Fehlmann Picomax 50 CNC conversion/refurb

[Agathon]

For induction motors, torque remains pretty constant over the rated speed range up to the rated speed, and is a result of the amount of current flowing through the windings. Although frequency controls the speed, as speed drops, the voltage required to drive that current through the windings also drops proportionally I.e. for a 3000rpm 240V motor, peak voltage will be around 120V when running at half speed.
Now because voltage is reduced, so is the power output, so if the above motor was rated at 1KW, at 1500RPM it would only be producing 500W. You could increase current (which some inverters can do to give a low speed torque boost), however you risk overheating the windings due to the extra current.

Above the rated speed/power, current becomes limited. So taking the above example motor, and trying to double it's speed to 6000RPM, you can do so by doubling the frequency, however unless you double the supply voltage, 240V will only be able to force half the current needed to get full torque through the windings, with the result you will only get half the rated torque.
The result is above the rating, the motor becomes power limited. You can have double the speed, but only half the torque, so even though the motor is spinning faster, you still only have 1KW of power.

This is why when fixed speed motors with gearing get replaced, they're often replaced with far bigger motors.
With gearing, say you take a 2Nm 3000RPM (probably about 600W), you gear it down 4:1 and get 8Nm at 750RPM.
To get that same torque at the same speed using direct drive, and still retain 3000RPM, you now need a motor capable of 8Nm and 3000RPM, so you need a motor with 4 times the power. (realistically you'd compromise with some gearing, a bit less torque, and running the motor so higher speeds are above the motor rated speed and into the derated/reduced current area).
That's the reason why most modern CNC machines come with such big spindles. For most end users, it not because they're going to be managing to use upwards of 10KW hogging metal with endmills, it's so they still have enough torque to drive a big facemill at a couple hundred RPM while still taking a decent depth of cut.

Very nicely and clearly explained. I was aware of the frequency voltage relationship, but hadn't really twigged the issue of running higher than the name-plate frequency and the consequent lack of volts. As the video shows, I don't really think that torque is going to be so much of an issue as far as the spindle goes, so I'm fairly hopeful about my plan to use the higher mechanical speed setting most of the time. We shall see.

Having looked into Brains more I understand your previous post and think that it all looks doable even for a novice like myself.