Don Labriola,
President QuickSilver Controls,
San Dimas, California

In a perfect motion system, motor turns a certain predetermined amount for every unit of electricity it is given. But if the load on the motor becomes too big, it doesn't matter how much power you try to feed it. Beyond a certain limit — maximum torque rating — motors can no longer turn. Motions become erratic, severely compromising accuracy. Why? Servo systems pick up on the resulting error right away, but open-loop systems don't. This is most troublesome when it appears in systems with stepping drive technology. Stepper systems are designed to provide position control without expensive feedback where precise motion is a requirement. Exceeding the available torque or other limits causes lost steps — failures to advance in position that go undetected.

To move the motor, currents to the stator phase windings are varied so as to produce a rotating magnetic field. The rotor attempts to align itself with the magnetic field, following the rotation and producing motion. The high pole count of most stepper motors — 100 poles for a common 1.8° stepper motor — requires 50 full electrical rotations of the phase currents for one rotor rotation. The phase currents are driven with a sine-cosine signal approximation; that is, one phase is driven with an approximation of a sine wave while the other is driven with an approximation of a cosine signal.

When full-stepping a motor, there are four full steps per electrical rotation. These may be located either at 0, 90, 180, and 270° in the case of wave stepping (when one phase is on) or at 45, 135, 225, and 315° with two-phases-on stepping. Half-stepping produces eight steps per electrical rotation — every 45° — while microstepping ranges from 16 steps per revolution to hundreds or even thousands of points on each electrical rotation. In fact, as we'll discuss further, this is the capability on which "hybrid stepper" solutions to lost steps are based. A hybrid stepper motor is actually a high pole count ac synchronous permanent-magnet motor that may be operated down to zero frequency.

Resonance problems

A motor produces torque only when its rotor is not aligned with the stator magnetic field. Torque varies in a roughly sinusoidal manner with this "error angle." Two things in a motor combine to effectively form a non-linear spring/mass rotary pendulum:

• The interaction between the stepper motor stator field and the rotor
• The rotor's moment of inertia.

Each step or fractional step applied to the motor windings shifts the equilibrium point of the pendulum, establishing a new error angle. The new error angle results in a new torque point, and the rotor — operating as a spring/mass rotary pendulum — attempts to follow. If the system is lightly damped (which is common) and the system is given enough time, the rotor overshoots the equilibrium point, ringing back and forth until it settles in. If the next step occurs when the system has sufficient speed while going in the opposite direction, then the peak instantaneous torque available may not be sufficient to keep the rotor within 6 180 electrical degrees. When this occurs, the system slips into the adjacent cycle of the error-torque sine wave. When this happens the stepper, in effect, has just lost four steps. If the rotor is not able to regain synchronization with the stator, many more steps may be lost.

A rotor's ringing as a rotary pendulum — associated with dips in torque available from an open-loop stepper — is commonly called low-frequency resonance. The motor, applied current, and load all affect this resonant frequency, resulting in low-frequency resonance usually around 50 to 150 rpm, corresponding roughly to 150 to 500 steps per sec.

Stepper correction

Microstepping reduces the amplitude of the torque variations between steps, which reduces the excitation of the pendulum resonance, and thus the likelihood that the error angle will get large enough to lose steps. (Note microstepping is most effective with motors that have been optimized for it. To illustrate, many stepper motors optimized for full stepping have a detent torque that aids full-step positions, but actually causes significant cogging when microstepping.)