Contact stresses in cylindrical contacts

[brkica]

I am trying to analyze the contact stresses in two cases of cylundrical contact:

Case 1: two perpendicular cylinders with different radii
Case 2: cylinder in a cylindrical socket

See also the attached file for explanation.

I assume there are analytical solutions for the contacts stress for these tweo cases.

Does anyone know a reference/book in which these cases are treated. I usually find other cases like sphere-flat plate, two sphere, conical indenter-flat plate, cylindrical indenter - flat plate, etc. I have not been able to find solutions for these two particalar cases.

Thanks in advance!

 

[flash3780]

What you're looking for is a Hertzian contact stress; there is a lot of literature on the subject. The best resource for information on Contact Mechanics is probably Ken Johnson's "Contact Mechanics" (I've been meaning to get a copy for myself). Johnson's book probably goes into more detail than you need about the derivation of the Hertzian contact equations.
A better resource for your particular problem would be Roark's Formulas for Stress and Strain. Roark's has simplified equations exactly describing the cases that you've drawn. (7th Edition, p 703)

Be mindful that your second case might be beyond the limits of Hertzian Contact; one of Hertz's primary assumptions is a small contact area relative to the significant dimensions of the contacting bodies. That being said, people use (abuse?) the formula in Roarks to calculate contact stresses in sleeve bearings all of the time. You could always do a quick plane strain FEA model to remove any doubt.

 

[brkica]

Flash,

thanks a lot. Tomorrow I will dig up Johnson's and Roark's book at the library and have a look at it.

As for the second case, a plane strain FEA will suffice to validate the formulae used.

 

[Keith1029]

I believe "Advanced Mechanics of Materials" by Boresi devotes a section to cylinders in contact. From what I can recall it covers a derivation for the general equation (regradless of contact angle). I don't have it with me though so I am not sure. Something to try though.