It is possible to approach the problem of assessing the vibration behavior of rail vehicles both theoretically and empirically [ 1, 2, 3]. Theoretical research has used numerical simulations to develop new approaches. Experimental approaches have relied on results from tests conducted in the lab on scale models [6,7] or on special test vehicles (13,14) and results from tests on the track [12,13].Numerical Simulation Applications are helpful tools for estimating and optimizing the dynamic performance of railway vehicles, both during the design phase and later on for investigating any problems.
In relation to experimental tests, which are costly and involve a large consumption of time and resources, numerical simulations have the advantage that they allow the investigation of the vehicle’s vibration behavior, even in extreme situations that cannot be highlighted in real test conditions [15,16,17,18].However, in the development of theoretical research into the evaluation of the vibration behavior of railway vehicles based on numerical simulation results, there are challenges in the stage of mechanical modeling of the vehicle-track system . It becomes difficult to do this when the combination of several vibration sources at the point of contact between the rail and wheel is taken into account .
The difficulties in modeling a railway vehicle are due to its complex mechanical system with specific vibration behavior, including rigid and flexible modes, either independent or coupled together. There are many sources of vibrations at the point of contact between the wheels and rails: irregularities in the rolling surfaces, constructive discontinuities on the rails, undulating wear or deviations from a circular wheel shape (eccentricity or ovality), polygonalization or plane placement, or flattening. The mechanical model of a vehicle-track system that takes into account all of these factors can produce complex numerical and mathematical models. These require long simulation times. Simple models can provide useful qualitative and quantitative information about the fundamental characteristics of vibrations in railway vehicles. For reliable results, complex models are needed that take into account several factors that influence the vibration behavior of the vehicle. The suspension is responsible for a large part of the vibration behaviour of a railway vehicle. The complexity of the suspension models will have a direct impact on the accuracy of the numerical simulation.
When it comes to assessing vibration comfort of the rail vehicle, accuracy is highly dependent on the carbody modeling. In previous research, it was found that the ride comfort of railway vehicles at high speeds is overestimated when a rigid car body-type model models the car body of the vehicle. It is essential to use a flexible carbody model in such research [ 40, 41].Traction rods are another major factor that affects the vertical vibration behavior of the railway vehicle. They ensure the transmission of forces between the car body & the bogie. The traction rod’s influence on the dynamic behavior of the railway vehicle is not well studied. There is much research on vertical vibrations and their impact on ride quality and comfort. Ma and Song incorporated the stiffness in the traction rod into the model of a metro vehicle to evaluate its impact on the vertical dynamic performance. [ 43]. Researchers recently conducted two studies, 44 and 45.
They were motivated by Tomioka’s and Takigami’s theory that bogies could be used to dampen vertical vibrations in railway vehicle car bodies. The study aimed to determine the effect of traction rods on the dynamic behavior and ride comfort of high-speed rail vehicles. These studies are unique in that they represent the traction bar as a non-linear element. In this paper, the effect of traction on the vertical vibration behavior of the railway vehicle’s car body, taking into account the damping of the traction bar, is analyzed. The results of numerical simulations based on the rigid-flexible coupled vehicle model with seven degrees of freedom are used to investigate the problem. In the vehicle model, the stiffness and damping characteristics of the traction bar are represented by a longitudinal KelvinVoigt model integrated into the secondary suspension model. The vertical vibration behavior of the railway vehicle’s car body is assessed using the power spectrum density of acceleration, the root-mean-square of acceleration, and the ride comfort indices by comparing three different cases: “without traction-rod,” “with traction-rod–with damping,” and “with traction-rod–without damping.” A specific secondary suspension model models each of these cases. In the first instance, a vertical KelvinVoigt model is used to represent the secondary suspension, while in the second, two KelvinVoigt models are used, one vertical, and the other longitudinal. In the third scenario, a vertical Kelvin Voigt system is combined with a longitudinal elastic component. The physical implications of the three scenarios of the study are analyzed in this context from the perspective of the effect of stiffness and damping on the vertical vibrations and ride comfort of the car body. The results for the cases “without traction bar” and “with traction bar–without damping,” which were verified in laboratory tests on a scale model, are qualitatively comparable to the results of the specialized literature. In contrast to previous research, the model of the traction rod represents both the stiffness and damping of the bar.
- Modeling and Equations of Motion for Railway Vehicles
- Model description of the railway vehicle
The mechanical model in this article was designed to study the effects of the traction bar on the vertical vibrations within the carbody of a railway vehicle. Figure 1. It is recommended that a rigid body be used. The vehicle car body is modeled as an Euler-Bernoulli beam. At the same time, the chassis, consisting of two bogies, four wheelers, and rigid bodies, are linked by Kelvin Voigt systems, which model the primary and secondary suspensions of the vehicle. Figure 2. ).Figure 1. The model is the mechanical of a railway vehicle. Figure 2. Model of vehicle suspension: A Secondary suspension model ( B The secondary suspension is modeled using a Kelvin Voigt vertical suspension system with stiffness of 2k. Ss The damping 2c ss ( Figure 2. For the case (a1)), it is possible to obtain the ‘without traction-rod.’ In the case of traction rods with damping, a longitudinal KelvinVoigt System with stiffness 2k is used.
The damping 2c tr The traction rod’s damping and elasticity are modeled in the secondary suspension model. Figure 2. (a2)). H is the distance between this system and the neutral axis on the carbody. C The distance from the center of gravity to the bogie’s axle is indicated by h B. The traction rod in the case “with traction–without damping” is modeled by an elastic element of stiffness 2k tr ( Figure 2. (a3)). The primary suspension is modeled as a vertical Kelvin Voigt system of stiffness 2k. Ps The damping 2c ps ( Figure 2. The vertical displacement of the car body corresponding to the bounce is denoted by z. The vertical displacement of the car body that corresponds to the bounce is represented by C. The pitch rotation angle is indicated by the. C The highlighting is in Figure 1. The vertical displacement is w C (x,t). This displacement is the result of the overlap between the exiles that correspond to the three modes of vibrations of the car body – the bounce, the pitch, and the first vertical bending mode, which corresponds to the relation.