Originally Posted by
m_c
A key thing to remember, is the motor is essentially a constant current device, as current = torque.
The problem is, as motor speed increases, the back EMF increases, meaning in order for the same current to flow through the motor, a higher voltage is required (the higher a motors inductance, the higher the voltage needed).
What the driver is attempting to do, is maintain the same current through the motor, regardless of speed.
So say you have a motor rated at 1A and 1V, while stationary, the driver will alter the output so 1A is flowing through the motor, which means the voltage across that winding will be 1V, regardless of the voltage being supplied to the motor.
However, as the motor starts to move, back EMF comes into play, so the drive then has to increase the voltage to maintain that 1A.
And this is where motor heating comes in to play. As motor speed increases, the more power it has to dissipate (stepper motors are pretty inefficient due to their cogging effect).
So using that example above, at idle it only has to dissipate 1W (1A x 1V) of power, however say you have a 50V supply, as speed increases to the point of reaching the maximum voltage, the motor is theoretically in constant current mode, up to the point it reaches maximum voltage, at which point it's having to dissipate 50W of power. Now once you pass that point, you enter constant power mode, as current will drop of as back EMF rises above the voltage, so the motor never has to dissipate more than 50W.
This is where selecting a supply voltage can be tricky. On something like a small mill running relatively slowly all day, you're not likely to have the motors running fast enough to get past the constant current stage to make use of a higher voltage, so even with the highest voltage possible, the motors are unlikely to see the full voltage.
However, on a router whirring around relatively fast, the power supply is going to be a limiting factor, but you're also likely to get past the constant current stage, and into the constant power stage. At that point it may sound like a good idea from a performance view, but it also means you're likely to be causing excessive motor heating. You can reduce current at this point to reduce heating, but then you lose torque throughout the speed range, so it's got to be a compromise.
It's worth noting Gecko's formula came from lots of experimentation, and is not an exact figure. It is however a very good ball park figure, and much more accurate than the multiple the motor voltage by a random figure formula.
Also, when I say dissipate power above, some will end up in kinetic energy (aka movement), while the rest will end up in heat (with a very minor amount making noise). As speed increases, the amount lost to heat increases, due to the inefficiencies caused by the cogging.
