I have quite a few tools, but I don’t yet have a lathe. In this case, I needed to mill grooves in the axles for my son’s Cub Scouts Pinewood Derby car.
There are plenty of pages out there that talk about using a hand drill to hold the axle and then polish it up, but to reduce friction even more ideally the wheel only makes contact at a few small points on the axle. Plus if you mill a groove, technically you have somewhere to store more graphite, which could possibly help improve lubrication over many runs (assuming it doesn’t just all fall out).
In my case, I was going for essentially one small point on the inner and outer edge of the wheel. This way the wheel shouldn’t wobble any more than when the entire axle is present.
Obviously a drill press would work better than a hand drill, since it is more stationary. For the cutting tools I had a set of jeweler’s files that work well for fine grinding like this. As for holding the tool I initially started by resting my hands on the drill press table and tried manually grinding down the area I wanted. I couldn’t get a very consistent result though, given occasionally the tool would get pulled more, causing it to graze the area where the wheel would make contact, ruining the smoothness of this area.
I then decided to make a tool holder of sorts by using a vise and a few blocks of wood (in this case oak) to hold the file in place. Then I could simply raise and lower the table to the correct height, then slide the vise along the table to grind the axle at the location I wanted without worrying about it running away from me.
It takes a bit of patience to adjust the table to the correct height, but with some practice I was able to finish the last axle in less than 10 minutes.
The head is also ground back with a triangle file to add a groove at the head as well as an angle to reduce the surface area touching the wheel. This I could do reliably enough by hand that I didn’t make another fixture for it.