| In complex cities(such as Chongqing)with many rivers and mountains,subway lines had to cross large rivers,so huge amounts of long-span bridges(LSB)have been designed and built to connect traffic on both sides,including super-long-span bridges with spans of more than 600 m.When the metro train passes through the bridge,the bridge vibration is caused,and the vibration of the bridge is transmitted to the metro train through the track,causing the vibration of the metro train,resulting in the vehicle-track-bridge coupled vibration.Compared with medium and small span bridges,the low stiffness characteristics of long-pan bridges aggravate the vehicle-rail-bridge coupled vibration.The resilient wheel is added rubber between the rim and the web,the wheel/rail interaction force is effectively reduced via the damping characteristics of rubber.At present,the resilient wheel has been applied to urban railway systems with small medium urban rail systems such as trams and light rails.Due to the concern for the environment and comfort in foreign countries,the resilient wheel is first used in subways,such as the Madrid Metro in Spain,the Monterrey Metro in Mexico,and the Copenhagen Metro in Denmark.However,due to the heavy axle and fast speed of the metro train,the application of resilient wheels in domestic metro train is limited.Therefore,from the perspective of dynamics,the resilient wheel is considered in the metro train,the influence of the resilient wheel on the coupled vibration of the metro train-track-LSB are investigated.The dynamic parameters of the resilient wheel suitable for the vehiclebridge coupled system are proposed.Considering the nonlinear factors of the rubber material of resilient wheel,the vibration reduction characteristics of the linear resilient wheel and the nonlinear resilient wheel in the vehicle-bridge coupled vibration are discussed,to promote the application range of the resilient wheel in the metro vehicletrack-LSB system,thereby reducing the vehicle-bridge coupled vibration.Firstly,the mechanics experiment of the resilient wheel rubber material is performed,and the mechanical relationship between rim and web of the linear resilient wheel and the nonlinear resilient wheel is discussed,and the multi-body dynamics model of the linear resilient wheel and the nonlinear resilient wheel is constructed.Based on the theory of train-track-bridge dynamic interaction,a coupled dynamic model of metro train-LSB considering resilient wheels(linear resilient wheels and nonlinear resilient wheels)is established,which includes four sub-models of resilient wheels,metro train,tracks and LSB.The wheel-rail relationship and bridge-rail relationship are adopted to realize the vehicle-bridge coupled.Based on multi-body dynamics,a metro train model with linear resilient wheels and nonlinear resilient wheels are established,with a total of 55 degrees of freedom.The nonlinear critical speed is adopted to verify the metro train model with resilient wheels,which proves the rationality of the model.The rail is simplified as an Euler beam.The LSB model is established via the finite element method(FEM),and the reliability of the LSB model is proved through modal tests and analysis of LSB natural vibration characteristics.The track irregularity is considered as the combined excitation of the American five-level spectrum(long wave)and Sato spectral(short wave).In order to ensure the stability of the calculation,the Newmark-β integral method is adopted to solve and iterate the motion equations of vehicles,tracks and bridges.Then,using the metro train-track-LSB coupled dynamic model considering the linear resilient wheel,the safety,stability,and dynamic performance of the long-span bridge are compared and analyzed,and the influence of the linear resilient wheel on the vehicle-bridge coupled vibration is studied.The dynamic parameters of the linear resilient wheel under the coupled vibration system of metro train-LSB are further optimized to provide reference for the subsequent dynamic research of the resilient wheel.On this basis,the influence of the optimized linear resilient wheel on the coupled vibration of metro train-LSB is studied.The results show that the resilient wheel has more advantages than the rigid wheel in the metro train-LSB coupled system.When the rubber stiffness of the resilient wheel is 30 M·N/m and 400 k N·s/m,the resilient wheel has a significant inhibitory effect on the system.Secondly,the viscoelastic properties of the rubber of resilient wheel are discussed,the mapping relationship between rubber resilient modulus and stiffness in resilient wheel system is deduced,and the stiffness characteristics of viscoelastic rubber material are determined.Based on the Yeoh constitutive model of rubber,the transient dynamic models of solid wheel,linear resilient wheel,nonlinear resilient wheel,and contact resilient wheel are established.The dynamic characteristics of four types of wheels under the action of wheel/rail force with variable wheel/rail contact point,and the response of different rubber materials to the dynamic characteristics of resilient wheels are studied.Results show that the resilient wheel reduces the wheel vibration compared with the traditional solid wheel.Considering that the rubber nonlinearity of the resilient wheel has an important influence on the dynamics,the contact nonlinearity between the components of the resilient wheel has no significant effect on the dynamics.The dynamic characteristics of resilient wheels increase with the increase of rubber hardness.Finally,adopting the coupled dynamic model of metro train-track-LSB considering linear resilient wheel and nonlinear resilient wheel respectively,the influence of linear resilient wheel and nonlinear resilient wheel on the coupled vibration system of metro train-track-LSB is studied.Results show that the nonlinear resilient wheel has better suppression effect on the coupled vibration of metro train-LSB than the linear resilient wheel.However,because the nonlinear characteristics of rubber hinder the stability of calculation and increase the cost,the linear resilient wheel has certain advantages for large-scale systems. |
