Theoretical and experimental study for implementation of the elliptical trajectory in dual-motor vibration system

In the petroleum drilling industry, the smoothly functioning vibrating screens play a critical role in control of solid–liquid and recovery of drilling fluid. Due to the mechanical coupling, the surface of the vibrating screen tends to produce unbalanced swings, which makes the motion trajectory inconsistent with the situation at the center of mass, thus affecting the screening efficiency. In order to reveal the reasons for the unbalanced swings of the vibration system and the principle of the trajectory equilibrium characteristics (TECs), the self-synchronization characteristics of two eccentric rotors (ERs) driven by elliptical trajectory dual-motor vibrating system are investigated. The kinematic differential equations of the vibration system are determined by the Lagrange method. Then, the conditions of synchronization and stability of the vibration system are determined, respectively, by the small parameter average approach and the Routh–Hurwitz criterion. Subsequently, the impact of the structural parameters about the synchronization stability is examined by numerical discussion. Furthermore, the effectiveness of the theoretical research is confirmed by comparing the results between dynamics simulation and experiment under different structural parameters. Finally, by focusing on the analysis of the trajectories of different measuring points in the experiment, the relevant conclusions on how to reduce the unbalanced swings and maintain the TECs of the vibration system are obtained. The elliptical trajectory form of the system is most affected by the motor installation angle and installation distance in vibrating body, while less affected by the installation deflection angle and installation offset distance between the motors. In addition, the elliptical trajectories of the oscillating body are in a good equilibrium when reducing the swing angle of the vibration system, in other words, increasing the installation angle and reducing the installation distance of the exciters in the stable state.