## Investigating Eddy Current Braking

##### Mark Fowler May 21, 2014

Have you ever wondered how a roller coaster or a train is brought to a stop? A braking effect produced by eddy currents is most likely the cause. Today, we’re going to discuss eddy current braking as well as investigate this phenomenon through an example model.

### Eddy Current Braking

*Eddy current braking* is an effect that occurs when an object’s motion slows down due to forces produced by eddy currents. Eddy currents are induced in a conductor due to time-varying magnetic fields or moving magnetic sources, such as magnets. The induced eddy currents, in turn, create a magnetic field that opposes the magnetic field of the source. The opposing magnetic field, produced by eddy currents, will eventually generate a braking force. When this happens in the eddy current brakes of a roller coaster or train, the vehicle is slowed down and eventually stops.

Here, we’ll explore this phenomenon through an alternative example of a magnet falling through a copper tube.

### Solving for the Magnet’s Terminal Velocity and Acceleration

In this model, a cylindrical magnet is dropped down a copper tube. During its fall, the magnet produces eddy currents on the tube walls. The magnetic field — generated by the eddy currents — opposes the magnetic field of the magnet, creating a braking force. This force gets stronger as the velocity of the magnet increases. At some point, the force of gravity equals the braking force produced, i.e., the magnet reaches terminal velocity.

The AC/DC Module contains a set of interfaces and features to help us solve for the magnet’s magnetic field, the magnetic field produced by the eddy currents, and the Lorentz force acting upon the magnet. With the software, we can solve for the dynamic equations of a falling magnet and calculate the magnet’s velocity and acceleration as it reaches terminal velocity.

This problem can be solved in a two-step process. First, we would need to solve for the vector potential field in and around the stationary magnet. Using the resulting solution as an initial condition, we can then perform a time-dependent study to solve for the falling magnet’s terminal velocity and acceleration.

### Results

Let’s have a look at the graphs after all of the necessary steps have been implemented.

Terminal velocity of the falling magnet versus time:

The falling magnet’s acceleration versus time:

We can see that the acceleration of the magnet decreases and becomes zero after 20 milliseconds, which agrees with the magnet’s constant velocity of 0.26 m/s after *t* = 20 ms.

Other factors can influence our results, like the thickness of the copper tube. What do you think happens if we use a copper tube that is twice as thick?

## Comments

Simone Angela WinklerMay 21, 2014 10:24 pmThis is nice – I am working on a related phenomenon in the frequency domain. Are the model files for this available for download?

Mark FowlerMay 23, 2014 9:58 amThanks for the question, Simone. You can download the model files for this example here: http://www.comsol.com/model/magnet-falling-through-copper-tube-13875 (also located in the “Further Reading” section, above). For this example, you will need to solve the Global ODEs and DAEs in the Time Dependent Study to solve for the dynamics. You can use the Frequency Domain Study to solve for the magnetic fields.

You will need to log into your COMSOL Access account to download the model files.