Microstepping of Stepping Motors

 

Introduction

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.

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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:

Where:

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.

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A common solution is to arrange the torques applied by the two windings so that their sum h has a constant magnitude equal to the single-winding holding torque. This is referred to as sine-cosine microstepping:

-- 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:

Where:

-- 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.

Detent Effects

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.

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These teeth are almost always rectangular, and I am aware of no detailed study of the impact of different tooth profiles on the shapes of these curves.