Download Damping effect due to Magnetic Field applied to Torsional Vibration

Effect of Magnetic Damping on Rotating Discs
Submitted by:
Abhishek Radhakrishnan
Supervisor: A/P Chew Chye Heng
Department of Mechanical Engineering
In partial fulfillment of the Requirements
for the Degree of Bachelor of Engineering
National University of Singapore
Session 2007/2008
SUMMARY
In this project, experiments were conducted to investigate the effect of magnetic damping
on rotating discs. A freely rotating disc made from a magnetic conducting material would
eventually come to a rest on its own, owing to natural damping factors such as friction
and air resistance. However, under the influence of a magnetic field, we expect the
damping behavior to deviate from normal conditions as this spinning disc, would now be
cutting various lines of flux that originate due to the present magnetic fields generated by
a present electromagnet.
Thus it is the purpose of this project to experimentally determine what orientation of
applied electromagnets and hence of magnetic fields would produce the most significant
damping effect. The damping of such discs by magnetic means can be very useful in
applications such as braking in large vehicles such as trains and roller-coasters. Since
magnetic braking is contact-less it produces no wear and tear as compared to friction
driven braking and requires less maintenance
It is concluded from this project that the use of a magnetic field is indeed feasible in order
to damp the rotation of a spinning disc and certain orientations are more effective than
others in achieving this result. Recommendations for improvement of the experimental
process have also been suggested in the form of testing the theory at higher rotation
speeds.
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ACKNOWLEDGEMENT
The author would like to express his sincere appreciation and deepest gratitude to the
following people, without whom this project’s success would never have been possible:
Firstly, the project’s supervisor, A/P Chew Chye Heng for his constant guidance, advice,
patience and understanding with regards to conducting and performing this project
through the course of the author’s final year.
Secondly, the staff and technicians at the Dynamics Laboratory who have consistently
provided support and concern for the well-being of the author and his project, especially
Mr. Ahmad Bin Kasa, Senior Technologist at the lab, who was pivotal in ensuring that
the project was carried out smoothly. Mr. Ahmad has been extremely helpful and
forthcoming in providing assistance, guidance and insight into making sure the project
produced results despite the several hiccups along the way.
Finally, the author would like to thank his family back in India for their endless moral
support as well as his second family in Singapore made up of his good friends in Sheares
Hall, especially the batch of graduating seniors.
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CONTENTS
SUMMARY
ii
ACKNOWLEDGEMENTS
iii
LIST OF FIGURES
vi
LIST OF TABLES
viii
LIST OF SYMBOLS
ix
1. Introduction
1
2. Literature Review
3
3. Theory of Magnetism
3.1 Magnetic Field Lines
10
3.2 Theory of Magnetic Damping
12
3.2.1 Eddy Currents
12
3.2.2 Magnetic Braking
13
3.3 Hazards of Electromagnetic Fields
15
3.3.1 Effect on Electronic Equipment and Loose Ferromagnetic Materials
15
3.3.2 Effects on Human Biological Effects
16
3.3.3 Types of Magnetic Shielding Methods
16
3.3.4 Use of Electromagnets
17
iv
4. Experimental Procedure and Results
4.1 Preliminary Experimental Requirement
18
4.2 Final Experimental Setup
19
4.2.1 Experimental Procedure
20
4.2.2 Selected Orientations
21
4.3 Results
24
5. Discussion
5.1 Explanation of Results
25
5.1.1 No Damping and Conventional Braking Arrangements
25
5.1.2 Single Magnet
26
5.1.3 Dual Magnets on One Side of Disk
27
5.1.4 Dual Magnets, One on Either Side of Disk
28
5.2 Inferences and Theoretical Agreement
28
6. Conclusion
6.1 Factors Affecting the Damping Effect
31
7. Recommendations
33
8. References
34
9. Appendices
9.1 Photos of Apparatus
36
9.2 Detailed Experimental Readings
40
9.3 Individual Decay Curves and Resolved Vectors
41
9.4 A Note on Maxwell’s Equations
48
v
LIST OF FIGURES
Figure 2.1
Conventional Setup for Magnetic Brake
3
Figure 3.1
Magnetic Field Lines
10
Figure 3.2
Measurement of Field Strength
11
Figure 3.3
Graph of Field Strength (Gauss) vs Applied Voltage (V)
12
Figure 3.4a
Principle of Magnetic Braking
13
Figure 3.4b
Eddy Currents in Moving Plate
13
Figure 3.5
Eddy Currents Induced using Right Hand Rule
15
Figure 3.6
Directions of F, B, J and v
15
Figure 4.1
Initial Experimental Setup
18
Figure 4.2
Final Experimental Setup
20
Figure 4.3
Schematic of Arrangements (a) to (j)
22
Figure 4.4
Experimental Setup for Arrangements (g) (h) (i) and (j)
23
Figure 4.5
Experimental Results of Speed vs. Time for 10 arrangements
24
Figure 4.5
Graph of Total Decay Time from 100rpm
24
Figure 5.1
Arrangement (a)
25
Figure 5.2
Arrangement (b)
25
Figure 5.3
Arrangement (c), (d), (e), (f)
26
Figure 5.4
Arrangement (g) and (h)
27
Figure 5.5
Arrangement (i) and (j)
28
Figure 9.1
Setup of Final Apparatus, Disc with No Damping
36
Figure 9.2
Setup for Arrangement (b), Conventional Damping Effect
36
vi
Figure 9.3
Setup for Arrangements (c) and (d)
37
Figure 9.4
Setup for Arrangements (e) and (f)
37
Figure 9.5
Setups for Arrangements (g) – (j)
38
Figure 9.6
Variable Power Source
38
Figure 9.7
Gauss Probe
39
Figure 9.8
Electromagnet
39
Figure 9.9
Graph and Schematic diagram for Arrangement (a)
41
Figure 9.10
Graph and Schematic diagram for Arrangement (b)
42
Figure 9.11
Graph for Arrangements (c) – (e) and Schematic diagram for
43
Arrangement (c) and (d)
Figure 9.12
Graph and Schematic diagram for Arrangement (e) and (f)
44
Figure 9.13
Graph and Schematic diagram for Arrangement (g) and (h)
45
Figure 9.14
Graph and Schematic diagram for Arrangement (i)
46
Figure 9.15
Graph and Schematic diagram for Arrangement (j)
47
vii
LIST OF TABLES
Table 3.1
Magnetic Field Strength for Varying Distance and Voltage
12
Table 4.1
Decay Times for Various Arrangements from 100rpm to Rest
24
Table 5.1
Decay Times for Various Arrangements Revisited
29
Table 9.1
Experimental Readings for Speed and Time for Arrangements (a) - (j)
40
viii
LIST OF SYMBOLS
B
magnetic flux density (Gauss)
F
volumetric force density (N/m3)
J
current density (A/m2)
v
velocity of the rotating disc (rpm)
σ
conductivity
ζ
damping ratio
ix
1. Introduction
Magnetic Damping is a phenomenon that has been observed for many years by which
vibrating, oscillating or rotating conductors are slowly be brought to rest in the presence
of a magnetic field. Using the knowledge of this phenomenon, which is a consequence of
Eddy current generation in a moving conductor, several applications can be thought of to
be utilized in the real world. Initially considered as a harmful side-effect of magnetic
induction, it has since been realized as a useful braking mechanism for moving objects.
