Shrink fit (INTERFERENCE)mild steel parts

Thanks for all the replies and comments
I found this formula from another forum .
is this a valet quotation
δ = R×α×(T - To)
Where,
δ = change in radius
R = radius at room temperature
α = coefficient of thermal expansion (11x10-6)
T = elevated temperature
To= room temperature
If I use this, then the delta diameter is 0.165 mm
Note that you also want to leave a bit of room in the 'expanded' diameter so that the two "drop fit" together. If you were to make your difference exactly .165mm (~6.5 thou), you would need to 'press' the two together, which likely cause it to not work (since the shaft would be warming/outer diameter cooling).
 
You design for interference at room temperature. Heating the outer part and cooling the inner part converts that to a slip fit so you can install it easily.
You can also increase the interference above the level you could press fit at room temperature.

You are limited by yield in the bore; too much stress and it stretches permanently.

More interference = higher contact pressure = higher torque carrying capability.

Pinning after the shrink, or shrinking with a key can vastly increase the torque carrying. Note that a classic keyway will be a dig stress riser. A round key might be better for fatigue/press fit stress reasons.

There are specialist retaining compounds that can deliver quite large shear strengths on even a slip fit.

Grit in the interface on a shrink can add some non-frictional interaction. IE shear stress that isn't dependent on interface force.

Can I see a sketch of the planned part, and how its loaded? There may be some modifications to improve fatigue resistance that could help a shaper part...

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I machined the hole to 0 .135 mm undersize on a total diameter of 39.865 mm. I heated the workpiece to approximately 600 degrees C . This 600 degrees C was not attentional . The target temperature was actually 300 degrees C but newer less the workpiece dropped in the hole like a slippery banana . After cooling down the fit looks fine. The rest if the piece is to be machined and than final fitment
 
I machined the workpiece to 0.135 mm undersized. The final diameter is 39.865 mm. I heated the workpiece to 600 deg C . This 600 deg C was unintentional , The target temp was 300 deg C. as I do not have a thermometer, but newer less, it dropped in the hole like a wet banana. After cooling down the fit looks fine. Now the rest of the machine work is to be done than final fitment and see of the old beast can be reinstated.
 
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