## Sizing a servo motor for a 4th (lathe) axis?

I have a small (~100kg / 220lb) 3 axis CNC machine that uses 60W servo motors, and want to add a 4th axis. From what I understand of the machine, it'll probably be easier for me to add another servo motor rather than a stepper.

Without going into lots of detail, the main focus of what I'd want to mill would be a 40cm (16") diameter (hollow) sphere, made from wood. A hollow sphere with a 40cm external diameter and 2cm wall thickness made from very dense wood should weigh around 9kg (20lb).

My machine's realistic cutting capacity is around 120ipm; which equates to about 5cm linear feed per second.

As a 40cm sphere has a maximum outside circumference of ~126cm, it would take about 25 seconds to cut this distance at 5cm per second. This means it'd need to be turned at approximately 2rpm.

Even a small object (5cm diameter; 16cm circumference) would need around 3 seconds to cut around the circumference; which is 20rpm. I.e. I don't need this axis to spin quickly for cutting duties.

Based on https://en.wikipedia.org/wiki/List_o...nts_of_inertia I calculate that my 9kg, 40cm sphere (with a 2cm wall thickness) would have a moment of inertia of approximately 0.212kg.m^2.

Given that torque = moment of inertia x acceleration; if I wanted to accelerate this sphere up to 2rpm (approx 12.6 radians per second) in 1 second I'd need:

0.212 x 12.6 = 2.7Nm

I have a 30W / 6000rpm DC motor that claims to provide 0.2Nm of torque (though I don't have a graph of rpm vs torque so I'm assuming it's not going to provide 0.2Nm of torque at 6000rpm)?

If I were able to reduce this motor by a ratio of 300:1, then ignoring efficiency losses I'd get a maximum of 20rpm, and 60Nm of torque (assuming 0.2Nm at 6000rpm).

Although the items I'm looking at milling will mostly be fairly evenly balanced around the axis, even if I had half of this 9kg ball as a point mass of 4.5kg (44 newtons) at 20cm from the axis, that would be a load of 44 x 0.2m = 9Nm.

Obviously I'm aware there are considerations on the forces of the cutting bit, and the desire for good acceleration for rapids, but are my workings above roughly on the right lines?

I.e. if I had a 30W 6000rpm motor, geared down at 300:1, does it seem reasonable that I'd be able to control and mill the outside of a 40cm diameter, 9kg, wooden sphere?