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研究生： 陳俞彤
Chen, Yu-Tung
論文名稱： 麥花臣懸吊系統之螺旋彈簧參數研究及作用力線之最佳設計方法
Parameter Study for Side Load Springs in Macpherson Strut Suspension and an Optimal Design Method for Force Action Line
指導教授： 劉至行
Liu, Chih-Hsing
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年： 2017
畢業學年度： 105
語文別： 英文
論文頁數： 190
中文關鍵詞： 螺旋彈簧 、側載彈簧 、麥花臣懸吊系統 、有限元素分析 、作用力線 、最佳設計方法
外文關鍵詞： Helical springs, Side load springs, Macpherson strut suspension, Finite element analysis, Force action line, Optimal design method
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    • 市面上之汽車麥花臣前懸吊系統由於機構設計的關係，導致一外力施加於減震器頂部支承，此外力若未與彈簧之反作用力重合，會產生一側向力施加於減震器的油封及活塞上，使得其在運作時摩擦力增加，亦容易造成減震器的疲勞壽命縮短、乘載舒適度降低，因此設計一個能改善此側向力之螺旋彈簧—側載彈簧，為本研究的重點。
    本研究針對麥花臣懸吊系統之側載彈簧進行參數研究，並探討各個參數對於作用力線的影響，有限元素軟體—LS-DYNA為本研究分析各種螺旋彈簧的工具。本研究探討的螺旋彈簧分別為直捲彈簧及C型彈簧，其中，直捲螺旋彈簧的設計參數包括彈簧及頂座之接觸圈數、節距控制、彈簧頂部及底部的偏移量；C型彈簧的設計參數依照螺旋彈簧的中心線的曲率分為三類，分別為等曲率、初始曲率為零之線性曲率、初始曲率不為零之線性曲率。本研究也提供建構彈簧輪廓及中心線之相關數學模型推導、作用力線之計算方式、有限元素模擬之相關參數設定，而為了驗證有限元素模擬結果的準確性，本研究採用一個中尺寸的螺旋彈簧進行實驗測試。本研究亦提出一個汽車螺旋彈簧作用力線之最佳化方法，藉此找出符合目標作用力線之最佳彈簧參數組合，並將最佳化得到之結果與有限元素模擬結果做驗證，結果顯示此最佳設計之側載彈簧的作用力線與目標力線一致。

    This study provides the parameter study for the side load springs used in Macpherson strut suspension systems, and investigates the effects of each parameter on the force action lines. Finite element analysis software, LS-DYNA, is used to analyze various kinds of helical springs. For cylindrical helical springs, the design parameters include the number of turns between spring and top seat, pitch control, and offset of upper and lower portion of spring. For C-shaped springs, the design parameters are divided into three groups according to the curvature of the curved centerline of helical springs, which are constant curvature, linear curvature with zero initial curvature, and linear curvature with initial curvature. The mathematical model for obtaining the profile of spring with three-dimensional curved centerline is also given in this study. Experimental test for a medium-sized helical spring is performed to verify the effectiveness of the FEA results. An optimization method to identify the optimal design of automotive coil spring with target force action line is proposed and validated by FEA results. The results show that the optimal design of side load spring can reduce the friction exerted on the damper rod to minimize the damper failure.

    摘要 i Abstract ii Acknowledgements iii Contents iv List of Tables vii List of Figures x Nomenclatures xvi Chapter 1 Introduction 1 1.1 Suspension System 1 1.2 Springs 7 1.3 Literature Review 8 1.4 Motivation and Objective 17 1.5 Outline of the Thesis 17 Chapter 2 Methodology 19 2.1 Basic Theory of Helical Spring 19 2.1.1 Spring rate of helical spring 20 2.1.2 Shear stress in helical spring 21 2.2 Force Line of Spring 22 2.3 Geometry Modeling 29 2.3.1 The process of geometry modeling 37 2.3.2 B-spline curve 40 2.3.3 The derivation of curved centerline with linear curvature 45 2.3.4 Obtaining profile of spring with coordinate transformation 48 2.4 Numerical Method 51 2.4.1 Numerical integration of functions 52 2.4.2 Numerical differential method 58 2.5 Taguchi Orthogonal Arrays and ANOVA 60 2.5.1 Introduction to orthogonal arrays 61 2.5.2 Analysis of variance 64 Chapter 3 Finite Element Model and Verification 72 3.1 The Process of the FEA 72 3.2 The Compression Test of Helical Compression Spring 74 3.3 FEM Model 77 3.4 The Card Setting in LS-DYNA 80 3.4.1 Material properties and units 80 3.4.2 Boundary conditions 80 3.4.3 Contact 81 3.5 FEA Results 81 3.5.1 Mesh convergence analysis 82 3.5.2 The comparison between simulation/experiment/theory 86 3.6 Discussion and Summary 87 Chapter 4 Parameter Study and Results 89 4.1 Reference Model 89 4.2 Material Property 98 4.3 Mesh Convergence Analysis 98 4.4 Cylindrical Helical Spring 102 4.4.1 Number of turns between spring and top seat 103 4.4.2 Pitch control 105 4.4.3 Offset of upper and lower portion of spring 110 4.4.4 ANOVA of Taguchi orthogonal arrays 119 4.4.5 Summary 122 4.5 C-Shaped Spring 123 4.5.1 Constant Curvature 125 4.5.2 Linear Curvature 128 4.5.3 Summary 137 Chapter 5 Force Line Optimization 139 5.1 Method for Force Line Optimization 139 5.2 Example 1 146 5.3 Example 2 151 5.4 Example 3 156 5.5 Summary 162 Chapter 6 Conclusions and Suggestions 163 6.1 Conclusions 163 6.2 Suggestions 166 References 167 Appendix A Control Points for Geometry Modeling of Spring 170 Appendix B Explanation of Parameters 175 Appendix C Results for Mesh Convergence Analysis 177 Appendix D Curve-Fitting Results 182 Appendix E Taguchi Orthogonal Arrays 187 Appendix F Coordinates for Piercing Points 189

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