# Eddy Current brakes operating at high speeds

1. May 29, 2017

### jmhumphrey

Hi all,

I'm currently working on eddy current brakes designed to stop a vehicle from speeds around 135 m/s. While researching eddy current brakes, I found the equations used to find the force generated tend to break down at higher speeds. The design is linear, stopping on an aluminum rail roughly 10.4 mm thick with a gap distance of 5.08 mm. The equation we have been using is
$$F = \frac{v A B^2}{\frac{\rho}{t}}$$
where v=velocity, A=area of magnet, B=magnetic field, rho=resistivity of the rail, and t=thickness of the rail.
Electromagnets are generating the B-field, and the skin effect has already been taken into account in the calculations.
My question is this: At what speeds does the equation tend to break down? Why does it break down, and is there any way we can predict the actual forces experienced at extremely high speeds?

Any help is greatly appreciated. Thanks in advance!

2. May 30, 2017

### Baluncore

Welcome to PF.

How do the equations break down? Do you have data showing actual versus predicted deceleration?

I would expect braking to be less at higher speeds due to skin effect. I would expect ρ to be a function of velocity at higher speeds when skin depth was less than t. How have you allowed for skin effect in the calculations?

3. May 30, 2017

### jmhumphrey

I haven't had the opportunity to test the vehicle, and likely won't be able to for some time. I was basing my concerns off of the following study by W.R. Smythe.

https://www.princeton.edu/ssp/joseph-henry-project/eddy-currents/eddy_current_brake.pdf

In the study, he notes that the actual eddy current forces generated were lower than predicted at higher speeds. Figure 5 is the predicted data, and figure 6 is the actual data. He said this could be due to properties of the metals; in his words, "A comparison of Figure 5 with Figure 6 indicates that our formula gives too rapid a falling off in torque at high speeds. It should be pointed out that other conditions, such as the degree of saturation of the iron in the magnet will upset the assumed relation between magnetomotive force and Φ and may modify equations 38, 29, 30, and 31 considerably."
To be honest, I'm not certain the equations will break down in the design I'm using. Smythe was dealing with rotational brakes, not linear ones, and I believe he was dealing with permanent magnets, not electromagnets. Smythe's reasoning seemed to reference the permanent magnets as the source of the lower-than-expected forces. However, I've seen several other sources saying eddy current brake force decreases unexpectedly at higher speeds, so I just wanted to confirm this wouldn't be a problem.

Skin effect has been factored into the calculations. Braking is higher at higher speeds, but only because force depends on velocity directly and the skin effect does not cancel out the higher force from the higher velocity. Skin effect does decrease the force generated. It is a function of velocity; it's used to find the frequency of the magnets, which are then used to calculate skin effect.

4. Jun 9, 2017

### Baluncore

It is important to understand what really causes the skin effect. A good conductor is highly reflective because the counter-current induced by the magnetic field in the surface cancels almost all the incident field.

The surface current therefore diffuses into a good conductor at a very low velocity, something of the order of 100 m/s. If the source of B travels faster than that figure, the magnetic field will be reflected from only a very thin layer on the metal surface before it is left far behind by the travelling source of B.

See attached.

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5. Jun 9, 2017

### HowlerMonkey

I would think the super high speed maglev trains use some sort of eddy current braking.

6. Jun 9, 2017

### Baluncore

A train is less likely to outrun the eddy current braking because a train tends to be long.
Yes, maglev trains do use eddy current braking. The field diffusing into the rail generated by the front of the train will continue to build up while the train passes and so will be available at the tail.
On the other hand, a short vehicle is unable to use the full thickness of the rail because it has passed before the field can diffuse far into the rail.