Research On Nonlinear Vibration Control Of Vehicle-Road Coupled Maglev Train

The nonlinear coupled vibration between the subsystems of maglev train will affect the safety and ride performance of the vehicle,and its vibration reduction control is a problem that must be solved in the application of low-speed maglev train.In the process of maglev train running,it will be affected by various reasons,resulting in nonlinear vibration of the car body,among which the periodic unsteady aerodynamic force is one of the main factors,however,aerodynamic lift is generally ignored in the existing theoretical research process,which affects the accuracy of the results.Based on magnetic levitation train as the research object,this paper studies the cause of the train system resonance occur between,dynamic characteristics and stability of the nonlinear coupling vibration analysis system,found the avoid maglev train control method of the coupling resonance for maglev trains structure parameters design and the improvement of system stability provides a theoretical basis and calculation method.Firstly,the single degree of freedom nonlinear vibration of maglev train under periodic unsteady aerodynamic disturbance is studied.Based on PD control,a single degree of freedom maglev vehicle body vibration model with periodic unsteady aerodynamic disturbance was established,and its nonlinear dynamic differential equation with positive stiffness was derived.The amplitude-frequency response curve of the vehicle body was obtained by solving it with multi-scale method.Secondly,the stability of the car body is analyzed,and the relationship between the nonlinear vibration of the car body and the control parameters and the equivalent mass of the maglev car body is obtained.Then,the negative stiffness control of the system is studied,and a bifurcation control method to change the system stiffness is obtained.The influence of velocity control parameters on the periodic and chaotic solutions is studied by using numerical theory,and the bifurcation parameter interval of control parameters is found.Secondly,a two-degree-of-freedom nonlinear vibration model of maglev train under unsteady aerodynamic disturbance is established.Based on the single degree of freedom,the influence of periodic unsteady aerodynamic force on the coupling resonance between the car body and the electromagnet of maglev train is studied by considering the relative motion of car body and maglev frame.The dynamic equation of car-electromagnet was established,and the amplitude-frequency response equation was deduced by using the multi-scale method.The amplitude-frequency curve of car-electromagnet was obtained according to the amplitudefrequency equation.The rule between the vibration amplitude of car-electromagnet and the parameters of spring stiffness,damping coefficient,control parameters and car-body mass between trains was analyzed by the curve.Then,the coupling nonlinear vibration between bridge and maglev train is studied.When the maglev train is suspended on the bridge,the maglev train and the bridge will produce a large vertical self-excited vibration.In order to analyze the resonance causes,considering the influence of elastic beam on maglev train,a two-degree-of-freedom coupled nonlinear model of bridge maglev train based on PD control was established,and the coupled dynamic equation of bridge and maglev train was derived,and the amplitude-frequency response curve of bridgemaglev train when coupling resonance occurred was obtained.The influence of control parameters,bridge parameters and electromagnet parameters on nonlinear coupled vibration of bridge-maglev train is analyzed,which provides theoretical reference for understanding and solving the self-excited vibration problem.Finally,the electromechanical coupling internal resonance between electromagnet and electromagnet circuit of maglev train is studied.The single point electromagnet model of maglev train was established,the electromechanical coupling relationship between track electromagnet and train electromagnet circuit was studied,the electromechanical coupling dynamic differential equation of magnetic track was listed,and the amplitude-frequency response curve was deduced when the frequency ratio of electromagnet and circuit system was approximately 2:1.The relationship between the nonlinear vibration of magnetic levitation electromagnet and coil equivalent resistance,coil turns,coil current and effective magnetic pole area is obtained by simulation.Then,the PD control algorithm commonly used in maglev train is used to analyze the stability,and the value range of displacement control parameters and speed control parameters is found.The results show that the coupling internal resonance for magnetic levitation trains track,electromagnet track and bridge can be effectively weakened by changing the control and structure parameters of the train.Therefore,the condition of internal resonance can be avoided as much as possible in the design of magnetic levitation parameters,and the value of control parameters can be increased to a reasonable range.