Magnetic braking is contact-less, unlike conventional friction-dependent mechanical
braking, hence produces far less wear and tear and requires little maintenance and
replacement and is therefore a subject of immense interest to engineers and physicists
alike.
The damping effects of magnetic induction are also proportional to the speed of the
moving object hence making the braking phenomenon extremely smooth. It is hence the
objective of this project to further investigate the aforementioned damping effects in the
case of rotating discs, with the focus being not on the strength of the magnetic field or the
speed of the disc, but on the various possible orientations of the applied magnetic field in
relation to the disc.
Hence, in short, the main aim of this final year project is to observe and note via
experiment, how various orientations of applied magnetic fields affect the damping of a
rotating disc. In this endeavor, a rotating disc is placed in the presence of various
1
combinations of magnetic field orientations in order to deduce which orientation
produces the most effective damping.
In addition to the main experiment, a literature survey has also been conducted and
included, which covers in detail the magnetic damping principles in practice today and
other studies related to the subject, along with the theories and principles of magnetism
involved in observing the phenomena.
2
2. Literature Review
2.1 The Conventional Direct Current Brake
The conventional electric brake consists of a conductor disc (or oscillating body) rotating
in between the two opposite poles of a magnet. The conductor disc revolving in the
magnetic field generates heavy circulating currents whose magnetic field reacts with that
of the permanent magnet to produce a drag of the kind that would occur if the disc were
immersed in a viscous fluid. This effect would be increased if the flux density through the
disc were raised by the use of stronger permanent magnet material, or by reducing the air
gap clearance, but these give little scope for practical control. If magnets are
progressively added until they cover the whole surface of the disc, the drag reaches a
maximum and then falls off because the path for the circulating current will have become
restricted, with the result that its resistance will rise. There are thus limitations to
adapting this frictionless brake arrangement for power uses, though it is excellent for
instruments and meters.
Figure 2.1: A conventional setup for a magnetic brake, with
the disc rotating between two opposite poles of a magnet
3
2.2 Regenerative Braking
Frictional braking has made such progress throughout the 20th century, mainly as a result
of research in friction materials, that its inherent limitations are often overlooked. Except
for stopping from slow speed, braking forces should be related to speed by dynamic
methods which remove most of the energy away for the braking mechanism and conserve
it by some regenerative system. In particular, the stored energy from the deceleration
should be made available from the acceleration stage which normally follows it.
Frictional braking is purely wasteful, tends to produce intense heating where it is least
wanted, causes wear and consequent maintenance, which neglected, can become
hazardous.
Early electric propulsion for both road and rail, showed that a c lose approach to this
dynamic regenerative ideal for braking could be achieved in practice. though by complex
and costly methods. These economic penalties were the direct result of electromagnetic
excitation. It was essential to have magnetic fields at full strength in the motors for
braking to be effective.
If a series motor is to be used for dynamic braking, it is necessary to have appropriate
field winding switching to ensure a power supply to provide the essential magnetic flux,
with the necessary precautions to see that the risk of failure is minimized. While these
conditions can be provided on a large scale, such as a railway, it can well be understood
that regenerative braking with conventional machines is regarded as uneconomic for road
vehicles. Fro safety reasons also, the magnetic flux should be present at full strength at all
4
times; this shows the great importance of permanent magnets for this purpose if they are
really permanent to withstand the severe operating conditions, mechanical as well as
electrical. For economic reasons also, this subject could not be considered before the
arrival of high-coercivity ferrite materials during the 1960’s. Their merits go well beyond
the vital safety need; it is now possible to have the simplest form of two-terminal
machines which will automatically give electrical braking without switching. Hence
dynamic braking, the most useful form in practice, can be automatically applied by an
electrical propulsion system using permanent magnet excitation. It becomes progressively
less effective as the speed is reduced and disappears as it comes to rest, so it must be
supplemented with frictional braking for the later stages and for parking.
2.3 Early Applications of Eddy Current Damping
Malcolm McCaig writes about a study conducted in 1962 to examine the efficiency of
magnetic systems for eddy-current brakes and advised that the thickness of the
conducting material should equal that of the necessary air-gap. Torque can be increased
by increasing the radius at which the magnets act, but if the rotor is a flat disc, the
magnets must not act so near the edge that the return paths for the eddy currents are
restricted. The watt-hour meter is one of the oldest and most common uses of eddycurrent brakes. The electrical arrangements of a watt-hour meter provide a torque that is
proportional to the product of the current time the voltage or the watts consumed. This
torque must drive something which has a resistance to motions that is a constant linear
function of speed. For many years a rather special type of steel horsehoe magnet was
5
always used, but this design is now obsolete. Good stability is the most important quality
of magnets for this application.
