Computer-Aided Analysis of Urban Railway Vehicles

SUMMARY

Computer-aided dynamic simulations are usually employed when designing modern urban railway vehicles. Even if the modeling procedure is similar to the one used for trains, specific features have to be taken into account for tramways: they are designed for low speeds (less than 80 km/h) and narrow curves (less than 20 m of radius). Moreover, in order to improve accessibility, low floor designs have been developed (the floor lying at about 300 mm above the rails level). The simulation procedure has therefore to take account of the occurence of multiple wheel/rail contacts or the modelization of independent wheels. A specific software well adapted to the computer-aided design of urban railway vehicles has been developed by the Faculte Polytechnique de Mons. It performs the following classical analyses:

lateral linearization, modal analysis and root locii plots;

vertical linearization and comfort prediction;

non-linear time simulation in straight track (limit cycles) and in curve (derailment study)

parametric analyses

The vehicle model is formed by combination of bodies ( or flexible bodies, rotating bodies like wheelsets or independent wheels) and interconnection elements ( spring and damper elements). Contact between rails and wheels is treated as a part of the rotating bodies. A residual formulation has been preferred. When combined with the use of a complete iteration matrix, this formulation is well adapted to the treatment of stiff differential equations. It is based on a fast determination of the residues of the dynamic equations combined with the calculation of the iteration matrix through a numerical derivation procedure. The advantages of the approach are discussed. The model of a partial low floor vehicle with wheelsets and independent wheels is described.