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.
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.
As seen in my draft plastic assembly, the required alignment between the rotor and stator in the gearbox is relatively tight. The difference in diameter between the inner race of the rotor and the outer surface of the stator is only about 0.2mm, which gives 0.1mm of clearance in normal operating conditions. A plastic drive train was never terribly likely to succeed. My next steps have been to machine the pieces of the gearbox critical to alignment out of aluminum, so as to ensure that the rotor and stator, (and also the gears) are held within some approximation of appropriate tolerances. The path of joints between the rotor and stator looks roughly like this:
The rotor attaches to the sun gear holder. The sun gear fits inside the holder, the shaft fits inside it. The shaft then fits into a bearing (unpictured above) that is inside the planet output. The planet output is then fit inside the output bearing, which fits into the front housing. The stator rests on the front housing. The rest of the components are necessary to transmit torque to the planet gears, or mount the overall motor, but I currently believe they shouldn’t be critical to maintaining rotor and stator alignment.
To verify that this would indeed work, I’ve sent off to have the sun gear holder, the planet output, and the front housing to be machined in 6061 Aluminum. I ended up using Xometry, which just farms the CNC jobs out to shops across the country. This was my first time using them, or having any parts CNC’d for that matter, so I was a little paranoid about getting appropriate drawings in place and trying to get all the tolerances into a suitable state.
In this drive train, there are several joints between parts that matter from a tolerance perspective. The sun gear fitting into the sun gear holder, the shaft bearing that sits in the planet output, the output bearing surface on the planet output, the bearing surface on the front housing, and the stator surface on the front housing. Ideally, each of these would form a relatively rigid connection under load. Thus I wanted to have something close to an interference fit.
The first part I made was the sun gear holder, and its primary interface is with the sun gear. The sun gear has an 8mm diameter, and my micrometer measured one sample at 7.998mm. Looking at Machinery’s handbook 30th edition, there is this chart showing standard tolerances for metric fits.
Then, for an 8mm shaft, the tables list:
However, using the quick turn Xometry feature only allows one to specify tolerances in the tightest as +- 0.001″, or +-0.025mm. +- 0.025mm is more than the entire range between the lowest size medium drive hole and the largest locational clearance hole. I also wasn’t exactly sure how rigid things needed to be, and didn’t want to mess with shrink fits or further post-machining operations, so did my initial drawings erring on the side of having too much clearance. I figured I could always use some retaining compound if need be. Thus I specified +0.04 -0.01 for that particular interface.
1 week after submitting CAD and drawings the sun gear holders arrived in the mail!
I also was surprised to receive an inspection report! Xometry claimed that I needed to pay extra to get one, so receiving it was a pleasant surprise. Reading the report, the measurement on the bore was claimed to be 7.99 or 8.00 for all 20 parts. So, I broke out my telescoping gauge and micrometer to measure that critical shaft interface myself to double check.
Lo and behold, smaller than I had specified, and right at the bottom end of a medium drive fit. Sure enough, the sun gear felt like it was going to take a significant amount of force to install. I went through and measured the dimensions on the first 10 parts using the same technique, for each part measuring at 4 different radial angles.
Overall, that is a relatively narrow spread, just +-0.015mm, however it is centered out of the tolerance band I had specified. Granted, I may not have yet mastered my telescoping gauge measuring technique, however, the impossible to manually press in gear seems to validate my results.
Next up, trying to assemble the sun gear into the holder anyways.