A Probabilistic Assessment Model for Train-Bridge Systems: Special Attention on Track Irregularities

In this paper, a probabilistic model devoted to investigating the dynamic behaviors of train-bridge systems subjected to random track irregularities is presented, in which a train-ballasted track-bridge coupled model with nonlinear wheel-rail contacts is introduced, and then a new approach for simulating a random field of track irregularities is developed; moreover, the probability density evolution method is used to describe the probability transmission from excitation inputs to response outputs; finally, extended analysis from three aspects, that is, stochastic analysis, reliability analysis, and correlation analysis, are conducted on the evaluation and application of the proposed model. Besides, compared to the Monte Carlo method, the high efficiency and the accuracy of this proposed model are validated. Numerical studies show that the ergodic properties of track irregularities on spectra, amplitudes, wavelengths, and phases should be taken into account in stochastic analysis of train-bridge interactions. Since the main contributive factors concerning different dynamic indices are rather different, different failure modes possess no obvious or only weak correlations from the probabilistic perspective, and the first-order reliability theory is suitable in achieving the system reliability.

Mathematical modeling of articulated passenger train spatial vibrations

The problem of high-speed railway transport development is important for Ukraine. In many countries articulated trains are used for this purpose. As the connections between cars in such a train differ from each other, to investigate its dynamic characteristics not a separate car, but a full train vibrations model is necessary. The article is devoted to the development of the mathematical model for articulated passenger train spatial vibrations. The considered train consists of 7 cars: one motor-car, one transitional car, three articulated cars, one more transitional car and again one motor-car. Differential equations of the train motion along the track of arbitrary shape are set in the form of Lagrange’s equations of the second kind. All the necessary design features of the vehicles are taken into account. Articulated cars have common bogies with adjoining cars and a transfer car and the cars are united by the hinge. The operation of the central hinge between two cars is modeled using springs and dampers acting in the horizontal and vertical directions. Four dampers between two adjacent car-bodies act as dampers for pitching and hunting and are represented in the model by viscous damping. The system of 257 differential equations of the second order is set, which describes the articulated train motion along straight, curved, and transitional track segments with taking into account random track irregularities. On the basis of the obtained mathematical model the algorithm and computational software has been developed to simulate a wide range of cases including all possible combinations of parameters for the train elements and track technical state. The study of the train self-exited vibrations has shown the stable motion in all the range of the considered speeds (40 km/h – 180 km/h). The results obtained at the train motion along the track maintained for the speedy motion have shown that all the dynamic characteristics and ride quality index insure train safe motion and comfortable conditions for the travelling passengers.

Analysis of generalized force and its influence on ride and stability of railway vehicle

Formulation of a rail vehicle model using Lagrange’s method requires the system’s kinetic energy, potential energy, spring potential energy, Rayleigh’s dissipation energy and generalized forces to be determined. This article presents a detailed analysis of generalized forces developed at wheel–rail contact point for 27 degrees of freedom–coupled vertical–lateral model of a rail vehicle formulated using Lagrange’s method and subjected to random track irregularities. The vertical–lateral ride comfort of the vehicle and the ride index of the vehicle are evaluated based on ISO 2631-1 comfort specifications and stability is determined using eigenvalue analysis. The parameters that constitute the generalized forces and critically influence ride and stability have been identified and their influences on the same have been analysed in this work.

Numerical analysis of beam rail bridges with random track irregularities

The study focuses on dynamic analysis of composite bridge / track structure / train systems (BTT systems) with random vertical track irregularities taken into consideration. The paper presents the results of numerical analysis of advanced virtual models of series-of-types of single-span simply-supported railway steel-concrete bridges (SCB) with symmetric platforms, located on lines with the ballasted track structure adapted to traffic of high-speed trains.

Numerical analysis of beam rail bridges - impact factors in the vertical deflection

The impact factors in the vertical deflection obtained in dynamic analysis of BTT systems - bridged / track structure / high speed train (BTT) - are discussed. The BTT system is one of 5 bridges spanning from 15 m to 27 m, modelled as simply supported beams loaded by ICE-3 trains traveling at high speeds. The two-dimensional, physically non-linear BTT model includes: viscoelastic suspension of rail vehicles on two independent axle bogies and non-linear one-sided wheel-rail contact springs according to Hertz theory, access zones for composite construction. The BTT system was divided into subsystems loaded with vertical interactions transmitted by elastic or viscoelastic and physically linear or nonlinear constraints. Using Lagrange equations and internal aggregation of subsystems, discretised according to the finite element method, matrix equations of motion of the subsystems were obtained, with explicit linear left sides and nonlinear implicit right sides, which were integrated numerically using the Newmark method with parameters βN=1/4, γN=1/2. The analysis focus on the effect of random track irregularities on the dynamic response of BTT systems.