## 8.1 Wheel/rail contact forces: effects of curving and applied traction

The greatest influences on tangential force are curve radius, applied traction, bogie design and applied cant. The effects of curve radius and applied traction on the magnitude and direction of tangential force are illustrated below for a vehicle with fairly conventional suspension. The magnitude of tangential force is shown as the so-called “traction ratio” i.e. the ratio of tangential to normal force, which is limited by the coefficient of friction (assumed here to be 0.4).

Calculations are shown of the tangential force at the leading and trailing wheelsets of a bogie for wheels on the high and low rails in a curve and for two conditions of applied traction: a coasting vehicle (T/N=0), and a locomotive or power car (T/N=0.28). The vehicle is curving at equilibrium cant. The range of applied traction in practice is typically 0<= T/N <=0.42. The traction that a locomotive or power car can apply is limited by available power at higher speed, and at lower speeds by available adhesion.

A bogie “steers” better i.e. with lower tangential forces, if the in-plane suspension is made more flexible: this allows the leading wheelset to become more radial and move towards the equilibrium rolling line. Applied traction counteracts this effect, and straightens the bogie out i.e. makes it curve more like a rigid bogie. Under high applied traction, wheels on the high rail are close to slipping even in gentle curves.

Increasing cant tends to move the trailing wheelset towards the inner rail, thereby allowing the leading wheelset to develop even higher “angle of attack”, greater tangential force and a greater difference in tangential force across a wheelset. Excessive cant exacerbates surface damage.

Conversely, under cant deficiency the trailing wheelset moves out to the high rail and the leading wheelset adopts a lower angle of attack. Tangential forces are very much more favourable. If movement towards the high rail gives more gauge face contact, lubrication should be provided to reduce wear.

For the leading wheelset the high rail wheel pushes the rail backwards and towards the inside of a curve for the full range of applied traction; the phase varies relatively little. This is consistent, for example, with the small (but significant) variation in direction of GCC cracks seen on the high rail. The direction of tangential force on the low rail is determined primarily by the angle of attack, which forces the rails to the inside of the curve (lateral force, corresponding to a phase of +90°). This is consistent with most damage seen on the low rail, particularly plastic flow. A longitudinal braking force is superposed on this for low applied traction, and a driving force for applied traction of T/N=0.28. For intermediate values of T/N, which are typical of metro vehicles with all wheels motored, there is a purely lateral force on the low rail.