Dynamics of synchronization for four hydraulic motors in a vibrating pile driver system

This article proposes a self-synchronous vibrating mechanism with four unbalanced rotors driven by four hydraulic motors mounted symmetrically on two coaxial rotating beams. Analytical expressions of the steady-state response for the multi-body vibrating system are deduced. The dimensionless coupling equations of the four unbalanced rotors are derived by virtue of the averaging method of modified small parameters. The synchronization and stability criteria are deduced using the existence and stability of the zero solution for the dimensionless coupling equations of the four unbalanced rotors. The coefficients of synchronization ability are defined. By numeric analysis, effect of the dynamic parameters on the characteristics of coupling dynamics for the unbalanced rotors is discussed to determine dynamic parameter intervals of synchronization stability. Computer simulations are carried out to verify the correctness of the theoretical analysis.