The point of the design exercise is to accommodate different diameters in the machine's envelope, right?
We are not talking about a design exercise - at least I wasn't. We don't have that luxury as hobbiests. Usually we are talking about improving an existing machine or fixing a broken one.
If we are talking about design, I'd go for a nice wide gear spread, a machine rigid enough to handle anything I'd likely throw at it. Enough power and torque to do the job. And a VFD or variable speed motor to fill in the gaps.
For an existing machine, we have the gears we got, the rigidity we got, the motor we got, and the capacity we got. The only things usually missing is the speeds between gears and often the desire for a lower speed than factory.
Sometimes we have broken gears to contend with, sometimes we have a blown motor that needs replacing, and sometimes we don't have the available power in the building or at the poles. Too often, the motor is the wrong voltage which often means a new motor and VFD.
The new motor can be same size for a mill, but a lathe can use a bit more oomph to spin it up and compensate by reducing the accel rate.
You replied to Slow Poke's post with a fine point:
Imagine going from machining 1" to 5" diameter. You drop the speed to 1/5. Reasonable to expect and want the same removal rate (cubic inches per minute), right?
No. It's not reasonable to expect the same removal rate. I would fully expect to reduce the removal rate. We are not using giant lathes in a production environment where time is money. We are hobbiests. More often than not, we are not operating at maximum either, so there is a little wiggle room.
I guess that is really the crux of the matter.
In my opinion if the speed goes down so does my expected removal rate.
On the other hand, if I understand you, you expect to maintain "maximum" removal rate at lower speeds. In this case, I agree that a VFD will not always achieve your expectations.
But I don't share your expectations. In my view
@slow-poke was totally in-line when he said that:
Seems like a good quality 3P motor and VFD could have accomplished the same results and be MUCH MUCH simpler.
For example some Yaskawa VFD's can produce full torque at VERY slow speeds. 90% of the "electronics" on that panel would simply disappear.
Wanna debate expectations? Or maybe just drop this again for now and wait till next time it raises its ugly head?
Wouldn't it be better to have some words we could both agree on? I believe that's possible. We don't disagree on the physics, and we don't disagree on the math either. It's just that we seem to have fundamentally different views of the priority - constant torque vs constant hp. I might be wrong, but I think that's only because we have different expectations.