The hunt for equilibrium

The railway vehicle use wheelsets formed of a pair of steel wheels fixed rigidly on an axle. This setup makes the wheels move together on track. The system evolved in time to what we know today: tronconic wheel profiles with inside flanges, rail profiles and inclination, bogies, suspensions and so on.

The tronconic shape of the wheel profile allows the wheelset to self-balance when riding on straight or curved track.

We all have used the basic explanation of the way the wheelset works on a curved track – the outer wheel moves on a wheel profile radius, Re, greater than the inner wheel radius, Ri. For equal rotations of the rigid wheelset, the two wheels move different lengths on the inside and inside rail, ideally remaining radial to the track curve due to the two running radii, Re and Ri.

On straight track, both wheels will ideally run on equal wheel profile radii Rs.

Any disturbance to this ideal equilibrium state will be naturally compensated during vehicle riding and the wheelset will tend to return to this equilibrium.

This ideal case works very well when the track and wheels are in good condition and at low enough speed.

When the speed increases above a critical value,  theseesaw movement of the wheelset no longer converges to the equilibrium state, oscillating for long time around it.

The wheelset describes a sinusoidal trajectory along the track, with slow or no attenuation (Knothe, Stichel – 2016). 

This movement of the wheelset “trying” to get to equilibrium but never “catching” it, is called “hunting”. The hunting oscillation of the wheelset was first defined in mathematical terms by W. Klingel in 1883. In his honour, the movement is called also Klingel hunting or Klingel oscillation.

One additional complication to all the above is that the wheelsets are usually mounted in pairs on a bogie; the hunting oscillation of one wheelset of a bogie will have an influence of the movement of the other.

Various solutions have been proposed and applied to reduce this movement or its damaging impact on the track or on the vehicle. A good track quality is always the desired state that will reduce the hunting oscillation. Any track irregularity is a potential trigger for the hunt.

The Switch Toe Trigger

On plain line sections of track there are no design induced triggers for the hunting oscillation.

When branching of the track is required, the design needs to include discontinuities of the running edge, at switch toes and crossings.

At the switch toe the track has, by design, a built-in irregularity that can/will trigger hunting.

When the wheel runs over the switch toe section, on the tangent switch rail side the wheel-rail contact patch runs on the stock rail, until the switch rail profile is thick enough to take the loading and comes in contact with the wheel. This change of the transversal position of the contact patch also changes the wheel profile radius.

Simplifying the phenomenon, we can say that …

Assuming no lateral movement of the wheelset, when the contact is on the stock rail, the wheel profile radius is Rt.

When the contact switches to the switch rail, the wheel profile radius switches to Rw, a bigger radius than Rt. This change triggers a lateral movement of the wheelset towards the opposite stock rail. And the hunting begins.

There are various designs trying to solve this problem, but two are my subject for today. Both of them trigger a gentler hunting, reducing the shock at the switch toes.

FAKOP – Kinematic gauge widening

In the mid-1980 BWG (since 1998 part of VAE Group) started the development of a new generation of German high-speed turnouts. Beside the general improvements of the turnout geometry, they have developed a kinematic gauge optimisation technology (in German, FAhrKinematische OPtimierung, FAKOP for short) with the aim to reduce the hunting movement of the bogie at the switch toes. The German FAKOP method consists in bending the stock rail outwards, increasing the gauge (A.Foan, Y. Bezin – 2019, M. Bugarin – 1995) to generate a controlled hunting before the wheel reaches the trigger point at the switch rail.

The increase in gauge required for FAKOP is up to 15mm.

The actual geometry of the bend evolved over time, and it is even to this day under a continuous process of improvement (A.Foan, Y. Bezin – 2019, B. Pålsson, J. Nielsen – 2012).

This bent stock rail solution significantly reduces the hunting movement over the modified section (Ping Wang – 2015) and it is in use on quite a few high-speed and conventional railways in Germany, China (Wang-2015), Spain (Bugarin – 1995), and considered for HS2 in the UK.

CATFERSAN – modified stock rail head

Soon after FAKOP was developed, a research project carried at the Railway Department of University of Cantabria School of Civil Engineering, Santander, Spain, developed an alternative solution for managing the hunting oscillation at switch toes. The method is called CATFERSAN (from Spanish CATedra de FERrocarriles … SANtander) and consist in reprofiling of the stock rail head on a similar section as the FAKOP method.

The result is similar; the change in rail head profile is slowly moving the contact patch on the stock rail on a smaller wheel profile radius, generating a controlled hunting before the opposite wheel gets in contact with the switch rail.

Both methods have been applied also for swingnose crossings.

Bugarin and Novales have produced a comparison of the two methods versus the straight stock rail.

The graph below (M. Bugarin, Novales – 2011) shows the simulated lateral displacement for a vehicle running at 300km/h on the through route of a high-speed turnout – Spanish design.

In his book (2015) Ping Wang presents track traces of Chinese high-speed turnouts with FAKOP solution.

And this is how a crooked (FAKOP) or a deeply worn (CATFERSAN) stock rail helps the bogie in its hunt for equilibrium at switch toes.

Further and more serious recommended reading is referenced below.

Now, a personal note …

Years ago, the resemblance of this comparison graph with a familiar software output fooled me so much, and it was one of the main arguments that turned me into a believer. I’ve even used it to convert others.

References:

W. Klingel (1883) Uber den Lauf der Eisenbahnwagen auf gerader Bahn. Organ fur die Fortschritte des Eisenbahnwesens in technischer Beziehung [This article I could not find, quoted in some of the references below as the first technical description of the Klingel movement]

***(2016) Deliverable D2.5 Radical S&C concept: Design concept evaluation study report. In2Rail. Innovative Intelligent Rail

M. R. Bugarin, J-M-G. Diaz-de-Villegas (1995) Desvios Ferroviarios [Raiway Switches and Crossings] Ingeniería Cántabra

M. R. Bugarin, J-M-G. Diaz-de-Villegas (1994) Geometric dynamic optimisation in turnout switches. Transactions on the Built Environment. WIT Press.

M. R. Bugarín, A. Orro, M. Novales (2011) High speed turnouts geometry. Journal of the Transportation Research Board. Volume 2261, Issue 1

Andy Foan, Yann Bezin (2019) Optimisation of railway Switches. PWI Journal, Vol 137.Pt2.

Klaus Knothe, Sebastian Stichel (2016) Rail Vehicle Dynamics. Springer International Publishing

B. A. Pålsson, J. C.O. Nielsen (2012) Track gauge optimisation of railway switches using a genetic algorithm. Vehicle System Dynamics. International Journal of Vehicle Mechanics and Mobility Volume 50

Ping Wang (2015) Design of High Speed Turnouts. Theory and applications. Academic Press. Elsevier.