03-11-2012, 01:13 PM
MAGNETIC BRAKING
ABSTRACT
In this paper the basic of magnetic braking are introduced. Firstly, a simple theory is proposed
using Faraday's law and the Lorentz force. With this theory magnetic braking on copper
rectangular sheet moving linearly through the magnet is explained. Secondly, a magnetic drag
force and a magnetic lift force on a magnetic dipole moving over a nonmagnetic conducting
plane are explained with image method based on Maxwell’s equations. At the end of the
seminar the practical uses of forces on moving magnets are shown.
INTRODUCTION
The topic of magnetic braking has dramatically increased in popularity in recent years. Since
1987, numerous articles about magnetic braking were published. These articles describe both
experiments dealing with magnetic braking, as well as the theory behind the phenomenon.
Magnetic braking works because of induced currents and Lenz’s law. If you attach a metal
plate to the end of a pendulum and let it swing, its speed will greatly decrease when it passes
between the poles of a magnet. When the plate enters the magnetic field, an electric field is
induced in metal and circulating eddy currents are generated. These currents act to oppose the
change in flux through the plate, in accordance with Lenz’s Law. The currents in turn heat the
plate, thereby reducing its kinetic energy.
The practical uses for magnetic braking are numerous and commonly found in industry today.
This phenomenon can be used to damp unwanted nutations in satellites, to eliminate
vibrations in spacecrafts, and to separate nonmagnetic metals from solid waste [1].
THEORY
The subject of magnetic braking is rarely discussed in introductory physics texts. To calculate
the magnetic drag force on a moving metal object is generally difficult and implies solving
Maxwell's equations in time-dependent situation. This may be one of the reasons why the
phenomenon of magnetic braking, although conceptually simple to understand, has not
attracted the attention of textbooks authors. A simple approximate treatment is however
possible in some special cases. In our seminar we will try to explain magnetic braking with
the understandable (simple) theory. Reports in literature have made the theory behind this
phenomenon easily accessible. First we will be interested in the braking of a rectangular sheet
moving linearly through the magnet.
2. 1 Magnetic braking of a rectangular sheet moving linearly through the magnet
A good source for explaining why this braking happens we find in [2]. We assume that the
speed of the sheet is sufficiently small that the magnetic field generated by the induced
current is negligible in comparison with the applied magnetic filed. Under this condition just
stated, the magnetic drag force is seen to arise from mutual coupling between the induced
current and the applied magnetic field.
PRACTICAL USE
Eddy currents brakes (magnetic brakes)
To slow vehicles down, we can use eddy current brakes (magnetic brakes). Eddy current
brakes are a relatively new technology that are beginning to gain popularity due to their high
degree of safety. Rather than slowing a train via friction, which can often be affected by
various elements such as rain, eddy current brakes rely completely on certain magnetic
properties and resistance.
The linear eddy current brake consists of an electromagnet, which is fixed on a train (vehicle).
This electromagnet is held at a definite small distance from the rail (approximately 7
millimeters). When electric current is passed through the electromagnet and the electromagnet
is moved along the rail, eddy currents are generated in the rail. These eddy currents generate
an opposing magnetic field, providing braking force. The first train in commercial circulation
to use such a braking is the ICE 3 (Figure 8).
The eddy current brake does not have any mechanical contact with the rail, and thus no wear
and tear of it, and creates no noise. Because the braking force is directly proportional to the
speed, the eddy current brake itself can never completely stop a train. It is then often
necessary to bring the train to a complete stop with an additional set of fin brakes (friction
brakes) or "kicker wheels" which are simple rubber tires that make contact with the train and
effectively park it.
Maglev Vehicles
Magnetic levitation (maglev) is a relatively new transportation technology in which
noncontacting vehicles travel safely at speeds of 250 to 300 miles-per-hour or higher while
suspended, guided, and propelled above a guideway by magnetic fields. The guideway is the
physical structure along which maglev vehicles are levitated. Figure 9 depicts the three
primary functions basic to maglev technology: levitation or suspension, propulsion and
guidance. In most current designs, magnetic forces are used to perform all three functions.
Figure 9: Three primary functions basic to maglev technology [7].
There are two primary types of maglev technology: electromagnetic suspension (EMS) and
electrodynamic suspension (EDS) [5].
Electromagnetic (attractive force) suspension (levitation)
Electromagnetic suspension (EMS) system depends upon attractive forces between
electromagnets and ferromagnetic (steel) guideway. Because the force of attraction increases
with decreasing distance, such systems are unstable and the magnets currents must be
carefully controlled to maintain desired suspension height. Furthermore, the magnet-toguideway
spacing needs to be small (at approximately 15 millimeters). On the other hand, it is
possible to maintain magnetic suspension even the vehicle is standing still, which is not true
for electrodynamic (repulsive force) systems. In the system in Figure 10 (left side), a separate
set of electromagnets provides horizontal guidance force, but the levitation magnets, acted on
by a moving magnetic field from the guideway, provide the propulsion force.
Figure 10: Schematic diagram of EMS and EDS maglev system [7].
CONCLUSION
In our seminar we look at the magnetic drag force and the magnetic lift force on moving
magnets. Understanding of both forces is now days very important for practical uses,
especially to design magnetically levitated (maglev) vehicles for high-speed ground
transportation.