臺灣博碩士論文加值系統

根據承受軸向力與軸向扭矩之圓柱形螺旋彈簧的12條微分方程式，本文利用Rayleigh-Ritz方法建立圓柱形螺旋彈簧的一維有限元素運動方程式，以使用在圓柱形螺旋彈簧的挫屈負荷與自然頻率分析。本文另利用文獻之轉置矩陣法(transfer matrix method)建立圓柱形螺旋彈簧挫屈負荷與自然頻率之分析模式，分析結果並與有限元素分析結果比較，以驗證本文有限元素分析模式。結合本文挫屈負荷與自然頻率之分析模式與文獻之作法，本文得到圓柱形螺旋壓縮彈簧之挫屈設計圖(buckling design charts)與頻率設計圖(frequency design charts)。繪製此兩種設計圖時，本文分別考慮圓柱形螺旋壓縮彈簧承受軸向力、承受軸向扭矩及同時承受軸向力與軸向扭矩。本文分析結果並與文獻的結果比較，以驗證本文所建立之分析模式之準確性與效率。同時本文亦探討彈簧之圈數與軸向負荷型態對圓柱形螺旋壓縮彈簧挫屈設計圖與頻率設計圖之影響。

Based on the equations of motion governing the natural vibration of helical springs subjected to static axial compression and twist, the present study develops the one-dimensional finite element equations of motion for the cylindrical helical springs which can be used in the analyses of buckling loads and natural frequencies. Using the transfer matrix method in the literature this study also solves the buckling loads and natural frequencies of cylindrical helical springs. Both results obtained by the transfer matrix method and the present finite element model are compared to verify the present finite element solutions. The present study also obtains the buckling design charts and frequency design charts of cylindrical helical springs by following the processes used in the literature. In producing the design charts, the present study considers the springs are subjected to axial compression, axial twist, and combined axial compression and twist, respectively. The present results are compared with that in the literature to demonstrate the accuracy and efficiency of the present analysis models. Also the effects of the number of turns of uncompressed helix and the three types of axial loads on the design charts are investigated.

摘要 I
ABSTRACT II
誌謝 Ⅲ
目錄 IV
附圖索引 VII
附表索引 IX
符號表 IV
第一章 緒論……………………………………………………………1
1.1前言………………………………….…………………….………1
1.1.1彈簧的種類………………………………………….….……...1
1.1.2彈簧材料的性質與選用……………………………….….…...4
1.2文獻回顧…………………………….………………….….……...5
1.3研究目的與內容…………………….……………………...……..8
第二章 建立圓柱形螺旋彈簧之運動方程式……………….....…….10
2.1圓柱形螺旋彈簧的幾何方程式………………….…………..….10
2.1.1空間曲線之路徑座標系統(path coordinate system)……....…10
2.1.2 Frenet-Serret 公式………………………………..…...……...12
2.1.3圓柱形螺旋彈簧的幾何方程式推導……….………….…….13
2.2圓柱形螺旋彈簧之運動方程式………………..………….…….16
2.2.1圓柱形螺旋彈簧的本構與靜平衡方程式..………………….16
2.2.2推導圓柱形螺旋彈簧之運動方程式..…………….……...….24
第三章 圓柱形螺旋彈簧有限元素運動方程式推導……………...….31
3.1 建立圓柱形螺旋彈簧元素之力與位移向量函數…………..….31
3.2有限元素運動方程式.…………………...….…………………...34
3.2.1圓柱形螺旋彈簧有限元素運動方程式推導………………...34
3.2.2圓柱形螺旋彈簧元素矩陣與力向量之估算………………...40
第四章　轉置矩陣法.…………………...….………………………….45
4.1轉置矩陣法求挫屈負荷(或共振頻率)及其模態……………….45
4.2求挫屈設計圖之流程與相關方程式推導……………...……….48
4.2.1相關方程式推導………………….....…………….………….48
4.2.2求挫屈設計圖之流程…………….....……………….……….50
4.3求頻率設計圖之作法……………….....….……………….…….52
第五章 圓柱形螺旋彈簧之挫屈分析與結果(使用靜態方法) ….….54
5.1承受軸向力螺旋彈簧之挫屈問題分析..….…………………….54
5.2承受軸向扭矩螺旋彈簧之挫屈問題分析….…………..……….63
5.3同時承受軸向力與軸向扭矩螺旋彈簧之挫屈問題分析…...….67
第六章 圓柱形螺旋彈簧之挫屈分析與結果(使用動態方法) …….76
6.1承受軸向力螺旋彈簧之挫屈問題分析….…………..……...….76
6.2承受軸向扭矩螺旋彈簧之挫屈問題分析………...…………....83
6.3同時承受軸向力與軸向扭矩螺旋彈簧之挫屈問題分析….…..89
第七章 結論與建議………………………………………………….93
參考文獻……………………………………………………………….95

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