旋轉雷立夫樑受週期性側向與軸向力之動態響應分析

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楊明倫(Ming-Lun Yang) 查詢紙本館藏

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機械工程學系

論文名稱

旋轉雷立夫樑受週期性側向與軸向力之動態響應分析
(Dynamic response analysis of a rotating Rayleigh beam with periodically radial and axial forces)

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摘要(中)

本文欲模擬車床加工中，均勻圓柱之工件的動態響應。預想之加工情況，為等速循環之連續切削，刀具作用於工件上之力可視作一移動之外力，除了對工件產生週期之側向力之外，對工件之軸向也會造成張力與壓力作用。文中將等速移動之側向力與軸向力表示為週期性之函數，利用傅立葉展開法，分析車削多個週期後，工件之動態響應。
　　理論上，工件可視為一旋轉之雷立夫樑，受到週期性運動相依之側向力，與週期性之軸向力。本文使用漢米爾頓定理，推導出此系統之運動方程式，並無因次化，代入以傅立葉展開之外力函數，再以格勒金法離散化系統運動方程式。接著，針對各個模態，以多重尺度法與數值方法做穩定性分析，以討論在各種條件下，系統之穩定特性。之後，以阮奇庫塔法，求解系統之微分方程組，得到位移響應，並經由快速傅立葉轉換得到頻譜圖，分析位移響應之頻譜特性。最後，再顯示穩定狀態下，旋轉樑隨時間之變形。

摘要(英)

This paper formulates the processing of the lathe. In this process, a turning tool moves along the workpiece repeatedly. It could be seem as a periodically moving load which includes radial motion-dependent force and axial tension and compression distributed forces. To analyze the dynamic response of the workpiece after numerous turning cycles, those external forces are periodic functions in the forms of Fourier series.
A rotating Rayleigh beam with periodically radial and axial forces was considered. The governing equations were derived by Hamilton’’s principle and expressed in a dimensionless form. The equation of motions was turned into discrete equations by Galerkin’’s method. For each mode, the stability of the rotating beam was analyzed by the method of multiple scales and Floquet theory. The differential equations were also solved by Runge-Kutta method. The phenomena of stability analysis and spectrum analysis are discussed. Finally, the time responses of the beam are showed and discussed.

關鍵字(中)

★ 動態響應
★ 穩定性分析
★ 多重尺度法
★ 旋轉雷立夫樑

關鍵字(英)

★ rotating Rayleigh beam
★ dynamic response
★ stability analysis
★ the method of multiple scales

論文目次

目錄………………………………………………I
圖索引……………………………………………III
表索引……………………………………………VII
第一章前言………………………………………1
第二章系統運動方程式…………………………4
2.1. 方程式推導…………………………………4
2.2. 無因次化系統方程式………………………6
2.3. 模擬外力形式………………………………7
2.3.1. 運動相依移動側向力……………………8
2.3.2. 軸向力……………………………………11
2.4. 離散化系統方程式…………………………13
第三章穩定性理論………………………………18
3.1. 多重尺度法…………………………………18
3.1.1. 軸向力的穩定性分析……………………19
3.1.2. 運動相依移動側向力的穩定性分析……32
3.1.3. 二次項穩定性分析………………………39
3.1.4. 模態耦合…………………………………41
3.2. 數值方法……………………………………48
第四章系統之數值結果與討論…………………51
4.1. 穩定性分析…………………………………51
4.1.1. 軸向力之影響……………………………52
4.1.2. 運動相依側向力之影響…………………56
4.2. 樑上單點位移………………………………59
4.3. 樑變形………………………………………65
第五章結論與建議………………………………66
5.1. 結論…………………………………………66
5.2. 建議…………………………………………67
參考文獻……………………………………………69

參考文獻

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指導教授

黃以玫(Yii-Mei Huang)

審核日期

2005-7-7

推文