隨著彈簧製造技術不斷提高，傳統的圓形截面壓縮彈簧無法滿足部分產業需求，取而代之的是異形截面彈簧的蓬勃發展。雖然矩形截面彈簧普遍常見，但是截面設計上的些微差異，卻是影響彈簧效能的重點。另一方面，彈簧預壓成形製程可使螺旋壓縮彈簧獲得更高的彈性限和允許負載，但通常僅被視為是製造過程，較少深入探討預壓機制。
本研究利用有限元素分析軟體 DEFORM，模擬不同截面形狀的桿件扭轉與彈簧壓縮。藉由面積、負載和最大剪應力等數據評斷較佳的矩形截面設計，改善其應力分布且達到維持彈簧常數又輕量化的目標。另一部分，利用DEFORM 模擬彈簧預壓成形，觀察預壓前、後彈簧的截面應力分布、特性曲線、彈簧常數，並與實驗比較，分析預壓成形對彈簧之影響。另外藉由文獻的理論分析，建立預測圓形截面壓縮彈簧預壓所需最大負載和預壓後回彈末高度的公式，再與模擬、實驗比對，並模擬不同尺寸彈簧，驗證預測公式的應用性。

With advanced spring manufacturing technology, traditional round cross-sectional compression springs cannot satisfy the needs of industry. Accordingly, profiled springs are increasingly developed. Although rectangular cross-sectional springs are generally used, slightly different cross-sectional design is the key to affecting the spring performance. On the other hand, spring presetting processes can increase the elastic limit and the allowable operating loads of the spring, but it is usually considered as a manufacturing process, and its mechanism is not investigated comprehensively.
In this study, a finite element analysis software DEFORM is used to simulate the torsion of bars and compression of springs with different cross-sectional shape, and find the preferred cross-sectional shape design by evaluating cross-sectional area, load, and maximum shear stress. The goal of design is obtaining uniform stress distribution with a larger spring constant and lighter weight. On the other hand, DEFORM is used to simulate spring presetting, and the characteristic curves and spring constant before and after presetting are compared with the experiments to analyze their effects on the spring of presetting. In addition, the prediction formulas of maximum load and final height of round wire spring presetting which is established by the theory of literature are compared with the simulation and experimental results. Spring presetting of different mean diameter of springs is also simulated to verify the applicability of the prediction formulas.

論文審定書 i
誌謝 ii
摘要 iii
Abstract iv
圖目錄 viii
表目錄 xii
符號說明 xiv
第一章緒論 1
1-1 前言 1
1-2 彈簧製造過程簡介 2
1-3 彈簧預壓成形簡介 5
1-4 文獻回顧 7
1-4-1 殘餘應力與預壓成形相關之文獻 7
1-4-2 彈簧應力設計相關之文獻 9
1-5 研究動機與目的 9
1-6 論文架構與研究流程 10
第二章理論基礎 12
2-1 圓形截面圓柱螺旋壓縮彈簧 12
2-2 矩形截面圓柱螺旋壓縮彈簧 13
2-3 彈簧預壓成形理論 14
2-3-1 預壓成形最大負載 14
vi
2-3-2 預壓後回彈末高度 19
第三章彈簧幾何設計及預壓成形有限元素分析 22
3-1 有限元素分析軟體 DEFORM 介紹 22
3-2 SAE9254 彈簧鋼之單軸拉伸試驗 22
3-3 圓形截面壓縮彈簧之預壓成形解析 27
3-3-1 幾何模型之建立 27
3-3-2 基本假設及參數設定 29
3-3-3 網格收斂性分析與劃分設定 31
3-3-4 預壓前後過程中負載與變形量之關係 33
3-3-5 預壓成形應力分布探討 36
3-3-6 預壓前後彈簧截面殘餘剪應力分布圖 38
3-3-7 預壓過程彈簧截面位置與剪應力變化之探討 40
3-4 矩形截面壓縮彈簧之模擬結果 41
3-4-1 幾何模型之建立 41
3-4-2 基本假設及參數設定 43
3-4-3 網格收斂性分析與劃分設定 43
3-4-4 預壓前後過程中負載與變形量之關係 46
3-4-5 預壓成形應力分布情形 48
3-4-6 預壓過程彈簧截面位置與剪應力變化之探討 50
3-5 矩形截面彈簧幾何設計 51
3-5-1 矩形截面桿件幾何模型之建立與模擬設定 51
3-5-2 桿件網格收斂性分析與劃分設定 52
3-5-3 桿件截面應力分布探討 54
3-5-4 扭矩、截面積與最大剪應力之比較 55
3-5-5 矩形截面彈簧幾何模型之建立與模擬設定 60
vii
3-5-6 彈簧網格收斂性分析與劃分設定 63
3-5-7 彈簧線截面應力分布探討 65
3-5-8 負載、截面積與最大剪應力之比較 66
第四章實驗與解析結果討論 70
4-1 彈簧預壓成形與負載量測實驗 70
4-1-1 實驗目的 70
4-1-2 實驗設備與實驗材料 70
4-1-3 實驗參數設定 72
4-1-4 實驗步驟與流程 72
4-2 實驗結果與解析結果比較 73
4-2-1 圓形截面彈簧之預壓最大負載與末高度 74
4-2-2 更改幾何尺寸驗證預壓預測理論公式 78
4-2-3 矩形截面彈簧之預壓最大負載與末高度 82
4-2-4 圓形截面彈簧之預壓前後彈簧常數比較 84
4-2-5 矩形截面彈簧之預壓前後彈簧常數比較 86
第五章結論 87
5-1 圓形截面壓縮彈簧之預壓成形 87
5-2 矩形截面壓縮彈簧之預壓成形 88
5-3 矩形截面彈簧之幾何設計 89
5-4 今後研究之課題 90
參考文獻 91

