Keywords: railway dynamics, wheel profile, curve negotiation.

This paper presents a methodology for optimal synthesis of railway wheel profiles, using an ideal equivalent conicity curve as an objective function. The optimization is performed using both genetic algorithms and traditional optimization methods, in order to approach as close as possible to the reference curve. The paper shows the results obtained for the case of a high-speed wheel profile, comparing the wear index obtained for a curved track with the original and with the optimized profile.

As it is well known, the geometry of wheel-rail contact has a significant influence on vehicle dynamic behaviour, the forces that will be transmitted to the track, the wear occurring in both the wheel and the heads of the rails, and on key parameters regarding security issues as the risk of derailment and stability. The geometric problem of wheel-rail contact is always given as a combination of a wheel profile and a rail profile, and the problem cannot be studied independently. It is therefore necessary to consider the geometric characteristics of the rail when performing a wheel profile optimization.

On the other hand, very small changes of the wheel and rail profiles can produce significant differences in contact parameters representing the geometric problem of the contact, such as the function of rolling radii difference between the wheels, directly related to the equivalent conicity of the wheelset. These differences in contact parameters lead to a final vehicle dynamic behaviour very different from the original. The high sensitivity of the contact curves to these small changes of the profiles makes the traditional optimization methods highly problematic. Using genetic algorithms, a relative maximum that can hardly improve initial performance of the wheel can be avoided, and they become a very suitable method for this type of problem. Finally, a traditional optimization method is applied in order to significantly improve the result obtained with the above procedure. The wheel profile is defined by straight and circular sections, with continuity of the first order derivative. In this way, the whole active section of the wheel profile can be defined with only four variables (radii of curvatures and limit points between sections), which are the variables of the optimization problem. With regard to the reference equivalent conicity curve, it is built in such a way that it remains constant and of low value for small lateral displacements of the wheelset (facing stability), and grows smoothly as the lateral displacement increases. The wheel profile corresponding to the flange area is not changed, assuring that safety against derailment is preserved.

As a result of the optimization, a modified wheel profile has been obtained. This wheel shows an equivalent conicity very close to the reference curve, which implies that curve negotiation will be improved maintaining the stability on a straight track. Some dynamic simulations in curves are shown in the paper. The dynamic behaviour of the vehicle with the original and with the optimized wheel profile is compared. It can be seen that wear indexes, lateral forces and risk of derailment are significantly reduced for several curve radii using the optimized wheel profile.

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