Study On The Nonlinear Fractional Derivatives Zener Model And Its Application Of Vehicle Track Coupling System

With the rapid development of high-speed railway network and the demand of safe operation and maintenance management during railway service period,the cumulative structural damage in high-speed railway ballastless track structure increases rapidly,such as rail corrugated wear caused by high-frequency wheel rail excitation,irregular wheel profile,fastener elastic bar fracture and track slab crack,etc.In order to accurately predict,analyze and control the high-frequency wheel-rail force,a large number of studies have been carried out on the high-frequency vibration dynamics of the wheel-rail coupling system,including the model refinement of the vehicle and track system,the wheel-rail interaction and the nonlinear dynamic model of viscoelastic rubber the vehicle track system.The dynamic properties of rubber materials are strongly dependent on the external load amplitude,frequency and ambient temperature,which result in the complex vibration characteristics of vehicle track coupling system under the extreme cold climate conditions and high frequency random excitation of wheel and rail.However,the factors often considered in the study of the existing railway system dynamics are not comprehensive enough,which makes the coupling vibration response of wheel-rail system still unsatisfactory in high frequency region.Therefore,it is of great significance to establish a more reasonable,accurate and efficient vehicle track dynamics model to improve the theoretical prediction ability in the high frequency range.This paper is supported by the National Outstanding Youth Science Foundation Project "Research on the Key Scientific Problems of Service Safety in High-speed Railway Track Structure(51425804)" and the scholarship under the State Scholarship Found organized by the "China Scholarship Council".The nonlinear dynamic model of vehicle track coupling system and its application in improving the vibration characteristics of track structure in extremely cold area are studied.The main research contents are as follows:1.The nonlinear Berg friction model and the fractional derivative Zener model were used to model the dependence of the load amplitude and frequency on the viscoelastic rubber material,respectively.A simplified Berg friction model is proposed and applied to the frequency domain analysis model,so that the fractional derivative Zener model of the nonlinear single degree-of-freedom(DOF)system can be solved directly in the frequency domain.The dynamic analysis of the single DOF system with viscoelastic rubber isolator is calculated and analyzed to verify the accuracy of the proposed nonlinear fractional derivative Zener constitutive model.2.Both the frequency and amplitude dependence of the dynamic behavior of the first suspension rubber springs and rail pads in the wheel-rail coupling system is considered,and the nonlinear fractional derivative Zener model of the vehicle track coupling system which models rail as beam element is established in time domain and frequency domain,respectively,and the simplified berg friction model method is used to improve the computational efficiency of the model in frequency domain.By comparing with the frequency domain response obtained by Fourier transform of the time domain results,the proposed model solved in the frequency domain directly is verified,and the calculation accuracy and parameter sensitivity analysis of the model are thoroughly studied.3.An accurate model of spatial vertical fractional derivative Zener of vehicle track coupling system is established by using the rigid mass block and Timoshenko beam,modeling the rail structure by finite element solid element,and combining the fractional derivative Zener model with higher expression accuracy for viscoelastic material dynamic behavior in high frequency.Combining the modal superposition method to solve the time/frequency domain dynamic response of the coupled system makes the proposed model not only have a high calculation accuracy,but also ensure a high calculation efficiency.Due to the vibration damping effect of the primary suspension system,the difference between the acceleration frequency response bogie under the two models of rail is negligible,and the accuracy of the wheel-rail force response of the Timoshenko beam t model of rail cannot meet the coupling vibration analysis in the high frequency range above 2000 Hz.When considering the elastic model of wheelset for the coupled vehicle-track system model,the difference of the bogie acceleration response is 11% at the first dominant frequency of wheel-rail resonance,and the effect of the acceleration response on the wheelset is great in the entire frequency domain.There are three additional response peaks at 118.4Hz,879.4Hz,and 2166.4Hz after considering the elastic model of wheelset,this is because the symmetrical load of the left and right rails excites the symmetric modes of the wheelset elastic model.However,the rail acceleration and wheel-rail force response under the two wheelset models are only significantly different at 118.4 Hz.4.The dynamic stiffness of the rail pad will be increased significantly and the damping decrease in the extreme cold environment,which will greatly affect the dynamic mechanical properties of the rail pad.A novel railway fastener system with thermoelectric generator and heater is presented.The thermoelectric generator integrated in the railway track system utilize the clean environmental thermal energy to provide sufficient power to heat the rail pad,that can ensure the optimal working temperature of the rail pad under the extremely cold weather condition,thereby improving the dynamic behavior of the track structure at the extremely cold temperature,and the feasibility of the proposed novel fastener system is verified through theoretical and experimental studies.Combined with the spatial vertical fractional derivative Zener model of the vehicle track coupling system proposed in this paper,the random vibration response of the wheel-rail coupling system with or without the novel fastener system is calculated and compared under extreme cold climate conditions.In the extreme cold weather condition,the vibration amplitude of the vehicle track coupling system equipped with the novel fastener system can be reduced by 41.5%,and the vibration energy is transferred to low frequencies.The reasonable working temperature range of the rail pad can be obtained according to the design guideline of railway track structure,which provides some reference for the design of railway track system in extreme weather.