A nonlinear approach for modeling rail flexibility using the absolute nodal coordinate formulation

Abstract

This paper describes a new nonlinear formulation based on the absolute nodal coordinate formulation (ANCF) for modeling the dynamic interaction between rigid wheels and flexible rails. The generalized forces and spin moments at the contact points are formulated in terms of the absolute coordinates and gradients of ANCF finite elements used to model the rail. To this end, a new procedure for formulating the generalized ANCF applied moment based on a continuum mechanics approach is introduced. The generalized moment is calculated using the spin tensor defined in terms of the gradients at the contact points, and therefore, the use of this approach does not require the use of angles. In order to have an accurate definition of the creepages, the location and velocity of the contact points are updated online using the rail deformations. An elastic contact formulation is used to define the contact forces that enter into the dynamic formulation of the system equations of motion. An elastic line approach is used to define the rail stress forces, and the relative slip between the rigid wheel and the flexible rail is iteratively updated using the deformations of the ANCF finite elements. The formulation proposed in this investigation is demonstrated using a five-body railroad vehicle negotiating flexible rails. In order to validate the ANCF rail model, the obtained results are compared with previously published results obtained using the floating frame of reference formulation that employs eigenmodes. The comparative study presented in this paper shows that there is, in general, a good agreement between the results obtained using the two different formulations.