| The construction of urban railway has greatly promoted the coordinated development of economy,traffic and environment in China’s metropolitan area.Under the background of increasing train operation speed and vibration reduction demand,the design of damping pad floating slab track(DPFST)also faces more stringent requirements and challenges.In fact,the service effect of the DPFST(safety,vibration reduction effect)is closely related to the real mechanical properties(temperature-,load-,and frequency-dependence)of the polymer elastic cushion(under rail elastic cushion,slab-track mats)and the field operation conditions(vehicle axle load,wheel-rail roughness,natural frequency of infrastructure under track).However,the above factors have not been considered in the design of the DPFST.Either from the perspective of the mechanics performance test method of elastic cushion products,the evaluation index,characterization model,or natural vibration characteristics of track system and dynamic simulation of wheel-rail coupled system,the research and application of design parameters in China lags behind in the world,which is bound to affect the service effect of DPFST.Therefore,accurately test and scientifically characterize the real nonlinear load-and frequency-dependent dynamic performance of the elastic cushion,carry out theoretical analysis and experimental verification of the natural frequency of the floating slab considering the real nonlinear loadand frequency-dependent characteristics of the elastic cushion,establish the vehicle-track coupled dynamic model considering the real nonlinear load-and frequency-dependent characteristics of the elastic cushion,evaluate and predict of the long-term fatigue aging mechanical properties and service life of the elastic cushion are of great significance and guiding value for the fine design of the DPFST of the new round of urban railway.The main research contents are as follows:1.Based on fractional derivative theory,a fractional derivative PT(FDPT)model reflecting temperature,load and frequency dependence was proposed by introducing polynomial function and exponential function.Taking a city railway as an example,the principle that the load service range of slab-track mats should be designed separately according to local conditions was clarified,and the error range in the existing specifications was corrected.The real nonlinear load-and frequency-dependent dynamic characteristics of the rail pad and three types(I-III type)slab-track mats were tested by using the microamplitude test method,which avoided the influence of the friction damping amplitude-dependent effect of the elastic cushion.The FDPT model was used to characterize the different nonlinear loaddependence characteristics(stiffness monotonically increasing,monotonically decreasing,decreasing first and then increasing)of elastic cushions.2.Considering the real nonlinear load-and frequency-dependence characteristics of the elastic cushion,and considering the difference of whether the track system has unsprung mass participating in the vibration,a scientific calculation method for the natural frequency of the DPFST was proposed.It can be seen that the natural frequency of DPFST is a dynamic range from the natural frequency without vehicle load to the natural frequency with vehicle load,rather than a fixed single value.The accuracy of the theoretical calculation method of natural frequency was verified by wheelset load-drop experiment and field measurement.Through harmonic response analysis,the effects of different parameters of the elastic cushions on the displacement admittance characteristics of the DPFST were compared.It was verified that the high-frequency tangential stiffness corresponding to the natural frequency of the track system can approximately reflect the vibration characteristics under the real nonlinear load-and frequency-dependent stiffness.3.Based on self-programming method(Matlab software)and secondary development of commercial software(Simpack-Simulink co-simulation),the FDPT model was used to replace the KV model,and the classical vehicle-track coupled dynamics model was improved.The vibration equations of rail and floating slab supported by FDPT model were derived.The constructing FDPT model in Simulink and the co-simulation method in Simpack were introduced.The correctness of the two simulation models was verified by comparing the effects of wheel-rail dynamic response(vertical and horizontal harmonic irregularity excitation)and the effect of FDPT model.4.The dynamic response of the wheel-rail coupled system considering the real nonlinear load and frequency dependent stiffness of the elastic cushion was calculated by using the improved vehicle-DPFST-infrastructure under track coupled dynamic model.The stiffness design method of elastic cushion was verified,that is,the traditional 4 Hz low-frequency secant stiffness was used to evaluate the dynamic displacement,and the high-frequency tangent stiffness corresponding to the natural frequency of track system under vehicle load was used to evaluate the vibration reduction effect(VRE).The influence of operating conditions such as different vehicle axle load,track irregularity and natural frequency of infrastructure under track on the VRE of DPFST was analyzed,which shows that the VRE was also a dynamic range.Taking a certain line as an example,according to the requirements of safe dynamic displacement and VRE,the stiffness limits of low-frequency secant stiffness and high-frequency tangent stiffness of slab-track mats were studied respectively,which provides a reference flow for the stiffness design of slab-track mats.5.Combined with the actual service conditions of track system elastic cushion,the shortcomings of fatigue test and aging test methods in the current specifications of elastic cushion were analyzed.The application conditions,advantages and disadvantages of Arrhenius equation,dynamic curve method and WLF equation for rubber material aging prediction were compared.Taking type-I rubber slab-track mats and type-II polyurethane slabtrack mats as examples,the traditional hot air aging test(without considering of service load),hot air aging test under static load(the full vehicle load)and thermal coupling aging test were designed.The aging characteristics of low-frequency secant stiffness and high-frequency tangent stiffness of slab-track mats under different test conditions were tested and analyzed.According to the service conditions(vehicle marshalling form,daily operation frequency)and environment temperature(high temperature duration days),the aging life of the stiffness of the type-I rubber slab-track mats was predicted by WLF equation method,and suggestions for improving the fatigue test and evaluation method of slab-track mats were given. |
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