A steel hub with bore radius is shrink-fitted inside a steel sleeve with outer radius…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Hooke's law for an isotropic solid

Problem

A steel hub with bore radius a=20 mma = 20\,\mathrm{mm} is shrink-fitted inside a steel sleeve with outer radius c=80 mmc = 80\,\mathrm{mm}; the common (interface) radius before assembly is b=50 mmb = 50\,\mathrm{mm}, machined with a radial interference δ=0.050 mm\delta = 0.050\,\mathrm{mm} (the sleeve's unstretched inner radius is δ\delta smaller than the hub's unstretched outer radius). Both parts are the same steel, E=200 GPaE = 200\,\mathrm{GPa}, ν=0.30\nu = 0.30. Treat each part as a long cylinder held far from its ends (plane strain), so that after assembly the interface carries a uniform contact pressure pp, with the hub's bore and the sleeve's outer surface both free of stress (σrr=0\sigma_{rr}=0 there). ((a)) Find the contact pressure pp at the interface. ((b)) Find the hoop stress σθθ\sigma_{\theta\theta} at the bore of the hub produced by the shrink fit.

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