Non-Contact Synchronous Phase Difference Detection in Dual-Motor Vibratory Systems by Dynamic Response Characteristics

In traditional vibration systems, phase difference measurement typically involves the direct installation of fiber optic sensors on rotors experiencing operational vibrations. However, practical applications are often constrained by the challenges of installing sensors in explosion-proof structures and the risk of sensor degradation due to exposure to slurry media. To address the safety and reliability challenges associated with direct measurement, an indirect phase difference detection method for dual-motor systems is proposed based on dynamic response analysis. The motion differential equations are established using Lagrange’s equations, and the steady-state responses along with phase difference expressions are derived through the small parameter averaging method. A synchronization phase equation is derived from the steady-state solutions, facilitating indirect modeling of phase differences. Additionally, an electromechanical coupling model is developed using the Runge-Kutta method to simulate how electromechanical characteristics affect synchronized phase differences. Simulation results indicate that the synchronized phase difference is correlated with structural parameters and changes as a function of motor installation distance. When the dimensionless parameter r _l reaches a critical value (approximately 6), the installation angle β becomes the predominant factor influencing phase synchronization. The indirect measurement model exhibits strong compatibility with arbitrary operational states of vibrating screens, showing high consistency between the predicted phase differences and both simulation and experimental results. This study constructs a non-contact monitoring framework by integrating vibration characteristic modeling and driving parameter analysis, providing valuable insights into phase detection under harsh vibrational conditions.