source: this website
A step motor is a constant output power transducer, where power is defined as torque multiplied by speed. This means motor torque is the inverse of motor speed. An interesting aspect of a step motor is that its power is independent of speed.
In general terms, torque is proportional to ampere-turns (current * the number of turns of wire in the winding). Since current is the inverse of speed, torque also has to be the inverse of speed. In an ideal step motor, as speed approaches zero, its torque would approach infinity while at infinite speed torque would be zero. Because current is proportional to torque, motor current would be infinite at zero as well. Electrically, a real motor differs from an ideal one primarily by having a non-zero winding resistance. Also, the iron in the motor is subject to magnetic saturation, as well as having eddy current and hysteresis losses. Magnetic saturation sets a limit on current to torque proportionally while eddy current and hysteresis (iron losses) along with winding resistance (copper losses) cause motor heating.
The first figure here shows an ideal motor’s natural speed-torque curve. Below a certain speed, called the corner speed, current would rise above the motor’s rated current, ultimately to destructive levels as the motor’s speed is reduced further. To prevent this, the drive must be set to limit the motor current to its rated value. Because torque is proportional to current, motor torque is constant from zero speed to the corner speed. Above the corner speed, motor current is limited by the motor’s inductive reactance. The result is a two-part speed-torque curve which features constant torque from zero speed until it intersects the motor’s natural load line, called the corner speed, beyond which the motor is in the constant power region.
A real step motor has losses that modify the ideal speed-torque curve, as shown in the second figure here. The most important effect is the contribution of detent torque. Detent torque is usually specified in the motor datasheet. It is always a loss when the motor is turning and the power consumed to overcome it is proportional to speed. In other words, the faster the motor turns the greater the detent torque contributes power loss at the motor’s output shaft. This power loss is proportional to speed and must be subtracted from the ideal, flat output power curve past the corner speed. Notice how the power output decreases with speed because of the constant-torque loss due to detent torque and other losses. The same effect causes a slight decrease in torque with speed in the constant torque region as well. Finally, there is a rounding of the torque curve at the corner speed because the drive gradually transitions from being a current source to being a voltage source.
Finally, the motor power output (speed * torque) is determined by the power supply voltage and the motor’s inductance. The motor’s output power is proportional to the power supply voltage divided by the square root of the motor inductance. As illustrated in the third figure here, if one changes the power supply voltage, then a new family of speed-torque curves results. As an example, if the power supply voltage is doubled then the curve has twice the torque at any given speed in the constant torque region. Since power equals torque times speed, the motor now generates twice as much power as well.
andreacollo 