Research On Synchronization Theory Of Vibration System Driven By Double-motor And Four-motor

In order to meet the vibration engineering needs of different machinery,it usually requires two or more motors to drive at the same time,and to achieve synchronous movement between them.In most cases,the structure of mechanical equipment will be greatly simplified when it utilizes vibration synchronization principle.Therefore,the vibration synchronization theory has great value in engineering application.As for the mechanical equipment,which uses the vibration synchronization,will show different synchronization status and different forms of movement,when it works in different vibration conditions(sub-resonance and super-resonance).At present,many scholars have conducted in-depth research on the synchronization of two-machine and multi-machine-driven vibration systems under super-resonance and ultra-far-resonance,however,there is little research on the synchronization of the mechanical equipment in the sub-resonance state.In this paper,three groups of dynamical models are selected to study the synchronization state in the sub-resonance and the super-resonance state,which has certain theoretical value and enrich the theory of vibration synchronization.In this paper,"Research on Synchronization Theory of Vibration System Driven by Double-motor and Four-motor" are selected as the topic.Based on three groups of dynamical models,two-machine-driven single-body dynamic model,four-machine-driven(two-reverse)single-body dynamic model,four-machine-driven(two-reverse)pairs of body dynamics model,the paper will study vibration synchronization theory in different types of resonance.The main content are as follows:(1)The introduction part summarizes the research status of vibration synchronization theory at home and abroad,and the research background and significance of this paper,and builds a theoretical basis for the discussion.(2)Taking single-body two-motor-driven dynamic model as the research objective,the synchronization condition of two vibrators is derived theoretically based on the small parameter average method.The stability criteria of the system are obtained based on the Hamilton principle.The amplitude-frequency and phase-frequency characteristics of the system are obtained numerically,and the region of synchronization and stability is obtained.In the simulation,the stable phase difference in the sub-resonance and the super-resonance region is obtained,which verifies the correctness of the numerical analysis.It is concluded that the phase difference of system is stable at 0 in the sub-resonance region,the displacement is larger in this region,and the vibration energy of the system is superimposed in this region,so the operating point of the system can be selected in the sub-resonance region;the phase difference of system is stable at ? in the super-resonance region,and the displacement is small,the system vibration energy offset each other in the region,so the system operating point should be selected to avoid this area.(3)Taking single-body four-motor-driven(two-reverse)dynamic model as the research objective,mechanism of system vibration synchronization are researched basing on the averaging method.The synchronization conditions of the system and the stability criterion are derived theoretically in the synchronization conditions.Through the numerical analysis,the stable phase difference and the synchronism capability coefficient curve of the vibration system are obtained in different resonance types.The comparison between simulation and numerical verify the theoretical derivation of the correctness and effectiveness.It can be shown that the stable phase difference of the system is 0 in the sub-resonance region,the displacement is superimposed vertically,the system has a large amplitude,and the sub-resonance region is selected as the working region of the system;while the phase difference of the system is stable at ? in the super-resonance region,the displacement will cancel each other,and the system is in a static state,so the region has no engineering application value.(4)Taking double-body four-motor-driven(two-reverse)of dynamic model as the research objective,the two criteria of the system synchronization are deduced basing on the averaging method and Hamiltonian principle,namely,the synchronization condition and the stability in the synchronization condition.The phase relation,synchronization ability and stability ability of the system are discussed numerically.Through simulation analysis,the numerical analysis is proved,which is the correctness of theoretical derivation.It is concluded that the relatived to the low frequency of the system in the sub-resonance region and the relatived to the high frequency of the system in the super-resonance region,the diversity phenomenon of the nonlinear system occurs,so the two regions can not be regarded as operating points of the system;relatived to the high-frequency of the system in sub-resonance region,the stability of system phase difference is in the vicinity of 0,and the displacement of the region is also a superposition state,the region can be selected as the work area.And the model can guide the research and development of new,long-distance,large-volume vibration conveying equipment,which is of great engineering application value.Based on the above research,the synchronization characteristics of three groups of dynamics models are analyzed under different resonance types.In the sub-resonant state of work,the main advantage is to save energy.The vibration machine operating has the advantage of being responsive to the stability of the amplitude in the super-resonance state.The research of this paper has a certain theoretical value,which provides a theoretical basis for the rational choice of the range of the structural parameters of the vibration system.Therefore,it is of great significance to study the vibration synchronization theory of mechanical system under different resonance types.