Study On The Theory Of Self-Synchronization For Multi-Body Vibrating Systems With Multiple Exciters

Self-synchronization of two unbalanced rotors in vibrating systems has opened up fresh opportunities in the vibration technology and resulted in the establishment of a new branch for vibration utilization.At present,a variety of vibrating machines with two exciters has been widely used in engineering fields,such as vibrating screens,vibrating conveyors,vibrating dehydrators,etc.However,three are not very good solutions to the following five shortcomings in the applications of vibrating machines so far.(1)During the working process,vibrating machines transfer dynamic forces to the foundation,which can be harmful to the foundations and surrounding buildings.The vibration isolation of vibrating machines is the first problem to be solved.(2)Because the power of vibrating motors is small,a large scale vibrating machine can not been driven by two vibrating motors.For the last decades,the attention of many researchers has been focused on how multiple exciters synchronize to implement the superimposition of their exciting forces in the given directions.(3)Self-synchronization of two exciters is only suitable for the vibrating system with small damping.How the multiple exciters can synchronize in a vibrating system with big damping?For example,two exciters in the vibrating hammer of pile drivers are synchronized by a pair of gears.(4)The dynamic characteristics of vibrating systems depend on the dynamic parameters of system.During the working process of vibrating machines,the variation of vibration material will modify the mass of the working body and hence the dynamic parameters of system.How to ensure the performance of vibrating machines is one problem that should be concerned on in the field of vibration utilization under the condition of variable vibration material.(5)Because the moment of inertial of exciters is big,the power of motors in a vibrating machine must be bigger to ensure that the system can start.But the motors operate at an under-load state during the usual working process,which increases heating energy consumption of the motors.This paper aims at the above five problems to investigate the theory of multiple exciters in multi-body vibrating systems.For the dual-body vibrating system with two exciters,such as a vibrating conveyor,synchronization ability coefficient,force transmission coefficient and characteristic amplitude are defined as the performance parameters of the system.Effects of the two design working frequency ratios in the vibration direction and vibration material coefficient on the synchronization ability coefficient,the force transmission coefficient and the characteristic amplitude are analyzed to determine the distributions of the three performance parameters in the space of the two frequency ratios.The effects of the mass ratio of the material box to the system on the distributions of performance parameters are discussed.The relation between the transport efficiency and the vibration amplitude of the material box is obtained by numeric analysis.By virtue of the above investigation results,the method of design for the dynamic parameters of the system is proposed to ensure the performances of synchronization and vibration isolation under the condition of variable transporting materials.Computer simulations are carried to verify the effectiveness of the proposed scheme.For linear vibrating machines of plane motions,according to the general dynamic symmetry of two exciters and the principle of motion selection for a single body vibrating system,a new mechanism of three-body vibrating system for plane motion is proposed to achieve the superimposition of four unbalanced rotors exciting forces in the given vibration direction by adding two accessorial rigid frames(ARFs)on the original body.The two ARFs can rotate around the spins fixed on the original body and their rotating planes are identical.Two exciters rotating in the same direction are symmetrically installed on each of ARFs,and the exciters on the two ARFs rotate in opposite directions.The synchronization criterion and the stability criterion are deduced by using the average method of modified small parameters.The design space of dynamic parameters that the four exciters can synchronize in the expected manner is determined by numeric calculations.Computer simulations are carried out to verify that the proposed mechanism can perform well.Furthermore,when the system operates stably,the power supply for one motor on each ARF is cut off,the four exciters still synchronize with small variations of the phase differences.This fact demonstrates that the proposed mechanism can operate in the vibratory synchronization transmission state to reduce the heating energy consumption of the motors.For space motion vibrating machines with two exciters,two ARFs rotating on non-uniplanar crossing axes are fixed on the original body to construct a new mechanism of three-body vibrating system.Two exciters rotating in the same direction are symmetrically installed on each ARF.The four exciters can synchronize to implement the screw motion of vertical transporting material of the body.The synchronization criterion and the stability criterion are deduced by using the average method of modified small parameters.The design space of dynamic parameters that the vibrating system undergoes the screw motion of the body is determined by numeric calculations.Computer simulations are carried out to verify that the four exciters can synchronize in the expected manner and that the system can operate in the state of vibratory synchronization transmission.For hydraulic pile drives with two exciters synchronized by a pair of gears,a new mechanism of five-body vibrating system is proposed to synchronize four exciters driven by four hydraulic motors in the big damping vibrating system.The equations of motion of the system are set up by using the Lagrange’s equations.The synchronization criterion and the stability criterion are deduced by the average method of modified small parameters.The domain that the four exciters drive synchronously the vertical piling motion is determined by numeric calculation.Computer simulations are conducted to verify the expected performances of the new mechanism.For the isolation vibration of vibrating machines,this paper proposes a new mechanism of multi-body vibrating system for the composite vibration isolation of four dual-exciter vibrating machines on the same rigid frame of vibration isolation(RFOVI).In this system,the eight exciters can rotate synchronously and the forces that the four vibrating machines act on the foundation are cancelled mutually.The synchronization criterion and the stability criterion for the eight exciters are deduced by the average method of modified small parameters.The domain of dynamic parameters that ensures the expected performances of the system is determined by numeric calculation.The results of computer simulation demonstrate that the eight exciters can rotate synchronously,the two exciters on each vibrating machine excite its vibration in the given direction,and the phase differences among motions of the four vibrating machines are opposite to cancel their forces acting on the RFOVI so that the RFOVI is static.