Frequency analysis of a typical planar flexible multibody system with joint clearances

A comprehensive study of the effect of joint stiffness on the vibration behavior of a typical slider-crank mechanism with a flexible component and joint clearances is presented in this paper. Firstly, the dynamic response of the ideal mechanism is obtained using both the floating frame of reference (FFR) and assumed modes methods. Based on the results, it is concluded that in mechanisms with high crank speeds, the fundamental natural frequency could be reachable by lower external excitation frequencies. Then, considering the joint stiffness between the slider and the ground as well as the coupler and the slider, the responses of both mechanisms with the ideal and imperfect joints are compared with each other. Having found the exact number of equations of motion equal to the number of degrees of freedom, a deeper insight into the vibration behavior of this typical mechanism considering the joint stiffness is obtained. Finally, Fast Fourier Transform (FFT) algorithm is implemented to find the frequency components of the transverse deflection of the coupler midpoint and the vertical displacement of the slider. It is, however, observed that variation of the joint stiffness in a reasonable range does not considerably change the frequency components of the response.