Hand Ergometer

[irving2008]

Hi Jonathan

I was half expecting you to investigate further :)

The radius is 90mm and there are 4 magnets. Fully energised they each generate 1.6 Tesla (core saturated magnetically) at the pole which is 20mm dia. I don't have the B-H curve (as you found, no data sheets online, but then this isn't their intended use) but I'm hoping to be able to calibrate it. The air gap to the rotor is 1mm. I kept it this size as think getting it smaller will require too much precision in mountings.

Now for some calcs....

torque = sigma * omega * B ^ 2 * p ^ 2 * a * d
sigma=rotor conductivity
omega=speed rads/sec
B = mag field Tesla
p = effective radius
a = pole area
d = disc thickness

sigma Al 6061 = 3.5e7
omega =6.3 rad/sec (60rpm)
p = .09m (200mm dia rotor, 20mm mag)
a = 0.01m^2*pi = 3.1416e-4
d=0.005m

using an online calculator whose URL I cant find right now the 4 magnets @ 1.6T generate a total of 1.36T yoked in a 7mm air gap. Therefore

max torque = sigma * omega * B ^ 2 * p ^ 2 * a * d
= 3.5e7 * 6.3 * 1.36^2 * .09^2 * 3.1416e-4 * .005
= 5.2Nm

Power= torque * omega = 5.2 * 6.3 = 32.8W

So will need to increase # of magnets to 8 x 40kg, or go to 40mm dia pole or increase rotor dia to 300mm to get to 60W. Also could consider some sort of epicyclic gear to rotate rotor faster e.g. 3 or 4 times but maintain it concentric to axle to minimise footprint.

edit: 27mm dia pole (70kg magnet) and 250mm rotor gives 91W

I did look at permanent magnets but the mechanical complexity of moving them and still measuring torque accurately got very messy (mechanical sizes were based on 3 pairs of 20mm x 10mm Neo magnets, I'd not recalculated based on electromagnets, my bad)