Keywords: railway transition curves, railway vehicle dynamical model, computer simulation, optimisation.

This paper represents new results obtained for the proper shape(s) of railway transition curves (TC). The authors use their original approach based on advanced software. In this software, a complete rail vehicle dynamical model of a two-axle freight car, the track discrete model, and non-linear description of the wheel-rail contact are used. Part of the software, being vehicle simulation software, is combined with library optimisation procedures into the final computer programme. With the use of this programme the shape of the polynomial TCs of any order greater than three can be directly optimised. Quality functions (QFs) are based on the system dynamical quantities, generated during the simulations.

Although the idea of the method and its tests have been presented earlier, they were further developed and possess two new features. First, the number of QFs implemented increased from 3 to 22. Their selection was also made, so that the four best ones were found. As a result not only is minimisation of the QF possible but also betterment in the vehicle dynamic behaviour is guaranteed. The second new feature is the possibility to optimise the shape of the TC not only for its arbitrary length. Now, the length of the TC can be free but takes account of quantities used in engineering methods for the determination of the TCs length.

The main difference between this and previous papers by the authors are the results of the calculation. Previously the results were tests with the route configurations adopted in order to check if the software works correctly. Now the results are optimisation results, corresponding to real railway routes. The entrance polynomial TCs of the 5th, 7th, 9th and 11th orders were tested to find their optimum shapes. The results for the 11th order are discussed but not illustrated. Curvature and superelevation ramp tangence as well as tangence of the superelevation ramp slope in the TCs' terminal points were and were not imposed during the calculations.

The main conclusion is that it is demonstrated that polynomial TCs with the biggest possible number of their terms have the smallest values of their QFs. This leads to the next conclusion that the use of the curves that satisfy the advanced geometrical demands, as those mentioned in the previous paragraph, is not the correct way to improve the dynamic properties of vehicle-track system using TCs. In this context, a serious difference between the curves of lower and higher degrees was revealed. The curves of the 5th and 7th orders have poorer dynamic properties than the 3rd order parabolic TC. The curves of the 9th and 11th orders possess better dynamic properties than the 3rd order parabola. It was shown that the use of polynomial TCs in railway conditions could be an advantage. This can only be achieved, however, for the curves of high order and preferably with the maximum number of the terms.

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