General equation for press/shrink fit stress?

In summary, the conversation discusses the presence of shear stresses in a shrink fit assembly, where a solid cylindrical shaft and a cylindrical hub are joined together by cooling and heating processes. The use of superposition is suggested to find the pressure causing the expansion and resulting in hoop stress in the assembly. The formula for calculating the hoop stress is also mentioned.
  • #1
cowpuppy
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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?
 
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  • #2
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
[tex]
\Delta R = \frac{qR^2}{Et}
[/tex]
The idea is then to find q that causes your interference R. Then your meridional stress is zero, while your hoop stress is
[tex]
\sigma_2 = \frac{qR}{t}
[/tex]

Good luck,
 

1. What is the general equation for press/shrink fit stress?

The general equation for press/shrink fit stress is: σ = (F * d) / (π * r^2 * t), where σ is the stress, F is the force applied, d is the interference or diameter difference between the outer and inner diameters, r is the radius of the smaller diameter, and t is the thickness of the part.

2. How is the general equation for press/shrink fit stress derived?

The general equation for press/shrink fit stress is derived from the principles of mechanics and the assumption that the contact pressure between the two mating parts is uniform. It takes into account the force applied, the difference in diameter, and the dimensions of the parts to calculate the stress at the interface.

3. What is the significance of the general equation for press/shrink fit stress in engineering?

The general equation for press/shrink fit stress is significant in engineering as it helps in determining the maximum stress that can be applied to a joint without causing failure. It is used in the design and analysis of press and shrink fit connections, which are commonly used in mechanical and structural assemblies.

4. Are there any limitations to the general equation for press/shrink fit stress?

Yes, the general equation for press/shrink fit stress has some limitations. It assumes a perfect fit between the two mating parts and does not take into account any variations in material properties or surface roughness. It also does not consider any external forces or thermal effects that may affect the stress at the interface.

5. How is the general equation for press/shrink fit stress applied in real-world applications?

The general equation for press/shrink fit stress is used in real-world applications by engineers and designers to determine the optimal dimensions and tolerances for press and shrink fit connections. It is also used to ensure that the applied force and dimensions of the parts do not exceed the maximum stress allowed for the material, thus ensuring the safety and reliability of the assembly.

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