Coupling Characteristics And Synchronization Mechnism In The Mechanical System With Pendulums Driven By Exciters

In this paper,the coupling characteristics and vibration synchronization of pendulums driven by exciters are presented,based on the theories of exciter synchronization and pendulum synchronization.Due to the existence of various coupling in such mechanical system,such as the coupling between exciters,the coupling between exciter and pendulum,and the coupling between pendulums.The coupling has the characteristics of complexity and variability,so its theoretical research is of great significance.In addition,the mechanism can be used to design many types of vibrating jaw crusher,compared with the conventional jaw crusher,and the vibrating jaw crusher has the advantages of larger crushing ratio and crushing ultra-hard raw materials.Therefore,this paper studies the coupling characteristics and synchronization mechanism of three kinds of the mechanical system with pendulums driven by exciters,based on the above theoretical research and the actual demand.Meanwhile,the influence of key parameters of the system,such as the mass of exciters,the mass of pendulums,the length of pendulums,etc.on the coupling dynamic characteristics of vibration of mechanical system and its stability is considered specially,so that the optimization of structural parameters of the system comes true,and this paper provides theoretical reference for the design of a new type of the vibration jaw crusher.The specific research contents are as follows:(1)With the plane motion,the dynamic model of a single pendulum driven by a single exciter is taken as the research object and the coupling dynamic characteristics of the vibration system is studied.Firstly,the Lagrange equation is used to establish the motion differential equation of the system,and the theoretical condition for linear motion of the main rigid frame is obtained,then the drift,harmonic amplitude,basic vibration amplitude are derived.Secondly,according to the theoretical derivation,the relationship between the parameter configuration and the motion characteristics of vibration system is obtained by qualitatively numerical analysis.Finally,the fourth-order Runge Kutta program is directly applied to the motion differential equation of system for simulation research.Through the comparative analysis of the theory,the numerical value and the simulation result,the correctness of the results of the study and the validity of methods are verified,this research can provide a theoretical reference for the design of a new vibrating equipment and also lay a theoretical foundation for the following problems of the coupling characteristics and synchronization of the mechanical system with multi-pendulums driven by multi-exciters.(2)With the plane motion,the dynamic model of double pendulums driven by double exciters is taken as the research object and the research on the synchronization mechanism and coupling characteristics is studied in detail.According to the dynamic model,the differential equation of motion is derived,then the vibration response of the system is obtained.Using the average method to deduce the theoretical criterion that the system can implement synchronization.The stability criterion is derived by introducing disturbance parameters.In the aspect of the qualitatively numerical analysis,the influence of the main parameters on the phase difference between exciters,the amplitude and the relative amplitude of pendulums,the amplitude of the rigid frame,the synchronization and stability of the system are obtained.Finally,based on the comparison between simulation results and theoretical numerical results,the correctness of the above theoretical derivation and research results is verified.The results show that the geometric and mass parameters of the pendulum directly affect the stability of the system with double exciters and double pendulums.In order to realize the application of this kind of synchronization mechanism in engineering,appropriate parameter configuration should be selected to ensure the phase difference between exciters and the relative amplitude between pendulums.(3)With the dynamic model of a single pendulum driven by double exciters is taken as the research object and the coupling and synchronization mechanism of the space system is studied in detail,two exciters are mounted on a pendulum and the rotating plane of exciters is interleaved with the movement plane of the pendulum in this system,.The purpose of this study is to provide a set of rules for the optimization and matching of system parameters for the development and the design of a new type of vibrating jaw crusher.Firstly,the mathematical model of the system is established and the vibration response,the criterion of synchronization and the criterion of stability are deduced.Through numerical analysis,the influence of the main parameter configuration on the characteristics of the vibration system is obtained.Finally,according to the comparison between simulation results and numerical analysis results,the correctness of the above theoretical method and results is verified.The results show that the key parameter configuration of the system has a great influence on the characteristics of the vibration system and the appropriate parameter configuration should be selected,according to the actual demand for the engineering.