ABOUT EDDY CURRENT

MAKING OF EDDY CURRENTS

What if the conductor you're moving through the magnetic field isn't a wire that allows the electricity to flow flow neatly away? You still get electric currents, but instead of flowing off somewhere, they swirl about inside the material. These are what we call eddy currents. They're electric currents generated inside a conductor by a magnetic field that can't flow away so they swirl around instead, dissipating their energy as heat. One of the interesting things about eddy currents is that they're not completely random: they flow in a particular way to try to stop whatever it is that causes them. This is an example of another bit of electromagnetism called Lenz's law (it follows on from another law called the conservation of energy).

Here's an example. Suppose we drop a coinshaped magnet down the inside of a plastic pipe. It might should take a half second to get to the bottom. Now repeat the same experiment with a copper pipe and we'll find our magnet takes much longer (may be three or four seconds) to make exactly the same journey. Reason for it is eddy current. When the magnet falls through the pipe, you have a magnetic field moving through a stationary conductor (which is exactly the same as a conductor moving through a stationary magnetic field). That creates electric currents in the conductor – eddy currents, in fact. Now we know from the laws of electromagnetism that when a current flows in a conductor, it produces a magnetic field. So the eddy currents generate their own magnetic field. Lenz's law tells us that this magnetic field will tryto oppose its cause, which is the falling magnet. So the eddy currents and the second magnetic field produce an upward force on the magnet that tries to stop it from falling. That is why it falls more slowly. In other words, the eddy current produce a braking effect on the falling magnet. It’s because eddy currents always oppose whatever causes them as brakes in vehicles, engines, and other machines.

EDDY CURRENT BRAKE WORKING

Suppose we have a railroad train that is actually a huge solid block of copper mounted on wheels. Let’s say it is hurtling along at high speed and we want to stop it. We could apply friction brakes to the wheels or we could stop it with eddy currents. For eddy current braking we put a giant magnet next to the track so the train had to pass nearby. As the copper approached the magnet, eddy currents would be generated (or ”induced”) inside the copper, which would produce their own magnetic field. Eddy currents in different parts of the copper would try to work in different ways. As the front part of the train approached the magnet, eddy currents in that bit of the copper would try to generate a repulsive magnetic field (to slow down the copper’s approach to the magnet). As the front part passed by, slowing down the currents there would reverse, generating an attractive magnetic field that tried to pull the train back a gain (again, slowing it down). The copper would heat up as the eddy currents swirled inside it, gaining the kinetic energy lost by the train as it slowed down. It might sound like a strange way to stop a train, but it really does work.We can also find the proof of it in many roller coasters cars, which use magnetic brakes like this, mounted on the side of the track, to slow them down. 

Fig: SIMPLE COPPER BLOCK TRAIN MOVING

Here simple copper block train moving from right to left, and I have embedded a giant bar magnet in the track to stop it. As the train approaches, eddy currents are induced in the front of it that produce a repulsive magnetic field, which slows the train down. If the train is moving really fast, this magnet might not stop it completely, so it will keep moving beyond the magnet. As it moves over past the other end of the magnet, the induced eddy currents will work the opposite way. Now they will produce an attractive magnetic field that rises to pull the train backward, but still trying to slow it down. The basic field that rises to pull the train backward, but still trying to slow it down. The basic point is simple: the eddy currents are always trying to oppose whatever causes them. An eddy-current brake consists of a stationary source of magnetic flux (permanent magnet or electromagnet) in front of which a conductor (metal disc, drum or rail) is moving. Because of the motion, the conductor experiences a time-varying magnetic flux density, which by virtue of Lenz’s law results in an electric field:

This electric field results in circulating currents in the conductor by virtue of Ohm’s law:

These currents are called “eddy-currents”. The interaction of eddy-currents with the flux density results in a force that opposes the motion:

Fig: Fundamental physics of eddy current

Fundamental physics reveal three important characteristics of eddy-current braking: - A braking force is induced without any mechanical contact between the rotor and the stator. Eddy-current brakes are thus wear-free. - The braking force is easily controllable by controlling the magnitude of the flux source.

REVIEW OF EXISTING EDDY CURRENT BRAKES

CONCEPTS

Eddy-current brakes are currently in use in three types of vehicles: commercial trucks, buses and some passenger trains. Eddy-current brakes used in trains are linear and 10 use the rail as an armature. They are also used in a variety of applications such as oil rigs, textile industry, etc. In trucks and buses, the eddy-current brake is often referred to as an “electromagnetic or electric retarder”. It is a single brake installed on the transmission shaft of the vehicle. It is used as a supplement to the main friction brake system to prevent it from overheating during downhill driving. The world leader in electromagnetic retarders is the French company Telma. 

Fig: Telma electromagnetic retarder 

The retarder consists of eight alternating-polarity iron-core electromagnets arranged in a circle faced on both side by two cast iron rotors. The rotors have an armature ring facing the electromagnets. The armature has fins on its back side in order to dissipate the braking energy through forced convection. The ring of iron on the outside of the rotor is called a “cheek” and guarantees the mechanical rigidity of the rotor. The performances of Telma’s retarders are listed in TABLE 1.

These retarders have disc outer diameters ranging from 352mm to 464mm and an air gap of 1mm or 1.4mm. Although the rated excitation current is not disclosed by the manufacturer, users have reported it to be within the 70-90A range.

