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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

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# Stresses with thickwalled tube theory

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