# General equation for press/shrink fit stress?

1. Sep 23, 2010

### cowpuppy

Shear stresses in shrink fit assembly?

I'm trying to figure out what shear stresses there would be from a shrink fit assembly, if any. You have a cylindrical solid shaft and a cylindrical hub, where the shaft diameter is greater than the hub's hole diameter. The shaft cooled and thus shrunk and the hub is heated and expanded so they will fit together, then allowed to come back to the original temperature.

Will either the shaft or cylindrical hub experience any shear stresses?

Last edited: Sep 23, 2010
2. Sep 24, 2010

### minger

Basically you can use superposition to find this. There is an interference, call it e. You can find the pressure which would cause that expansion e. The stress in the shaft from the interference will then be the stress caused from that pressure.

It should be all hoop stress if I'm not mistaken. Looked it up, from Roark, you have the radial displacement
$$\Delta R = \frac{qR^2}{Et}$$
The idea is then to find q that causes your interference R. Then your meridional stress is zero, while your hoop stress is
$$\sigma_2 = \frac{qR}{t}$$

Good luck,