Many laboratory instruments such as balances can be damped buy a conducting sheet
moving in the gap of a permanent magnet. Moving coil instruments are often damped by
eddy-currents induced in their own coil. The decree of damping depends upon the
external resistance. Sensitive instruments such as galvanometers are critically damped for
one particular value of the external resistance. If the resistance is much lower than this
critical value the instrument is too sluggish, and if the resistance is much higher, they
continue to swing for a long time.
2.4 Brake Run
A brake run on a roller coaster is any section of track meant to slow or stop a roller
coaster train. Brake runs may be located anywhere along the circuit of a coaster and may
be designed to bring the train to a complete halt or to simply adjust the train's speed. Of
late, magnetic brakes or ‘eddy current brakes’ are being increasingly used for this
purpose. Modern roller coasters use this type of braking, but utilize permanent magnets
instead of electromagnets. These brakes require no electricity; however, their braking
strength cannot be adjusted.
Magnetic braking is a relatively new technology that are beginning to gain popularity due
to their high degree of safety. Rather than slowing a train via friction (such as fin or skid
brakes), which can often be affected by various elements such as rain, magnetic brakes
6
rely completely on certain magnetic properties and resistance. In fact, magnetic brakes
never come in contact with the train.
Magnetic brakes are made up of one or two rows of very strong Neodymium magnets.
When a metal fin (usually made of copper and brass) passes between the rows of
magnets, eddy currents are generated in the fin, which creates a magnetic field opposing
the fin's motion. The resultant braking force is directly proportional to the speed at which
the fin is moving through the brake element. This very property, however, is also one of
magnetic braking's disadvantages in the eddy force itself can never completely stop a
train. This effect of magnetic braking can be explained by an example in which the train's
speed is halved as it passes through each set of brakes. The train's speed (in any unit)
would initially be 40, then 20, 10, 5, and so on. It is then often necessary to bring the train
to a complete stop with an additional set of fin brakes or "kicker wheels" which are
simple rubber tires that make contact with the train and effectively park it.
Magnetic brakes can be found in two configurations:
* The brake elements are mounted to the track or alongside the track and the fins are
mounted to the underside or sides of the train. This configuration looks similar to
frictional fin brakes.
* The fins are mounted to the track and the brake elements are mounted to the
underside of the train. This configuration can be found on Intamin's Accelerator Coasters
(also known as Rocket Coasters) such as Kingda Ka at Six Flags Great Adventure. This
configuration is probably less expensive, as far fewer magnets are required.
7
In terms of pros, magnetic braking is virtually fail-safe because it relies on the basic
properties of magnetism and requires no electricity. Magnetic brakes are also completely
silent and are much smoother than friction brakes, gradually increasing the braking power
so that the people on the ride do not experience any unpleasant feelings. Many modern
roller coasters, especially those being manufactured by Intamin, have utilized magnetic
braking for several years. Another major roller coaster designer implementing these
brakes is Bolliger & Mabillard in 2005 on their Silver Bullet inverted coaster and in 2006
on Patriot. These later applications have proven effectively comfortable and relevant for
these inverted coasters which often give the sense of flight. There also exist third party
companies such as Magnatar tech. which provide various configurations of the
technology to be used to replace and retrofit braking systems on existing roller coasters to
increase safety, improve rider comfort, and lower maintenance costs and labor.
However, the main disadvantage of magnetic brakes is that they cannot completely stop a
train, so they cannot be used as block brakes. They also cannot be conventionally
disengaged like other types of brakes. Instead, the fins or magnets must be retracted so
that the fins no longer pass between the magnets. These are the most effective brakes that
slow the train quickly, and these are failsafe. Accelerator Coasters, for example, have a
series of magnetic brake fins located on the launch track. When the train is launched, the
brakes are retracted to allow the train to reach its full speed. After the train is launched,
the brake fins are raised to safely slow the train down in the event of a rollback.
8
2.5 Magnetic Damping of Rotating Shaft
Finally, in a Final Year Project study conducted by Cai Zhemin, a student at the National
University of Singapore, results of an experiment to observe the damping effect on a
rotating shaft showed that the velocity at which the shaft rotates will affect the magnitude
of the eddy currents induced. Hence, the higher the speed of rotation, the greater will be
the opposing force acting on the shaft and thus, the greater will be the damping effect.
Hence it will not be in the focus of our experiment to re-prove experimentally this fact
that can be predicted by theory according to the Lorentz force density equation
F = J x B = σ (v x B) x B
that shows that the opposing force that causes the damping effect is proportional to the
velocity of the rotating shaft.
9
3. Theory of Magnetism
3.1 Magnetic Field Strength
For the purpose of this experiment two horse-shoe shaped electromagnets were made use
of in order to generate our required magnetic field. Once supplied with a voltage, the
magnetic field would be generated from the electromagnet’s poles. In most applications
of a magnetic braking mechanism (as seen in the previous section) the oscillating object
to be damped is places in between the two opposing poles of the horseshoe. However, for
our investigation, the disc is to be placed parallel to the lateral face of the magnet.
The field line distribution for the typical horseshoe magnet is show in the Figure 3.1. It is
known and can be seen from the lines that the magnetic field strength decreases as the
distance from the face of the magnet increases.
Figure 3.1: Magnetic Field Lines for typical horseshoe magnet. Field lines get further
apart as distance from the magnet increases, hence field intensity decreases.
10
Thus it was sensible for us to measure the magnetic field strength using a gauss meter at
an increasing distance from the face of the magnet as this is how the disc would
eventually be placed and hence this would be the point where the area of the disc cut the
magnetic flux lines generated by the magnet (Figure 3.2).
Figure 3.2: Field strength was measured with increasing distance from the magnet
From the measurements taken in the laboratory, the author arrived at Table 3.1 below
which shows the relation between applied voltages to the magnet, distance of the gauss
probe from the magnet and finally the magnetic field strength read by the probe. One can
see a rough inverse polynomial relation between distance and magnetic field strength,
and this agrees with what is known from theory. Also, there is a direct linear
proportionality relation between the field strength and the applied voltage, as illustrated
by the graph in Figure 3.3.
