Predicting elastic and plastic wheel deformation

[RayRoc]

I am trying to predict elastic wheel deformation. I am not quite sure how to do it. How might one approach the problem?

Take a steel wheel: 6 in. diameter, 2 in. thick, with a contact force of 1000lbs

E = 30,000,000 psi
Poisson ratio: .27

Would one calculate this in finite layers? Considering sections at a time and applying shear modulus through the layers to find the finite stress of the steel?

I have seen the stress distribution of a steel wheel against a track, and it looked like a strait coulomb from the contact area to the axial. Can it be as simple as:

Contact pressure = (volume of wheel displaced/ volume of .5 the wheel cross section) * Poisson ratio * E

There are of course many effects not realized by such a simplistic view especially when one wants to find the conditions that will cause plastic deformation at the contact area; which is ultimately what I want to know.

The gears in my head have failed, the more I think about this problem the louder the grinding noises.

 

[minger]

Contact stresses for a cylinder on a cylinder are as follows. The area of contact is a narrow rectangle of width 2b, and length l, where l is the length of the cylinders, and
$$b = \sqrt{ \frac{2F}{\pi l} \frac{ (1-\nu^2_1)/E_1 + (1- \nu^2_2)/E_2}{1/d_1 + 1/d_2} }$$
With the maximum pressure being
$$p_{max} = \frac{2F}{\pi b l}$$
You can apply this to a cylinder in contact with a plane by making $$d_2 = \infty$$

edit: Just seen that you're looking for deformation, not stress. Let's see...stress in the z-direction, perpendicular to the contact line is:
$$\sigma_z = \frac{-p_{max}}{ \sqrt{1+ z^2/b^2}}$$
Perhaps you could integrate that from z = 0, to z = r to calculate the summation of strain?

 

[oswaler]

As a scientist, there are several potential approaches to predicting elastic and plastic wheel deformation. One approach could be to use mathematical modeling, where you would input the known parameters of the steel wheel (diameter, thickness, contact force, elastic modulus, Poisson ratio) and use equations and simulations to predict the deformation under different conditions. This could involve breaking the wheel into finite layers and calculating the stress distribution through the layers to determine the potential for plastic deformation.

Another approach could be experimental testing, where you would physically apply different forces and measure the resulting deformation of the wheel. This could help validate the predictions from the mathematical model and provide more accurate data for real-world conditions.

Additionally, considering the complexities and variables involved in predicting elastic and plastic deformation, it may be beneficial to collaborate with other experts in the field, such as engineers or materials scientists, to gather different perspectives and approaches.

Ultimately, the best approach may depend on the specific goals and constraints of the project, but a combination of mathematical modeling and experimental testing could provide the most comprehensive understanding of the problem. It is also important to constantly evaluate and refine the approach as new information and data is collected.