含呼吸式裂紋之曲柄滑塊機構橈性連桿的振動與疲勞裂紋成長耦合分析

連桿在高速運動時，其變形對構運動位置有很大影響，隨著精密機械或微機電的應用，撓性連桿的振動與疲勞評估，日益重要，為確保機構零件之安全，疲勞裂紋成長的評估，是一個值得探的課題。在文獻中，撓性連桿的振動分析，已被許多學者探討，但含裂紋的連桿的振動分析，鮮少被探討，至於含裂紋的連桿的疲勞裂紋成長分析，更未有學者加以研究。本文考慮在曲柄-滑塊機構中，分析含裂紋之撓性連桿的橫向振動問題。首先我們假設連桿為Timoshenko樑，以漢米爾頓(Hamilton)原理求得運動方程式和邊界條件，而連桿在滑塊的那一端為移動的邊界條件與實際狀況相同，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數值方法來探討連續和呼吸式裂紋模態的暫態振幅，並探討振動與疲勞裂紋成長耦合分析。結果顯示，自然頻率不受曲柄轉速率的影響、裂紋深度比愈深時，震動振幅亦會變大。綜合振動與疲勞的研究，解決振動與疲勞交互影響的盲點，在研究與應用上具有貢獻。

關鍵字

振動；疲勞；曲柄滑塊；呼吸式裂纹

並列摘要

Based on Timoshenko theories, the vibration and fatigue analyses are combined to discuss the vibration behavior of a cracked rod of crank-slider mechanism with the crack growth in this study. The natural frequency is changed when the crack is growing. Therefore the amplitude of vibration is affected by the loading frequency. The model of breathing crack is applied to simulate the opening and closure crack, which affects the behavior of vibration. The analysis of vibration and fatigue for a cracked rod are coupled in this study. The interaction between vibration and fatigue are determined and discussed. At first, the connecting rod is assumed as Timoshenko’s beam, then the equations of motion and boundary conditions are derived by Hamilton’s principle, that the moving boundary conditions of connecting rod at one end of slider are considered. Moreover, using the Galerkin method with mode shape function that satisfies the boundary conditions, the equations of motion are reduced to Mathieu equations. And then, Runge-Kutta method is used to determine the transient amplitude for breathing crack model. The modified Forman equation is used to determine the rate of fatigue crack growth, and the crack depth is corrected cycle by cycle. When the crack depth ratio increases, the amplitude increases.

並列關鍵字

fatigue ； vibration ； breathing crack ； Timoshenko ； flexible connecting Rod

參考文獻

1. Lowen G. G. and Jandrasits W. G. , “Survey of Investigations into the Dynamic Behavior of Mechanisms Containing Links with Distributed Mass and Elasticity”, Mechanism and Machine theory, Vol. 7, No. 1, pp. 3-17, 1972

2. Erdman A. G. ,Sandor G. N. , and Oakberg R. G. , “A General Method for Kineto-Elastodynamic Analysis and Synthesis of Mechanisms”, Journal of Engineering for Industry, pp. 1193-1205, Nov. 1972

3. Viscomi B. V. and Ayre R. S. , “Nonlinear Dynamic Response of Elastic Slider-Crank Mechanism”, Journal of Engineering for Industry, pp. 251-262, Feb. 1971

5. Fung R. F. , “Dynamic Responses of the Flexible Connecting Rod of a Slider-Crank Mechanism with Time-Dependent Boundary Effect”, Computers & Structures, Vol. 63, No. 1, pp. 79-90, 1997

6. Fung R. F. , “Dynamic Analysis of the Flexible Connecting Rod of a Slider-Crank Mechanism”, Transactions of the ASME, Journal of Vibration and Acoustics, Vol. 118, No. 4, pp. 687-689, Oct. 1996

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含呼吸式裂紋之曲柄滑塊機構橈性連桿的振動與疲勞裂紋成長耦合分析

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