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Magnetic Field Strength (Gauss)
Voltage (V)
2
4
6
79
173
267
8
16
23
2
4
6
1
2
2.5
Distance (cm)
0
22
3
1
1
0
5
10
15
8
372
31
8
3
10
468
38
10
3.5
12
567
47
12
4
Table 3.1: Magnetic Field Strength values for varying Distance and Voltage
Field Strength vs Voltage for varying distances from pole
600
500
Field Strength (G)
400
0cm
5cm
10cm
15cm
Linear (0cm)
300
200
100
0
0
2
4
6
8
10
12
14
-100
Voltage (V)
Figure 3.3: Graph of Field Strength (Gauss) vs Applied Voltage (V)
3.2 Theory of Magnetic Damping
3.2.1 Eddy Currents
An eddy current (also known as Foucault current) is an electrical phenomenon discovered
by French physicist León Foucault in 1851. It is caused when a moving (or changing)
magnetic field intersects a conductor, or vice-versa. The relative motion causes a
circulating flow of electrons, or current, within the conductor. These circulating eddies of
12
current create electromagnets with magnetic fields that oppose the effect of the applied
magnetic field in accordance Lenz's law. The stronger the applied magnetic field, or
greater the electrical conductivity of the conductor, or greater the relative velocity of
motion, the greater the currents developed and the greater the opposing field. Eddy
currents create losses through Joule heating. More accurately, eddy currents transform
useful forms of energy, such as kinetic energy, into heat, which is generally much less
useful.
3.2.2 Magnetic Braking
Figure 3.4a: Principle of Magnetic
Braking. As the moving plate
penetrates into the magnetic field,
eddy currents are generated
Figure 3.4bEddy currents in the
moving plate retard its movement.
Braking force is proportional to
velocity, conductivity, and flux
density
To present the principle involved in magnetic braking, the author refers to the structure in
Figure 3.4a. In this structure, an electromagnet generates a flux density B in the gap. This
field will be assumed to be constant. A pendulum-like piece, made of a conducting
material is placed such that it can move into the gap. If the current in the electromagnet is
zero, the oscillation of the pendulum is not affected by the structure. If the current in the
13
coil is not zero, the movement of the conducting plate, into the magnetic field (Figure
3.4b) generates induced currents in the plate itself. The flux of the induced currents is
such that it opposes the field B, since, initially, in the plate, the field was zero. According
to Lenz’s law, the induced currents tend to maintain this condition. The electric field due
to the induced currents is given by E = v×B , and get
J = σ E = σ v× B
The rate at which the plate penetrates into the gap is responsible for the magnitude of the
induced currents. The volumetric force density f is
f = J × B = σ (v × B) × B
If all vectors are mutually orthogonal, as is the case in our example, the force is
F = σ vB 2Vol
and its direction, given by the cross product J × B , opposes the direction of v, where F is
the volumetric force density (N/m3), J is the current density (A/m2) and B is the magnetic
flux density (Tesla). This has the effect of damping the movement of the plate into the
gap. This principle is used extensively on locomotives and trucks. Conducting discs are
installed on the axes of the vehicle and electromagnets are placed around them such that
the discs move in the gap of the electromagnets. When the mechanical brakes are applied,
a current is passed through the electromagnet and the braking effects of the mechanical
and magnetic brakes are added together. Again, one must note that electromagnetic
brakes cannot be uses to completely stop a vehicle, but only slow it down, as it is
dependent on v.
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In this project, eddy currents are generated in the disc and these eddies give rise to the
resistive force experienced by the disc. Figures 3.5 and 3.6 show how the direction of
Eddy currents is found using the right hand rule and how the resultant force can be found
using Fleming’s left hand rule.
Figure 3.5 (above left): Schematic diagram of Eddy Currents Induced using Right Hand Rule
Figure 3.6 (above right): Directions of F, B, J and v using Right and Left hand rules
3.3 Hazards of Electromagnetic Fields
Static electromagnetic fields have been known to cause problems such as effects on
electronic equipment, unwanted magnetic forces on surrounding ferromagnetic materials
and human biological effects.
3.3.1 Effect on electronic equipment and loose ferromagnetic materials
Electronic equipment can be affected by magnetic fields if not properly shielded. For
instance, mobile phones, watches, cameras and credit cards can be damaged by fields
above 10G. Also, bioelectronic devices such as the cardiac pacemakers can be affected
by magnetic fields. A magnetic field of about 5G can interfere with the operation of such
devices. Magnetic fields can also attract surrounding ferromagnetic materials and this can
15
be dangerous. Loose objects may ‘fly’ towards the magnet and injure or even kill
individuals. Hence, it is important to make sure that equipment and magnets are shielded.
3.3.2 Effects on Human Biological Effects
It is still a controversy on whether electromagnetic fields will cause human biological
effects such as cancer, depression and Alzheimer’s diseases. Although there have been
studies that testify the biological effects of exposure to static electromagnetic fields, there
is no adverse health effects. In 1997, Lai and Singh [3] examined that the
Deoxyribonucleic acid (DNA) single-strand break in the brain cells of rats being exposed
to a magnetic field of 5G. Also, in another study in 2003, Rosen [4] examined that cells
that are exposed to a 1250G static magnetic field has resulted in an effect on the function
of their cell membranes. However, these studies which associated cancer with magnetic
fields were inconsistent and there were insufficient evidence to show the exposureresponse relationship between magnetic field exposure and cancer cases. Overall, there is
a weak association between human health effects and static electromagnetic field. Till
today, there is no strong evidence to prove that static electromagnetic fields will cause
hazards to human health.
3.3.3 Types of Magnetic Shielding Methods
There are two basic methods to mitigate magnetic fields, namely, the passive and active
shielding technique. These methods can be used together or separately.
In passive shielding method, a nickel-iron alloy, commonly known as Mu-metal, is often
used to screen equipments from magnetic fields due to its high magnetic permeability.
Mu-metals divert the magnetic flux towards them instead of the surrounding. Hence, the
magnetic field from the electromagnet will be greatly reduced by the shielding material.
16
However, Mu-metals tend to be more expensive due to their high permeability. For a less
expensive choice, a ferromagnetic and conductive shielding material such as steel can be
used.
