Allowable Stresses In A Rail At Wheel/Rail Contact

[Ussuri]

Firstly, this is not a railroad question. I have a site where we fabricate steel structures to support oil and gas developments. These structures can be quite heavy. The site uses a railroad system and purpose designed bogies to move these around.

The bogies consist of 4 x 200mm diameter wheels. The rails are BS75R. We are looking to work out the maximum load we can apply to the rail at the wheel/rail interface. The loadings is applied very infrequently, and wheel speeds are very very low at 20rpm.

I have done some simple calculations to calculate surface and subsurface stresses at the contact point. I am looking for some published guidance which might suggest limits for the stresses developed in the rail. I would have thought there would be something but I cannot find much. The best I have found is in the "Wheel/Rail Interface Handbook" which says the maximum subsurface shear stress should not exceed the plastic limit.

I wondered if this is more akin to railroads used in mining operations instead of normal rail applications.

Any suggestions would be appreciated

 

[ornerynorsk]

Do the wheels have any width to them?

It is better to have enough ideas for some of them to be wrong, than to be always right by having no ideas at all.

 

[Ussuri]

The wheels are 100mm wide, between the wheel rims, the rail has a running surface 60mm wide.

 

[SwinnyGG]

The best I have found is in the "Wheel/Rail Interface Handbook" which says the maximum subsurface shear stress should not exceed the plastic limit.

This seems extremely clear.. what about this limit don't you like?

 

[MikeHalloran]

I didn't retain any data from when I worked for a crane manufacturer, but I do remember that 200mm is damn small even for a crane wheel. I think standard railroad axles are bigger than that, and the wheels are upwards of 30 inches in diameter.
... and the wheel running surfaces are tapered.
... and the rails are slightly crowned.
... so that a four-wheel bogie will tend to center itself between the rails _without_ requiring contact of the flanges and the railhead except on very tight curves.

Why not use standard-ish railway parts that are already in production?



Mike Halloran
Pembroke Pines, FL, USA

 

[Ussuri]

Thanks folks

jgKRI, nothing insofar as it goes, but it is a single line reference in a textbook. I thought (mistakenly maybe) there would have been something contained within a standard, code, guideline somewhere which was more in depth. Maybe railroad, mining, cranes, p-way etc.

Mike, the site infrastructure is existing so changing components is not something that will be entertained.

 

[SwinnyGG]

Did you read through the actual wheel/rail contact book, or just skim a google doc?

It contains a MASSIVE amount of information. The answer you're asking for is in that book, and so are the calculations which support the answer, and so are the derivations of those calculations from first principles in many cases... it is a very in-depth book.

 

[Ussuri]

Unfortunately, I do not have the complete reference, only Chapter 3 (which deals with the contact analysis) and because it is purchased per chapter the cost was restricted. I will look to purchase a personal copy.

 

[dhengr]

Ussuri:
You are asking for the impossible (certainly unlikely data/research). The AAR (Association of American Railroads) has rooms full of info. and data on this subject. Wheel and rail wear and damage are a really big deal to them. But, they are working with radically different wheel dias., loads, velocities/rpms, ton/miles etc. etc. It is basically a Hertz bearing stress problem btwn. the wheel and the rail head, but it is very difficult to define the rail and wheel shapes, geometry and dias., so elaborate long hand calcs. are somewhat suspect when using the basic theory on the subject. Millions of ton miles of testing have refined the RR’s understanding of this problem and improved geometries, etc. The basic calcs. do give you a range of stresses and deformations and some handle on the problem, but in the final analysis, you have to just make an engineering judgement, coupled with some experience and testing/inspection of your own wheels and rails and load history. I wouldn’t let the big-wigs ask me how big a load can we carry, but rather, lets look at each extra big load and make an engineering judgement of the damage it might cause, you have to splain his to them. How badly do you want to move that load, are you willing to replace some wheels and rail? This type of admonition and discussion is important because we can’t give them an exact answer to a problem like this. You and I didn’t pick the wheel dia. or the rail head shape, they did, so they are kinda stuck with it. The plant and carts were designed for 300T loads, really big loads at the time, but now they want us to move 600T loads with the same equip. We will abuse the rail and the wheels, and we will want to inspect them for this once we are applying these larger loads, I’ve done this many times for short moves of heavy loads. You are basically dealing with shop carts, I’ve designed many of them, and irrespective of wheel/rail interaction, I would probably be more concerned that nothing on the cart actual be near failure. You’ll dent or work harden the rails and wheels, but that’s wear-n-tear and abuse, once or twice a year; I don’t want an axle or bearing or some frame member on the cart to fail during this move.

