A History of Railway Vehicle Dynamics
Coning of the wheel tread was well-established by 1821. George Stephenson in his
“Observations on Edge and Tram Railways”2 stated that:
It must be understood the form of edge railway wheels are conical that is the outer is rather less than the inner diameter about 3/16 of an inch. Then from a small irregularity of the railway the wheels may be thrown a little to the right or a little to the left, when the former happens the right wheel will expose a larger and the left one a smaller diameter to the bearing surface of the rail which will cause the latter to lose ground of the former but at the same time in moving forward it gradually exposes a greater diameter
to the rail while the right one on the contrary is gradually exposing a lesser which will cause it to lose ground of the left one but will regain it on its progress as has been described alternately gaining and losing ground of each other which will cause the wheels to proceed in an oscillatory but easy motion on the rails.This is a very clear description of what is now called the kinematic oscillation, as shown in Figure 2.1.The rolling behaviour of the wheelset suggests why it adopted its present form. If the flange is on the inside the conicity is positive and as the flange approaches the rail there will be a strong steering action tending to return the wheelset to the centre of the track. If the flange is on the outside the conicity is negative and the wheelset will simply run into the flange and remain in contact as the
wheelset moves along the track. Moreover, consider motion in a sharp curve in which the wheelset is in flange contact. If the flange is on the inside, the lateral force applied by the rail to the leading wheelset is applied to the outer wheel and will be combined with an enhanced vertical load thus diminishing the risk of derailment. If the flange is on the outside, the lateral force applied by the rail is applied to the inner wheel, which has a reduced vertical load, and thus the risk of derailment is increased.As was explicitly stated by Brunel in 1838 (see Vaughan3) it can be seen that for smal displacements from the centre of straight or slightly curved track the primary mode of guidance is conicity and it is on sharper curves, switches, and crossings that the flanges become the essential mode of guidance.Lateral oscillations caused by coning were experienced from the early days of the railways. One solution to the oscillation problem that has been proposed from time to time, even down to modern times, was to fit wheels with cylindrical treads. However, in this case, if the wheels are rigidly mounted on the axle, very slight errors in parallelism would induce large lateral displacements that
would be limited by flange contact. Thus, a wheelset with cylindrical treads tends to run in continuous flange contact.In 1883 Klingel gave the first mathematical analysis of the kinematic oscillation4 and derived the relationship between the wavelength L and the wheelset conicity l, wheel radius r0, and the lateral distance between contact points 2l as