Keywords: curved track, steady curving, flexible rail, multibody dynamics, trajectory frame, railroad vehicle.

Kinematics for a flexible track modelled with the moving shape functions method is summarized in this paper. Also, the equations of motion of a vehicle body described in a trajectory frame of reference, and the multibody vehicle-track system equations of motion are presented. The shape functions method is based on the floating frame of reference formulation and it uses shape functions defined in the trajectory frame of reference to describe deformation. The moving shape functions used are those for a beam under a moving load on a Winkler foundation. The fact that these functions are not fixed with respect to the body frame introduces new terms for the inertia forces appearing in the track.

Railroad vehicles negotiating a curved track show a steady state curving behavior. This curving behavior is analyzed in this paper. The linear model is summarized and, based on it, the flange normal contact force is calculated. The calculation of the steady curving of a railroad vehicle on a curved track using the formulation is presented.

As an application of the moving shape functions method for modelling rail flexibility, simulations were done for an unsuspended wheelset travelling with a forward velocity of 30 m/s on a curved track. The track curvature was varied to study the curving behavior on flexible tracks. The results showed that the effect of the track flexibility in the behavior of the wheelset and the effect on the wheel-rail lateral impacts. Results were compared with the behavior on rigid tracks. Steady curving of the wheelset were obtained for rigid and flexible tracks, and also compared with the classical simplified linear method. Good agreements were obtained when the radii of curvature was such that does not produce flange contact. The curves with permanent flange contact showed larger differences when the flexibility increases.

Although the problem was formulated here in terms of a simple wheelset, the proposed formulation can be applied to more complex vehicle models travelling on arbitrarily shaped rails. The equations of motion can be linearized around the calculated steady curving and the stability can be analyzed. The method applied allows the use of very long tracks, as no boundaries are needed to describe the track deformation, making the stability analysis using eigenvalue analysis possible.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)