臺灣博碩士論文加值系統

網格搭建在有限元素分析中為重要的技術，直接影響模擬的準確度和
計算效率，若使用 Moldex3D 自動建立的 BLM 網格(Boundary layer
meshes)，雖然快速簡易但網格品質較差，但使用六面體網格(Hexahedron)
或三角柱網格(Prism)，能大量提升網格品質，唯須手動建立且較耗時，因
此本研究建立三種網格，分別是 Prism+Hexa 網格、Mostly Hexa 網格與
BLM 網格，將不同網格之模擬結果與實驗之流動波前形狀、光程差分佈
照片比較，來驗證模型準確度，從研究結果得知，Mostly Hexa 網格可獲
得較正確的模流分析結果，其次是 Prism+Hexa 網格，而最差的是 BLM 網
格。透過收斂性分析，建立不同尺寸的 Mostly Hexa 網格，藉由模擬與實
驗的比對，得知 0.04mm 的網格尺寸可獲得較正確的模流分析結果。
為了改善光學鏡片形狀精度的問題，業界常見以總體積補償法來優化
翹曲品質，但是由於產品的不等向收縮，往往很難達到產品所有部位之精
度要求，本研究使用 Moldex3D 提出之全方位體積收縮補償法(3D volume
shrinkage compensation method)，以雙面非球面鏡片為模型，使用網格品質
最佳的 Mostly Hexa 網格進行模仁補償，從結果顯示，對於光學鏡片之外
徑與中心厚度之尺寸精度均有明顯改善。
關

In finite element analysis, mesh generation is an important technique, which
directly affects the accuracy and computational efficiency of the simulation.
Using BLM (Boundary layer meshes) automatically is fast and easy in Moldex3D,
but the mesh quality is not excellent. If using Hexahedron or Prism mesh can
greatly improve mesh quality but consuming more time. Therefore, this study
generate three kinds of meshes, Prism + Hexa mesh, Mostly Hexa mesh and BLM
mesh. To verify the accuracy of model, we compared the results of simulation
with experimental melt front and optical retardation. The results of the study
shows that the Mostly Hexa mesh can bring the correct molding simulation results.
The results of molding simulation of Prism+ Hexa mesh are not so correct. And
the results of molding simulation of BLM mesh are incorrect. Then, through the
convergence analysis, we generate the different size for Mostly Hexa mesh. By
comparing the simulation with the experiment, we found that the mesh size of
0.04 mm can bring the through correct molding simulation results.
In order to improve the shape accuracy of optical lenses, industry often use
the total volume compensation method to optimize the warpage. However, due to
the unequal concentration of the product, it is difficult to meet the requirements
of all parts of the product. In this research, we use 3D Volume shrinkage
compensation method (3DVSCM) for cavity compensation. In conclusion, using
3DVSCM obviously improves the outer diameter and center thickness of the
optical lens.

目錄
摘要 ........................................................................................................................ I
ABSTRACT ........................................................................................................ II
致謝 .................................................................................................................... III
目錄 ..................................................................................................................... IV
圖目錄 ............................................................................................................... VII
表目錄 .................................................................................................................. X
緒論 ..................................................................................................... 1
1-1 前言 .................................................................................................. 1
1-2 文獻回顧 ........................................................................................... 3
1-2-1 網格種類與品質 ............................................................................. 3
1-2-2 有限元素法收斂性分析相關文獻 .................................................. 4
1-2-3 Grid-refinement study 相關文獻 ...................................................... 5
1-2-4 模仁收縮補償法相關文獻 .............................................................. 5
1-3 研究動機與目的 ............................................................................... 6
1-4 研究流程 ........................................................................................... 7
基本原理與理論模式 ......................................................................... 9
2-1 網格性質 ........................................................................................... 9
2-2 光學理論 ......................................................................................... 13
2-2-1 雙折射現象 ................................................................................... 13
2-2-2 應力光學定律 ............................................................................... 13
2-3 應力偏光儀 (HIGH SPEED QUANTITATIVE PHOTOELASTIC ANALYZING SYSTEM) 14


V

2-4 全方位體積收縮補償法 ................................................................. 15
模型設定方法 ................................................................................... 17
3-1 鏡片模型 ......................................................................................... 17
3-2 模流分析軟體簡介 ......................................................................... 18
3-3 材料簡介 ......................................................................................... 19
3-4 成型條件設置 ................................................................................. 21
3-5 適當網格評估 ................................................................................. 26
3-5-1 網格形式探討與網格品質提升 .................................................... 26
3-5-2 決定最適當網格尺寸 .................................................................... 33
3-6 實體網格製作 ................................................................................. 39
3-7 全方位體積收縮補償法於光學鏡片之模仁補償 .......................... 42
3-7-1 業界總體積補償法模擬流程 ........................................................ 43
3-7-2 全方位體積收縮補償法模擬流程 ................................................ 44
結果與討論 ....................................................................................... 46
4-1 短射驗證與光程差驗證 ................................................................. 46
4-2 P5 鏡片網格品質造成總光程差計算誤差 ...................................... 46
4-3 P5 鏡片網格形式探討與實驗比對 ................................................. 47
4-4 P4 鏡片網格形式探討與實驗比對 ................................................. 50
4-5 流道網格對於模流分析的影響 ...................................................... 54
4-6 適當網格評估小結 ......................................................................... 56
4-7 決定適當網格尺寸 ......................................................................... 57
4-7-1 Hexa+Prism 之網格尺寸探討 ......................................................... 57
4-7-2 Mostly Hexa 之網格尺寸探討 ........................................................ 60


VI

4-7-3 BLM 之網格尺寸探討 .................................................................... 62
4-8 決定適當網格尺寸小結 ................................................................. 65
4-9 全方位體積收縮補償法於光學鏡片之模仁補償結果 ................... 67
4-10 鏡片外徑尺寸改善 ....................................................................... 67
4-11 鏡片中心厚度之改善 ................................................................... 69
4-12 鏡片體積精準度之改善 ............................................................... 70
結論與未來展望 ............................................................................... 72
5-1 結論 ................................................................................................ 72
5-2 未來展望 ......................................................................................... 73
參考文獻 ............................................................................................................. 76

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