Right now. The OP mentioned a item in Wkipedia about hunting oscillation. Following posts have written mainly about flange contact causing squeal. This is at low speed and there willl be PSRs in place to prevent derailment.
This is not quite the same, however. Leaving out all the algebra, if you look at the conicity of the tread in the link I posted the moving wheelset will tend to stabilise with bearing contact with the rail in the centre due to the cone shape of the tread.
Now, as I understand it, sideways movement will cause one wheel to rise on its cone, the other to fall, Either the wheelset will correct itself or there will be a sliding contact due to the circumferential speed being different.
When it enters a curve the outside wheel will have to travel further than the inside one, it will also be tending to move outwards, the outside wheel rising up the shape of the tread where the circumference is greater, the inside wheel moving down the shape of the tread where the circumference is less. Thus the difference in distance travelled tends to be evened out and reduce the tendency for sliding.
The amount of this movement will be controlled by controlling the speed of the train relative to the tightness of the curve and the amount of cant, or superelevation, in the track
However at near to the maximum speed you have a very delicately balanced system, where any perturbation such as a defect in the track can set it to swinging.
This of course is describing a wheelset on its own where it will tend to position itself parallel to a radius of the curve. However wheelsets are mounted in pairs in a rigid frame and so are kept aligned to the frame. Thus we have another source of instability which is what link
http://www.railway-technical.com/whlbog.shtml describes.
All this was known about to railway engineers but until the middle of the twentieth century they simply bulit a design and ran it to find out the speed it would become unstable and set a speed limit somewhere below. Thus passenger trains generally did not exceed 80mph, and the typical four wheeled goods wagon less than 40mph. I once caught a train out of St. Pancras. It was about half an hour late and set out to make up time. I dont know what speed it was doing but the noise in the coach where I was was deafening. It isnt often I'm scared but I was then!
The first task facing British Railways in 1966 was to work out exactly what the wheelset on its own was doing and, more importantly, quantify it, and then design a computer to describe the most stable tread profile.
The next stage was to study the behaviour of various designs of suspension and derive computer models for their design. This is what the
High Speed Freight Vehicle The work that was done formed the basis of every succeeding rail vehicle from the Sprinters to the Eurostar. It was the first chapter of any succeeding textbook of railway vehicle design, just as much a milestone as the firetube boiler and blastpipe had been acentury before.
