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[HarryCole]

Hi! I’m working on a shrink-fit joint where a thin-walled 304 stainless sleeve is installed into a bored pocket in a much larger 4140 steel housing. The sleeve carries only light axial loads, but I want to size the interference so the hoop stress doesn’t crush or ovalise it. Most interference-fit guidance assumes shaft-and-hub geometry, which doesn’t translate well to a thin liner.
How do you estimate hoop stress for a thin sleeve-in-bore to pick a safe fit?

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[Noah Carter]

Compared to thick-walled situations, hoop stress is much more sensitive. A simplistic approach is to consider the casing as a thin-walled cylinder and the body as solid, then use the basic Lame equations for hoop stress:

σθ = pr/t

where p = radial interference pressure, r = mid-radius of the casing, t = wall thickness of the casing.

Interference determines p as follows: p = (δi/r) x (Es/(1−𝝂s2p); where δi = radial interference, Es = volumetric modulus of stainless steel, 𝝂s = Poisson’s ratio.

Axial stress is generally negligible for light loads, but the situation changes if you have long, thin casings with end constraints. The key point is high stress for thin wall = small interference. Prevent permanent ovalization by keeping hoop stress from 304 stainless (yielding about 205 MPa) ~0.4-0.5·σ_y lower.

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