# How to calculate pad deformation

• luuurey
In summary: Sorry.In summary, the conversation discusses a standard contact stress problem involving the deformation of a pad under a cylinder. The person asking the question has searched various sources but cannot find information on the local deformation of a pad. They are also struggling to understand the equation commonly used for this type of problem. Experts suggest looking at a specific link and recommend further reading on the subject in a book called "Contact Mechanics" by Johnson. The conversation ends with the expert declining to provide further information.
luuurey
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.

This is a standard contact stress problem where have you looked?

Studiot said:
This is a standard contact stress problem where have you looked?

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.

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?

luuurey said:
But how does everyone find out this? It looks like everyone just copy this without understanding.

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.

Studiot said:
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?

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?

Last edited:
Studiot said:
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:
$$\frac{1}{E} = \frac{1-υ_1^2}{E_1} + \frac{1-υ_2^2}{E_2}$$
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?

Studiot said:
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.
$$\frac {1}{E} = \frac{1}{E_1} + \frac{1}{E_2}$$
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.

cronanster said:
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.

I'm asking you how we get the frist equation for a? Sorry, I cannot find out.

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.

## 1. What is pad deformation?

Pad deformation is the change in shape or structure of a material caused by external forces, such as pressure or weight. In the context of calculating pad deformation, it refers to the change in shape of a pad (typically made of rubber or foam) when weight is applied to it.

## 2. Why is it important to calculate pad deformation?

Calculating pad deformation is important in order to ensure the structural integrity and stability of a material or object. It can also help determine the amount of weight or pressure a pad can withstand before it deforms, which is crucial for safety and performance purposes.

## 3. How is pad deformation calculated?

Pad deformation is calculated by dividing the force applied to the pad by its area. This results in a measure of pressure, known as the stress. The stress is then used in conjunction with the material's properties (such as elasticity and stiffness) to determine the amount of deformation that will occur.

## 4. What factors can affect pad deformation?

The material properties of the pad, such as its elasticity and stiffness, can greatly affect pad deformation. Other factors include the amount and distribution of weight or pressure applied, as well as external factors such as temperature and humidity.

## 5. How can pad deformation be minimized?

To minimize pad deformation, it is important to choose a material with suitable properties for the intended use and to distribute weight or pressure evenly across the pad. Additionally, regular maintenance and proper storage of the pad can also help prevent excessive deformation over time.

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