Sun gear holder shrink fit

As discussed last time, the sun gear holders I had CNC machined unintentionally had a slightly undersized bore that the sun gear was going to fit into.  The allowance was large enough, that there was no way I was going to press it into place as is.  So, I decided to try a shrink fit, but before I did I wanted to do some math to verify that it was possible with the temperatures I could easily achieve and that I wasn’t going to explode (or even just fracture) the aluminum part from over-stressing it.

All the math

Referring again to the Machinery’s Handbook, it has a formula for a steel shaft / cast iron hub, and also for a steel shaft and hub, but nothing for a steel shaft and aluminum hub.  I’ll just do a minimal derivation with some simplifying assumptions here to see how close it is.

First, I’ll assume a solid block of aluminum hub, and a solid shaft.  In actuality, the hub is only 15mm external diameter, and the shaft (sun gear), is hollow with a 4mm internal diameter.  Next, 6061 aluminum has a yield strength of 386MPa, I’ll aim for 200MPa maximum.  The modulus of elasticity is 68.9GPa.  That works out to 200MPa / 68.9GPa = 0.0029 mm of shrink per mm of diameter.  Thus for an 8mm diameter shaft, I could have a maximum shrink of 0.023mm.  My shaft is 7.998mm, which means that the holes should be no smaller than 7.975mm.  I have some parts that big, but maybe only half of them.  However, given that my simplifying assumptions were conservative, I’m probably in the right ballpark for all of them.

Giving it a try

I don’t have any dry ice on hand, but I do have compressed air canisters and a heat gun.  So I pre-cooled the sun gear in the freezer.  Then I heated up the sun gear holder with my heat gun set to maybe 260C.  Next, I turned the compressed air canister upside down and performed a final cooling pass on the sun gear holder.  After that I — very quickly — set the holder and gear on my press and forced them down together.

They fit!

Granted, there is probably no way I am ever taking them apart now, but I guess I don’t have a pressing need to try.