The Double Pendulum Model And Analysis Of Nonlinear Dynamic Characteristics Of The Pantograph Of A High-speed Train

The pantograph of a high-speed train is an important device for supplying thetrain with electric energy. With higher speed of the train, the practical workingconditions are more complicated. In order to ensure the stability of electric currentflowing, the dynamic model of the pantograph should be built reasonably and itsdynamic characteristics should be analyzed. Considering the structure nonlinearity,friction and the special excitation from the catenary, the nonlinear dynamiccharacteristics of the pantograph become a worth study problem. In this thesis, thesingle arm pantograph was studied, the double pendulum model of the pantographwas developed, in which the catenary was described as a variable stiffness spring, anda square angular velocity damping torque was used to describe the nonlinear dampingtorque of the hydraulic vibration damper. Considering the nonlinear factors caused byhydraulic damping and the interaction between the catenary and the pantograph, themotion differential equations based on the double pendulum model were establishedand the dynamic characteristics of the pantograph of high-speed train were analyzed.The main works included in the thesis are as follow：1. The structures and operating characteristics of the catenary and pantographwere introduced in brief. The researches of the dynamics of the pantograph in homeand abroad were summarized. The models of the pantograph and the catenary wereintroduced in detail. Then the related knowledge of nonlinear dynamics and Lagrangeequation were simply described.2. The single arm pantograph was studied. The double pendulum model of thepantograph was developed, in which the interaction between the pantograph and thecatenary and the effect of the hydraulic vibration damper were considered. Themotion differential equations based on the double pendulum model were establishedin Lagrange equation, and then were simplified. Then they were changed intonon-dimensional form.3. The multi-scale method was carried out to solve the non-dimensionalequations and the first-order approximate solution was got.1:1internal resonance wasinvolved and the averaged equations in the Cartesian coordinate system were got. Themotion characteristics were analyzed in the numerical method, when the system is in 1:1internal resonance. The results show that the system occurs the quasi-periodicmovements and chaos under the taken parameters. Therefore the1:1relationship ofthe natural frequencies should be avoidable, when the pantograph is designed.4. The numerical simulation was used to analyze the motion differentialequations. The dynamic characteristics were analyzed considering the pendulumlength ratio and the speed of the train separately. The bifurcation maps of the systemof which the bifurcation parameters were the pendulum length ratio and the speed ofthe train separately were acquired with the numerical simulation; and the timehistories, the phase maps, Poincaré maps and spectrograms were also acquired. Theresults show that the system occurs quasi-periodic movements and chaos，and whenthe speed is different，there is quasi-periodic movements in the system.The researches of the thesis enrich the pantograph model and improve theunderstanding for the dynamic characteristics of the pantograph of the high-speedtrain, and provide a reference for the design of the nonlinear dynamic characteristicsof the pantograph of a high-speed train.