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# Deformation of Rail

## Deformation of Rail

(OP)
I have a 29-1/2 ft diameter piece of 40# ASCE rail track. On this track there are 16 wheels 2" wide each with each wheel supporting approx 12,000 lbs of load. Does anyone know how to calculate the load capacity of 40# rail?

Thanks

### RE: Deformation of Rail

1. 29-1/2 foot diameter rail?

2. What do you think the stress is under each wheel right now? Assuming every wheel is uniformly loaded at 12,000 lbs each, and whatever you assume is correct for the compression surface (loaded area) of each wheel and the track?

### RE: Deformation of Rail

(OP)
Hi

Sorry for the delay. The rail is formed into a 29-1/2 ft diameter circle. 5 equal pieces of rail stock are formed, cut and trimmed to make the circle.

The 16 wheels are mounted to a table with each wheel assumed to be carrying an equal load of 12,000 lbs each. The wheels are 6.66" in diameter, made from 1045 HRS which have been flame hardened to about 55 RC 3/16" deep, and each have about 1.875" of line contact on the rail. The table indexes 45 degrees once every 30 seconds and from what I can understand using a Hertzian calculator that is on line I come up with about 98,000 lbs of force on each of the wheels with about 30,000 lbs of shear stress about .03" deep in the in the rail. From what I can see, 40# rail is pretty close to 1055 carbon steel and from the info I see on carbon steel it has about 100,000 lbs of tensile (compressive) strength. Since the rail is wearing rather quickly I'm assuming that these numbers are correct and that the wheels are deforming the top of the rail a little bit every time the table rotates. If what I explained is correct, then the next issue is what to do to increase the longevity of a replacement rail (possibly of a different material) as the life span of the present rail is not very impressive.

This isn't my area of expertise.

Thanks again,

### RE: Deformation of Rail

Hmmmn.

Can you photograph each axle, each wheel - one of each set?

There's a skidding or a rubbing motion in there someplace that is "rubbing" the two surface together rather than just letting them "roll" across each other. That "skidding" (non-rotating) motion between the two is what I am suspicious of.

### RE: Deformation of Rail

Wearing in what way?

The line contact is not uniform due to the crown on the top of the rail, so you may be getting much more stress in the center; more if the wheels are also crowned. For reference ordinary train wheels are conical.

Of the potential defects in the design:

1) Wheels not conical to match turning radius see https://en.wikipedia.org/wiki/Rail_profile#Conical...
2) Wheels not aligned, causing shearing loads
3) Insufficient number of wheels
4) Wheels not bearing identical loads due to vertical mismatch or platform lack of flatness
5) Radius of wheels too small
7) If there is a system to force the table to rotate about an axis it may not be centered on the curve of the rail

If there is damage only at the index positions, I would look at some lift system that unloads the wheels at the index positions. Even a set of small hydraulic jacks with .1 inch travel would be more than enough to prevent the wheels from leaving dents at the index positions; depending on the pressure and size you could remove any fraction up to the full load allowing the wheels to carry the load only while turning.

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