Subsurface stresses elliptical contact area

[arnoldh]

Dear Forum,

I am trying to calculate the different subsurface stresses over the depth for an elliptical contact area. I have formulas for a line contact and a point contact on a flat surface, but not the formulas for an elliptical contact, which should be the ones in a ball bearing. Can anybody provide the required formulas to calculate the required sigmas and/or tau for an elliptical contact?

Many thanks in advance for you help.

Regards,

Arnold

 

[dimjim]

This might help.

http://www.mech.uwa.edu.au/DANotes/MST/contact/contact.html

 

[Fugeguy]

See:

http://books.google.com/books?id=Hr...ris&sig=C9Ie3AjmFsOzisONPEj6vOiClbI#PPA108,M1

Eq. 6.25

http://books.google.com/books?id=Hr...ris&sig=C9Ie3AjmFsOzisONPEj6vOiClbI#PPA112,M1

http://books.google.com/books?id=Hr...ris&sig=C9Ie3AjmFsOzisONPEj6vOiClbI#PPA127,M1

http://books.google.com/books?id=Hr...ris&sig=C9Ie3AjmFsOzisONPEj6vOiClbI#PPA133,M1

Hope that helps.

 

[volpegrigia]

If you have the formulae for point contact, then you have the formulae for elliptical contact. Point contact is a special case of elliptical contact (at least it is treated that way by all of the texts I have.
The issue you will have to calculate the subsurface stress, is the ability to calculate incomplete elliptical integrals of the first and second kind.
The best treatise of its kind, is in AB Jones book (published in the '40s and out of print). If you are interested I can upload a PDF file with the section you will need.

 

[arnoldh]

Dear all,

first of all, thanks for your help and the great links.

volpegrigia: if you could upload a pdf of the needed section this would be great (not only for me, I guess.

Many thanks in advance.

Regards,

Arnold

 

[volpegrigia]

here you go!