Keywords: optimisation, numerical simulation, curved track, transition curves, vehicle dynamics, railway vehicle, vehicle-track interactions.

The issues discussed in this paper concern the search for the proper shape of railway transition curves (TCs). It is intended to exploit advanced vehicle models, dynamic track-vehicle and vehicle-passenger interactions, with optimisation methods for this purpose. The search for proper shape means, to the authors, the evaluation of the curve properties based on chosen dynamic quantities and generation of such a shape with optimisation methods. The studies presented, and to be done in the future, describe the features of the numerical tests.

Recently, an increase in the number of publications on TCs, both the railway and road ones, can be noticed. Also a qualitative change in their content is observed. It consists in attempts to diverge from the standard and to look for modern methods for evaluation of TC properties. Despite this, limitations visible in the earlier works still exist. Namely, the analysis is rare which exploits advanced dynamics of vehicle-track system. We have the use of advanced vehicle models and the precise description of vehicle-track interactions in mind, here. Also the use of the optimisation methods directly in formation of TCs is rare if not unheard-of.

The aim in the present paper is to describe the elaboration and tests of the method of TC optimisation. The scope of the studies comes out from the demands to be satisfied. So, mathematical methods for the optimisation need to be used. Dynamic quantities being the result of the simulation of the railway vehicle advanced model should be exploited in the determination of quality functions (QFs) in the optimisation process. The possibility of calculating a dozen or so different QFs should be ensured in the software. Search for optimum solutions with QFs based on traditional criteria should be possible. The possibility to take account of fundamental demands concerning TCs should be preserved. Two-axle vehicle models as well as vertically and laterally flexible track models need to be used. Account must be taken of non-linear geometry and forces in wheel/rail contact. A polynomial TC will be optimised. The highest order of the polynomial should equal at least 12. Optimisation of the entrance and exit TCs and of both simultaneously should be possible.

The idea and software presented appeared to be the effective tool in optimising the form of the polynomial TCs. It proved true for the different QFs tested. The polynomial coefficients for the optimised TCs were calculated. In future the following issues are worthy of continuation. More QFs should be proposed and tested. Some could take account of the several factors simultaneously or be calculated for the selected parts of the TCs. Optimisations for the exit TCs and the routes including the entrance and exit TCs should be undertaken.

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