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How to calculate pad deformation

  1. Dec 30, 2012 #1
    Could someone please show me how to calculate the deformation of a pad (ideal material with the same elasticity at all directions) under a cylinder ? Thank you very much.
  2. jcsd
  3. Dec 30, 2012 #2
    This is a standard contact stress problem where have you looked?
  4. Dec 30, 2012 #3
    I have checked all websides. Everywhere is written about the standart stress problem such as a stressing a whole subject or strain, but there is no word about the local deformation of a pad. It is combimation of more types of deformations.
  5. Dec 30, 2012 #4
  6. Dec 31, 2012 #5
    Thank you.

    But I feel like I live in a stupid world. This equation is written everywhere:
    \frac{1}{E} = \frac{1-υ_1^2}{E_1} + \frac{1-υ_2^2}{E_2}
    But how does everyone find out this? It looks like everyone just copy this without understanding.

    For example check Wikipedia: http://en.wikipedia.org/wiki/Contact_mechanics
    I cannot understand. Where do all the equations come from?
  7. Dec 31, 2012 #6

    Vanadium 50

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    Stop right there. The fact that you don't understand it does not mean that the people who wrote it down don't understand it. That's illogical, and frankly, insulting to them.

    Studiot pointed you to a link, and discussed how what was there had your situation as a limiting case. If you don't like or understand that, be specific about what you don't like or understand. Don't just make wild accusations.
  8. Dec 31, 2012 #7
    The question is commonly addressed by mechanical engineers (as with my link).
    It is also standard stuff in standard books such as Roark or Pilney
    If you are interested in the background then post more details of your application and interest.
  9. Dec 31, 2012 #8
    Thank you. I would like to understand more and deeper. For example where do we get the equation from Wikipedia?
  10. Dec 31, 2012 #9
    Sorry to tell you this but you put something into this discussion.

    What do you want to know and at what level?
    Last edited: Dec 31, 2012
  11. Dec 31, 2012 #10
    How can I calculate a curvature (and the maximum deformation) of shape of a pad if I put a cylinder on it? (like that http://upload.wikimedia.org/wikipedia/commons/4/41/Kontakt_Kugel_Ebene.jpg)

    I read the article on Wikipedia, but I didn't get where does this equation come from:
    \frac{1}{E} = \frac{1-υ_1^2}{E_1} + \frac{1-υ_2^2}{E_2}
  12. Dec 31, 2012 #11
    What was wrong with the link I offered?

    The Wiki formula is not the one you want directly.
    Do you understand what the symbols mean in it?
  13. Dec 31, 2012 #12
    I understand that it's sth. like calculating efective elastic modulus of two serial springs.
    [tex]\frac {1}{E} = \frac{1}{E_1} + \frac{1}{E_2}[/tex]
    E is elastic modulus.
    It's because we can say it's like two springs. One is the object and second is the pad.
    And it is almost all I know about it.

    I know what υ is. But I don't know how we get this.
  14. Dec 31, 2012 #13
    I really don't understand what your question is.

    On the one hand you say you want to calculate the deformation.

    But you keep posting a formula that connects two elastic constants, Poisson's ratio and Young's modulus and does not contain an expression for deformation.

    Further you keep ignoring a link to an article that discusses deformations specifically on page 8.

    Most articles (eg Wiki) only discuss stress.

    In order to derive a strain or deformation you need to solve an elliptic integral or use the approximation offered.
  15. Dec 31, 2012 #14
    Ok. So how would you calculate the deformation of a pad if you put an cylinder on it. How would you calculate the distribution of normal force along the curvature?
  16. Dec 31, 2012 #15
    As Studiot has pointed out, what you are looking for is in that link. No, it doesn't go line by line on the derivation, but you should be able to work backwards to see where it came from.

    Read through that link again, all pages, and if you still don't understand, come bak and ask.
  17. Dec 31, 2012 #16
    I'm asking you how we get the frist equation for a? Sorry, I cannot find out.
  18. Jan 4, 2013 #17
    My involvement with this subject has been through the design, implementation and failure investigations of bridge roller bearings supporting many thousands of Tonnes.

    You will find all you could ever need including discussions and analysis at various levels in

    Contact Mechanics by Johnson (Cambridge University Press)

    I do not propose to post further in this thread.
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