THEORETICAL ANALYSIS OF EDDY CURRENT

Method of theoretical analysis of the eddy-current brake

The purpose of the analytical model is to rapidly provide insight into the fundamental physics of eddy-current braking, and preliminary design data which verifies whether the performance and size are compatible with the envisioned application. The analytical modeling of eddy-current brakes has been studied previously. The scope and complexity of the models vary greatly. Several publications only aim at providing a simple and restrictive model of eddy-current braking, others attempt to analyze the fundamental characteristics of the torque-speed curve. Several complex analytical models have been proposed using Coulomb’s method of images, while others have solved Maxwell’s equations more generally. An interesting method has been proposed in several publications. This method is based on a layer approach and is sometimes referred to as the Rogowski’s method. It offers a very rigorous and methodical approach without excessive complexity and unlike most other methods, it allows describing the air gap and the air beyond the disc. It is most extensively described in. The method proposed in the present chapter is derived from this method. It is worth noting that only one publication reports an attempt to optimize the design of an eddy-current brake and investigate the impact of design parameters on performance.

Theoretical analysis derivations

Below shows the basic eddy-current brake considered for the purpose of the analytical model. Only the rotor and the permanent magnets of alternate polarities are represented. The stator back-iron is not represented but is located in the plane immediately on top of the permanent magnets.

Fig: Eddy current brake

The problem is most easily described in a cylindrical coordinate system (r r,θ r,z r). The disc material is considered linear, whether magnetic or not. The problem can then be solved by superposition of two sub-problems: a static problem and an eddy-current problem. In the static problem, only the stator magnetization is considered. There are no eddy-currents. For the eddy-current problem, it is assumed no stator magnetization, only eddy-currents in the disc.

The geometry of the problem is invariant in the radial direction in the region of interest, i.e. from the inner radius to the outer radius. The magnetic field generated by the magnets is strictly confined to the (θ r,z r) plane. If the width of the ring is much greater than its thickness, then it may be assumed that the eddy-currents are infinite in the radial direction and that the return paths of the currents have a negligible effect on the overall problem. The problem can thus be reduced to a two-dimensional approximation, in the (θ r,z r) plane.

Fig: Eddy current path

The geometry is divided into 3 regions: air gap, disc and air beyond the disc. The stator is modeled as a region of infinite permeability by the means of a boundary condition for the air gap. The figure below shows the decomposition of the geometry into regions, where g is the air gap width and e is the thickness of the disc. 

Fig: Two dimensional region

USE OF EDDY CURRENT BRAKE

Despite being invented over a century ago, eddy current brakes are still relatively little used. Apart from roller coastres, one area where they are now finding applications is in high-speed electric trains. Some versions of the German Inter City Express (ICE) train and Japanese Shinkansen (“bullet train”) have experimented with eddy-current brakes and future versions of the French TGV are expected to use them as well. You will also find eddy current brakes in all kinds of machines, such as circular saws and other power equipment and they are used in things like rowing machines and gym machines to apply extra resistance to the moving parts so your muscles have to work harder.

HOW DOES AN EDDY CURRENT BRAKE STOP SOMETHING MOVING?

Suppose we have a railroad train that's actually a huge solid block of copper mounted on wheels. Let's say it's hurtling along at high speed and we want to stop it. We could apply friction brakes to the wheels —or we could stop it with eddy currents. How? What if we put a giant magnet next to the track so the train had to pass nearby. As the copper approached the magnet, eddy currents would be generated (or "induced") inside the copper, which would produce their own magnetic field. Eddy currents in different parts of the copper would try to work in different ways. As the front part of the train approached the magnet, eddy currents in that bit of the copper would try to generate a repulsive magnetic field (to slow down the copper's approach to the magnet). As the front part passed by, slowing down, the currents there would reverse, generating an attractive magnetic field that tried to pull the train back again (again, slowing it down). The copper would heat up as the eddy currents swirled inside it, gaining the kinetic energy lost by the train as it slowed down. It might sound does work. You'll find the proof of it in many rollercoaster cars, which use magnetic brakes like this, mounted on the side of the track, to slow them down. Artwork: Here's our simple copper block train moving from right to left, and I've embedded a giant bar magnet in the track to stop it. As the train approaches, eddy currents are induced in the front of it that produce a repulsive magnetic field, which slows the train down. If the train is moving really fast, this magnet might not stop it completely, so it'll keep moving beyond the magnet. As it moves past the other end of the magnet, the induced eddy currents will work the opposite way. Now they'll produce an aatractive magnetic field that tries to pull the train backward, but still trying to slow it down. The basic point is simple: the eddy currents are always trying to oppose whatever causes them.

ELECTRICITY AND MAGNETISM GO HAND IN HAND:

Wherever you get electricity, you get magnetism as well, and vice versa. This is the basic idea behind electricity generators and electric motors. Generators use some kind of movement (maybe a wind turbine rotor spinning around) to make an electric current, while motors do the opposite, converting an electric current into movement that can drive a machine (or propel something like an electric car or electric bike). Both kinds of machine (they are virtually identical) work on the idea that you can use electricity to make magnetism or magnetism to make electricity. To make electricity, all you have to do is move an electrical conductor (like a copper wire) through a magnetic field. That's it! It's called Faraday's law of induction after English scientist Michael Faraday, who discovered the effect in the early 19th century. If you connect the wire up to a meter, you'll see the needle flick every time you move the wire (but only when you move it). If you were clever, you could figure out some way of removing the electricity and storing it: you'd have made yourself a miniature electric power plant.