Hoop stress is a lot more sensitive than in thick hub cases. A simple approach is to treat the sleeve as a thin-walled cylinder and the housing as rigid, then use the basic Lame’s equations for hoop stress:

σθ = pr/t

p = radial interference pressure, r = sleeve mean radius, t = sleeve wall thickness.

The interference sets p via: p = (δi/r) x (Es/(1−𝝂s2p); with δi = radial interference, Es​ – stainless steel bulk modulus, 𝝂s​ = stainless Poisson’s ratio.

Axial stress is usually negligible for light loading, unless you have long, thin sleeves with end constraints. The key is that thin wall = high stress for small interference. Keep hoop stress < ~0.4–0.5·σ_y of 304 stainless (about 205 MPa yield) to avoid permanent ovalisation.