光學鏡片之有限元素網格品質探討暨模仁全方位體積收縮補償法之研究

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：80

、訪客IP：18.119.119.252

姓名

蔡嘉軒(Chia-Hsuan Tsai) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

光學鏡片之有限元素網格品質探討暨模仁全方位體積收縮補償法之研究
(Investigation of finite element mesh quality and 3D volume shrinkage compensation method in core and cavity design for optical lenses)

相關論文

★ 田口分析法驗證射出參數對光碟機面板翹曲變形量之研究	★ 聚丙烯射出成型品表面具抗沾黏特性之研究
★ 從模流到結構的集成分析光學鏡片之模仁變形研究	★ 應用反應曲面法進行鏡筒真圓度之射出成型參數優化
★ 冠狀動脈三維重建之初步架構	★ Zienkiewicz動態多孔彈性力學模型之穩定性探討
★ 外加磁場輔助射出成型對於導電高分子複合材料的磁性纖維配向與導電度之實驗與模擬	★ 骨板與骨釘之參數模型應用於股骨骨折術前規劃
★ 光學鏡片模具之異型水路最佳化設計	★ 傳統骨板與解剖骨板對於固定Sanders II-B型跟骨骨折力學分析
★ 以線性迴歸分析驗證射出成型縫合角與抗拉強度呈正相關	★ 異形水路模具設計對於金屬粉末射出成型槍機卡榫影響之研究
★ 槍機卡榫模流分析參數最佳化之研究	★ 聚碳酸酯與碳纖維複合材料之射出參數對於縫合線強度之研究
★ 運用田口方法分析ABS塑膠材料之射出成型參數對拉伸強度的影響	★ 化學發泡射出成型製程條件對聚丙烯與聚苯乙烯之影響

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

至系統瀏覽論文 ( 永不開放)

摘要(中)

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

摘要(英)

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.

關鍵字(中)

★ 射出成型
★ 光學鏡片
★ 收斂性分析
★ 全方位體積收縮補償法

關鍵字(英)

★ injection molding
★ optical lens
★ convergence analysis
★ 3D volume shrinkage compensation method

論文目次

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

參考文獻

參考文獻 [1] G. WARREN, W. Anderson, J. THOMAS, and S. Krist, "Grid convergence for adaptive methods," in 10th Computational Fluid Dynamics Conference, 1991, p. 1592. [2] R. H. Macneal and R. L. Harder, "A proposed standard set of problems to test finite element accuracy," Finite elements in analysis and design, vol. 1, no. 1, pp. 3-20, 1985. [3] A. Cifuentes and A. Kalbag, "A performance study of tetrahedral and hexahedral elements in 3-D finite element structural analysis," Finite Elements in Analysis and Design, vol. 12, no. 3-4, pp. 313-318, 1992. [4] S. E. Benzley, E. Perry, K. Merkley, B. Clark, and G. Sjaardama, "A comparison of all hexagonal and all tetrahedral finite element meshes for elastic and elasto-plastic analysis," in Proceedings, 4th international meshing roundtable, 1995, vol. 17, pp. 179-191: Sandia National Laboratories Albuquerque, NM. [5] J. E. Walz, R. E. Fulton, and N. J. Cyrus, "Accuracy and convergence of finite element approximations," NATIONAL AERONAUTICS AND SPACE ADMINISTRATION HAMPTON VA LANGLEY RESEARCH CENTER1968. [6] I. Babuska and B. Szabo, "On the rates of convergence of the finite element method," International Journal for Numerical Methods in Engineering, vol. 18, no. 3, pp. 323-341, 1982. [7] A. D. Cheng, M. Golberg, E. Kansa, and G. Zammito, "Exponential convergence and H‐c multiquadric collocation method for partial differential equations," Numerical Methods for Partial Differential Equations: An International Journal, vol. 19, no. 5, pp. 571-594, 2003. [8] P. J. Roache, "Perspective: a method for uniform reporting of grid refinement studies," Journal of Fluids Engineering, vol. 116, no. 3, pp. 405-413, 1994. [9] C. J. Roy, "Grid convergence error analysis for mixed-order numerical schemes," AIAA journal, vol. 41, no. 4, pp. 595-604, 2003. [10] L. Eça and M. Hoekstra, "Evaluation of numerical error estimation based on grid refinement studies with the method of the manufactured solutions," Computers & Fluids, vol. 38, no. 8, pp. 1580-1591, 2009. [11] 張英 et al., "使用三維厚度變異進行射出成型翹曲變形探討," 台灣區模
具工業同業公會 , 2009.

77

[12] 黃聖智, 王珉玟, 陳昱廷, 林明哲, and 蔡元勛, "雙面非球面鏡片射出成
形暨模仁補償研究,"
台灣模具工業同業公會 , 2015.
[13] 曾琛涵, 黃招財, 劉育志, 楊文禮, and 張榮語, "全方位體積收縮補償法
於模具設計之優化 "
台灣模具工業同業公會 , 2016.
[14] M.-H. Wang, J.-Y. Lai, C.-H. Hsu, Y.-C. Tsai, and C.-Y. Huang, "Boss recognition algorithm for application to finite element analysis," ComputerAided Design and Applications, vol. 14, no. 4, pp. 450-463, 2017. [15] 王培仁, 張元榕, 游朝凱, 邱顯森, and 楊文賢, "射出成型光學鏡片的模
擬與驗證,"
台灣模具工業同業公會 , 2009.
[16] A. Adhikari, T. Bourgade, and A. Asundi, "Residual stress measurement for injection molded components," Theoretical and Applied Mechanics Letters, vol. 6, no. 4, pp. 152-156, 2016. [17] 尹文, 陳俊生, 劉冠群, and 杜承翰, "COC 射出成型試片光學性質的探
討 "
龍華科技大學學報第三十一期 , 2011.
[18] 陳夏宗, 樓映帆, 魏子翔, and 蕭翰薪, "應用壓力-溫度-比容(PvT)圖探
討成型參數與收縮率關係之研究 "
中國機械工程學會第三十四屆全國學
術研討會論文集 2017.
[19] Grid-Refinement Study, "https://www.zhihu.com/question/24348363."

指導教授

鍾禎元(Zhen-Yuan Zhong)

審核日期

2019-8-22

推文