“…From equations (1) to (4), it can be derived that the motion of a wheelset is closely correlated with the rail vibrations. Besides, the wheel–rail vertical force can be calculated by d’Alembert principle, that is (Xu and Zhai, 2020a)withwhere Fϕ, Fz, and FG, respectively, denote the wheel–rail force induced by the rolling, bounce, and gravitational effect of the vehicle; m denotes the mass of a body; Ix, Iy, and Iz denote the moment of inertia of a body around the X -, Y -, and Z -axis, respectively; when j=1,2, y¨b,j, ψ¨b,j, ϕ¨b,j, and …”
Modelling of vehicle–track interaction has long been a hot and interesting topic. In multibody dynamics based on force-equilibrium methods, Hertzian contact and creep theories have been applied in vehicle–track model constructions. In another aspect, the complementarity-based methods have also been widely used in establishing vehicle–track interaction, but still having drawbacks on characterization of wheel–rail contact geometry/creepage in three-dimensional space. In this study, we draw essences from methodologies of refined wheel–rail coupling models and energy-variational principle, and a model for vehicle–track three-dimensional interactions with inclusion of rail irregularity excitations is newly developed. This model possesses high accuracy compared with Hertzian contact, FastSim, and vehicle–track coupled model in the middle-low frequency domain, and also, the advantages in computational stability are possessed. In this model, the unevenness of rail irregularities at the three-dimensional space is preliminarily considered by taking a hypothesis of normal distribution and accordingly, the wheel–rail three-dimensional constraint equations are presented. Extensively, a series of numerical examples are shown to verify the effectiveness and engineering practicability of this model. Besides, the influence of rail three-dimensional irregularities on the dynamic performance of vehicle–track systems is further explored, which shows when the trochoid of the wheel–rail contact points changes rapidly, the additional inertial effects brought out by rail irregularities might exert great influence on wheel–rail forces.
“…From equations (1) to (4), it can be derived that the motion of a wheelset is closely correlated with the rail vibrations. Besides, the wheel–rail vertical force can be calculated by d’Alembert principle, that is (Xu and Zhai, 2020a)withwhere Fϕ, Fz, and FG, respectively, denote the wheel–rail force induced by the rolling, bounce, and gravitational effect of the vehicle; m denotes the mass of a body; Ix, Iy, and Iz denote the moment of inertia of a body around the X -, Y -, and Z -axis, respectively; when j=1,2, y¨b,j, ψ¨b,j, ϕ¨b,j, and …”
Modelling of vehicle–track interaction has long been a hot and interesting topic. In multibody dynamics based on force-equilibrium methods, Hertzian contact and creep theories have been applied in vehicle–track model constructions. In another aspect, the complementarity-based methods have also been widely used in establishing vehicle–track interaction, but still having drawbacks on characterization of wheel–rail contact geometry/creepage in three-dimensional space. In this study, we draw essences from methodologies of refined wheel–rail coupling models and energy-variational principle, and a model for vehicle–track three-dimensional interactions with inclusion of rail irregularity excitations is newly developed. This model possesses high accuracy compared with Hertzian contact, FastSim, and vehicle–track coupled model in the middle-low frequency domain, and also, the advantages in computational stability are possessed. In this model, the unevenness of rail irregularities at the three-dimensional space is preliminarily considered by taking a hypothesis of normal distribution and accordingly, the wheel–rail three-dimensional constraint equations are presented. Extensively, a series of numerical examples are shown to verify the effectiveness and engineering practicability of this model. Besides, the influence of rail three-dimensional irregularities on the dynamic performance of vehicle–track systems is further explored, which shows when the trochoid of the wheel–rail contact points changes rapidly, the additional inertial effects brought out by rail irregularities might exert great influence on wheel–rail forces.
“…The vehicle-track interaction model in the framework of elastic and multibody dynamics was developed in many works, for example, Xu and Zhai (2019), Xu et al (2020), Yang et al (2020) and Zhai et al (2009), as shown in Figure 1. The dynamic equations of motion for vehicletrack interaction can be unified as…”
“…The vehicle–track interaction model in the framework of elastic and multibody dynamics was developed in many works, for example, Xu and Zhai (2019), Xu et al (2020), Yang et al (2020) and Zhai et al (2009), as shown in Figure 1. The dynamic equations of motion for vehicle–track interaction can be unified aswhere bold-italicM, bold-italicC, and bold-italicK denote the mass, damping, and stiffness matrices respectively, bold-italicF denotes the loading vector, subscripts ‘V’ and ‘T’ denote vehicle subsystem and track subsystem respectively, ‘VT’ and ‘TV’ denote the interaction between the vehicle and the tracks, bold-italicX¨, bold-italicX˙, and bold-italicX denote the acceleration, velocity, and displacement vector respectively.Figure 1.Vehicle–track interaction model (a) side view; (b) end view (the subscript ‘c’ and ‘w’ denote the car body and the wheelset and symbols ‘y’, ‘z’, ‘ψ’, ‘β’, and ‘θ’ denote the transverse, bounce, yaw, pitch, and ...…”
In this work, an entire multi-rigid-body system with two-stage suspension systems is assumed to run on a slab track system, where the elastoplasticity of the track slab is modeled by Mindlin plate theory considered in a framework of three-dimensional vehicle–track dynamic system. Considering the elastoplasticity of track slabs, the nonlinearity and time- and stress-dependent track slab stiffness matrices must be accounted for in the time-domain dynamic solutions; therefore, a two-step iterative algorithm separating the vehicle–track system into vehicle–rail subsystem and track slab system is developed to solve the dynamic equations of motion for vehicle–track interactions. The numerical studies have shown the accuracy and efficiency of this method in calibrating the vehicle–track dynamic behavior in conditions of track slab elastoplastic deformation. Besides, it has shown that the longitudinal unevenness of the track support stiffness has significant influence on the plasticity of track slabs.
“…Based on the findings of train/vehicle-ballastless track coupled dynamics 30 – 36 , considering the train load, gravity load of slab track, temperature gradient load of slab track, and contact nonlinearity of slab track, a high-speed train-CRTS III slab track on subgrade coupled dynamic model is established. The initial track states and system dynamics under different temperature gradient loads of slab track are studied and analyzed in depth.…”
Temperature is an important load for ballastless track. However, there is little research on the system dynamic responses when a train travels on a ballastless track under the temperature gradient of ballastless track. Considering the moving train, temperature gradient of slab track, gravity of slab track, and the contact nonlinearity between interfaces of slab track, a dynamic model for a high-speed train runs along the CRTS III slab track on subgrade is developed by a nonlinear coupled way in ANSYS. The system dynamic responses under the temperature gradient of slab track with different amplitudes are theoretically investigated with the model. The results show that: (1) The proportions of the initial force and stress caused by the temperature gradient of slab track are different for different calculation items. The initial fastener tension force and positive slab bending stress have large proportions exceeding 50%. (2) The maximum dynamic responses for slab track are not uniform along the track. The maximum slab bending stress, slab acceleration, concrete base acceleration appear in the slab middle, at the slab end, and at the concrete base end, respectively. (3) The maximum accelerations of track components appear when the fifth or sixth wheel passes the measuring point, and at least two cars should be used. (4) The temperature gradient of slab track has a small influence on the car body acceleration. However, the influences on the slab acceleration, concrete base acceleration, fastener tension force are large, and the influence on the slab bending stress is huge.
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