Magnetic Resistance Exercise Bike Theory Question

[JustRob]

I am an electrical engineer disabled in a snow sking accident and am now a quadriplegic. I'd like to design an exercise arm bike and make it magnetically resisted because friction resisted is not conducive to minute changes in resistance.

I have a magnetic resisted trainer for a road bicycle where you take the front wheel off of a road bike, fasten the forks in the trainer frame and the back tire sets on a roller. At one end of this roller is a small aluminum disk roughly 1/8" thick and 4" in diameter and attached to the spinning roller. On one side of the spinning disk is a disk the same diameter with six 3/4" diameter magnets (appear to be ceramic) arranged around the perimeter of the 4" disk evenly spaced (as if every 10 minutes around a clock). This disk is fixed and cannot move.

On the other side of the spinning aluminum disk is an identical magnet disk with magnets configured the same way but allowed to rotate 30 degrees. The strength of the magnetic field is varied by rotating one magnet disk causing the magnets to more eclipse the corresponding magnet on the other side of the spinning aluminum disk.

I can't find good information explaining the theory behind this. I have read all of the wiki pages on eddy current brakes. I'd like to see an equation that would explain what is going on. I got 1" neodymium magnets and positioned them around a 5" disk with a 1/8" thick disk between but the resistance is minute. I suspect it is because the rotational velocity is no where near as fast as the road bike trainer. I have also been told that the thickness of the spinning disk between is too thin.

Any help or direction is GREATLY appreciated!

Thanks

 

[mfb]

Eddy currents require a variable magnetic field - I don't know the relative orientation of your magnets, but one setting will have a very inhomogeneous magnetic field, and the other configuration will have a more uniform field.

I suspect it is because the rotational velocity is no where near as fast as the road bike trainer.

Probably. Alternative explanations would be a bad placement of the magnets (field too uniform), or weak magnets.

I have also been told that the thickness of the spinning disk between is too thin.

I would try to get a thickness similar to the size of the magnets, but that might depend on details of the implementation.

 

[JustRob]

I ultimately would like to use either one or two electromagnets. With that said and the knowledge that it is a changing magnetic field let me ask you this.

If I change the configuration so that on one side of the aluminum wheel I'm spinning is an electromagnet facing the wheel with a 1/16" airgap and mounted toward the outer perimeter of the spinning wheel and opposing it on the other side of the spinning wheel an identical electromagnet mounted with the same air gap.

The electromagnet on one side would be powered so that the center is north pole and the intensity be sinusoidal from minimum to maximum magnetic field.

The opposing electromagnet would have a steady state south pole field where the intensity would vary the strength of the resistance.

Do you forsee that working?

 

[mfb]

Why do you want to vary both?
The setup will give a deceleration, which depends on the currents in the electromagnets, sure.

 

[JustRob]

The electromagnet set up with the sinusoidal variation would provide the varying magnetic field to induce the eddy current and braking action. The steady state magnetic field I thought I'd use the magnitude to provide more or less resistance.

I guess what I'd could do is have one electromagnet set to constant full power with maximum magnetic field and simply vary the magnitude of the dc sine wave powering the opposing electromagnet.

By deceleration do you mean it will creating a resistance to someone spinning the shaft which would be attached to the spinning aluminum disc between the electromagnets?

 

[mfb]

No, not that. You need a spatial variation, this automatically translates to a time-dependent variation for the rotating disk.

By deceleration do you mean it will creating a resistance to someone spinning the shaft which would be attached to the spinning aluminum disc between the electromagnets?

Right

 

[JustRob]

No, not that. You need a spatial variation, this automatically translates to a time-dependent variation for the rotating disk.Right

Sorry but I'm confused. No, not what? By spatial variation do you mean a distance from the spinning disc variation? If so doesn't a sinusoidal magnetic field strength simulate that? If it is more like having magnets pass by each other would just cycling power on and off to one electromagnet work?

The setup will give a deceleration, which depends on the currents in the electromagnets, sure.

Again confused, do you feel this will work to resist someone pedalling the handles?

 

[mfb]

No, not what?

No, not what you posted.

Here is an image:

A permanent magnetic field with a rotating disk. All the time, parts of the disk enter the magnetic field, and other parts leave it, leading to a time-dependent field for those regions, and therefore a braking force.

do you feel this will work to resist someone pedalling the handles?

I think that is the whole point of the device?

 

[JustRob]

Just to be crystal clear:

That spinning disc is just all aluminum?

I appreciate all the help. Would a crude equation describing the resistance be:

F = ω * β * A

where;
F: force resisting the disc
ω: rotational velocity of the disk
β: magnetic field strength
A: magnetic field area

And again, I realize it is very crude.

 

[mfb]

Anything conducting will work, aluminium is conducting.

This equation cannot be right, as you can check via the units. In addition, it does not include the conductivity of aluminium.
Playing with the units, $\frac{1}{s^2} T^2 m^6 \sigma \mu_0$ with a conductivity $\sigma$ has the units of a force, but I am not sure how to construct the length to the 6th power and if that has anything to do with the force.

 

[Newsome]

I have a magnetic resisted indoor trainer for a road bicycle where you take the front wheel off of a road bike, fasten the front forks in the trainer ... I can't find good information explaining the theory behind this.

 

[mp3car]

Not sure this adds a whole lot, but perhaps it will add something... My elliptical machine uses a magnetic resistance setup, it's pretty simple. When you "pedal" the elliptical, it spins an iron flywheel, and there is a semi-circular (maybe about 6" long) permanent magnet that is positioned so that it's parallel lengthwise to the direction of rotation (picture placing a slightly curved hand close to a bicycle wheel, with your hand parallel to the bike frame (almost like your drinking water from your hand). There is a small motor that changes the distance between the magnet and the iron flywheel to change the resistance... a very simple design...

 

[Sprintman]

i know this is years later, but simply attaching magnets to the frame so the allow rim passes the magnets will create the eddy force resistance. I do the same thing on my rollers. 3 rare Earth magnets mounted about 2 mm from the aluminum rollers provides all the resistance I need. The faster I pedal, the more resistance. I have PowerTap pedals on order so I can measure the difference between magnets on vs magnets removed. WOrks great and I don't have to mount my bike on any trainer, I just hop on the rollers and go. Next I'll replace the permanent magnets with an electromagnet on a resistance control (rheostat or whatever to vary the DC power to the EM). V 3 would be an arduino controller and raspberry pi app to control the power to the EM. v4 would then be to connect it to Zwift. OR, I can leave it as is with my $8 magnets and rollers I got for free. Lots of YouTubes out there for people that did the same thing

 

[Sprintman]

Alloy rim I meant. . typing too fast with my formerly fat fingers. There is actually a trainer that has this setup (permanent magnets on the frame where the alloy rim passes). but same old same old. . you got to connect your bike to the trainer. I'd rather just ride outdoors or if its raining dogs and cats like today, just throw the bike on the rollers and WALLA, instant sweat to bug the wife. I thought about sneaking some magnets to a race and attaching them to one of my competitors frames right where the wheel passes - of course that was years ago before carbon frames.

 

[berkeman]

Welcome to PF, @Sprintman -- avid MTB'er here.