當金屬板材完軋過後，板材內部容易產生不均勻的殘留應力，進而產生如邊波浪以及中間波浪等缺陷，此時拉伸矯直製程為修正板形之一種方式。
若利用有限元素法探討板材之拉伸矯直製程時，在建造模型時，因波浪缺陷有許多種，且模型內所有元素之輥軋後殘留應力需逐一輸入，相當耗費時間，本研究目的為針對執行完軋後的缺陷板材於拉伸矯直製程之有限元素模擬時，設計一程式以其能快速完成板材的建模，藉以省去極大部分建模的時間。
本研究結合有限元素分析軟體Marc與C語言，設計可建構經過輥軋後有邊波浪缺陷以及中間波浪缺陷的板材於拉伸矯直製程之有限元素3D模型的自動化建模程式，僅需藉由程式之問答介面輸入材料參數、平板長寬高、波浪類型、波浪個數、波浪大小、波浪位置、平板區輥軋後殘留應力、拉伸率等資訊，有限元素模型即可自動產生。
本研究所得之自動建模程式有三項特點，第一項為可節省95%以上的建模時間；第二項特點為輸入方式簡易；第三項為不管板材缺陷與分佈有多複雜，自動建模程式皆能輕易完成模型建造。
最後，本研究利用所設計之程式順利完成大量模形模擬，並結合田口法，探討具單一邊波缺陷板材的其波浪與板材相對尺寸變異與不同拉伸率對殘留應力消除率之影響。

In metalworking, rolling processes tend to induce non-uniform residual stress distributions in workpieces, resulting in various defects, such as edge waves and center buckles of the piece. Thus, tension leveling is commonly employed to correct these defects.
The finite element method (FEM) can be employed to examine the performance levels of tension-leveling processes. However, developing an FEM model is extremely time-consuming because deformation types may vary, and all residual stress elements of the defective workpiece after rolling must be individually input into the model. Therefore, the present study involves designing a program that rapidly models defective sheet metal workpieces, facilitating finite element analysis and substantially reducing modeling times when FEM is employed to simulate the performance levels of tension leveling processes of defective workpieces after rolling.
Using Marc, a finite element analysis solution, and the C programming language, an automated modeling program was developed to construct finite element 3D models of the tension-leveling processes used to treat workpieces that exhibit edge wave and center buckles after rolling. Users simply input relevant data, such as material parameters, sheet specification, wave type, wave quantity, wave size, wave position, residual stress distribution following the rolling process, and tensility, into the Q&A interface and the program automatically generates a finite element model.
The proposed automated modeling program reduces modeling times by more than 95%, presenting a simple data input interface that easily and automatically generates models regardless of the complexity of the defects or distributions.
In summary, numerous model simulations were successfully completed using the proposed program. Combined with the Taguchi method, the proposed program can be used to observe workpieces that demonstrated asymmetrical edge wave defects, demonstrating how variations in relative wave-workpiece sizes and the tensile variations affected the removal rate of residual stress.

論文審定書 I
誌 謝 II
摘 要 III
Abstract IV
第 一 章 緒論 1
1. 1研究目的 1
1. 2 文獻回顧 2
1.2. 1輥軋結果 2
1.2. 2輥軋矯直 4
1.2. 3拉伸探討 6
第 二 章 研究方法 14
2. 1模型建立 14
2. 2假設條件 14
2.2. 1網格設定 14
2.2. 2材料性質 15
2.2. 3邊界條件設定和負載設定 15
2. 3初始條件 16
2. 4模擬分析 21
第 三 章 自動建模之套裝軟體的製作 34
3. 1如何降低建模時間? 34
3.1. 1為何建模會耗費時間? 34
3.1. 2利用command 34
3.1. 3 Command是什麼呢? 35
3.1. 4 GUI轉成command 35
3.1. 5製作command所遇困難 36
3. 2自動建模之套裝軟體的製作 36
3.2. 1 command與C語言做結合 37
3.2. 2如何利用C語言 38
第 四 章 軟體使用方法 44
4. 1建模軟體介紹 44
4.1. 1軟體使用說明 44
4.1. 2 注意事項 44
4.1. 3成果展現 45
4.1. 4模型問題 45
4.1. 5安裝步驟 46
4. 2不同拉伸率對殘留應力消除率之影響 47
4.2. 1改變尺寸比例對殘留應力消除率之關係 47
4.2.1. 1田口法 48
4.2.1. 2直交表的應用 48
4.2.1. 3如何選擇直交表 48
4.2.1. 4邊波板不同拉伸率對應之殘留應力消除率以及邊波板每階段拉伸率對應之殘留應力消除率增加率之算法 49
4.2. 2改變尺寸對邊波影響之結果 51
4.2. 3波浪板最佳反應因子 51
第 五 章 結論與未來展望 76
5. 1 結論 76
5.1. 1 自動建模軟體結論 76
5.1. 2 田口法與波浪模擬之結論 77
5. 2未來展望 77

