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Understanding the wheel/rail interface – part one

The 50-year gap between the end of the ‘first generation’ tramways in the UK and the introduction of ‘second generation’ lines has meant that much of the accumulated experience of planners, engineers and builders has been lost. This loss of knowledge and the misplaced belief that heavy rail experience could be read over into tramway track design has resulted in a number of expensive problems.

In these articles I will concentrate on the misapprehension that wheel-flange guidance from the integral check of girder (grooved) rail is undesirable and must be avoided. This can result in curving problems and tracks becoming life-expired far sooner
than necessary.

Introducing the issues

First generation British tramways – and the majority of networks outside the UK, both long established and new – ensured that outer and inner rails of curved tracks (known as low and high) each provide a nominal 50% of the lateral thrust needed to get a car round a curve. To achieve this checks had sufficient thickness to accommodate the same level of wear as the gauge-face.

France has opened 34 modern tramways, all having similar design parameters including the adoption of girder rail known as SEI 35G or, where appropriate, the closely-related SEI 35GP. The equivalent German standard, (Ri60-10 or Ri 60) has a very similar railhead profile. In the same period, the eight modern tramway systems in the British Isles [1] (each built to a unique specification) between them have adopted four different profiles, including both French and German standards, with some networks using more than one.

Confined street layouts demand severe curve radii and hence involve inescapable constrained-curving. In such circumstances, competent track designs match wheel-flange profiles with gauge-faces and checks. If the wheel-flange properly aligns with the groove sides of the girder rail (grooved rail) then all four wheels of the trucks or bogies share lateral thrust, the inside faces of diagonally opposite wheels assisting in constraining yaw. In effect, it spreads the turning force between four thrust faces, collectively reducing wear on individual surfaces.
An additional benefit is that the inner leading wheel-flange will deter its opposite number from climbing out of its groove.

To some extent, the high-rail integral check guides the trailing axle away from centre, forcing the wheelsets to align as closely as possible to the track. This eases the attack angle and reduces stress on both the leading outer wheel-flange and the high-rail gauge-face.

Second-generation logic

A lack of detailed tramway ‘engineering memory’ in the UK meant that when the time came for the mode’s reinstatement, a team of highly qualified railway engineers was recruited to design the first second-generation street tramway. Instead of questioning the purpose of numerous infrastructure facets, they designed from first principles.

Numerous subsequent technical reports published by railway-oriented engineers stressed that girder rail integral ‘keeps’ should play no part in vehicle guidance, their only purpose being on paved tracks to maintain a clear flangeway. It is difficult to understand why railway engineers seem so unaware of constrained-curving, or fail to grasp the lateral forces involved in negotiating the severe curves inherent in urban systems.

A knowledge of high-speed or suburban railway track geometry does not necessarily mean that the engineer has sufficient proficiency to design an urban tramway.

Wheel/rail technology

For railed vehicles rounding a bend, dynamic behaviour modifies a combination of centrifugal and tread steering forces determined by speed, track radius, track cant and vehicle wheelbase. Forces opposing movement include air resistance, bearing friction and rolling resistance.

Railway permanent way engineers state that vehicle primary performance and steering force occurs in a tiny interface area between the coned wheel tread and the transversely-radiused railhead, known as the contact patch. The fundamental differences between railway and tramway technologies are best explained by a (necessarily simplistic) review of the factors involved in persuading flanged wheels to follow those parallel rails, both in a straight line and around curves.

Proportional circumferences of a wheelset comprising an axle and pair of inflexibly connected wheels with coned treads varies with any offset from the track centre, the sideways shift altering the relative distance each wheel traverses per revolution. That introduces ‘hunting’ – a minute self-righting zigzag motion about the neutral position – which in normal conditions on tangent track is insufficient to involve flange-root contact with the track gauge corners, and generally flanges take no part in keeping vehicles on the rails. The result is a vehicle that rolls along the track with a comfortable, flowing movement. When approaching critical speed this predictable controlled hunting can evolve into more violent oscillations, constrained only by flange contact with the gauge-face, which suspensions of high-speed vehicles control with complex stiffening and damping.

This hunting effect can pose significant problems with four-wheel trucks on tramcars or four-wheel railway vehicles. British Rail spent a lot of time and effort seeking to improve the high-speed ride of four-wheel vehicles, with limited success. The much-maligned Class 14X Pacer trains use a bus body mounted on a modification of the existing freight vehicle underframe (HSFV1), with poor curving performance – as many disgruntled commuters will still attest. Tramcar speeds are modest and rarely induce severe hunting, particularly once single-truck vehicles with long cantilevers ceased to be common, however the problem has arisen again with some of the modern articulated designs, with resulting constraints on operating speeds – particularly on city centre curves.

