## Stepper Motor Thermal Coefficient

You’ve probably seen this exchange on whatever DIY 3D printing forum you monitor:

1. My stepper motors get scorching hot, what should I do?
2. Turn down the current!
3. That worked great, but …
4. … now all my objects have a shift in the middle.
5. Your motor is losing steps: turn up the current!
6. Uh, right.

So, with that setup on the bench, I ran a simple experiment with current, temperature, and heat transfer. Most DIY 3D printers have stepper motors attached to a plywood chassis or plastic holder, so the first data point comes from a motor with no mechanical thermal path to the outside world (which is the Basement Laboratory at 14 °C ambient).

Running at about 1200 step/s with a winding current of 1 A peak from a 24 A supply, the motor stabilized at 52 °C = 125 °F after half an hour.

Both windings have a 2 Ω resistance and carry 1 A peak = 0.7 A rms, so the total power dissipation is:

`2 × [(1 A / √2)2 × 2 Ω] = 2 W`

That’s the same power produced with the motor stopped at a full step position, where the peak current flows in a single winding and the other winding carries zero current:

`(1 A)2 × 2 Ω = 2 W`

The temperature rise suggests a thermal coefficient of about 19 °C/W = (52 °C – 14 °C) / 2 W.

The next current setting on the driver is 1.46 A, which doubles the power dissipation to 4.3 W. Assuming a large number of linearities, that would cook the motor at 82 °C = 180 °F above ambient. Even though the motor could probably withstand that temperature, for what should be obvious reasons I didn’t go there.

Instead, I parked the motor atop a big CPU heatsink harvested from an obsolete PC, sans thermal compound, mechanical fitting, and anything more secure than gravity holding it in place:

The results:

 Ambient 14 °C Winding 2 ohm A pk A rms Power W Case °C °C/W amb °C/W incr 1.00 0.71 2.0 28 7.0 7.0 1.46 1.03 4.3 42 6.6 6.2 1.91 1.35 7.3 63 6.7 6.9

The thermal coefficients represent the combination of all interfaces from motor case to ambient, but the case and heatsink stabilized to about the same temperature, so the main limit (as always) will be heat transfer to ambient air. Obviously, the heatsink sits in the wrong orientation with little-to-no air flow, not to mention that the butt end of a stepper motor isn’t precisely machined and has plenty of air between the two surfaces. Improving all that would be in the nature of fine tuning and should substantially lower the coefficient.

What’s of interest: just perching the motor on a big chunk of aluminum dropped the case temperature 24 °C without no further effort.

Blowing air over the case (probably) won’t be nearly as effective. Epoxy-ing a liquid-cooled cold plate to the end cap would improve the situation beyond all reasonable bounds, plus confer extreme geek cred.

Hmmm, the Warehouse Wing does have some copper tubing…