Water Cooled Stepper Motors: Flow Calculation

A discussion on the Makergear Google Group about a heated enclosure prompted me to run the numbers for cooling stepper motors with water, rather than fans and finned heatsinks.

The general idea comes from my measurements of the air-cooled heatsink stuck to a stepper’s end cap. The metal-to-metal conductivity works surprisingly well and reduces the case temperature to slightly over ambient with decent airflow through the heatsink; epoxying a cold plate to the end cap should work just as well. A NEMA 17 stepper case is 42.3 mm square, so a standard 40 mm square CPU cooling plate will fit almost exactly.

The question then becomes: how much water flow do you need to keep the motors cool?

Some numbers:

• Water’s heat capacity is 4.2 J/g·K
• 1 J = 1 W·s, 1 W = 1 J/s
• NEMA 17 motors dissipate about 5 W (13 W if you’re abusing them)
• We’ll cool all four motors in parallel, for a total of 20 W
• Allow a 5 K = 5 °C temperature rise in each cold plate

Rub them all together:

(20 J/s) / (5 K * (4.2 J/g·K)) = 0.95 g/s

For water, 1 g = 1 cc, so the total flow is 1 cc/s = 3600 cc/h = 3.6 liter/h, which, here in the US, works out to a scant 1 gallon/hour. It’s tough getting a pump that small and cheap flowmeters run around 0.5 liter/m…

If you don’t want a pump. put an aquarium up on a (sturdy) shelf and drain it through the cold plates. A cubic foot of water, all eight gallons and sixty-some-odd pounds of it, will last 8 hours, which should be enough for most printing projects.

If you want reliability, drain the coolers into a sump with a float switch (high = on), put another float switch (high = off) on the aquarium, and have the pump top up the aquarium. If the pump fails, your steppers stay cool for the next 8 hours. Heating the water about 5 °C during 8 hours won’t require active cooling.

Now, managing the hoses leading to the X axis stepper may be challenging, but a cable drag chain would control the rest of the wiring, too.