On curved track, the contact patch on the outside wheel shifts laterally towards its larger radius and the inside wheel towards the smaller radius, balance depending upon curvature severity. The majority of railway tracks have sufficiently large radii to enable a combination of wheel coning and super-elevation to mitigate the differences in rail lengths. One of the effects of super-elevation (or cant) is that it counters centrifugal force that would otherwise thrust the outer flange against the gauge corner, allowing trains to negotiate a bend without flange contact. This is known as free-curving. (Figure 1)

Centrifugal force thrusts the moving mass towards the outside of the curve, whilst the raised high-rail opposes this lateral acceleration with gravity to produce balance at a defined line speed. Equilibrium depends upon the relationship between cant angle, curve radius and velocity, too slow resulting in cant excess – when gravity causes an inward force or cant deficiency.

The physics of cornering

A truck does not sit squarely on curved track. Each wheel is misaligned from the track centre-line, the outside wheel of the leading axle presenting a positive angle with the rail and its inside wheel a negative angle. The trailing axle does the reverse. (Figure 2)

On gentle curves associated with mainline railways, tread conicity laterally shifts the rolling radius of the leading axle to match the linear difference in rail length. This slightly increases the attack angle of the front wheel but the generation of creep forces (micro-creep) prevents flange contact.

The trailing axle attempts to align itself radially, which further skews the leading axle to present a greater positive attack angle with the rail, although the frame constrains the axles from twisting and longitudinal forces drive the misaligned wheelset around curves with the truck moderately skewed outwards at the leading end (Figure 3). Around tighter curves, increasing attack angles render creep forces insignificant and by forcing the outer wheel onto its flange-root radius, substantially amplifies the relative circumferential difference of the two wheels.

It is important to understand that free-curving applies only on moderate curves. At higher speeds or on tightly curved track we enter the realms of constrained-curving, where a higher turning force invokes friction between flange and rail. As curves become tighter the situation is exacerbated and in addition to hard flange contact, the difference in length between high and low rails becomes too great to accommodate. Simple calculation will also show that on the tight curves of a street tramway the different rail lengths of the inner and outer rail cannot be compensated for by conicity and flange-root running, resulting in slip-skip of the wheels and corrugation of the track [2].

With unchecked rail, the only force available to increase direction change is reaction between the misaligned leading outer flange and the gauge-corner of the high rail, that additional stress perhaps becoming sufficient for the wheel to literally climb out of engagement with the gauge face of the outer rail and a derailment ensues. To prevent derailment it is then necessary to install an additional rail, a check rail, alongside the low rail to transmit a percentage of lateral thrust via the low-wheel flange-back.

Railway vs. tramway

The minimum free-curve radius is the point at which railway and tramway dynamics become separate technologies. Consider the rolling radius difference between the two rails forming a 90° standard-gauge curve: heavy rail systems measure radii in kilometres, a severe mainline 1km (0.6-mile) curve having a mere 0.13% discrepancy, whilst meandering branch lines are rarely less than 400/500m radius, again a minor variance in the order of 0.25%. Coning and superelevation accommodate those differences.

By contrast, first generation tramway engineers strove to deal with minimum radii going down to 35ft/12m or less when shoehorning their tracks around street corners. The resulting length variance, about 12%, made friction between wheel and rail an inescapable burden. [3] Harsh attack angles associated with tramway curves render creep forces insignificant and directional change relies totally upon lateral thrust through wheel-flanges, which suffer friction far beyond anything most railway engineers have to consider.

Most second-generation tramways have 20m radius curves where the variation is a still significant, 7%[4], far in excess of anything wheel coning can accommodate. To compensate, the outer wheel endeavours to make the inner wheel revolve more rapidly than the ideal and if successful, the consequence is positive scuff on the low rail. Less likely, the inner wheel tries to make the outer wheel turn slower, success resulting in negative scuff on the high rail. Either of these occurrences will impose twist that increases friction between high gauge-face and flange of the outer leading wheel and attempts to enlarge an already severe attack angle, the additional stress heightening the likelihood of wheel climb and scuffing will result in wheel wear and rail corrugation. Yet although corrugation forms for various reasons, it is not inevitable.

Applying full steering force only through friction between the high-rail gauge-face and leading offside wheel-flange is to ‘design-in’ excessive wear and increase derailment potential, which tramway engineers alleviate by using a sacrificial check.

Grooved rail history

During the horse-drawn era, groove profiles had a wide slot and a guard too oblique to offer guidance, which was of relatively little importance since around curves horses hauling those trams automatically applied the necessary lateral force through their traces.

After the introduction of integral power units in the form of steam trams, Legrand reinvented and patented a girder rail, this time with a guard having a near vertical inner face. The inference is obvious; his redesigned guard allowed both sides of wheel-flanges to share lateral thrust. It is interesting to note that a few tramways, in the UK including those in Hull and Doncaster, adopted a centre-grooved rail with the flange shaped so that both sides of it provided lateral guidance and offered a smooth ride across mechanical (fishplated) rail joints.

In the UK at the beginning of the 20th Century, tramway electrification led to the introduction of two complementary rail profiles, one each for tangent and curves, the latter checks having additional thickness accommodating similar wear to that on the gauge face. More than a century later, why do contemporary British engineers reject that expertise?


Feature originally appeared in Tramways & Urban Transit – July 2015 issue (931).