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Assuming you have a high quality printer with a fast processor, will you see a noticeable improvement by upgrading from 16X/32X microstepping drivers to 64X/128X microstepping drivers? (e.g. smoother surface finish). In what ways do they perform differently from the more common 16X or 32X stepper drivers. I'm thinking the RAPS128, Silencioso, and Trinamic drivers vs the DRV8825, A4988 and A4988.

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You will likely not see a noticeable improvement by upgrading from a 16x or 32x to a 64x or 128x microstepping driver. Depending on the motors you're driving and the size of the load you could actually see a decrease in quality.

Although microstepping increases theoretical resolution it does not necessarily increase accuracy. The reason is that microstepping significantly limits the incremental torque of the motor. This means that you may ask for a step but not get one because the torque of the step won't be enough to actually turn the shaft.

As an example: a motor running in full steps will have 100% of its rated holding torque. Moving to 16 microsteps/full steps drops this to ~10%, 128 drops it to ~1%.

The practical effect of this is that in high torque situations (such as printing at fast speeds) the motor may end up skipping some of the steps. In this way the increase in resolution can actually lead to a decrease in accuracy (smaller steps but they may not actually be taken).

A relevant calculation to do would be to work out what the different number of microsteps to full steps works out to in terms of horizontal, vertical, or whatever movement the motor drives. You can do this by measuring how far the stepper moves said surface in one revolution provided you know the number of steps it takes per revolution.

Example:

With no microstepping: 1 turn/inch * 200 steps/turn = 200 steps/inch or .005 inch/step (127 micron resolution)

With 16x microstepping: 16 * 200 steps/inch or .0003 inch / step (8 micron resolution)

In this example 128x microstepping would be absolutely foolish. Every situation is different and you should use this information to make a decision based on your setup. Many manufacturers have recommendations on how far their motors can be microstepped.

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    $\begingroup$ I think the sentence "As an example: a motor running in full steps will have 100% of its rated holding torque. Moving to 16 micro-steps/full steps drops this to ~10%, 128 drops it to ~1%." misses something important about stepper motors. A stepper motor torque-vs-position-error curve is like a sin curve. There is zero torque at zero displacement, and maximum torque at one full-step displacement. This doesn't change with micro-stepping. (cont) $\endgroup$
    – cmm
    Commented Dec 2, 2017 at 21:23
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    $\begingroup$ Thus, if you are taking 1/128th of a full step, it will truly give you very little torque. OTOH if you happen to stop, given a full step, at 1/128th of a step in error, you will also have a very small torque toward the correct position. $\endgroup$
    – cmm
    Commented Dec 2, 2017 at 21:23
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Prints benefit from higher microstepping in two ways:

Noise level

Using microstepping reduces noise from your printer's operation.

Print quality

Using higher resolution microstepping does not increase the physical accuracy of your prints meaningfully, but it can reduce surface artifacts such as moire.

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