In active shielding, active cancellation loops is used and the region to be shielded is
sensed using a feedback system. The system will then impose a current on the conductors
to reduce the magnetic field. Active shielding is usually used for full-room shielding. In
many cases, active shielding is used to supplement passive shielding. However, for
shielding a magnet, passive shielding will be sufficient.
Hence, with proper shielding, the hazards due to magnetic field can be greatly reduced.
3.3.4 Use of Electromagnets
The magnets used in the experiment are electromagnets as the magnetic field can be
effectively contained within a small area when in use. Measured magnetic flux densities
are about 50 G at 1 cm away from the magnets, decreasing to about 5 G at 15 cm from
the magnets at maximum voltage settings. Also, during transportation from place to
place, with no power supply, the electromagnets will not generate a magnetic field. This
ensures that no electrical or magnetic devices are accidentally exposed to the magnetic
field.
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4. Procedure and Results
4.1 Preliminary Experimental Requirement
For the purpose of the experiment the author was provided with two horseshoe shaped
electromagnets with a power rating of 12 volts each. Since the aim was to observe the
effect of their magnetic fields on a freely rotating disc, a suitable experimental setup was
necessary. The initial setup arrangement involved fabrication of a circular disc of
conducting material which was to be mounted on a steel shaft that would be held in place
and rotate on two bearings housed at either end of the shaft. One end of the shaft would
be connected to a drive motor which would power the rotation of the disc and then
disengage once a satisfactory speed was reached. The other end of the shaft was to be
connected to a small signal analyzer that would produce a voltage versus time output
which could then be calibrated to give a speed versus time decay output. The
experimental setup plan is shown in Figure 4.1
Figure 4.1: Initial Experimental Setup
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4.1.1 Shortcomings of the Initial Setup
After fabricating most of the apparatus required for the setup, with the help of the
laboratory technologists, including the disengaging mechanism for the drive motor, the
circular rotating plates along with the collars by which they would be mounted on the
shaft, and finally the shaft itself, problems started to arise in the form of the bearings in
use suffering from far too much internal damping to be of any use. Hence fresh bearings
for the experiment were procured from SLS Bearings Pvt. Ltd. Deep groove bearings
with only one axis of rotation were chosen so as to ensure smooth undamped rotation of
the shaft and the disc. However, even with the inclusion of the new bearings, there were
several issues with the straightness of the shaft and its alignment with the bearings, which
was still giving rise to heavily damped rotation of the shaft and disc, even in the absence
of any magnetic field. Such conditions were absolutely not useful for our experiment and
thus with little time left on our hands and the current setup being unable to allow for any
testing or readings to be taken, other alternatives needed to be explored.
4.2 Final Experimental Setup
With time running out and the original design springing up one problem after another, the
author was fortunate enough to discover in the laboratory a prefabricated disc, shaft and
bearing mechanism of suitable material and size (Figure 4.2). The 29.6 kg steel disc-axle
unit measured 30cm in diameter and turned out to be a good magnetic conductor.
Preliminary tests were carried out to ensure that the magnetic damping effect was indeed
visible. Better yet, not only was the size of the new disc more suitable than the previous
design, the internally housed bearings were of extremely superior quality, the entire shaft
19
itself being exceptionally well balanced allowing for minimal damping under natural
conditions and hence proving to be ideal for observation of changes in damping
phenomena.
Figure 4.2: Final Experimental Setup
4.2.1 Experimental Procedure
Discovery of the new apparatus came a little too late however, and pressed for time and
results, fabrication of a new motor driving unit and output analyzer system did not turn
out to be feasible. However, it was better late than never and the experiment was
continued by driving the rotating disc manually and readings were taken using a
stopwatch and a tachometer. In order to reduce and remove sources of inaccuracy such as
human error, readings were taken several times and the experiments were repeated
several times over and the readings averaged out.
20
The initial part of the experimental procedure involved connecting up the electromagnet
to the variable power source according to the required polarity as per the arrangement
being tested. For all arrangements and experiments, power was supplied at the maximum
of 12 volts in order to observe the greatest possible damping effect. The distance was also
kept constant between the magnet and the disc, at 1cm, and thus with these two variables
being maintained at constant throughout the project, the only variable that would effect
the damping phenomena would be the orientation of the magnet.
After the magnet(s) were connected, the voltage was set to 12v with the power still being
in the ‘off’ position. The disc was turned and spun and the instantaneous rotational
velocity in rpm was measured by the tachometer that was placed in a fixed position
throughout the project. Timing of the mechanical decay was commenced the moment the
speed of the disc reached 100rpm and the tachometer continued to record the
instantaneous velocity at intervals of 10s until the minimum recordable speed (30rpm) of
the tachometer was reached. The disc however was allowed to continue spinning until it
finally came to rest and the total time from 100rpm to rest was recorded. The experiment
was then repeated for the various magnet orientations, with the only difference being that
the power supply was switched ‘on’ as soon as the disc reached 100rpm and timing
commenced at the same instant as well.
4.2.2 Selected Orientations
Results were recorded and then plotted in terms of Speed vs. Time for each orientation.
Figure 4.3 shows the various orientations and combinations of the magnets that were
21
chosen for investigation. Figure 4.4 shows photographs of the setups for the more
complex arrangements of the magnets (g)-(j).
Figure 4.3: Arrangements (a) to (j) of the various orientations of magnetic fields for experiment
Arrangement (a) corresponds to the disc spinning freely in the absence of any applied
magnetic field and subject only to natural damping factors.
Arrangement (b) corresponds to the conventional setup of the magnetic brake, as
discussed and seen in Section 2 of this paper, with the disc rotating between two opposite
poles of the magnet
Arrangement (c) corresponds to a single magnet applied to the left side of the disc’s
center when the disc is viewed rotating CCW. The North Pole of the magnet is above the
South Pole.
Arrangement (d) corresponds to a single magnet applied to the left side of the disc’s
center when the disc is viewed rotating CCW. The South Pole of the magnet is above the
North Pole.
