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I know that stepper motors are usually driven with current-limiting chopper drivers and hence the applied voltage doesn't really matter (or does it?) and that's why specs of stepper motors don't state a max voltage but a max current instead.

However, I'd like to drive a Nema23 with a SparkFun Monster Moto Shield and an Arduino Uno.

This is the info I have about the motor Motor specs

How do I calculate the DC voltage I can apply to the VMOT of the motor driver shield without frying the motor?

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From the data sheet at Sparkfun for the motor shield, the absolute maximum voltage is 41 volts and the absolute maximum current is 30 amps. For normal operation, input voltage is 9-16 volts.

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    \$\begingroup\$ yeah the shield is not the problem. The question is what's the maximum voltage for the stepper motor \$\endgroup\$ – user1282931 May 20 at 22:20
  • \$\begingroup\$ @user1282931 The voltage for the stepper motor depends on your application. The higher the voltage, the more torque your motor will have, especially when moving at higher speeds. However, the higher your voltage, the more power your stepper driver will have to dissipate when the motor has reached steady state current (pretty much when your motor is sitting still, but still has power applied). The motor will be able to withstand any voltage that your motor driver can. \$\endgroup\$ – ambitiose_sed_ineptum May 20 at 22:35
  • \$\begingroup\$ "The motor will be able to withstand any voltage that your motor driver can" are you sure about this? \$\endgroup\$ – user1282931 May 20 at 22:39
  • \$\begingroup\$ Nema 23 is a motor size standard, you are going to need to pick one and look at the data sheet. \$\endgroup\$ – zeta-band May 20 at 23:01
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Within the ample insulation rating stated, motors would be damaged by current, not voltage. So within a reasonable range, voltage is just not an issue, so long as the chopping drive does not exceed the rated current.

As already pointed out, the motor drive you want to use does itself have a voltage limit, so you want to stay well within that. This is especially true if your mechanical system may ever backdrive the motor - some types of power supply will see the bus voltage rise under such conditions of regeneration, so it's best to stay well within the limit.

Realistically, you might shop for a 24v supply, though going higher could be reasonable. If your performance need is low even a 12v one may work. Your driver of interest is a bit overkill for a NEMA23 frame motor.

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There is one number which you need to get: the phase resistance of your windings.

Let's say, as an example, that your windings are 2 ohms each. Then, for a perfect bridge, you would want an 8 volt supply. 8 volts divided by 2 ohms is 4 amps.

Note that this will produce a motor with less torque than specified, especially at high step rates. When voltage is applied to an inductor, the relationship $$V = L \space di/dt $$ will hold, a low V means that the current in the winding cannot change quickly.

And, of course, your bridge will probably have some voltage drop, so you'll need to use slightly higher voltage to compensate.

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