In this paper, a novel dynamic model of coupling translation joints with subsidence for time-varying load in a planar mechanical system is established. One translational joint has four working scenarios, which are free motion, one corner rub-impact, two adjacent corners rub-impact and two opposite corners rub-impact. However, the rub-impact of double coupling translation joints are not a simple superposition of these scenarios, but rather a more complex rub-impact configuration that should be considered in this model. An adaptive fourth-order Runge–Kutta method is utilized to solve the dynamic differential equations. After that, we discuss the dynamic behavior of the rub-impact coupling by taking a triplex member of the crosshead slider, piston rod and piston slider as an example in the reciprocating compressor system. The results show that the double coupling translation joints experience free motion, continuous contact motion and rub-impact motion. The difference is that, in the rub-impact motion, for the crosshead slider there only appears one single corner and two adjacent corners impacting the guide, while the coupling piston slider experiences multiple rub-impact situations including one single corner, two adjacent corners and two opposite corners impacting the guide. Moreover, the results reveal that the subsidence has a significant influence on the rub-impact behavior of the coupling translation joints, and the greater the subsidence, the more severe the vibration response of the slider impacting the guide. Finally, in this rub-impact coupling system, the existence of chaotic behavior is confirmed by the Poincare section and the largest Lyapunov exponent approaches.

Coupling rub-impact dynamics of double translational joints with subsidence for time-varying load in a planar mechanical system

Oblique collisions are more likely to happen in the realistic translational joint with clearance, compared to the full front impacts. It can be a quite demanding task to evaluate how oblique contact influences the system responses. In this connection, a modified model to assess the contact forces generated in the 3D translational clearance joint is presented, together with its application in a double crank mechanism. The influence of the oblique impact, as well as the geometrical changes of the contact region, is introduced to this model. The effects of impact velocity and initial inclination angles were numerically analyzed in a two-body oblique contact system as a demonstrated example. Referring to the simulation results obtained from software ANSYS/LS-DYNA, the accuracy of the proposed model was proved. Numerical investigations were carried out for a double crank mechanism with rigid bodies to study the effects of crank speed and clearance size on the dynamic behaviors. Poincare portraits and acceleration of the output element were utilized to assess the system behaviors. The results demonstrate that the translational clearance and oblique contact can have a remarkable influence on the system responses. Furthermore, an experimental rig was established based on a mechanical press to achieve some experimental validations.

Dynamic analysis of the double crank mechanism with a 3D translational clearance joint employing a variable stiffness contact force model

Clearance joint appears in the multibody system and it could cause the uncertainty of motion A general method for dynamic modelling and analysis of slider-crank mechanism with multiple clearance joints is presented and discussed in this work The contact-impact characteristics of clearance joint are described by the nonlinear continuous contact force model With flexible link taken into account, the dynamic characteristics of slider-crank mechanism with multiple clearance joints are analyzed based on the presented model Then, the dynamic response of a flexible slider-crank mechanism is measured to clarify how to clearance joints can cause the vibration phenomenon of multibody system Moreover, the stability and chaos analysis are conducted with the purpose of performing a parametric study, which quantifies the effects of clearance size and rotational speed on dynamic behavior of multibody system with multiple clearance joints The numerical results indicate that the dynamic behavior of a flexible slider-crank mechanism depends on the characteristics of clearance joints

Kinematic accuracy and nonlinear dynamics of a flexible slider-crank mechanism with multiple clearance joints

Joint clearance serves as a crucial element of nonlinearity in multibody systems. The quantization of the system chaos is conducive to not only the understanding of the nonlinear nature but the rationalization of system controlled parameters. In the present work, the system dynamics for the planar slider-crank mechanism with multiple clearance joints is depicted by the correlation dimension and bifurcation actions. Considering the obliqueness of the slider, the general configuration of the planar joint is proposed. Generalized coordinates and the Lagrangian approach are adopted to derive the dynamic motion equations. The effects of clearance size and driving speed on the bifurcations of the dynamic response are investigated. Furthermore, the fractal dimension of the strange attractor is identified by the correlation dimension from time series. Based on the Cao method, the Mutual Information (MI) function, and the Grassberger-Procaccia (G-P) algorithm, the controlled factors in the evaluation of correlation dimension are cautiously determined. Ultimately, the compound effect of translational and revolute clearance joints on the mechanism dynamics is featured. The numerical results testify that the correlation dimension of the slider displacement approximately saturates beyond a specific translational clearance value. Moreover, with the parameters used in this work, the complexity of system response seems to be more sensitive to the variation of translational clearance size than with the revolute joint.

Yunqing Zhang

Papers

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