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Rail Wheel Design - Hertz Contact Stress Limit in Stainless?

Rail Wheel Design - Hertz Contact Stress Limit in Stainless?

Hi all

I've got a small application that needs an underwater linear guide.  Unfortunately I can't use plastics in this application, so I'm left with austenitic stainless steel only, and there aren't too many off-the-shelf solutions in stainless.

I am considering using grooved rollers on a round rail.  I can calculate the Hertz contact stress for this arrangement easily enough, but I'm not sure where to set my limit.  Some rules of thumb I've seen like "2 x UTS" and "< 4 GPa", refer to bearing steels only.  I haven't seen a good reference for unhardened steels, and stainless in particular.  So how much contact stress should I allow on 304 (or 17-4) stainless rails and wheels?

Should I use the maximum sub-surface shear stress?  If the maximum shear is about 1/3 of the contact stress then the contact stress should be no more than 3/2 * yield, or about 350 MPa.  That seems fairly low (that means I would need a 1.5" diameter x 1" wide wheel just to carry 500 lb)!

I don't think crane rails & wheels are hardened.  Is there a calculation for sizing those?  

Should I be worried about galling?  I've seen galling stress threshold limits as low as 1 MPa for stainless, which would seriously limit the load.  Should I nickel plate the wheels?

Thanks in advance.    

RE: Rail Wheel Design - Hertz Contact Stress Limit in Stainless?

The few miles of crane rail I've bought were pretty damn hard.

Mike Halloran
Pembroke Pines, FL, USA

RE: Rail Wheel Design - Hertz Contact Stress Limit in Stainless?

250-300 Brinnell hardness is about typical for crane rail right?  That's about Rockwell C 30, which is close to what I can get with 17-4PH Stainless (and a damn sight softer than bearing steels, which are about RC 60).  So I think the crane wheel sizing formulas (or charts) might still be suitable.  What did you use to size your crane wheels?

RE: Rail Wheel Design - Hertz Contact Stress Limit in Stainless?

I found a reference that suggests a minimum of 370-400 BHN.

The Boss sized the rail and wheels; he was tight-lipped about exactly how.

We bought the wheels from a supplier in Taiwan; they supplied rating spreadsheets, but I don't recall a mention of what basis they used.


Mike Halloran
Pembroke Pines, FL, USA

RE: Rail Wheel Design - Hertz Contact Stress Limit in Stainless?

CMAA #74 is used to size wheels on underrunning cranes.  Table gives allowable loads based on wheel tread width and diameter but I didn't see the equations on which the tables are based.  You may be able to back calculate and get an approximation.;prodid=72

RE: Rail Wheel Design - Hertz Contact Stress Limit in Stainless?

Thanks for that reference.  The wheel tables in CMAA #74 are pretty consistent.  Using my Hertz contact formula I get:

For 200BHN - Contact Stress Limit = 700 MPa (102 ksi)
For 260BHN - Contact Stress Limit = 800 MPa (116 ksi)
For 320BHN - Contact Stress Limit = 825 MPa (120 ksi)  

which corresponds (very roughly) to 75-100% UTS, or 125-200% yield from what I read of the crane rail properties.  That's something anyway.

Annealed 304 has about the same hardness and UTS as 200BHN crane steel, but the chemistry is different (much less carbon for instance) so I can't be 100% positive that I can use the same contact stress limit.

I wish I had a reference for (Hertz) contact stress limit in stainless steel!

RE: Rail Wheel Design - Hertz Contact Stress Limit in Stainless?


A static hertzian contact analysis is a good starting point.  But to determine the maximum allowable contact stress, you will need to characterize your load/life cycle conditions, for both the roller and rail surfaces.  Subsurface shear stress would probably only be a limiting factor if your parts had a hard, strong outer case structure.  Otherwise, the surface contact stress will be your limit.

With a round roller/straight rail contact, the roller naturally has higher stress due to its smaller radius of curvature.  To equalize the relative fatigue lives, it may be beneficial to make the roller somewhat harder than the rail.  The roller may also be subject to a greater number of load cycles than the rail, if the roller diameter is small and the average rail travel distance is long.

Most corrosion resistant steels tend to gall/fret quite readily.  Most metals do have a galling/fretting contact stress limit, but as you noted, it is usually quite modest.  If your parts are submerged in clean fresh water, a light oxide film on the surface of the parts may actually help with the galling/fretting condition, since the oxide film will inhibit the local cold-welding at the contact.

Depending upon the loads you need to support, you might be able to find some suitable commercial components.  There are through-hardened 440C cres track rollers and rail available.  Or an alternative might be hardened steel with thin-dense chrome plating for corrosion protection.

Hope that helps.


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