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# Hertz contact stress3

## Hertz contact stress

(OP)
Please can anyone help with using Hertz contact stresses? I am designing some equipment for a customer who requires I use a safety factor of 4 on proof strength and 6 on ultimate strength. This is fine when it comes to bending and shear stresses etc, however I'm not sure "what to do" with Hertz stresses. Part of the design uses a hardened steel roller, dia 12 mm, (440C, UTS 930MPa) on a flat steel plate (En24T, proof 650 MPa UTS 850 MPa), loaded both statically and slow moving. I've calculated the compressive and shear stresses according to Roark Table 33 case 2a, however I don't know what to do with them!  They are 504 MPa and 168 MPa. I've done the American Railway Engineering Association allowable loading check from the text and my loading has a reserve factor of over 4.
Cheers.

### RE: Hertz contact stress

The limits normally adopted for Hertz's contact stresses are 4 times the allowable stress for linear contact and 5.5 times for point contact. You could divide the Hertz stresses by the same factors before comparing them to your allowables.

prex

http://www.xcalcs.com
Online tools for structural design

### RE: Hertz contact stress

(OP)
Thanks prex but I don't know the allowables. The Hertz stress is a compressive stress and the peak shear stress is subsurface. I only have material tensile strength information.

### RE: Hertz contact stress

Your allowable is the minimum of Y/4 and U/6, right?
Take the Hertz contact stress intensity (surface stress), divide it by 4 if it is a linear contact (cylinder onto flat) and compare the result to your allowable.

prex

http://www.xcalcs.com
Online tools for structural design

### RE: Hertz contact stress

(OP)
I'm with you prex! It's the tensile vs compressive I'm not sure about. Can I compare a Hertz compressive stress with an allowable based on a tensile material strength? Also what do I do with the subsurface shear stress that I have calculated?

Cheers

### RE: Hertz contact stress

Essentially you're comparing stress intensity with the material yield stress and so it is irrelevant whether or not the principal stress is compressive or tensile. The value of stress intensity is always positive.
The shear stress limit is generally half the allowable stress intensity limit. If you're comparing bending stresses, for example, with a quarter of yield then by the same token the shear stress should be compared with one eighth of yield.

corus

### RE: Hertz contact stress

(OP)
Thanks for your help prex and corus.

Prex - could you please give me a reference for your advice "The limits normally adopted for Hertz's contact stresses are 4 times the allowable stress for linear contact and 5.5 times for point contact"? I need to write up my calcs and submit to my customer.

### RE: Hertz contact stress

Don't know if this will be useful for you, but my reference is the italian code for structural steel 'D.M.9/1/96', where at point '4.7-Fixed and sliding supports' it is said:

#### Quote:

The contact pressures, calculated with Hertz formulae, must be:
-for linear contact: σl≤4 fd
-for point contact: σp≤5,5 fd
fd is the calculation strength or allowable stress.

prex

http://www.xcalcs.com
Online tools for structural design

### RE: Hertz contact stress

FYI-
ASME B&PV Code Sec IID allows 1.6xDesign Stress for Bearing Stress on Pressure Vessel Design

### RE: Hertz contact stress

(OP)
Does any one else know any limits please for Hertz stress, as the 4 times allowable seems high? The Tribology Handbook page E1.2 concerning contact between a ball and a plane or between two balls states "At heavy loads plastic flow takes place, beginning when Hertz pressure reaches 1.8 x yield stress in tension of softer body"

Cheers
Rattler

### RE: Hertz contact stress

This has always been confusing and
I have not seen definitive answers.
Ball bearings are often life tested with
stresses in the 350000 PSI range.
The 350000 is more than 2.5 times the
UTS of the bearing rings materials
which have uts values around 123000 PSI.
These are surface pressures and not
bending stresses but bearing stresses.
I have also seen unusually high surface
stresses in gears without failure.
I think bearing stresses are published for
some materials.  Surely they exceed the
uts of the materials.

### RE: Hertz contact stress

Well, ultimately the thing that really determines how much surface stress you can stand is the subsurface shear stress. In a situation with purely compressive direct stresses, no material failure can occur, no matter how high those stresses are. The more closely the Hertzian conditions approximate this ideal limiting case, the higher the Hertzian compressive stresses you can stand.

### RE: Hertz contact stress

Rail-wheel allowables from 1.6 to 2.0 times the UTS of the softer material, i think are in DIN (German) standards. Also quoted in Hydraulic gates and Valves by Jack Lewin

### RE: Hertz contact stress

also in EM1110-2-2703, plate B-90 that is a Corps of Engineer manual available on the web, there is implied a factor of 2 times yield for allowable hertz stress, wheel on rail

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