滑蓋機構是滑動式手機及滑動式平板電腦的關鍵零組件，此機構的運動主要是靠一個或數個特殊形狀的扭轉彈簧來提供動力源，而手機及平板電腦“輕、薄、短、小”的要求造成扭轉彈簧在微小線徑的幾何條件下，需達到“大行程、大推力及高壽命”的嚴苛設計要求，因此造成扭轉彈簧的設計異常困難。為解決此問題，本論文乃構思如何將傳統應用於降低實驗次數的“田口實驗方法”應用至扭轉彈簧的尺寸參數設計，並結合工程力學的基本觀念及計算幾何的數學基礎來確保彈簧幾何形狀的合理性。首先，本論文以“能量法”的觀念推導出扭轉彈簧在滑蓋機構中推移一段固定行程的運動方程式，由此方程式求出無運動干涉的扭簧尺寸參數；接著，以此扭簧尺寸整理出合理的參數組合，做為田口法的控制因子及變動水準，然後以有限元素法計算出直交表中每一組扭簧尺寸在整個運動行程中的最大應力，以利求出“最大應力最小化”的參數組合，藉以解決先前所提的“高壽命”設計要求。但誠如先前所言，扭轉彈簧的設計需“同時”達到“大行程、大推力及高壽命”的嚴苛設計要求，因此本論文再嘗試將模糊理論導入田口法，發展出“多重目標演算法”，以解決“最大應力最小化”與“固定作用力”雙目標函數之最佳化設計問題，藉此得到扭轉彈簧之最佳化尺寸參數。
本論文除了理論推導外，並開發電腦程式及使用商用CAE軟體，使整個數學推導過程及所提出的演算法皆能連貫，快速得到最佳的扭轉彈簧尺寸參數。由最終的計算結果所得的扭轉彈簧可驗證本論文所提出的“運動幾何計算+田口實驗方法+多重目標演算”可達到“大行程、大推力及高壽命”的嚴苛設計要求。

The slide mechanism is a key component of sliding mobile phones and sliding tablet PCs. The movement of the slide mechanism mainly relies on one or more specially-shaped torsion springs as the power source. Compact size and light weight are major design trends for mobile phones and tablet PCs, and necessitate the stringent design requirements of “large traveling distance, high elastic force, and long service life” for torsion springs of small diameter, rendering their design exceptionally difficult. To solve this problem, this study proposes an application of the Taguchi method (which is conventionally used to reduce the number of experiments in material testing) to the design of dimension parameters for torsion springs. The geometry of the spring is ensured by taking into account basic concepts of engineering mechanics and mathematical foundations of computational geometry. First, based on the concept of “energy method”, this study developed motion equations for a torsion spring traveling a fixed distance, as in the slide mechanism. The equations were then used to obtain dimension parameters for a spring with no self-interference. Reasonable parameter combinations obtained were in turn used as control factors and change levels for the subsequent Taguchi method. Finally, the finite element method was applied to determine the maximum stress within the entire movement of each spring dimensional group in the orthogonal array, and parameter combinations were obtained that minimized this maximum stress to best meet the design requirement of long service life.
As previously mentioned, the torsion spring design must satisfy the stringent requirements of “large traveling distance, high elastic force, and long service life”. Hence, this study attempted to incorporate fuzzy set theory into the Taguchi method and develop a multiple performance characteristics index that could solve the optimization problem of dual-target functions of minimized maximum stress and fixed acting force, yielding the optimal torsion spring dimensions.
In addition to discussing its theoretical foundations, this study also developed computer programs and used commercial CAE software to achieve consistency throughout the entire mathematical deduction process and the proposed algorithms, resulting in rapid calculations of optimal torsion spring dimensions. The final torsion spring dimensions can be used to verify that the proposed method - which combines motion geometry, the Taguchi method, and a multiple performance characteristics index - can satisfy the challenges of “large traveling distance, high elastic force, and long service life”.

1. 馬愛軍、王旭，Patran和Nastran有限元素分析，清華大學出版社，北京，2005。
2. S. Moaveni, Finite Element Analysis Theory and Application with ANSYS, 3rd Edition, Pearson Prentice Hall, New York, 2007.
3. M. J. Turner, R. W. Clough, H. C. Martin, and L. C. Topp, "Stiffness and Deflection Analysis of Complex Structures," J. Aeronent Sci., Vol. 23, No. 9, 1956.
4. 王國強，實用工程數值模擬技術在ANASYS上的實踐，西北工業大學出版社，西安，2000。
5. J. F. Besseling, "The Complete Analogy Between the Matrix Equations and the Continuous Field Equations of Structural Analysis," International Symposium on Analogue and Digital Techniques Applied to Aeronautics, Liege, Belgium, pp. 223-242, 1964.
