I really wouldn't do this on your lathe @Janger. For that, a 3phase motor and VFD is best by a very wide margin. You will LOVE the end results with a smoother motor and smoother startup even at normal speed.
But I'd say go ahead and try it on your sander. Those centrifugal switches have significant hysteresis - the drop in speed is much lower than the drop out. Some basic experimentation will nail down what they are. In fact, you can even measure the start coil voltage so you don't have to depend on your ears. That said, your ears and your eyes can easily tell when it happens.
I'll resist a long detailed lesson on how the two motor types differ. @whydontu has said it well. Single phase motors try to do what 3ph motors do naturally by deliberately using a start winding with a phase shift induced by a capacitor to get the motor going. Basically turning 1 phase into 2 phase just to get it going. Then once it is going, a centrifugal switch kills the start winding and capacitor(s) so only one phase runs the motor.
It's not common, but some single phase motors have 2 capacitors. The centrifugal switch only kills one if them and the start winding is always energized through the other cap. I'd be remiss if I didn't say that there are even some single phase motors that have no switch and run full time on the start winding.
Back to single phase VFDs. Again, go ahead and try it on your sander. I'd always recommend 3ph over single but I also understand it might be more than you want to chew on right away even though it's really the easier path. Just be aware of the switch, find its set points and run your VFD accordingly. If the VFD has an over-ride start frequency, set it to 60 so your motor will always start at that frequency and then turn it down. Otherwise, it could try to start at a lower frequency than the drop out speed - ya, magic smoke is a bad thing. If it doesn't have that, you will have to remember to start at 60 not whatever it was set to last. This is a recipe for a problem the day you turn 65 - maybe sooner in your case!
In any event, I doubt you can get much range out of a single phase VFD. But maybe that's enough. Only you know what you need.
But I'd say go ahead and try it on your sander. Those centrifugal switches have significant hysteresis - the drop in speed is much lower than the drop out. Some basic experimentation will nail down what they are. In fact, you can even measure the start coil voltage so you don't have to depend on your ears. That said, your ears and your eyes can easily tell when it happens.
I'll resist a long detailed lesson on how the two motor types differ. @whydontu has said it well. Single phase motors try to do what 3ph motors do naturally by deliberately using a start winding with a phase shift induced by a capacitor to get the motor going. Basically turning 1 phase into 2 phase just to get it going. Then once it is going, a centrifugal switch kills the start winding and capacitor(s) so only one phase runs the motor.
It's not common, but some single phase motors have 2 capacitors. The centrifugal switch only kills one if them and the start winding is always energized through the other cap. I'd be remiss if I didn't say that there are even some single phase motors that have no switch and run full time on the start winding.
Back to single phase VFDs. Again, go ahead and try it on your sander. I'd always recommend 3ph over single but I also understand it might be more than you want to chew on right away even though it's really the easier path. Just be aware of the switch, find its set points and run your VFD accordingly. If the VFD has an over-ride start frequency, set it to 60 so your motor will always start at that frequency and then turn it down. Otherwise, it could try to start at a lower frequency than the drop out speed - ya, magic smoke is a bad thing. If it doesn't have that, you will have to remember to start at 60 not whatever it was set to last. This is a recipe for a problem the day you turn 65 - maybe sooner in your case!
In any event, I doubt you can get much range out of a single phase VFD. But maybe that's enough. Only you know what you need.