1.林靜妤，完軋AA5052鋁合金板經拉伸矯直後其殘留應力分佈之有限元素分析，國立中山大學機械與機電工程學系，中國機械工程學會第二十九屆全國學術研討會論文集，台灣，2012年
2.余杰霖，具中間波浪之完軋鋁合金板經拉伸矯直製程後其殘留應力分佈之有限元素分析，國立中山大學機械與機電工程系，碩士論文，台灣，2013年
3.Nakayama, Y., T. Takaai, and S. Kimura. "Evaluation of surface residual stresses in cold-rolled 5083 aluminum alloy by X-ray method." Mater. Trans., JIM 34.6 (1993): 496-503.
4.Razny, W., et al. "The influence of some rolling parameters on the residual stresses after rolling." Journal of materials processing technology 60.1 (1996): 81-86.
5.Dixit, U. S., and P. M. Dixit. "A study on residual stresses in rolling." International Journal of Machine Tools and Manufacture 37.6 (1997): 837-853
6.Huh, Hoon, et al. "The parametric process design of tension levelling with an elasto-plastic finite element method." Journal of Materials Processing Technology 113.1 (2001): 714-719.
7.趙麗麗、張以都，基於MSC的板材冷軋殘餘應力分佈的數值仿真，中國有色金屬學報，第五十七卷，第一期，2005。
8.尹曉輝、李响、劉靜安、蔣程非,鋁合金冷軋及薄板生產技術，冶金工業出版社，2010。
9.Yang, Zhao, et al. "Application of full restart method in FEM analysis of plate rolling." Mechanic Automation and Control Engineering (MACE), 2010 International Conference on. IEEE, 2010.
10.Abdelkhalek, Sami, et al. "Strip flatness modelling including buckling phenomena during thin strip cold rolling." Ironmaking & Steelmaking 37.4 (2010): 290-297.
11.Guo, Remn-Min. "Optimal profile and shape control of flat sheet metal using multiple control devices." Industry Applications, IEEE Transactions on 32.2 (1996): 449-457
12.Yoshida, Fusahito, and Masaki Urabe. "Computer-aided process design for the tension levelling of metallic strips." Journal of Materials Processing Technology89 (1999): 218-223.
13.Morris, J. W., et al. "Formation of residual stresses owing to tension levelling of cold rolled strip." Ironmaking & steelmaking 28.1 (2001): 44-52.
14.Doege, E., R. Menz, and S. Huinink. "Analysis of the levelling process based upon an analytic forming model." CIRP Annals-Manufacturing Technology 51.1 (2002): 191-194.
15.Park, Kee-Cheol, and Sang-Moo Hwang. "Development of a finite element analysis program for roller leveling and application for removing blanking bow defects of thin steel sheet." ISIJ international 42.9 (2002): 990-999.
16.LI, Sheng-zhi, et al. "Numerical simulation of continuous tension leveling process of thin strip steel and its application." Journal of Iron and Steel Research, International 14.6 (2007): 8-13.
17.Jamshidian, M., et al. "ANALYSIS OF STRIP RESIDUAL CURVATURES IN ANTI-CROSSBOW CASSETTE IN TENSION LEVELING PROCESS."
18.曾清宏，鈑金矯直張力與矯直力之有限元素探討，國立雲林科技大學機械工程系，碩士論文，雲林，台灣，2010年。
19.Liu, Zhifang, Yongqin Wang, and Xingchun Yan. "A new model for the plate leveling process based on curvature integration method." International Journal of Mechanical Sciences 54.1 (2012): 213-224.
20.Tanner, D. A., and J. S. Robinson. "Modelling stress reduction techniques of cold compression and stretching in wrought aluminium alloy products." Finite elements in analysis and design 39.5 (2003): 369-386.
21.Prime, Michael B., and Michael R. Hill. "Residual stress, stress relief, and inhomogeneity in aluminum plate." Scripta Materialia 46.1 (2002): 77-82.
22.Koc, Muammer, John Culp, and Taylan Altan. "Prediction of residual stresses in quenched aluminum blocks and their reduction through cold working processes." Journal of materials processing technology 174.1 (2006): 342-354.
23.唐志濤、劉戰強、艾興、萬熠，基於裂紋柔度法的鋁合金預拉伸板內部殘餘應力測試，中國有色金屬學報，第十七卷，第九期，第1404-1409頁，2007。
24.S. X. Yuan, X. Q. Li, S. Ma, Y. C. Zhang and Y. D. Gong , “ Measurement of the Residual Stresses Distribution in Thick Pre-stretched Aluminum Plate”, Precision Mechanical Measurements, Vol. 7130 , 2008.
25.張圓圓，鋁合金厚板淬火過程及預拉伸熱-力仿真與實驗研究，中南大學，碩士論文，中國，2008年。
26.廖凱、吳運新、龔海、閆鵬飛、郭俊康，鋁合金厚板淬火－預拉伸應力預測與測試，中國有色金屬學報，第二十卷，第十期，第1901-1906頁，2010。