Research On Dynamics Of The Linkage Mechanism With Cracked Links

The linkage mechanism is widely used in various types of machines as the dynamic parts. Due to various factors, the components of linkage mechanism are easy to crack. Cracks existing in the linkage mechanism not only change the crack stress and strain field of tip area, but also affect the dynamic characteristics of the linkage mechanism. If these cracks can not be detected in time, the vibration of linkage mechanism may make rapid expansion of the crack, which causes the fracture of components, and then causes devastating damage to the machine. The linkage mechanism is comprised of components, which should be considered as elastomer when the dynamic characteristics of linkage mechanism with cracked components are analyzed. It has important theoretical significance and practical value for analyzing impacts of vibration on crack and crack identification. This paper is to solve problems about dynamic characteristics of the linkage mechanism, the main content of this paper include the following:According to the finite element theory, the vibration theory and the theory of fracture mechanics, the dynamic model of a crack beam element is established. First of all, using the finite element displacement method, the kinetic energy and elastic potential energy of the crack beam element is obtained. The formula of the strain energy which is released by crack growth is introduced based on the theory of fracture mechanics. then, the expression for potential energy of open crack beam element and breathing crack beam element are derived, and finally, the dynamic equations of cracked beam which contained open crack and breathing crack by using Hamilton’s principle are obtained.Using the finite element theory, the linkage mechanism is divided into many beam element model, if no cracks in the beam element, it is considered as non-cracked beam element model, otherwise, it is considered as cracked beam, and obtain the corresponding coordination unit matrix and coordinate transformation matrix, integrate the cracked beam element model and the non-cracked beam model which is previously established, the dynamic model of linkage mechanism with cracked components is obtained.Using the method of multiple scales, the mechanism of the parameter excitation and the forced vibration of the linkage mechanism with cracked component, the studies indicate that the nonlinear crack parameter excitation and the outer excitation exist in the linkage mechanism with cracked component system. The crack parameter excitation is caused by the motion of the surface of breathing crack, and the outer excitation is caused by the self-excited inertial forces of the system. The coupling phenomenon of both the parametric vibration and the forced vibration of the system may take place under the influence of both the crack parameter excitation and the outer excitation.Applying synthetically the implicit time integration framework and the modified Newton iteration, obtain iterative framework of solving nonlinear equation. First of all, applying the theory to solve the cantilever beam and simply supported simple beam structure of the cracked state natural frequency, the result was presented and validated through experiment, next, the natural frequency and mode shape of four bar mechanism with cracked connecting rod is obtained through simulation, the result was presented and validated through experiment, and finally, study the nonlinear dynamics of four bar mechanism with cracked connecting rod when the crank worked at uniform circular motions.Carrying out the experiment about cracked structure and linkage mechanism with cracked connecting rod, test the cantilever beam and the simply supported beam with crack and four bar mechanism with cracked connecting rod, to verify the correctness of the method.