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Predicting elastic and plastic wheel deformation

  1. Feb 10, 2009 #1
    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.
     
  2. jcsd
  3. Feb 11, 2009 #2

    minger

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    Science Advisor

    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
    [tex] 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} } [/tex]
    With the maximum pressure being
    [tex] p_{max} = \frac{2F}{\pi b l} [/tex]
    You can apply this to a cylinder in contact with a plane by making [tex]d_2 = \infty [/tex]

    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:
    [tex]\sigma_z = \frac{-p_{max}}{ \sqrt{1+ z^2/b^2}}[/tex]
    Perhaps you could integrate that from z = 0, to z = r to calculate the summation of strain?
     
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