Study On The Theory Of Self-synchronization For Four-Hydraulic-Motor Vibrating Pile Driver System

Vibrating pile driver is one of the key equipment in construction industry, which is widely used in pile driving and drawing operations of large-scale infrastructure projects such as urban construction, bridges and ports. Vibrating pile driver can be divided into two categories: electric pile driver and hydraulic pile driver, while hydraulic pile driver is characterized with FM convenience, high pile driving efficiency, low noise, impact resistance and wide applicable range. Currently, vibrating pile driver operates synchronously through rigid transmission gears, which are damaged frequently by the impact, decreasing pile driver’s reliability and shortening its life. But the discovery of self-synchronization phenomenon and establishment of self-synchronization theory open a new opportunity for vibrating machine design, namely, if the vibrating system meets specific conditions, multi-eccentric-rotor synchronization can achieve self-synchronization to make excitements be stacked up in a specific direction. Based on general dynamic symmetry and movement selection principal of vibrating system, this paper proposes a new sub-resonant vibrating mechanism driven by four hydraulic motors which can implement self-synchronization, establishes a new theory that hydraulic motors drive four eccentric rotors in vibrating pile driver, and explorers an analytical method of four-eccentric-rotor self-synchronization theory. Eliminating gear synchronizer based on self-synchronous theory to design a machine, can greatly simplify the structure of vibrating pile driver and improve the reliability of the transmission system, which provides a theoretical basis for the design of new vibrating pile driver. The study results in this paper are yielded as follows:(1) This paper proposes a self-synchronous vibrating mechanism with four eccentric rotors rotating in the same direction driven by four hydraulic motors mounted symmetrically on two coaxial rotating beams, and two eccentric rotors are mounted symmetrically on each coaxial rotating beam, whose rotating plane is proportional to perpendicular plane of pile direction at a certain angle called vibration exciting angle, and the two rotating planes on the beams are symmetric to perpendicular plane of pile direction, thus making excitements of the four eccentric rotors be stacked up in the pile direction.(2) Hydraulic drive system of vibrating pile driver is designed and the mathematical model of the electric motor-pump-hydraulic motor drive system in quasi-steady-state operation is derived based on energy transmission process in vibrating pile driver system. The kinetic energy, the potential energy and the viscous dissipation function of the system are established by coordinate transformation, and then applying these three items into the Lagrange’s equations, the equations of motion for the system are obtained.(3) Analytical expressions of the steady-state response for pile driver multi-body vibration system are deduced through modal analysis. The dimensionless coupling equations of the four eccentric rotors are deduced by virtue of the modified average method of small parameters. Based on the existence and stability of the zero solution for the dimensionless coupling equations, the condition of implementing the synchronization is derived, and the problem of synchronization stability of the eccentric rotors is transformed into the problem of zero solution stability for both the four eccentric rotors’ angular velocity perturbation parameters general system and the three phase perturbations parameters general system. Self-synchronization stability condition is obtained using Lyapunov stability criterion and Routh-Hurwitz stability criterion.(4) Based on the principle of minimum energy operation, the calculation method of generalized dynamic symmetry angle of the four eccentric rotors is proposed, and generalized dynamic symmetry coefficient of the four eccentric rotors is defined. Numerical analysis is done through programming to study the relationship between general dynamic symmetric angle, general dynamic symmetric coefficient and Structural and dynamic parameters of the system, which provides a parameters design rule for self-synchronous ability and maximizing excitement of the vibrating pile driver.(5) The movement selection principle for sub-resonant self-synchronous vibrating system is proposed. For sub-resonant vibration systems, horizontal elliptical motion (over resonance) makes the average phase difference between two pairs of eccentric rotors approach π, prompting system to vibrate vertically; and vertical vibration also makes the average phase difference between two pairs of eccentric rotors approach π, prompting system to vibrate vertically. This characteristic is called movement selection principle for the sub-resonant vibration system. Based on this principle, sub-resonant vibration system in this paper will be able to achieve vertical stable vibration to pull or drive pile, which is a major feature of sub-resonant vibrating system.(6) Taking advantage of Runge-Kutta method, the software of computer simulation for the four-hydraulic-motor vibrating pile driver system is developed. Through computer simulation, the impact of the difference of structural parameters, dynamic parameters of the system and the difference of initial phase on self-synchronous operation is studied to verify the correctness of the theoretical analysis.