Adhesion railway
An adhesion railway relies on adhesion traction to move the train, and is the most widespread and common type of railway in the world. Adhesion traction is the friction between the drive wheels and the steel rail. Since the vast majority of railways are adhesion railways, the term adhesion railway is used only when it is necessary to distinguish adhesion railways from railways moved by other means, such as by a stationary engine pulling on a cable attached to the cars or by a pinion meshing with a rack.
The friction between the wheels and rails occurs in the wheel–rail interface, or contact patch. The traction force, the braking forces and the centering forces all contribute to stable running. However, running friction increases costs, due to higher fuel consumption and increased maintenance needed to address fatigue damage and wear on rail heads and on the wheel rims and rail movement from traction and braking forces.
Variation of friction coefficient
, or friction, is reduced when the top of the rail is wet or frosty or contaminated with grease, oil or decomposing leaves, which compact into a hard slippery lignin coating. Leaf contamination can be removed by applying "Sandite" from maintenance trains, using scrubbers and water jets, and can be reduced with long-term management of railside vegetation. Locomotives and trams use sand to improve traction when driving wheels start to slip.Effect of adhesion limits
Adhesion is caused by friction, with maximum tangential force produced by a driving wheel before slipping given by:where is the coefficient of friction and is the weight on the wheel.
Usually the force needed to start sliding is greater than that needed to continue sliding. The former is concerned with static friction, or "limiting friction", whilst the latter is dynamic friction, also called "sliding friction".
For steel on steel, the coefficient of friction can be as high as 0.78, under laboratory conditions, but typically on railways it is between 0.35 and 0.5, whilst under extreme conditions it can fall to as low as 0.05. Thus a 100-tonne locomotive could have a tractive effort of 350 kilonewtons, under the ideal conditions, falling to 50 kilonewtons under the worst conditions.
Steam locomotives suffer particularly badly from adhesion issues because the traction force at the wheel rim fluctuates and, on large locomotives, not all wheels are driven. The "factor of adhesion", being the weight on the driven wheels divided by the theoretical starting tractive effort, was generally designed to have a value of 4 or slightly higher, reflecting a typical wheel–rail friction coefficient of 0.25. A locomotive with a factor of adhesion much lower than 4 would be highly prone to wheelslip, although some three-cylinder locomotives, such as the SR V Schools class, operated with a factor of adhesion below 4 because the traction force at the wheel rim does not fluctuate as much. Other factors affecting the likelihood of wheelslip include wheel size, the sensitivity of the regulator and the skill of the driver.
All-weather adhesion
The term all-weather adhesion is usually used in North America and refers to the adhesion available during traction mode with 99% reliability in all weather conditions.Toppling conditions
The maximum speed at which a train can proceed around a turn is limited by the radius of turn, the position of the centre of mass of the units, the wheel gauge and whether the track is superelevated, or canted.Toppling will occur when the overturning moment due to the side force is sufficient to cause the inner wheel to begin to lift off the rail. This may result in loss of adhesion – causing the train to slow, preventing toppling. Alternatively, the inertia may be sufficient to cause the train to continue to move at speed, causing carriages to topple completely.
For a wheel gauge of with no canting, a centre of gravity height of and a speed of, the minimum radius of curvature is. For a modern, exceptionally high-speed train at, the minimum radius would be about. In practice, the minimum radius of turn is much greater than this, as contact between the wheel flanges and rail at high speed could cause significant damage to both. For very high speeds, the minimum adhesion limit again appears appropriate, implying a radius of turn of about. In practice, curved tracks used for high speed travel are superelevated, or canted, so that the minimum radius of curvature is closer to.
During the 19th century, it was widely believed that coupling the drive wheels would compromise performance, and this was avoided on engines intended for express passenger service. With a single drive wheelset, the Hertzian contact stress between the wheel and rail necessitated the largest-diameter wheels that could be accommodated. The weight of locomotives was restricted by the stress on the rail, and sandboxes were required, even under reasonable adhesion conditions.
