Hand Ergometer

[Jonathan]

I had hoped to use a stepper motor with DC energised windings but some experiments by Jonathan showed that probably wasn't going to work either.

I think a DC motor could be made to work quite easily, particularly if it's separately excited. There are quite a few available second hand, the problem is people like using them to make (not very good) wind turbines, so the prices on eBay are inflated. Using eddy currents seems more elegant, but the DC motor does give the option of using the energy generated for something useful - e.g. powering laptop. From a quick google search it looks like we can expect about 30-60W from two arms.

The cage is mounted on bearings concentric to the axle the hand cranks act on and is allowed to rotate a limited amount as it reacts to the torque applied to the rotor. A load cell measures this torque (<£10 on eBay).

I recently needed some load cells for a project where I need to measure torque, so I got some of the cheapest 20kg 'hanging scales' on eBay and dismantled them. I've not actually made the circuit yet, but it looks like it wont be difficult to use the load cells they contain. That makes is <£4 for the load cell.

The rotation speed of the rotor, nominally 60rpm, is measured with a photosensor and speed, torque and magnet current is all fed to an Arduino computer which then calculates the actual load in watts being applied and displays on a small TFT colour display. It will also provide time info and control the magnet current to vary the gear/terrain for interval training

It looks like the radius of your disc at the center of the magnets is about 75mm, so at 60rpm that's 0.5m/s. You're going to need a high flux density in the aluminium disc to generate much force due to eddy currents at that low speed. It's annoying that there's not much information about the 500N electromagnets on eBay. I think we can work out the flux density at the pole face required to lift 50kg, estimate the reluctance of the magnetic circuit, then use that to work out the torque/speed characteristic. Another approach is I could model in FEMM, using the dimensions of the magnet and making an educated guess for the rest. Either way I suspect you might need either some sort of gearing between the handles and disc, a bigger disc, copper disc, or more electromagnets.

I've got plenty of permanent magnets you're welcome to which would probably be suitable, although it would mean changing the design somewhat since you'd have to move the mangets to control the torque.

[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)

[irving2008]

Been looking for plastic internal (annulus) gear rings, to create an epicyclic gear train, but can't find a UK supplier. Any ideas?

Alternatives are a timing belt to drive the rotor at, say, 5x crank speed so can use smaller lighter magnets but that adds equal complexity

[FatFreddie]

Been looking for plastic internal (annulus) gear rings, to create an epicyclic gear train, but can't find a UK supplier. Any ideas?

Is this something that could be 3D printed? Not sure what sort of strength / wear characteristics you'll need...

I'm happy to have a go if you want to try it - max size is about 200 x 200 by 100 mm deep though print time / warping might be a problem if using the full envelope. I've got plenty of PLA in - not tried ABS or nylon yet but willing to experiment.