22
Arrangement (e) corresponds to a single magnet applied to the right side of the disc’s
center when the disc is viewed rotating CCW. The North Pole of the magnet is above the
South Pole.
Arrangement (f) corresponds to a single magnet applied to the right side of the disc’s
center when the disc is viewed rotating CCW. The South Pole of the magnet is above the
North Pole.
Arrangement (g) corresponds to two magnets applied to both left and right side of the
disc’s center when the disc is viewed rotating CCW. The South Pole is higher on the left
and the North Pole is higher on the right.
Arrangement (h) corresponds to two magnets applied to both left and right side of the
disc’s center when the disc is viewed rotating CCW. The North Pole is higher on both
sides
Arrangement (i) corresponds to two magnets applied to either side of the disc itself.
Both magnets have their North Poles higher.
Arrangement (j) corresponds to two magnets applied to either side of the disc itself. One
magnet has its North Pole higher and the other has its South Pole higher.
Figure 4.4: Experimental Setup for Arrangements (g) (h) (i) and (j)
23
4.3 Results
The results of the experiments with the various orientations of the magnetic fields and
their effect on the damping of the disc are shown in the form of speed versus time curves
in Figure 4.5. In addition, Table 4.1 shows the comparison of the various orientations
along with their total time taken for the disc to come to rest from a speed of 100rpm.
Speed (RPM)
Decay Curves for Various Orientations
110
100
90
80
70
60
50
40
30
20
10
0
0
50
100
150
200
a
b
c
d
e
f
g
h
i
j
250
Time (s)
Figure 4.5: Experimental Results of Speed vs. Time for 10 arrangements
Total Decay Time
5:15
4:10
3:17
3:19
3:15
3:24
2:39
2:12
2:10
2:57
Table 4.1: Total Decay Time from
100rpm for each arrangement
Total Deca y Time
6:00
Time (s )
Arrangement
a
b
c
d
e
f
g
h
i
j
4:48
3:36
Total Decay Time
2:24
1:12
0:00
a
b
c
d
e
f
g h
i
j
Orientation
Figure 4.5: Graph of Total Decay Time from 100rpm
24
5. Discussion
5.1 Explanation of Results
5.1.1 No Damping (a) and Conventional Braking Arrangements (b)
Figure 5.1: Arrangem ent (a)
120
100
80
60
40
20
0
0
50
100
150
200
250
a
T i m e ( s)
Figure 5.2: Arrangement (b)
120
100
Sp eed (rp m)
80
60
40
20
0
0
50
100
150
20 0
250
b
Ti me ( s)
From the results obtained in the Figure 5.1 above, it is seen that the disc in the absence of
any magnetic fields undergoes natural damping and hence decelerates at a roughly
constant rate due to air resistance. It takes 5min 15s to come to rest from 100rpm (Table
25
4.1). In Figure 5.2, when the magnetic field is applied in its standard orientation (b), the
rate of decrease increases, i.e. the disc slows down faster (4min 10s). By using our left
and right hand rules, the figure shows that the direction of the Lorentz force generated in
the disc is opposite to the direction of motion, hence producing a retarding effect.
5.1.2 Single Magnet
Figure 5.3: Arrangement (c) (d) (e) (f) - clockwise from top left
1 20
1 00
Sp ee d (r p m )
80
60
40
20
0
0
20
40
60
80
T i me ( s)
1 00
12 0
140
c
d
e
f
The graph in Figure 5.3 shows roughly the same degree of decay when it comes to the
application of a single magnet, regardless of the polarity or which side of the central axis
is used. As can be seen from the same diagram on the right of the graph, using right hand
rule, due to each pole’s magnetic field acting on the disc, eddy currents are generated in a
particular direction and hence the resultant Lorentz force experienced at each point of the
disc that crosses these flux lines has a direction corresponding to the cross product of the
current density J and the flux density B. The direction can be seen to be opposite the
direction of velocity in all four arrangements, producing a similar retarding force and
26
hence similar decay time. Each arrangement (c), (d), (e) and (f) has shorter decay times
than undamped motion from 100 rpm (3min 17s, 3min 19s, 3min 15s, and 3min24s
respectively).
5.1.3 Dual Magnets on One Side of Disk
Figure 5.4: Arrangement (g) and (h)
120
100
(g)
80
Speed (rpm)
g
60
h
40
(h)
20
0
0
20
40
60
80
100
120
Time (s)
With the addition of our second electromagnet at the same applied voltage as the first, a
significant in decay time is again shown and hence a considerable increase in damping
force. From the schematic above it is once again seen that the forces lining up in a
direction that opposes the motion and since there are more poles in action for
arrangements (g) and (h), an expected increase in decay rate and drop in decay time to
2min 12s and 2min 39s respectively is also seen. Also from the graph in Figure 5.4 it is
more evident at this stage that the speed decay versus time is non-linear but exponential
rather, owing to the fact that the retarding force is a function of the instantaneous velocity
hence the rate of deceleration decreases with time.
27
5.1.4 Dual Magnets, One on Either Side of Disk
Figure 5.5: Arrangement (i) and (j)
Left View
Front View
Right View
120
100
(i)
Speed (rpm)
80
60
40
(j)
20
0
0
20
40
60
80
100
Time (s)
120
i
j
Finally, arrangement of dual magnets set up on either side of the disc results in readings
similar to the previous case of having them both on the same side. By theory shown on
the right of Figure 5.5, the forces again oppose the direction of the motion at each point
on either side. Since there are again more poles generating the flux lines, more eddy
currents are generated and hence the retarding force increases as compared to the case of
single magnets, giving decay times of 2min 10s and 2min 57s for (i) and (j) respectively
5.2 Inferences and Theoretical Agreement
Table 5.1 below lists the various decay times for the different arrangements and their rate
of decay can be seen from Figure 4.5 in the previous section or in the records of readings
in Appendix B.
