Study On Synchronization Theory Of The Vibrating Systems Driven By Multiple Motors

In practical engineering,in order to achieve the synchronization characteristics required in engineering,and to improve the efficiency and yield,two or multiple motors often need to be installed on machines to work together.Therefore,it is necessary to study the theory of self-synchronization of vibrating system.In the existing vibration machines for engineering applications,the vibration machine designed by using synchronous principle has the advantages of energy saving,high efficiency and simple structure,and it occupies little space in the installation of production equipment,so it is an significant development direction of vibration machinery.At present,the vibrating synchronization of the vibrating system driven by two motors or multiple motors under far resonance has been studied by predecessors,and few studies have been done on near resonance.In order to fill the blank of this field,this paper puts forward three kinds of dynamic model of vibrating system,studies the synchronization principle of vibrating system on near resonance and super resonance,analyzes the coupled dynamic characteristics,obtains some synchronization criterion and stability criterion,and determines the reasonable selection region of the working point of the system base on its actual needs.In this paper,the three kinetic models proposed,the dynamic model of single-frame three-motor-driven vibrating system,double-frame three-motor-driven vibrating system,double-frame four-motor-driven（two-reverse）vibrating system with plane linear motion,are chosen as the study object,respectively.And by means of theoretical deduction,numerical analysis,computer simulation,the dynamic coupling characteristics and self synchronization of the system under different resonance types are studied.For the dynamic models of three typical vibrating systems,the differential equations of the systems are derived by the Lagrange equation,and the nonlinear dynamic analysis method is used to deduce the theory,then the synchronization criterion of system synchronization is obtained;the synchronization stability conditions are derived by the Routh-Hurwitz criterion or the Hamilton principle;numerically,the characteristic parameters of the vibrating system are analyzed in detail;finally,the correctness of the theoretical results and the feasibility of the method are verified by computer simulation.The main contents are as follows:（1）In the introduction,it summarizes the research status of vibrating synchronization theory at home and abroad,gives the research background and significance of this study,and put forward the basic research framework of this paper.（2）Taking the dynamic model of single-frame three-motor-driven vibrating system with same rotation direction in a plane is considered as the object of study,and the vibrating synchronization mechanism and stability of them under different resonance conditions are emphatically studied.The synchronization criterion of the vibrating system and the stability criterion of the system under synchronous state are derived by means of the average method and the Routh-Hurwitz criterion,respectively;numerically,the trend of characteristic parameters such as the maximum coupling torque,vibrating synchronization ability and ability of synchronization stability and the phase difference between unbalanced rotors are discussed,and coupling dynamic characteristics of the system are studied,then the steady state of system in different regions are obtained;the feasibility of the research method and the accuracy of the theoretical results are verified by the simulations of the vibrating system by Runge-Kutta method.In the course of research,according to the ratio of working frequency to natural frequency,the motion state of frame can be divided into two types:（ⅰ）sub-resonance state,in this case,the phase differences between three unbalanced rotors both are 0,then the exciting forces are added in a same direction;（ⅱ）the super-resonance state,in this case,the phase differences between the three unbalanced rotors both are 2π/3,then the vector sum of exciting forces is 0,and in this case,in order to realize that the phase differences between the exciters both are zero,the control synchronization should be adopted.（3）Based on the dynamic model of double-frame three-motor-driven vibrating system,the synchronization theory of double-frame three-motor-driven vibrating system with linear motion on various resonance states is studied.The synchronization criterion of the vibrating system is obtained by theoretical deduction,based on the Hamilton principle,the energy equation is derived,then the simplest analytical expression of the stability criterion of the system under synchronous state is obtained;in the numerical study,the changes of characteristic parameters of the vibrating system such as the amplitude frequency characteristics,the maximum coupling torque,synchronization ability,the synchronous stability ability,the phase difference between unbalanced rotors and the phase lag angles of frames are discussed,finally,some simulation results are given.In the analysis process,with the two natural frequencies of system as nodes,the whole frequency interval can be divided into three resonance regions,and the resonance states of the three resonance regions are respectively:（ⅰ）sub-resonance state(i.e.ω_m0<ω₁);（ⅱ）near sub-resonance state(i.e.ω₁<ω_m0<ω₀);（ⅲ）super-resonance state(i.e.ω_m0>ω₀).Through analysis,in the sub resonance and super resonance state,the phase differences between the three unbalanced rotors both are 2π/3,and the vector sum of exciting forces is 0,and the frames are at rest;in the near sub-resonance state,the phase differences between the three eccentric rotors both are within the interval of（-π/2,π/2）,so the exciting forces of them are superimposed,and the motions of the two frames in the x-direction are a harmonic vibration with the inverse phase,the amplitudes of them are superposed.（4）Taking the dynamic model of double-frame four-motor-driven（two-reverse）vibrating system with plane linear motion is considered as the object of study,the synchronization theory on double-frame four-motor-driven vibrating system with linear motion is studied.The synchronization criterion and the stability criterion in the synchronous state are obtained by theoretical deduction.The change trends of the amplitude frequency characteristic,the maximum coupling torque,the synchronization ability,the synchronization stability ability and the phase differences of the unbalanced rotor with the synchronous speed of the system are numerically analyzed.According to the value of the two natural frequencies of the system,the frequency interval can be divided into three regions,and it is found that the vibrating system exhibits a nonlinear system diversity in the sub-resonant region of the low natural frequency and in the super-resonant region relative to the high natural frequency,but in these two regions,the displacement of two frames are very small.In the region between two natural frequencies,the phase differences between the two unbalanced rotors on the same frame is belong to the interval of（-π/2,π/2）,the exciting forces of them are superimposed.The phase differences between the two unbalanced rotors on the different frame is belong to the interval of（π/2,3π/2）,the exciting force of them are in the opposite direction.By analysis,it is concluded that two frames operate with inverse phase in this region.Therefore,it is the best choice region for the working point of the system.Finally,the work done in the full text is summarized,then the existing problems and the next research also be pointed out.