曲柄滑塊機構之含裂紋撓性連桿的振動分析

Vibration Analysis of the Cracked and Flexible Connecting Rod in a Crank-Slider Mechanism

林魁偉(Kwei-Wei Lin)

指導教授 ： 施延欣

中原大學/工學院/機械工程研究所/碩士(2001年)

https://doi.org/10.6840/cycu200100394

摘要

摘要

本文考慮在曲柄-滑塊機構中，分析含裂紋之撓性連桿的縱向振動與橫向振動的問題。首先我們假設連桿為Euler樑，以漢米爾頓(Hamilton)原理求得運動方程式和邊界條件，再以滿足邊界條件的模態函數，利用Galerkin方法來推導出Mathieu方程式。然後再利用Runge-Kutta數值方法來探討曲柄轉速率對橫向振動角頻率比( )、曲柄對連桿長度比( )與裂紋深度比(a / R)等參數對暫態振幅的影響。結果顯示，自然頻率不受曲柄轉速率的影響、曲柄對連桿長度比增加時，橫向振幅會變大、當裂紋深度比愈深時，橫向振幅亦會變大。

關鍵字

振動分析 ； 曲柄-滑塊機構 ； 含裂紋撓性連桿

並列摘要

Abstract

Considering a crank-slider mechanism, the analysis of the longitudinal and transverse vibration of the cracked flexible connecting rod is analyzed in this study. First of all, the connecting rod is assumed as the Euler’s beam, then the equations of motion and boundary conditions are derived by using Hamilton’s principle. Moreover, by using the Galerkin method with mode shape function that satisfies the boundary conditions, the equations of motion are reduced to the Mathieu equations. And then, Runge-Kutta method is employed to determine the transient amplitude, some parameters, such as the ratio ( ) of rotating angular velocity of the crank to natural frequency of transverse vibration for the link without crack, the ratio ( ) of the crank length to connecting rod length, and the ratio (a / R) of crack depth to radius of link, influence the amplitude. The results reveal that the natural frequency of connecting rod is not influenced by the angular velocity. While the ratio of the crank length to connecting rod length increases, the transient transverse amplitude increases, too. The ratio of crack depth increases, the transverse amplitude increases a little.

並列關鍵字

Cracked and Flexible Connecting Rod ； Crank-Slider Mechanism ； Vibration Analysis

參考文獻

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