Directional stability and hunting instability
It may be thought that the wheels are kept on the tracks by the flanges. However, close examination of a typical railway wheel reveals that the tread is burnished but the flange is not—the flanges rarely make contact with the rail and, when they do, most of the contact is sliding. The rubbing of a flange on the track dissipates large amounts of energy, mainly as heat but also including noise and, if sustained, would lead to excessive wheel wear.Centering is actually accomplished through shaping of the wheel. The tread of the wheel is slightly tapered. When the train is in the centre of the track, the region of the wheels in contact with the rail traces out a circle which has the same diameter for both wheels. The velocities of the two wheels are equal, so the train moves in a straight line.
If, however, the wheelset is displaced to one side, the diameters of the regions of contact, and hence the tangential velocities of the wheels at the running surfaces, are different and the wheelset tends to steer back towards the centre. Also, when the train encounters an unbanked turn, the wheelset displaces laterally slightly, so that the outer wheel tread speeds up linearly, and the inner wheel tread slows down, causing the train to turn the corner. Some railway systems employ a flat wheel and track profile, relying on cant alone to reduce or eliminate flange contact.
Understanding how the train stays on the track, it becomes evident why Victorian locomotive engineers were averse to coupling wheelsets. This simple coning action is possible only with wheelsets where each can have some free motion about its vertical axis. If wheelsets are rigidly coupled together, this motion is restricted, so that coupling the wheels would be expected to introduce sliding, resulting in increased rolling losses. This problem was alleviated to a great extent by ensuring that the diameters of all coupled wheels were very closely matched.
With perfect rolling contact between the wheel and rail, this coning behaviour manifests itself as a swaying of the train from side to side. In practice, the swaying is damped out below a critical speed, but is amplified by the forward motion of the train above the critical speed. This lateral swaying is known as hunting oscillation. Hunting oscillation was known by the end of the 19th century, although the cause was not fully understood until the 1920s, and measures to eliminate it were not taken until the late 1960s. The maximum speed was limited not by raw power but by a possible instability in the motion.
The kinematic description of the motion of tapered treads on the two rails is insufficient to describe hunting well enough to predict the critical speed. It is necessary to deal with the forces involved. There are two features which must be taken into account:
- the inertia of the wheelsets and vehicle bodies, giving rise to forces proportional to acceleration;
- the distortion of the wheel and track at the point of contact, giving rise to elastic forces.
An analysis of the kinematics of the coning action yields an estimate of the wavelength of the lateral oscillation:
where d is the wheel gauge, r is the nominal wheel radius and k is the taper of the treads. For a given speed, the longer the wavelength and the lower the inertial forces will be, so the more likely it is that the oscillation will be damped out. Since the wavelength increases with reducing taper, increasing the critical speed requires the taper to be reduced, which implies a large minimum radius of turn.
A more complete analysis, taking account of the actual forces acting, yields the following result for the critical speed of a wheelset:
where W is the axle load for the wheelset, a is a shape factor related to the amount of wear on the wheel and rail, C is the moment of inertia of the wheelset perpendicular to the axle, m is the wheelset mass.
The result is consistent with the kinematic result in that the critical speed depends inversely on the taper. It also implies that the weight of the rotating mass should be minimised compared with the weight of the vehicle. The wheel gauge appears in both the numerator and denominator, implying that it has only a second-order effect on the critical speed.
The true situation is much more complicated, as the response of the vehicle suspension must be taken into account. Restraining springs, opposing the yaw motion of the wheelset, and similar restraints on bogies, may be used to raise the critical speed further. However, in order to achieve the highest speeds without encountering instability, a significant reduction in wheel taper is necessary. For example, taper on Shinkansen wheel treads was reduced to 1:40 for both stability at high speeds and performance on curves. That said, from the 1980s onwards, the Shinkansen engineers developed an effective taper of 1:16 by tapering the wheel with multiple arcs, so that the wheel could work effectively both at high speed as well as at sharper curves.