Are the cones mainly for keeping the train centered, or for allowing the outer wheel on a turn to be effectively larger? Not sure if the differential effect is an added benefit that isn't really necessary, or if it is the main goal of the design.
The conical section of the wheels is mostly intended to prevent hunting on straight track, and the shape can't be made too aggressive without increasing the wear on wheels on rails. So on curves the superelevation is added to provide the extra force required.
Because conical wheels do increase wear and can contribute to oscillation in their own way, there have been experiments with cylindrical wheels especially on higher-speed trains---BART is a well known example. It ultimately didn't work very well and so they have been re-trueing the wheels to a non-cylindrical profile, although still not quite a traditional conical one. Basically in higher-speed operation the re-centering effect is too significant and causes one wheel to "chatter," which over time creates a significant vibration in the rail. Trouble is cylindrical wheels tend to cause the same thing to happen on the other side. It was a very hard problem before computer modeling became available.
I've never heard about that theory as for why superelevation/cant is supposedly being used until now.
Given that most of the time you'll end up with a remaining net force to the outside of the curve even after application of cant, it doesn't seem to make that much sense, either.
I think for low-speed freight the balance needs to be pretty close on to ideal to meet regulations, e.g. FRA regulations give calculations for acceptable ranges. But since it's dependent on running speed it's hard to get correct for freight and passenger mixed operation which is the subject of this FRA report that has a lot of detail on the calculations: https://railroads.dot.gov/sites/fra.dot.gov/files/fra_net/19...
I see what you mean with regards to how it's also described on Wikipedia – only I've got some currentish (European) literature in front of me which claims that cant and the resulting cant deficiency/excess are only of secondary importance with regards to wheel and rail wear (the main factors are simply the curve radius itself and the construction of the running gear of the trains operating over the curve), and as such the main importance of cant is simply ride comfort. Likewise it also claims that according to some practical experiments done by some infrastructure operators, no link could be found between occurrences of cant excess for slower moving heavy freight trains and increased maintenance requirements (Which interestingly somewhat contradicts the corresponding supposition given in your FRA document...).
This also matches the evolution of the design rules on the German national railways – in the 80s there still used to be a relatively elaborate system of determining the allowable cant excess for slower moving trains depending on the annual tonnage of that kinds of trains, but since then at some point that system got dropped and has been radically simplified: The regular cant is simply 55 % of the equilibrium cant and it's up to the design engineer to deviate from that value if necessary (when the speed distribution varies from that of a normal mixed-traffic route).
Interestingly all of that somewhat contradicts the statements given in your linked FRA document. To some extent this can probably be explained by European freight trains being shorter, somewhat lighter (lower axle loads) and also nowadays slightly faster than their American counterparts, and also due to traditionally using somewhat higher allowable cant deficiency values, especially with regards to passenger rolling stock. It likely doesn't explain everything, though, but I don't know enough, either, to reconcile those two differing points of view.
Or, looked at the other way, when the track curves, then the axle becomes uncentered.
(PhD was 'Residual stress in rails', for what that's worth. Judging from the profiles of the rails I saw, direct contact with the wheel flange plays a substantial role in keeping the train in place on curved track. But on roughly straight track, I'm satisfied that the argument about conicity applies).
The London Underground has some lines that are horrifically loud. The squealing must surely be at dangerous sound levels. I’d always assumed it was the flange against the rail, and you appear to be confirming that?
But it mostly (totally?) happens on very tight curves. It shouldn't happen much or at all on gentler curves.
(Of course, this is circular, because I'm kind of defining "gentler" and "tight" based on whether they cause flange squeal. Still, there's a point - there is something like a threshold of curve tightness where flange squeal becomes much more probable.)
I surmised this running 2 motors up a 3%(?) grade with 20k ton gross at 10mph. It's about the only explanation I could come up with is that the running gear was twisting under the gravity and the energy being put down to work against it. It might also just be a stringline sort of effect dragging the motors to one side of the track and pressing the flange. Maybe one of the rail engineers will come holler at me for my poor trainhandling skills.