On the influence of crosswind on the overturning stability of railway vehicles

Abstract

In recent years modern railway vehicle design shows a trend to faster, lighter and more energy efficient railway systems. These developments unfortunately alter the crosswind stability in a negative manner and so the risk of overturning of railway vehicles during operation in strong winds becomes a critical issue. The risk of overturning is quantified by the probability that a railway vehicle capsizes. To improve the crosswind stability it is very important to know the influence of the design and excitation variables on the wheel unloading of the railway car. Sensitivity coefficients of the design and excitation variables with respect to the probability of failure are calculated and the most influential variables are accentuated. Stochastic modeling of the systemThe railway vehicle is simulated in the commercial MBS-Code ADAMS/RAIL. The wind induced forces and moments which are acting on the vehicle are modeled as concentrated forces and moments. As shown in figure 2 an artificial gust scenario is designed for the crosswind characteristic [3], in which the amplitude A and the duration T of the exponential gust are modeled as stochastic variables. Not only the amplitude and the duration but also the aerodynamic coefficients C y,z,mx,my,mz of the railway vehicle are uncertain. Altogether there are seven stochastic variables z describing the excitation of the system [4]. As the excitation of the nonlinear railway vehicle model is a stochastic process the response of the railway car is also stochastic and so the probability of failure that the railway vehicle turns over can be computed. Failure means, that the wheel unloadings of the windward wheels exceed a certain limit. Carrarini [1] proposed a Probabilistic Characteristic Wind Curve (PCWC) (figure 3) where the failure probability P f is shown as a function of the mean wind velocity u 0 . The probability of failure has been calculated by a FORM and a Line Sampling analysis. Using FORM the probability of failure is approximated by the standard normal cumulative distribution function (CDF)where β = z is in the space of the stochastic variables the shortest distance from the origin to the limit state function g(z) = 0, which separates the failure from the safe domain. The point with the shortest distance to the origin lying on the limit state function is the so-called Most Probable failure Point (MPP). Sensitivity calculationsLocal sensitivity calculations concerning the 7 stochastic excitation variables z and concerning 9 deterministic design parameters θ have been done. At the MPP gradients of the distance β with respect to the excitation variables z and gradients with respect to the design parameters θ