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Stresses with thickwalled tube theory

  1. Feb 5, 2009 #1
    Hello


    A ring should be mounted on a solid shaft. The rings inner diameter is smaller than than the shaft diamater so it will be forced on.
    for my problem the inner diamater for the ring is 90mm -50 [tex]\mu[/tex]m
    the shaft is 90mm + 20[tex]\mu[/tex]m

    so there can be a difference of 110 [tex]\mu[/tex]m.
    This should give a certain stress after mounting the ring.

    That stress is what I need to calculate

    Im using thickwalled tube theory. plane strain.
    I have attached a figure to make it easier...

    If the radial stress in the ring starts with
    S_radial=A - B/r^2
    A, B are constants as we know.

    with BC:
    S_radial(r=OR)=0
    S_radial(r=IR)= -Pi

    so A=B/(OR^2)

    and at the inner radius the stress is equal to the inner pressure: -Pi
    So A=-Pi/(1/OR^2 -1/IR^2)/)

    So the radial stress for the ring is :
    SigmaRing=[-Pi/(1/OR^2 -1/IR^2)]/OR^2 + [Pi/(1/OR^2 -1/IR^2)]*1/r^2

    If I do equlibrium for the solid shaft:
    Witch BC:
    Sigmaradial(r=0)=0
    and Sigmaradial(r=IR)= -Pi

    The constants A=0 and B=Pi*(IR^2)
    So that stress is Sigmar=-Pi(IR^2)/r^2

    What should I do to introduce the radial missmatch of 110 micro meters?
    And after that how do I get the stress in the ring with my material data below ?

    E-modulus ring =540 GPa
    Poissons ring = 0.24
    E-modulus shaft=205 GPa
    Poissons shaft = 0.3


    Thanks for any help
     

    Attached Files:

    Last edited: Feb 5, 2009
  2. jcsd
  3. Feb 6, 2009 #2

    nvn

    User Avatar
    Science Advisor
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    ladil123: For an answer to this question, see my post in thread 289475.
     
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