The wheels may be 100mm wide, but the rail head is only 60mm wide and it is crowned and shaped, so the actual running surface is a fairly narrow line at the center of the rail head and in the middle third of the wheel. You will dent the rail and you will move some metal plastically, work hardening it. I’m not familiar with the handbook you are talking about, but I imagine it is an agglomeration of much of the earlier research and testing done the RR’s, etc. But, remember that anything you see in a handbook will likely have a fair FoS because they too are admitting that they don’t have an exact answer to this problem. And, they are wanting to talk about millions of ton/miles, not two moves per year. Some riggers will say that if you can pull the carts up out of the railhead dents the wheels make you can move it, but they are likely going to scrap the rail after the move. So, you should probably initiate some sort of an inspection program of your equipment as you do more of these heavy loads.

 

[Ussuri]

dhengr

Thank you. I have redesigned the carts to accommodate the higher loading. We will fabricate replacements for these. So it does ultimately come down to the local interface at the rail and the foundation below it. My hertz based hand calcs suggest local deformation at the rail, giving a dent. In the real world I'm inclined to think they wont even notice a dent or flat spot. It will be relatively small.

This may be an example of analysis versus design, I am focusing too much on the theoretical interface instead of asking what the consequences are. In the case where I am locally deforming/work hardening the rail, I cannot envisage a case where this 'failure' is catastrophic (such as an axle failure), so it maybe is a case of, acknowledge it will occur, plan for the occurrence (may need to pull harder to move it), and clean up afterwards (inspect replace etc).

 

[dhengr]

Ussuri:
I would use the biggest wheels, axles, and bearings that I could, consistent with headroom and lifting issues. But, I’ve designed dozens of shop carts with 8, 10, 12” wheels, and nobody payed much attention to their cap’y. once they were on the shop floor, expect that they did roll and didn’t drop the load. Pay some attention to getting that load nicely distributed to all four wheels on the shop cart. Heck, you could use Hellman rollers on flat pls. on the shop floor for some of those heavy loads and short moves. Obviously, the ties, grade beams under the rails, the foundations must be considered, but they are short term loads/deflections, spring like, and again, only happen a few times a year.

“In the real world...,” re: the rail dents, etc., the rigger or the shop foreman will just say, ‘we need a bigger Cat to pull this mother. I was once involved, only tangentially, in the following situation: Two RR engines, a loaded heavy duty railcar and a caboose, a special RR move. The engineers knew the best joint in the south to get BBQ’ed. pork sandwiches for lunch, so they pulled off on a siding, parked the train and we had a very good lunch, very good conversation and all. We came out, walked across the highway, and down a block or so, and the heavy duty railcar was sitting in the dirt almost up to the axles. In an hour or two the vibrating engines had caused the siding rails to spread, and the railcar just settled down into the ties and soil. I was glad I didn’t have to make that phone call, because there weren’t a lot of happy campers on that one.

 

[chicopee]

Get some references from Timoshenko prolific work on structures and stress analysis. There is may be something useful as I remember that he has done analysis on railway tracks. AISC also has material on cranes that my be useful.

 

[Black Phoenix]

It's really hard to give any specifics with such a broad question, but generally with rails you should be distributing loads over multiple wheels as opposed to having beefier wheels (rails themselves are pretty soft and will be a maintanence issue if heavy loads keep moving on it). It's significantly better to have 64 normal axles (better yet, taking them from your local railway supplier) over 16 beefy customized axles.

For railroad systems I'm familiar with, the typical axle load limit will be about 20 tons in extreme cases, but typically 12 tons. In first order, the wheel speed does not matter. These numbers are for 1520 mm railways, but they should be an OK first order guess for similar rail systems. Still, if it's a very customized system, then the maximum loads can significantly differ (particularly if steel type in rails, gauge, wheel profile, rail profile change).

The question kinda brought to mind a starting-testing launch table for USSR rockets (this one:

https://cont.ws/uploads/posts2/267791.jpg).

To carry large loads it employed 256 (IIRC) axles (re-using them from normal railways). This would give it about 3000 tons nominal capacity (at 12 tons per axle), which fits well with its purpose (it must be able to hold a fully fueled N-1 rocket, which was about 2900 tons, and move an unfueled rocket stack up to about 400 tons in mass).

If your bogies were designed for 300 tons, then to increase capacity to 600 tons with existing wheels & cart designs your best bet will be doubling the number of axles - that's my opinion. Doubling number of axles will be playing it safe, but it's unclear if that's a reasonable answer here. I'm not sure I understand the entire setup here (how many axles, does the cart have one bogey or multiple bogies, how is the load mounted on them, etc). Maybe it's possible to connect two carts/bogies into one "wagon" and double effective axle count that way. Searching for alternate wheels or rails is an option, but then you absolutely have to do a full study on what happens to your rails under those loads.

Overloading rails is pretty bad, apart from basic mechanical problems (you can twist rails out of their mounting pads, push them apart) it may cause issues like rails getting splits and cracks - the rail head can detach from the rail base and cause the entire thing to derail while it's carrying something.