I have always heard that the purpose of the taper on railroad wheels is to allow them to differ their rotation speed when rounding a curve because the distance traveled is greater on the outside rail than it is on the inside rail.
However, when a wheel-set enters a curve, the centrifugal force pushes the wheel-set outward so that the outer wheel rides up to a larger diameter of its taper, which would force it to rotate slower while it must travel a greater distance than the inside wheel. At the same time, the inside wheel would ride down to a smaller diameter, which would cause it to rotate faster while it must travel a lesser distance than the outside wheel. This would create a conflict with the slower, outside wheel traveling farther than the faster, inside wheel. If the purpose of the cone taper is to compensate for the difference in distance traveled, it would seem that the cone taper on each wheel should be reversed. Perhaps this common explanation for the taper is incorrect.
I wonder if the true explanation for the taper is that the conflict it creates tends to keep the wheel-set centered while it travels the curve, or in other words, to fight the centrifugal force so the outer wheel flange does not bear against the outer rail. It does this on straight track. Any thoughts on this?
The outer wheel has been pushed up hard against the outer rail. Hence it has its greatest diameter running on the outer rail. The inner wheel has its smallest diameter running on the inner rail.
For any given rotational speed, the outer wheel (greater diameter) will cover a greater distance than the inner wheel (small diameter). This is thecorrect way round.
You misunderstand what is happening. The wheels must rotate at the same speed because they are locked to the axle. When the outside wheel completes one revolution, the inside wheel will also have completed one revolution. Because the outside wheel has moved to the larger diameter part of the taper the wheel will cover more distance in one revolution of the wheel (and axle), than the inside wheel. Since the distance around a curve on the outside rail is greater this will all balance out.
Yes this also happens, but it is more a function of the pair of axles (and four wheels) being mounted in a truck.
Forget about the speed of rotation. It’s not relevant here. What is inportant is that the outer wheel moves further with each rotation. The inner wheel moves a lesser distance with each rotation. Thus the wheelset finds a happy medium where the two are not sliding or are least sliding as little as possible. Obviously there will be turns that are too tight such as yard and industry tracks and the flange will come into play. But on most mainline track the wheelset will find this happy medium and very little wear will occur.
Thank you all for this clarification. It does make sense when I look at it that way. I realize that the two wheels are locked together and must turn at the same RPM, but I was visualizing a conflict from wanting to turn at different speeds. But the explanation of covering different distances while running at the same speed is easy to visualize now that I think of it.
Think of it this way…the taper is constantly forcing the wheel/wheel set to track and try to come back to dead center, the truck side frames hold them wheel square to the track…the flange is the safety system, which comes into play only when the centrifugal forces exceed the ability of the taper to force the wheel back to center.
Under perfect circumstances, where the super elevation is perfectly matched to the speed of the car, all the track is correctly aligned, and the wheels set is “perfect”, the flange will never touch the rail head.
Of course, nothing is ever perfect, but the taper still helps “steer” the wheel.
Worn side bearings, bad track, or binding bolster plate among other things will cause a wheel set to “hunt” for the dead center…you most likely have seen a car in a train that seems to be bouncing side to side while the rest of the cars don’t.
The difference between the ID gauge of the track, and the OD gauge of the flanges is different, to allow for the difference in travel distance in curves.
As was pointed out, one wheel will have to travel farther than the other…if the flange and track were exactly matched in width, the flanges would bind in any curve…but because there is “play” in there, it can move to the outside and use the flange to steer without binding up.
Looking back, I must admit to being startled when I discovered that I had analyzed this issue of wheel taper while completely overlooking the fact that wheels are coupled, and therefore cannot turn at different speeds. But I mistakenly came into the problem thinking about a differential being produced by the wheel tapers, and that led to the concern about the wheel taper direction being backwards.
Under the heading: Directional Stability and Hunting Instability, I see nothing about the explanations or the diagrams that I would question. However, under the next heading, Effect of Lateral Displacement, I see much to question.
In the first sentence, they state that when the wheelset displaces to one side, the diameters of the regions of contact change, and become different for the two wheels. By “region of contact,” they are referring to the generally round (I have heard elliptical) load bearing contact of the wheel to the rail. I am not sure why that would change if the wheelset displaced laterally. Perhaps it does because it moves to a different part of the wheel and rail, where the contours may differ. But, in any case, I don’t see why a change in the size of contact would affect anything to do with tracking (or with wheel velocity as their explanation continues).
It would seem that the issue affecting tracking is that the point of contact moves to a zone of greater or lesser diameter of the tapered wheel. They seem to link a difference in the size of the region of contact with a change in wheel velocity. I do not understand what they mean by the parenthetical modification of the term, velocity with the term, linear. But I conclude that if the wheelset displaces to one side on straight track (they are referring
Murphy Siding, have you not been paying attention? [;)]
The wheels are tapered. That is, they have a smaller diameter on the outside than they do on the inside.
The wheel on the inside of the curve rides on the outside of the wheel (which has a smaller diameter), while the wheel on the outside of the curve rides on the inside of the wheel (which has a larger diameter).
Let’s say that the difference in diameter between the inside and the outside of the wheels is 1 inch. That means that wheel on the outer track of the curve will travel about three inches further than the wheel on the inner track of the curve for each rotation of the axle.
As the track distances are not nearly that great between the inner and outer rails, the wheels can adjust themselves accordingly so that the radiuses are appropriate to the actual distances that need to be travelled.
