Vibration Analysis of a Slider-Crank Mechanism by Finite Element Method

滑塊－曲柄機構撓性連桿的振動分析

馮榮豐(Rong-Fong Fung) ； 施延欣(Yan-Shin Shih) ； 陳信宏(Hsin-Hung Chen)

《中華民國振動與噪音工程學會論文集》 1994 (1994/06) Pp. 35-43

https://doi.org/10.30028/CSSVANNUAL.199406.0035

摘要

本文研究滑塊－曲柄機構撓性連桿的振動分析，假設連桿為Timoshenko樑，並利用Hamilton原理來推導運動方程式及邊界條件。連桿與滑塊的連接點受限在水平向的導槽作運動，由此束縛條件，得到一個方程式來描述此移動邊界的運動現象，此點與一般文獻假設的簡支撐邊界條件不同。最後以Runge-Kutta數值積分法求得連桿中點及滑塊端軸向，側向變形及截面轉角的暫態振幅。

並列摘要

Tranditionally, mechanisms have been designed on the basis of an assumption that is all members in a mechanism being rigid bodies. However, a mechanism operated at a high-speed condition, a perturbative motion about the position predicted by use of the rigid-body assumption will be observed. There will be some problems in mechanisms when the amplitudes of vibrations are greater than allowable limits. To have a more accuracy in the performance of the slider-crank mechanism, the dynamic analysis of the elastic connecting rod is interested.
In this paper, the vibration analysis of a high-speed slider-crank mechanism with a flexible connecting rod is studied. The equations of motion of Timoshenko beam and its corresponding boundary conditions are developed by Hamilton's principle, which are transformed into a set of ordinary differential equations by use of finite elemen method.
The realistic operation condition is that the crank rotates, and the end of connecting rod moves reciprocally with slider along the horizontal guide. The geometric constraint of the end of connecting rod is derived and introduced into the equations of motion and boundary conditons. It is found that the boundary conditions of the connecting rod moving with slider are the moving boundary supports, but not the simply supported ones assumed in all references.
Finally, the Runge-Kutta numerical method is applied to obtain the transient amplitudes which are compared with those of considering the flexible rod to be Euler beam or assuming the ends of connecting rod are simply supported.