Multi-Mode)模式參數表	                   73
表 4.7.1 PTT、Giesekus (Multi-Mode) 流變模式參數表	   82
 
圖目錄
圖 1.1.1 CAE應用於射出成型示意圖	                    2
圖 2.2.1 Burger 模式之應變與時間關係示意圖	           11
圖 3.1.1 PMMA結構式	                                   24
圖 3.1.2 COP結構式	                                   25
圖 3.2.1研究流程圖	                                   26
圖 3.3.1平板夾具旋轉流變儀示意圖	                   27
圖 3.3.2不同流變儀黏度量測範圍	                           28
圖 3.4.1光學鏡片示意圖	                                   32
圖 3.4.2 Moldex3D分析模型圖	                           32
圖 3.4.3 Moldex3D模型網格圖	                           33
圖 3.5.1 PMMA(Kurary GH-1000S)穩態剪切黏度溫度掃描	   35
圖 3.5.2 COP(Zeonex480R)穩態剪切黏度溫度掃描	           36
圖 3.5.3 COC(Topas 5013L-10)穩態剪切黏度溫度掃描	   36
圖 3.5.4 PMMA(Kurary GH-1000S)穩態剪切黏度（無加熱罩）	   37
圖 3.5.5 PMMA(Kurary GH-1000S)穩態剪切黏度（有加熱罩）	   38
圖 3.5.6 COP(Zeonex480R)穩態剪切黏度（無加熱罩）	   38
圖 3.5.7 COP穩態剪切黏度（有加熱罩）	                   39
圖 3.5.8 PMMA(Kurary GH-1000S)動態頻率測試	           40
圖 3.5.9 PMMA(Kurary GH-1000S)動態頻率測試	           40
圖 3.5.10 COP(Zeonex480R)動態頻率測試(230~260℃)	   41
圖 3.5.11 COP(Zeonex480R)動態頻率測試(270~290℃)	   41
圖 3.5.12 COP(Zeonex480R)之N1測試	                   42
圖 3.5.13 PMMA(KuraryGH-1000S)之240℃之應變與時間之關係圖	                                                   43
圖 3.5.14 PMMA(KuraryGH-1000S)之250℃之應變與時間之關係圖	                                                   44
圖 3.5.15 PMMA(KuraryGH-1000S)之260℃之應變與時間之關係圖	                                                   44
圖 3.6.1 DMA夾具示意圖	                                   45
圖 3.6.2 PMMA(Kurary GH-1000S)之DMA溫度掃描	           46
圖 3.6.3 COC(Topas 5013L-10)之DMA溫度掃描	           46
圖 3.6.4 PMMA與COC儲存模數比較圖	                   47
圖 3.6.5 PMMA與COC損失模數比較圖	                   47
圖 3.6.6 COC(Topas 5013L-10)之DMA頻率掃描	           48
圖 4.1.1 Burger模式之應變與時間關係擬合圖	           50
圖 4.1.2 PMMA(Kurary GH-1000S)蠕變階段擬合結果	           51
圖 4.1.3 PMMA(Kurary GH-1000S)240℃回復階段擬合結果	   51
圖 4.1.4 PMMA(Kurary GH-1000S)250℃回復階段擬合結果	   52
圖 4.1.5 PMMA(Kurary GH-1000S)260℃回復階段擬合結果	   52
圖 4.1.6 PMMA(Kurary GH-1000S)在240℃改變蠕變時間之擬合結果(應力:50Pa)	                                           55
圖 4.1.7 PMMA(Kurary GH-1000S)在250℃改變蠕變時間之擬合結果(應力:50Pa)	                                           55
圖 4.1.8 PMMA(Kurary GH-1000S)在260℃改變蠕變時間之擬合結果(應力:50Pa)	                                           56
圖 4.2.1 COP(Zeonerx480R)黏度與Cross模式回歸數值比較	   59
圖 4.2.2 PMMA(Kurary GH-1000S)黏度與Cross模式回歸數值比較	                                                   59
圖 4.2.3 COP(Zeonerx480R)實驗值與回歸數值WLF比較	   60
圖 4.2.4 PMMA(Kurary GH-1000S)實驗值與回歸數值WLF比較	   60
圖 4.2.5 改變材料之黏度n值	                           61
圖 4.2.6改變材料之黏度Taus*值	                           61
圖 4.3.1 Cox-Merz 黏度關係式驗證	                   64
圖 4.3.2 Laun's經驗式N1對剪切率關係圖	                   64
圖 4.3.3 COP(Zeonex480R)應力緩和時間對剪切率圖	           65
圖 4.3.4 PMMA(Kurary GH-1000S)應力緩和時間對剪切率圖	   65
圖 4.3.5 改變W-M模式之m值	                           66
圖 4.3.6 改變W-M模式之k值	                           66
圖 4.4.1 PMMA(Kurary GH-1000S)利用DMA損失模數做線性回歸圖	                                                   69
圖 4.4.2 COC(Topas 5013L-10)利用DMA損失模數做線性回歸圖	   69
圖 4.4.3 PMMA(Kurary GH-1000S)在流變儀得到之參數比較	   71
圖 4.4.4 COP(Zeonex480R)在流變儀得到之參數比較	           71
圖 4.4.5 PMMA(Kurary GH-1000S)中aT對溫度做圖	           72
圖 4.5.1 COP利用Maxwell方程式回歸參數與實驗值儲存模數圖	   74
圖 4.5.2 COP利用Maxwell方程式回歸參數與實驗值損失模數圖	   74
圖 4.5.3 PMMA利用Maxwell方程式回歸參數與實驗值儲存模數圖	                                                   75
圖 4.5.4 PMMA利用Maxwell方程式回歸參數與實驗值損失模數圖	                                                   75
圖 4.6.1 Shear viscosity master curve (Tr:260℃) and PTT fitting (e:0.1) for COP(Zeonex480R)	                   77
圖 4.6.2 Shear viscosity master curve (Tr:240℃) and PTT fitting (e:0.8) for PMMA(Kurary GH-1000S)	           77
圖 4.6.3 COP(Zeonex480R) e、x回歸參數與實驗值相比較	   79
圖 4.6.4 PMMA(Kurary GH-1000S) e、x回歸參數與實驗值相比較	                                                   79
圖 4.7.1 COP(Zeonex480R) Giesekus回歸參數與實驗值相比較	   81
圖 4.7.2 PMMA(Kurary GH-1000S) Giesekus回歸參數與實驗值相比較	                                                   81
圖 4.8.1四種黏彈模式和實驗值的光彈條紋比較圖	           83
圖 4.9.1改變材料黏度之n變化	                           85
圖 4.9.2澆口附近區域放大圖	                           85
圖 4.9.3 Taus*變化總合光彈條紋圖	                   85
圖 4.9.4改變材料黏彈性m之變化圖	                           87
圖 4.9.5改變材料黏彈性k之變化圖	                           87

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