Dynamic Response and Nonlinear Characteristic Analysis of Rigid–Flexible Coupling Mechanism with Lubricated Revolute Clearance and Prismatic Clearance

Revolute and prismatic pair clearances are common in various mechanisms, and their motion state seriously affects the accuracy of the mechanism. Adding lubricant to a kinematic pair can effectively counteract the adverse influence of a collision force. Thus, this work introduces an advanced modeling method that considers the combined effects of a lubricated revolute and prismatic clearance, as well as component flexibility, and studies the influence of their coupling effect on the dynamic response and nonlinear characteristic of mechanisms. The specific content of this paper is as follows: Firstly, revolute lubrication clearance and prismatic pair clearance models are established. Secondly, rigid components and flexible components are described based on the reference point coordinate method and absolute nodal coordinate formulation. Then, based on the Lagrange multiplier method, a rigid–flexible coupling dynamics model with revolute lubrication clearance and prismatic clearance is established. Finally, the dynamic responses of the mechanism are analyzed, including the displacement, velocity, and acceleration of the slider, the driving torque of the crank, and the center trajectories of the revolute clearance and prismatic clearance. Qualitative research is conducted on the nonlinear characteristics of the system through a phase diagram and Poincaré map. This quantitative study is conducted on the nonlinear characteristics of a system using the maximum Lyapunov exponent. The influences of different parameters on the dynamic response and nonlinear characteristic of the mechanism are analyzed. The results indicate that lubrication effectively reduces the influence of the clearance on the dynamic response and nonlinear characteristic of the mechanism, resulting in a decrease in the peak dynamic response and a weakening of the chaotic phenomenon. Further, as the driving speed increases, the dynamic viscosity decreases the clearance value increases, and the stability of the mechanism decreases.