Studies on Vibration and Synchronization Characteristics of an Anti-Resonance System Driven by Triple-Frequency Excitation

In the continuous drilling process of oil wells, to achieve the efficient screening of drilling fluids by the vibrating screen while ensuring the safety of the screening operation, an anti-resonance system driven by two exciters with triple-frequency (denoted as 3:1 frequency ratio) is proposed. Initially, differential motion equations are formulated utilizing Lagrange’s equation, followed by the definition of vibration isolation coefficients adopting ratios. Triple-frequency synchronization and stability criterion between two eccentric blocks are subsequently elucidated via the asymptotic method and Routh–Hurwitz criterion. Concurrently, the effects of structural parameters on vibration isolation capacity, steady-state trajectory, and the triple-frequency synchronization phase are investigated through numerical computation. Ultimately, the reliability of the theoretical study is corroborated by simulation analysis. Results indicate that under the allowable system parameters for the practical project, the amplitude of the vibration body can exceed three times that of the isolation body; the two solutions of the stable phase difference (SPD) are different by π, one of which is stable and the other is unstable, and the stability of phase difference is determined by the sign of the stability coefficient. This work is useful for developing new vibrating screens and other multi-frequency vibration machines.