Keywords: railway dynamics, hunting, dynamic stability.

Bi-conical axles and bogies are milestone-features of trains, as a means of providing cornering capacity and dynamic stability. Modern day bogies reached a remarkable stage of development compared with early designs, yet the dynamic stability of trains still contends with the ability of going through tight curves and requires, in high-speed lines, radii greater than 5 km and a very demanding level of accuracy and maintenance.

This paper addresses the dynamic characteristics of a different family of guiding systems that follow a reference located on the rail ahead of the wheel. These systems can be optical devices focused on the rail or simply a pair of rollers running on the lateral faces of the rails.

The equations are presented and solved for the frequency response function. The most relevant parameter is found to be the guiding length, the distance between the wheel and the reference point. A system with a positive guiding length (reference point ahead of the wheel) is always stable; with a negative length (reference point behind the wheel) is unstable; and in the limit of a null guiding distance the response is marginally stable, similar in several ways to the typical response of isolated railway axles (axles without bogie).

Provided the guiding length is positive, initial perturbations decay exponentially, without hunting. The demonstration is presented for straight sections but the statement finds a direct analogy in any other track geometry because the system is linear. Looking at the transfer functions of the lateral movement of bogies and of this new guiding system, we find a different pattern: absence of resonance and a lower response to perturbations of small wavelength. The transfer function of the system presented in this paper is broadly independent of the characteristics of the wheel-rail contact and is not affected by the vertical suspension of the vehicle. Therefore, that suspension can be designed to maximize comfort without regard to dynamic stability. The behaviour of the new system in curves depends on a set of parameters: the trains may exhibit an over-turning tendency in curves, like the Talgo trainsets, or compensate that tendency in a number of ways.

The conclusion is that this type of guiding system has less stringent requirements concerning the radius of curvature and the geometrical accuracy of the head of the rails and the thread of the wheels. A possible drawback is that these trains would only move forward in normal conditions (like automobiles) and not in both directions (like most trains). Another possible inconvenience is that most of these systems need some degree of automatic control if the lateral faces of the wheels are used, because that part of the rail is not completely available in switches and other special locations.

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