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.
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.
Look here, put the radius of the second cylinder = ∞ http://www.mech.utah.edu/~me7960/lectures/Topic7-ContactStressesAndDeformations.pdf
Thank you. But I feel like I live in a stupid world. This equation is written everywhere: [tex] \frac{1}{E} = \frac{1-υ_1^2}{E_1} + \frac{1-υ_2^2}{E_2} [/tex] 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?
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.
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.
Thank you. I would like to understand more and deeper. For example where do we get the equation from Wikipedia?
Sorry to tell you this but you put something into this discussion. What do you want to know and at what level?
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: [tex] \frac{1}{E} = \frac{1-υ_1^2}{E_1} + \frac{1-υ_2^2}{E_2} [/tex] http://en.wikipedia.org/wiki/Contact_mechanics
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?
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.
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.
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?
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.
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.