Dynamic study of a dual-mass nonlinear system with piecewise stiffness driven by three non-ideal motors

Abstract

In the petroleum industry, vibrating screens are crucial equipment for separating rock chips from drilling fluids. However, the accuracy of dynamic characteristics in vibrating screens is often insufficient due to their simplified modeling as linear vibration systems. In this study, we propose a dual-mass nonlinear vibration system with piecewise stiffness driven by three non-ideal motors to better capture the nonlinear vibrations characterized by multi-degree of freedom (DOF). To investigate the dynamic characteristics of this system, we first establish the absolute and relative differential motion equations using the Lagrangian method and linearize the piecewise linear elastic force through asymptotic approximation. The synchronization conditions are then theoretically deduced based on mean small parameter method, followed by deriving a stability criterion using Poincare-Lyapunov method. Additionally, a mathematical model for non-ideal induction motors to analyze their impact on torque balance in the synchronous state is presented. Furthermore, we numerically investigate how structural parameters influence the system’s synchronization ability, stable phase difference, mass center trajectory, and amplitude frequency characteristics. Finally, simulation results validate the theoretical findings and numerical analysis, emphasizing that the synchronization ability of the system is significantly influenced by both the eccentric rotor mass ratio and motor mounting angles. Additionally, it is observed that under different synchronization conditions, the mass center trajectory is affected by piecewise nonlinear stiffness.