28
Arrangement
Total Decay Time
a
5:15
b
4:10
c
3:17
d
3:19
e
3:15
f
3:24
g
2:39
h
2:12
i
2:10
Table 5.1: Decay Times for Various Arrangements
As expected and predicted by theoretical application of laws of magnetism, the
introduction of a magnetic field interacting with a moving conductor such as our rotating
disc will produce a damping effect as seen by the reduction in time between (a) and (b) or
between (a) and (c), (d), (e) or (f) where a single magnet was introduced perpendicular to
the face of the disc. Orientations (c) to (f) show roughly the same decay times indicating
that polarity and position are not a factor as theoretical laws show that the net result will
always oppose the change that is producing the current. In these arrangements the
magnetic field was measured to be stronger at the surface of the disc from the poles than
in the case of (b) hence the faster decay rates in comparison. This could be a result of the
design of the magnet wherein the flux originating from a particular face may not be
identical to that at a different face even at the same applied voltage (see Appendix A).
As for arrangements (g), (h), (i) and (j), which are using in fact now twice as many
magnets at the same power rating, we expect more flux lines to be cutting the moving
conductor hence a greater retarding force to be experienced. The author worked out that
the directions of these forces and in each case irrespective of polarity as positioning the
forces counteract the rotation. Besides the significant drop in decay timing, another
significant feature is observed. In both pairs of arrangements (g)-(h) and (i)-(j), it is seen
that the NS-NS orientation of the magnetic couple produce a shorter decay time. That
means when the magnets are aligned such that like poles are at the same level (beside
each other in the former case and opposite each other in the latter), there is a greater
29
j
2:57
damping effect. What is even more uncanny is that both sets of NS-NS arrangements i.e.
(h) and (i) result in almost identical decay times, suggesting that the effect of the damping
is not dependent so much on how the magnets are positioned, but more on the orientation
of their polarity. The sheer number of magnets surely increases the strength of the
magnetic field present hence with two magnets producing the field we witness more
damping than in the case of one. However within the magnet pairs the difference is due to
the polar alignment. When like-poles are aligned the damping effect is even more
prominent. This could be because the magnetic field strength itself at the poles is lesser
when unlike poles are aligned. This could be due to the North and South Pole field lines
interacting when they share the same space and reduce each of their individual strengths
at the magnet’s poles by cancelling parts of each other out. With the same power supply
of 12v, the Gauss Probe too showed stronger magnetic flux density at the poles of the
magnet in the NS-NS arrangement which would thus contribute to the larger damping
effect witnessed experimentally. Hence orientations (h) and (i) were the most effective
for damping, with decay times of 2min 12s and 2min 10s respectively.
30
6. Conclusion
Thus it can be seen from the experiments that the effect of an applied external magnetic
field does indeed produce a damping effect in a conducting disc that is rotating within the
range of the lines of flux. What’s more is that from our experiment, novel applications of
this principle, using orientations that are not in common practice or haven’t been studied
extensively before, have also been shown to be feasible in producing desired and
effective damping effects. Positioning the electromagnets perpendicular to the face of the
disc significantly reduces the time for it to come to rest and sever factors listed below
were also found to affect the damping extent.
Hopefully in the future the results of this experiment can be applied to real world
situations where critical damping is required on various scales, be it in vehicles such as
roller coasters or subway trains, or even minute applications such as balances, meters and
optical disc drives.
6.1 Factors Affecting Damping Result
6.1.1 Speed of Disc
The speed of the disc is by theoretical definition critical in determining the instantaneous
damping force induced. At higher speeds the damping force will be larger and will
gradually decrease. It would be interesting to test our experiment at much higher speeds,
in the range of several hundred rpm. However the results obtained would still be the same
as the decay from 100rpm onwards would not be affected by the previous speed and
damping and would continue as seen in this experiment. What would be more evident
however would be the exponential decrease in the deceleration of the disc which is only
31
marginally visible in our experiment (see Appendix). Hence magnetic damping alone can
never bring the body to a stop, but only slow it down until natural damping takes over.
6.1.2 Air Gap
The distance between the magnet surface and the conductor disc also plays and important
part in the damping as the magnetic flux density decreases by an inverse polynomial
function as distance from the magnet increases. Thus since the damping effect is directly
related to the flux density, a cheaper alternative to raising the voltage in order to raise the
flux intensity would be to close up the gap between magnet and conductor. However,
caution must be exercised to secure the magnet and the disc firmly so that they do not
attract one another and come into contact as this could be dangerous to both human and
machine when high speeds are involved.
6.1.3 Number of Magnets
Similarly as above, the number of magnets present logically will increase the flux density
at the surface of the conductor. This causes generation of more eddy currents at the
various points and thus a larger damping is experienced. However in order to optimize
their utilization, the magnets should be placed strategically so that their fields don’t
cancel one another out.
6.1.4 Orientation of Magnets
As our experiment has concluded, rather than position, the orientation of the magnets can
improve the damping efficiency of the setup. By having a N-S -N-S arrangement, i.e.
having like poles positioned at the same level in relation to the disc, rather than unlike
poles, engineers can maximize the effect of their magnetic fields and hence arrive at the
best possible critical damping function for the moving object.
32
7. Recommendations
The recommendations for this experiment revolve around improving the accuracy of the
measured results by fine tuning the experimental procedure. It would be ideal to have a
drive motor to power the rotation of the shaft so that a higher constant velocity could be
reached before the motor is disengaged. The use of a signal analyzer would also help in
taking down the readings electronically in terms of voltage versus time which could then
be converted to speed versus time decay.
It will also be of interest to see how the inclusion of more magnets and hence various
arising permutations of orientations would affect the damping. More studies could be
carried out into determining the theoretical values of the eddy currents, damping ration
and Lorentz force and these could be verified experimentally using appropriate devices
such as Eddy Probes if available in the laboratory.
Finally, more measures could be put in place in order to minimize the present ambient
damping factors, such as air resistance, by conducting the experiment in a vacuum and by
making sure the environmental magnetic field count is minimized. Also, one must keep
in mind that unless one waits for a significant amount of time between experimental runs,
there will constantly been some residual magnetization present in both the disc and the
magnet itself, even when the power is switched off, which could affect readings and
results. This could be minimized by having an identical alternative setup so that
experiments could still be run on one setup while the other is being demagnetized.
