Confirming PSU spec for steppers.

[Jonathan]

Looks like you're after an explanation of why, not what...

I would consider the voltage you get from the common formulas (20*V, 32*L^0.5 etc) to be a 'recommended minimum'. You will get better torque at high speed if you use 70-75V, plus seems a waste to get PM752 drivers if you're only going to run them on 42V.

A linear power supply handles current surges better than a switch mode power supply (smps), which means you can safely use a lower rated current than the smps. A 500VA transformer is fine for 3 motors, probably 4 and that's only 500/70=7.1A.

The current in a 2-phase stepper motor on a microstepping driver is, at intermediate speed, approximately sinosoidal and out of phase by 90°. This means that the maximum current is the maximum of I*(sin(thing)+cos(thing)), which is I*2^0.5 where I is the current in one phase - so 2.1*1.414=2.97A. This is 70.7% of 4.2A. Similarly if you work out the rms current for both phases (just integrate the previous formula squared etc), it is 2.1A - hence 50%. I'm guessing this is where your 50%-70% approximation comes from.