Microstepping of Stepping Motors
Microstepping serves two purposes. First, it allows a stepping motor to stop and hold a position between the full or half-step positions, second, it largely eliminates the jerky character of low speed stepping motor operation and the noise at intermediate speeds, and third, it reduces problems with resonance.
Although some microstepping controllers offer hundreds of intermediate positions between steps, it is worth noting that microstepping does not generally offer great precision, both because of linearity problems and because of the effects of static friction.
Sine Cosine Microstepping
Recall, from the discussion in Part 2 of this tutorial, on Stepping Motor Physics, that for an ideal two-winding variable reluctance or permanent magnet motor the torque versus shaft angle curve is determined by the following formulas:
a -- torque applied by winding with equilibrium at angle 0.
b -- torque applied by winding with equilibrium at angle S.
h -- holding torque of composite.
x -- equilibrium position.
S -- step angle.
This formula is quite general, but it offers little in the way of guidance for how to select appropriate values of the current through the two windings of the motor.
-- single-winding holding torque
((π / 2) / S)θ -- the electrical shaft angle
Given that none of the magnetic circuits are saturated, the torque and the current are linearly related. As a result, to hold the motor rotor to angle θ, we set the currents through the two windings as:
-- current through winding with equilibrium at angle 0.
-- current through winding with equilibrium at angle S.
-- maximum allowed current through any motor winding.
Keep in mind that these formulas apply to two-winding permanent magnet or hybrid stepping motors. Three pole or five pole motors have more complex behavior, and the magnetic fields in variable reluctance motors don't add following the simple rules that apply to the other motor types.
Limits of Microstepping
The utility of microstepping is limited by at least three consideraitons. First, if there is any static friction in the system, the angular precision achievable with microstepping will be limited. This effect was discussed in more detail in the discussion in Part 2 of this tutorial, on Stepping Motor Physics, in the discussion of friction and the dead zone.
The second problem involves the non-sinusoidal character of the torque versus shaft-angle curves on real motors. Sometimes, this is attributed to the detent torque on permanent magnet and hybrid motors, but in fact, both detent torque and the shape of the torque versus angle curves are products of poorly understood aspects of motor geometry, specifically, the shapes of the teeth on the rotor and stator.