6. R. J. Melosh, "Basis for the Derivation of Matrics for the Direct Stiffness Method," AIAA Journal, Vol. 1, No. 7, pp. 1631-1637, 1963.
7. R. E. Jones, "A Generalization of the Direct Stiffness Method of Structural Analysis," AIAA Journal, Vol. 2, No. 5, pp. 821-826, 1964.
8. J. R. Cooke and D. C. Davis, Applied Finite Element Analysis – An Apple II Implementation, John Wiley & Sons, Inc., New York, 1986.
9. S. Moita and M. Soares, "Analyses of magneto-electro-elastic plates using a higher order finite element model," Journal of the Composite Structures, Vol. 91, pp. 421-426, 2009.
10. K. Alnefaie, "Finite element modeling of composite plates with internal delamination," Journal of the Composite Structures, Vol. 90, pp. 21-27, 2009.
11. R. D. Cook, Finite Element Modeling for Stress Analysis, John Wiley & Sons, Inc., New York, 1995.
12. Y.-L. Hsu, Y.-C. Hsu, and M.-S. Hsu, "Shape Optimal Design of Contact Springs of Electronic Connectors," Transactions of the ASEM, Vol. 124, pp. 178-183, 2002.
13. 鄭崇義，田口品質工程技術理論與實務，中華民國品質學會，台北，2000。
14. G. Taguchi, Introduction to Quality Engineering. , Asian Productivity Organization , Tokio, Japan:, 1990.
15. 田口玄一，田口統計解析法，五南圖書出版公司，台北市，2003。
16. 鄭燕琴，田口品質工程技術理論與實務，中華民國品質學會，台北，1998。
17. 羅錦興，田口品質工程指引，中國生產力中心，台北，1999。
18. A. Kunjur and S. Krishnamurty, "A Robust Multi-Criteria Optimization Approach," Mech.Mach.Theory, Vol. 32, pp. 797-810, 1997.
19. G. Derringer and R. Suich, "Simultaneous Optimization of Several Response Variables," Journal of Quality Technology, Vol. 12, pp. 214-219, 1980.
20. E. A. Elsayed and A. Chen, "Optimal Levels of Process Parmeters for Products with Multiple Characteristics," International Journal of Production Research, Vol. 31, pp. 1117-1132, 1993.
21. A. I. Khuri and M. Conlon, "Simultaneous Optimization of Multiple Response Represented by Polynomial Regression nctions," Technometrics, Vol. 23, pp. 363-375, 1981.
22. L.-I. Tong, C.-T. Su, and C.-H. Wang, "The Optimization of Multi- Response Problems in the Taguchi Method," International Journal of Quality& Reliability Management, Vol. 14, pp. 367-380, 1997.
23. Y. S. Tarng, W. H. Yang, and S. C. Juang, "The Use of Fuzzy Logic in the Taguchi Method for the Optimization of the Submerged Arc Welding Process," International Journal of Advanced ManufacturingTechnology, Vol. 16, pp. 688-694, 2000.
24. J. Y. Kao and Y. D. Pan, "Optimization of Tool Geometryin Face Milling Operation Using the Fuzzy-Based Taguchi Method," Journal of Technology, Vol. 16, pp. 709-716, 2001.
25. L.-I. Tong and C.-T. Su, "Optimization Multi-response Problems in the Taguchi Methodby Fuzzy Multiple Attribute Decision Making," Quality and Reliability Engineering International, Vol. 13, pp. 25-34, 1997.
26. 鐘煥章和陳玉銘，滑蓋機構及應用該滑蓋機構之攜帶式電子裝置，中華民國專利I318669，蘇泰克貿易有限公司，英屬維爾京群島，2006。
27. 林明璋，「滑蓋手機之機構研究」，碩士論文，逢甲大學材料與製造工程研究所，台中，2007。
28. 陳盈璋，「滑蓋彈簧應力分析與尺寸參數設計」，碩士論文，國立臺灣科技大學機械工程研究所，台北，2007。
29. 蔡意輝，「滑蓋彈簧之壽命分析」，碩士論文，國立臺灣科技大學機械工程研究所，台北，2008。
30. 馬揚傑，「扭力彈簧之電腦輔助應力分析」，碩士論文，國立臺灣科技大學機械工程研究所，台北，2009。
31. 張敬民，「應用基因演算法於滑蓋手機彈簧結構最佳化設計」，碩士論文，國立高雄第一科技大學機械與自動化所，高雄, 2009。
32. 柯定成，「大型滑蓋之結構分析與尺寸參數設計」，碩士論文，國立臺灣科技大學機械工程研究所，台北，2010。
33. 陳信志，「可變動力行程半自動滑蓋之參數化設計」，碩士論文，國立臺灣科技大學機械工程研究所，台北，2010。
34. D. L. Logan, Mechanics of Materials, Harpercollins College Div, New York, 1991.