As has been pointed out by others above, they turn the same speed, but cover the differing distances of the rails in a curve without slipping by riding on different diameters of their tapers.
Wikipedia is hardly an authoritative source for anything, although the folks who post there seem to like to think so.
I suspect that the problem here lies in the term ‘speed’. The wheels, being linked by a solid (very solid) axle, must turn at the same rotational velocity – one might call that speed. However, if they are riding at different points on the rims – which they usually are – one wheel will be riding on a larger diameter than the other. Therefore the tangential velocity of the rim with the larger diameter will be greater than the tangential velocity of the other, and the wheelset will move in a curved path towards the wheel riding on the smaller diameter. Tangential velocity of the wheel might also be referred to as ‘speed’. The overall rate of forward progess of the wheelset – measured, perhaps, at the midpoint of the axle – might also be referred to as ‘speed’. If neither wheel is slipping, that velocity will be the same as the average of the tangential velocity of each wheel…
The English language, she is a great and wonderful thing – but only when people use technical terms correctly, and avoid trying to use non-technical terms to describe technical concepts.
I’m going to make up some numbers here to clarify what the Wikipedia article is talking about in terms of linear speeds of the wheels.
Let’s say that an axle is turning at one revolution per minute (1 rpm). If a wheel attached to that axle has a diameter of 20 inches, then that wheel is moving at a speed of approximately 63 inches per minute. If a wheel attached to that axle has a diameter of 21 inches, then that wheel is moving as a speed of approximately 66 inches per minute. Same axle, different linear speeds.
That’s why a tapered wheel can negotiate a curve without slipping. The smaller diameter wheel on the inside rail moves at a slower speed than the larger diameter wheel on the outside rail.
.[:I] OK maybe not enough attention, but I’m still having some doubts in the logic of what you’re saying.
As I understand what is being explained here, when a track turns to the left, for example, the wheels and axle moved to the right. This causes the wheel on the left side to ride on a spot that has a smaller diameter than the wheel on the right side is riding on. So far, so good. That is a pretty good explanation of stagger on the wheels of a racecar, to help it turn left. However, what pushes those wheels left or right must be centrifical force-correct? If so, differences in the speed of a train going around the corner would cause differences in how far left or right the wheelsets move. It would seem like that would mess up the theory that the wheels move to the correct spot to make all the math work, about diameter and distance traveled. (?)
So when Wikipedia refers to linear speed of the wheel, they are referring to distance the wheel travels per unit of time as opposed to the number of revolutions per minute? So the outer wheel is moving ahead faster to compensate for the fact that it has a longer distance to cover.
(Heaven help me…) I am not a mathematician, nor an engineer, nor an expert in anything mechanical, so please indulge me for a few minutes.
What we are talking about is a set of dynamic forces that strive for equilibrium…yes? The car doesn’t want to turn, so it attempts to maintain its tangential motion along the curve. But, the flanges , which in turn are affixed to wheels physically attached to a solid axle, require it to conform to the centreline path between the rails…on average,…or at least to the line imparted to its movement by direct contact with the inner edge of the outer rail head.
These radial forces, not the tangential ones that want to keep it going in a straight path, impart the major dynamic because they cause the wheels to place a changing length of running surface on the railhead. This changing length means that for any one revolution of the rigid axle, the outer wheel will travel farther than the inner, as was made clear earlier. This should not be astounding because along the arc of the curve, the outer rail is longer, as the formula for the circumference of a circle showed us in grade school.
There will be some scrubbing, though, because both axles in the truck are parallel. If/when one is perpendicular to the tangent of the curve along its own axis (the axle is pointing directly down the radius toward the curve’s centre), the other must not be. One axle is always going to be slightly askew. In truth, neither is ever perfectly oriented toward the circle’s centre, and therefore both axles will cause their rigidly fixed wheels to scuff while they track in a direction slightly off axis toward the centre of the curve.
The effect of the train wanting to travel in a straight line to overcome the curvature of the tracks is very, very small, particularly at the speeds that trains in the US travel. Of course, trains that are designed to travel at higher speeds have curves with correspondingly higher curvatures. How often (when travelling on a train) do you feel yourself thrown to one side as the train negotiates a curve?
Wheel tracking predominates at almost any speed that the train can safely navigate.
I was going through my Dad’s garage because the dipstick on the tractor went missing and I blamed it on the squirrels instead of my own absent mindedness last time I changed the oil, and I came across a manuscript to a conference paper V Milenkovic (1970), The Generalized Problem of Lateral Guidance and Stability in Wheeled Vehicles, which addresses many of the same issues as the Wikipedia article. Yes, the Wikipedia generally has it right on this one and the anomomous contributer knows what they are talking about. You can notice the British variants on English in the article along with references to work done in Great Britain on the wheel-on-rail stability problem, the basic theoretical work being done there in the 1960’s.
The first kind of instability in wheel-rail guidance is what the article calls the kinematic instability of the tapered wheelset, which is the widely-accepted term and explanation. The flanges have nothing to do with the trajectory – they are there as a backup for sharp curves or when the excursions get too large – and the cone taper steers the wheels. Yes, the wheels are connected with a solid axle, which means each wheel goes through the same rotation angle as the wheelset moves down the track, but the wheel riding up on the larger part of the cone taper goes farther for a given angle of rotation, which steers the wheel away from the wheel that is high on the taper and towards the opposite wheel that is low on the taper until the situation is reversed and the wheelset steers back the other way. The wheelset will meander back and forth in a wavy motion according to the equation given in the Wikipedia article.
A second kind of instability is given in the linked