This is part of my series of material that I edited out from my books prior to publishing. I usually cut whole sections like this when I realize they’re redundant or don’t fit well in the context. This is copy/pasted directly from my draft files with no additional editing, just for fun.
I’ve tried a lot of different ways to explain motor load angles and microsteps.
Consider again the motor trying to lift a heavy load. Each added microstep increases the torque, and we can directly predict that torque based on the number of microsteps traversed. Then, if the line to the load suddenly snaps, the rotor will rapidly spring towards the coil current angle as the built-up load angle torque accelerates the rotor. It will continue accelerating until the rotor catches up with the coil energization and reaches zero load angle at some speed.
- If we only advanced a few small microsteps before freeing the rotor, it will have little load angle, meaning little torque, and thus not accelerate very much. Speed when it reaches zero load angle will be low.
- If we advanced many microsteps (up to a full step) before unlocking the rotor, there will be a large amount of torque, and a rather violent initial acceleration. Speed when it reaches zero load angle will be high, and oscillation is likely.
It should be obvious that freeing the rotor after a small microstep will produce a gentler acceleration than freeing the rotor after a full step. Gentle is good. But we don’t operate 3D printers with locked rotors, so why is this important?
This case of the released rotor springing forward is similar to operation of a lightly-loaded stepper at low speeds, where the rotor has time to largely settle to a stop between steps. Coil currents change much faster than rotors can accelerate, so the load angle changes caused by the driver advancing the coil energization can be considered instantaneous at low running speeds. Thus:
- A stationary, fully-settled rotor that abruptly experiences a large change in the coil current angle (such as a full step) will violently accelerate towards the new position, overshoot, and oscillate before it settles.
- A stationary, fully-settled rotor that experiences a very small change in coil current angle (such as a small microstep) will have a very minor acceleration. This small disturbance can then be repeated many times in succession to produce the same total travel as the single large step.
[diagram showing coarseness of stairstep vs oscillation]
The conclusion here is that taking many small steps produces much smoother and gentler motion than a few large steps. Microstepping thus reduces the oscillations that lead to motor resonance, and decreases torque ripple and vibration through the drivetrain. As a consequence, microstepped steppers often provide more usable torque and smoother torque at low to intermediate speeds. Quarter stepping is better than half, and 1/8th stepping is better than quarter, and so on.