I also had a chance to do these tests with Ferrofluid quantity fill vs. RPM in small diameter skateboard hub motor wheels. We get asked all the time how Statorade will work in RC style motors spinning at high RPM's, and so I've wanted to actually characterize rather than just extrapolate. Direct drive skateboard motors in particular are prone to overheating issues and have a lot of merit for testing.

We had someone drop off an Inboard electric skateboard with damaged controller that provided a good candidate motor for these experiments. I put tape over the 3 vent holes that are normally on the outside of the hub.

The motors were run from up to 2500 rpm with wind speed going from 0-40 kph.

With 1mL, the effect of Statorade peaks clearly at around 500 rpm. With 2mL, it peaks at more like 800 rpm. And with 3mL it seems to plateau a little around 1250 rpm.

What interested me most was to see how these results compare with larger diameter motors. In theory, the centripetal accelleration on the fluid is

acc = (2 * Pi * RPM / 60)^2 * r

So doubling the RPM would result in four times the force away from the stator core, while doubling the radius of the motor at the same RPM should double the force. If we have a motor with twice the radius, we should expect the max RPM we can spin it at for the same force on the Statoarde to decrease by 1/Sqrt(2).

If we look at my previous post on the Cromotor, that has an air gap diameter of about 200 mm. The acceleration on the FF is

10.9 m/s^2 at 100 rpm (just over 1g)

43.8 m/s^2 at 200 rpm (almost 4.5g) and

98.7 m/s^2 at 300 rpm (exactly 10g)

At 300 rpm in that motor we're dealing with 10g forces on the fluid, no surprise that small volumes would flatten out and a larger fill was needed. When you spin the motor at 400 rpm the force is ~18g, and at 500 rpm the G forces at the magnets reach 28g. I've done lots of tests of standard DD hub motors at 400 rpm in the wind tunnel and with sufficient QTY Statorade definitely still works well, so forces up to 20g appear fine.

On this skateboard wheel, the air gap diameter is more like 45mm. For this we have

500 rpm = 6.3g

800 rpm = 16g

1250 rpm = 39g

On a skateboard wheel, 1250 rpm is about 20 kph / 12 mph. Not super fast, but not a useless speed either and well in the ballpark of what these hubs would be doing up a hill climb.

Going in the other sense to bigger hubs, I also tested the large diameter BionX D motor, see

https://endless-sphere.com/forums/viewtopic.php?p=1361795#p1361795

On that one, the 300 rpm test corresponds to a force of 16g on the motor.

Anyways I'm hoping that by collecting more info like this over a range of wheel diameters and rpm's, we can also come up with some good rule of thumb guidelines for Statorade fill levels based on some simple equations given

a) diameter of the motor

b) width of the stator

c) the motor RPM.

And also have a reasonable max RPM number where modest amounts of FF cease to have much of an effect as the acceleration is just too high. For instance, an 80mm outrunner motor spinning 4000 rpm? G force at the magnets is over 700g, and for sure that's way too much for FF to bridge the gap.