[1] 賴耿陽譯, “彈簧之設計及製造”, 復漢出版社, 臺南, 1996, pp. 115-122.
[2] 張英會、劉輝航、王德成, “彈簧手冊”, 北京機械工業出版社, 北京, 1997, pp. 77-118.
[3] R. Z. Wang, “Review on the Residual Stress Through the Course of Manufacture Technique for the Cold Formed Circular Coil Spring”, China Surface Engineering, Vol. 19, No. 6, 2006, pp. 1-12.
[4] A. M. Wahl, “Mechanical Springs”, 2nd ed., Penton Pub. Co., Cleveland, 1963, pp. 59-61.
[5] M. Shimoseki, M. Oshida, “Variation of Height due to Pre-setting in Coil Spring”, Transactions of Japan Society for Spring Research, Vol. 1975, No. 20, 1975, pp. 70-74.
[6] R. G. Budynas, J. K. Nisbett, “Shigley’s Mechanical Engineering Design”, 10th ed., McGraw-Hill, New York, 2015, pp. 510-522.
[7] 成大先, “機械設計手冊”, 化學工業出版社, 北京, 2008, pp. 152-153.
[8] 劉松柏編譯, “彈塑性力學基礎”, 五南圖書, 臺北, 2008, pp. 182-183. (F. Yoshida, 1997)
[9] J. Matejicek, “Residual Stresses in Cold-coiled Helical Compression Springs for Automotive Suspensions Measured by Neutron Diffraction”, Journal of Materials Science and Engineering A, Vol. 367, No. 1-2, 2004, pp. 306-311.
[10] T. Yoshida, “Software Skill for Metal Forming Analysis (I): FEM codes”, Journal of the Japan Society for Technology of Plasticity, Vol. 56, No. 649, 2015, pp. 124-128.
[11] M. Shimoseki, T. Hamano, T. Imaizumi, “FEM for spring”, Japan Society for Spring Research, Tokyo, 2003, pp. 180-198.
[12] Peter R. N. Childs, “Mechanical Design Engineering Handbook”, 1st ed., Butterworth-Heinemann, London, 2013, pp. 625-647.
[13] K. Maki, K. Yoshida, “Fabrication of Ultrafine Shaped Wire by Drawing for Micro
Spring Application”, The Proceedings of the Japanese Spring Conference for the Technology of Plasticity, Vol. 216, 2014, pp. 89-90.
[14] M. T. Todinov, “Maximum Principal Tensile Stress and Fatigue Crack Origin for Compression Springs”, International Journal of Mechanical Sciences, Vol. 41, No. 3, 1999, pp. 357-370.
[15] T. Imaizumi, T. Ohkouchi, S. Ichikawa, “Shape Optimization of the Wire Cross Section of Helical Spring”, JSME International Journal, Series C, Vol. 36, No. 4, 1993, pp. 507-514.
[16] J. Francu, P. Novackova, P. Janicek, “Torsion of a Non-circular Bar”, Engineering Mechanics, Vol. 19, No. 1, 2012, pp. 45-60.
[17] S. Timoshenko, J. Goodier, “Theory of Elasticity”, 3rd ed., McGraw-Hill, New York, 1970, pp. 309-313.
[18] 張莉、李升軍, “DEFORM 在金屬塑性成形中的應用”, 機械工業出版社, 北京, 2009, pp. 43-72.
[19] ASTM., “Standard Test Methods for Tension Testing of Metallic Materials”, E8/E8M-15, U.S.A., 2015, pp. 8.
[20] 陽旻企業股份有限公司 http://www.yangmin.com.tw/list/cate-22372.htm