I have not read this in full. But it seems to me that a simple calculation to study ratings of fuses and breakers is to use the Isquare R value.
SIMPLY:
Determine the current drawn when the motor stalls = 6.25AMPS.
Continuous CURRENT rating should be nearest (just over) 120% of that = 7.5Amps.
MAX. Current rating should be not exceeding 150% of the continuous current rating = 9.375A. (Perhaps break the rules and use a 10A fuse!) - So an 8A SLOW BLOW fuse should manage this.
But please be aware that fuses are simply resistors, with a thermal "inertia" - so take time to heat to failure point.
So the energy needed to blow a fuse is time dependant. For starting motors - or resisting stalling - or preventing stall currents from cooking the motor, you have to be aware of the time element.
Here's a graph of I versus Time.
View attachment 155128
I presume the motor will take maybe 5 or 10 seconds of stall without vaporising the internal insulation? (Burn-out).
But if you had a momentary stall on the lathe and quickly hit the stop button - say within 2 seconds - you would not want the motor to burn-out or fuse to blow?
That leaves you (say) between 3 and 10 seconds of "safe" use - but something that will blow before the Motor fries and lets all the smoke escape! - Then that can give you an "IsqR" value for the fuse.
This is what manufacturers of proper equipment do for "the layman" so he can but his drill, lathe, washing machine or TV and it "works OK".
But you are asking about doing all that yourself.
You can see from the graph that at RATED current, the fuse relating to the graph will virtually NEVER blow. But at 150% of rated current it will blow in something like 2 seconds. So following this logic, you want something that is rated a bit closer than 150% of rated current, maybe 130% of rated current? - which is close to the 8A rating for a fast blow fuse - like regular cheap fuses...
A slow-blow fuse is a different curve to a fast blow fuse - this graph is for industrial fast-blow fuses. You could try a 6A slow-blow, as this will probably manage your use as the motor isn't actually drawing rated current when cutting, (stop-start). But will blow in seconds (not minutes I reckon) on a stall. Just time for a quick button hit ?? - and if it blows it is cheaper and quicker to replace than the motor.
A 10A fuse "regular" (= fast-blow) - I reckon - will put the motor at a lot of risk as it will take the starting current for your motor if starting on full load. But if the motor fries in >10 seconds at less than 10A then the fuse won't give you the protection you need.
Hope this doesn't sound too confusing or technical?
Conclusion - try a 5A or 6A SLOW-BLOW. - to be safe.
K2