Keywords: high speed, bearing flexibility, critical speed.

Railway multibody models usually ignore the flexibility of the rolling bearings, assuming that it is much smaller than the flexibility of the primary suspension elements. However, this assumption is not necessarily valid for high speed vehicles, which have a much stiffer primary suspension. In this paper a model to obtain the stiffness parameters of a typical configuration of railway bearings is developed and applied to a high speed vehicle bearing system.

In this paper a bearing model has been developed, which takes into account the real geometry of the bearings and races for a more precise calculation of the forces transmitted through the different contact patches.

It has been demonstrated that the interaction of rollers and races can never be considered as Hertzian contact, as the shape of the contact area goes from ellipsoidal to trapezoidal as the load increases, including a mixed contact shape when only one of the roller end is in contact with the race. Hertzian contact implies a unique type of contact through all the loading cases, with a loss of precision in the areas where it does not behave in this way. The methodology has been applied to a bearing set used in high speed vehicles, with the following results:

1. The stiffness matrix of the bearing set has been obtained. Individual stiffness values are highly dependent on the mounting clearance. A priori, this dependence cannot be neglected for high speed dynamic analyses.
2. The inclusion of bearing stiffness in a high speed vehicle can affect the theoretical values of the primary suspension, i.e. reduce longitudinal stiffness up to 10% or lateral stiffness up to 32%. This effect will decrease the dynamic stability of the vehicle.
3. It can also affect the transmission of the lateral force, displacing the lateral force position closer to the wheelset axis. This effect, which is positive for the dynamic behaviour of the vehicle, is negligible for the stiffness values of the primary suspension and the bearing set of the studied vehicle.

Moreover, a polyvalent and adaptable bearing model has been developed that allows the calculation of various characteristics and variables. This model can be further used for other studies that need individual roller characteristics, such as contact geometry or maximum pressures in the races.

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