33
8. References
1. McCaig, Malcolm, “Permanent Magnets in Theory and Practice”, 2nd Edition,
Pentech Press, 1987
2. Furlani, Edward P., “Permanent Magnet and Electromechanical Devices”,
Academic Press, 2001
3. Baostos, Joao P.A. and Nathan Ida, “Electro-magnetics and Calculation of
Fields”, 2nd Edition, Springer 1997
4. Polgreen, G.R, “New Applications of Modern Magnets”, Macdonald, 1966
5. Moon, Francis C., “Magneto-Solid Mechanics”, John Wiley and Sons, 1984
6. Lai, H., and N.P. Singh, Acute Exposure to Magnetic Field Increases NA Strand
Breaks in Rat Brain Cells, Bioelectromagnetics 18, pp. 156-65, 1997
7. AD Rosen: Effect of a 125 milliT static magnetic field on the kinetics of voltage
activated Na+ channels in GH3 cells. Bioelectromagnetics 24:517-523, 2003
8. David Jiles, “Introduction to Magnetism & Magnetic Materials”, Chapman &
Hall, 1991
9. Jefferson Lab ESH&Q Manual, “Hazards”, September 2006
http://www.jlab.org/ehs/manual/EHSbook-523.html
10. John Moulder, “Static EM Field”, 2005 http://www.mcw.edu/gcrc/cop/staticfields-cancer-FAQ/toc.html#Q7
11. Nathan Ida, “Engineering Electromagnetics”, Springer, 2000
nd
12. Hammond, P., “Electromagnetism for Engineers”, 2 Edition, Pergamon Press,
1978
34
13. Cai, Zhemin. “Damping Effect due to Magnetic Field applied to Torsional
Vibration”, Final Year Project, National University of Singapore, 2007
14. A Gallery of Magnetic Fields, www.coolmagnetman.com/gallery/imageset.html
15. Wikipedia, the free encyclopedia,
a. Mu-metals, http://en.wikipedia.org/wiki/Mu-metal
b. Eddy Current, http://en.wikipedia.org/wiki/Eddy_currents
c. Lorentz Force, http://en.wikipedia.org/wiki/Lorentz_force
d. Magnetic Field, http://en.wikipedia.org/wiki/Magnetic_field
e. Eddy Current Brake, http://en.wikipedia.org/wiki/Eddy_current_brake
f. Brake Run, http://en.wikipedia.org/wiki/Brake_run
35
9. Appendix
9.1 Pictures of Experimental Setup and Apparatus
Figure 9.1: Setup of Final Apparatus. Disc with No Damping
Figure 9.2: Setup for arrangement (b), conventional damping effect
36
Figure 9.3: Setup for arrangements (c) and (d)
Figure 9.4: Setup for Arrangement (e) and (f)
37
Figure 9.5: Setups for Arrangements (g) (h) (i) (j)
Figure 9.6: Variable Power Source for Electromagnet, set to 12V for
our experiment
38
Figure 9.7: Gauss Probe to measure Magnetic Flux Density
Figure 9.8: Electromagnet
39
Tim e (s)
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
Total Decay Time
a
100
97
93
88
84
80
76
72
69
65
61
57
54
51
48
44
41
38
35
32
30
5:15
c
100
94
87
80
74
67
62
55
49
43
39
34
30
3:17
b
100
95
90
84
79
75
70
65
60
55
51
47
43
38
35
31
4:10
3:19
d
100
93
86
79
72
65
59
53
47
42
37
32
30
3:15
3:24
Magnetic Field Orientation
e
f
100
100
94
94
87
87
80
81
74
75
67
69
61
63
55
56
49
51
44
45
39
41
33
35
30
30
2:39
g
100
92
83
74
66
58
51
45
39
34
30
2:12
h
100
90
81
72
63
54
46
38
31
2:10
i
100
90
80
71
61
51
43
35
30
2:57
j
100
93
84
77
71
65
58
52
46
40
35
30
9.2 Experimental Readings
Table 9.1 Experimental Readings of Speed for different times and arrangements
40
9.3 Individual Graphs and Diagrams for Arrangements
9.3.1 Arrangement (a)
120
100
Speed (rpm)
80
60
a
40
20
0
0
50
100
150
200
250
Time (s)
Figure 9.9: Graph and Schematic diagram for arangement (a)
41
9.3.2 Arrangement (b)
120
100
Speed (rpm)
80
b
60
40
20
0
0
50
100
150
200
250
Time (s)
Figure 9.10: Graph and Schematic diagram for arangement (b)
42
9.3.3 Arrangement (c), (d), (e) and (f)
120
100
c
Speed (rpm)
80
d
60
e
40
f
20
0
0
20
40
60
80
100
120
140
Time (s)
(c)
(d)
Figure 9.11: Graph for arrangement (c) – (f), and Schematic diagram
for arangement (c) and (d)
43
(e)
(f)
Figure 9.12: Schematic diagram for arangement (e) and (f)
44
9.3.4 Arrangement (g) and (h)
120
100
Speed (rpm)
80
g
60
h
40
20
0
0
20
40
60
80
100
120
Time (s)
(g)
(h)
Figure 9.13: Graph and Schematic diagram for arangement (g) and (h)
45
9.3.5 Arrangement (i) and (j)
120
100
80
Speed (rpm)
i
60
j
40
20
0
0
20
40
60
80
100
120
Time (s)
(i)
Figure 9.14: Graph and Schematic diagram for arangement (i)
46
(j)
Figure 9.15: Graph and Schematic diagram for arangement (j)
47
9.4 Notes on Maxwell’s Equations
When using the Maxwell’s equations, the variations in the currents and charges of the
source are more or less synchronized with the variation in the electromagnetic field,
except for a slight delay in the field as a result of the propagation speed of
electromagnetic waves in the medium. To facilitate the prediction of magnetic field and
Lorentz’s forces, the delay effect is ignored and stationary current is assumed at every
instant. The evaluation of the forces will be presented later. This quasi-static
approximation is valid as long as the changes in time are small and the studied
geometries are considerably smaller than the wavelength.
48