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.

ii

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

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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

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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

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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

Arrangement (c) and (d)

43

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

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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

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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.

3

Figure 2.1: A conventional setup for a magnetic brake, with the disc rotating between two opposite poles of a magnet

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 eddy-

current 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.

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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.

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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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Distance (cm)0 2 4 6 8 10 12

0 22 79 173 267 372 468 5675 3 8 16 23 31 38 4710 1 2 4 6 8 10 1215 1 1 2 2.5 3 3.5 4

Voltage (V)Magnetic Field Strength (Gauss)

Table 3.1: Magnetic Field Strength values for varying Distance and Voltage

Field Strength vs Voltage for varying distances from pole

-100

0

100

200

300

400

500

600

0 2 4 6 8 10 12 14

Voltage (V)

Fiel

d St

reng

th (G

)

0cm5cm10cm15cmLinear (0cm)

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 3.4bEddy currents in the moving plate retard its movement. Braking force is proportional to velocity, conductivity, and flux density

Figure 3.4a: Principle of Magnetic Braking. As the moving plate penetrates into the magnetic field, eddy currents are generated

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 , and get E = v×B

J = E = v Bσ σ ×

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 = (v B) Bσ× × ×

If all vectors are mutually orthogonal, as is the case in our example, the force is

2 F vB Vσ= ol

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 exposure-

response 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.

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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.

Arrangement Total Decay Timea 5:15b 4:10c 3:17d 3:19e 3:15f 3:24g 2:39h 2:12i 2:10j 2:57

Decay Curves for Various Orientations

0102030405060708090

100110

0 50 100 150 200 250Time (s)

Spee

d (R

PM)

abcdefghij

Figure 4.5: Experimental Results of Speed vs. Time for 10 arrangements

Total Decay Time

0:00

1:122:24

3:364:48

6:00

a b c d e f g h i j

Orientation

Tim

e (s

)

Total Decay Time

Table 4.1: Total Decay Time from 100rpm for each arrangement

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: Arrangement (a)

0

20

40

60

80

100

120

0 50 100 150 200 250

Ti me ( s)

a

Figure 5.2: Arrangement (b)

0

20

40

60

80

100

120

0 50 100 150 20 0 250

Ti me ( s)

Spee

d (r

pm

)

b

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

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

Figure 5.3: Arrangement (c) (d) (e) (f) - clockwise from top left

0

20

40

60

80

1 00

1 20

0 2 0 40 60 80 1 00 12 0 140

T i me ( s)

Sp

eed

(rp

m)

c d e f

26

h

Figure 5.4: Arrangement (g) and (h)

00 20 40 60 80 100 1

Time (s)

20

40

60

80

100

120

20

Spee

d (r

pm)

g

h

ence similar decay time. Each arrangement (c), (d), (e) and (f) has shorter decay times

an undamped motion from 100 rpm (3min 17s, 3min 19s, 3min 15s, and 3min24s

th

respectively).

5.1.3 Dual Magnets on One Side of Disk

(g)

(h)

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

Figure 5.5: Arrangement (i)

20

80

100

120

Spee

d (r

pm)

and (j)

00 20 40 60 80 100 120

Time (s)

40

60

i j

.1.4 Dual Magnets, One on Either Side of Disk

similar to the previous case of having them both on the same side. By theory shown on

int

currents are generated and hence the retarding force increases as compared to the case of

5.2 Inferences and Theoretical Agreement

Finally, arrangement of dual magnets set up on either side of the disc results in readings

the right of Figure 5.5, the forces again oppose the direction of the motion at each po

on either side. Since there are again more poles generating the flux lines, more eddy

single magnets, giving decay times of 2min 10s and 2min 57s for (i) and (j) respectively

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.

Left View Right View Front View

(i)

(j)

28

29

Arr e f g h i jTotal Decay Time 5:15 4:10 3:17 3:19 3:15 3:24 2:39 2:12 2:10 2:57

angement a b c d

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

esign of the magnet wherein the flux originating from a particular face may not be

entical to that at a different face even

h are using in fact now twice as many

magnets at the same power rating, we expect more flux lines to be cutting the moving

be

e irrespective of polarity as positioning the

e significant drop in decay timing, another

s of arrangements (g)-(h) and (i)-(j), it is seen

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

Table 5.1: Decay Times for Various Arrangements

d

id at the same applied voltage (see Appendix A).

As for arrangements (g), (h), (i) and (j), whic

conductor hence a greater retarding force to

the directions of these forces and in each cas

forces counteract the rotation. Besides th

significant feature is observed. In both pair

that the NS-NS orientation of the magnetic

experienced. The author worked out that

30

.e.

g

itioned, but more on the orientation

f their polarity. The sheer number of magnets surely increases the strength of the

ore

ould be because the magnetic field strength itself at the poles is lesser

hen 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

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.

damping effect. What is even more uncanny is that both sets of NS-NS arrangements i

(h) and (i) result in almost identical decay times, suggesting that the effect of the dampin

is not dependent so much on how the magnets are pos

o

magnetic field present hence with two magnets producing the field we witness m

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 c

w

of 12v, the Gauss Probe too showed stronger magnetic flux density at the poles of the

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/static-

fields-cancer-FAQ/toc.html#Q7

11. Nathan Ida, “Engineering Electromagnetics”, Springer, 2000

12. Hammond, P., “Electromagnetism for Engineers”, 2nd

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

9.2 Experimental Readings

Tim

e (s

)a

bc

de

f0

100

100

100

100

100

100

100

1097

9594

9394

9492

2093

9087

8687

8783

3088

8480

7980

8174

4084

7974

7274

7566

5080

7567

6567

6958

6076

7062

5961

6351

7072

6555

5355

5645

8069

6049

4749

5139

Mag

netic

Fie

ld O

rien

tatio

ng

hi

j10

010

010

090

9093

8180

8472

7177

6361

7154

5165

4643

5838

3552

3130

4690

6555

4342

4445

3440

100

6151

3937

3941

3035

110

5747

3432

3335

3012

054

4330

3030

3013

051

3814

048

3515

044

3116

041

170

3818

035

190

3220

030

Tota

l Dec

ay T

ime

5:15

4:10

3:17

3:19

3:15

3:24

2:39

2:12

2:10

2:57

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)

0

20

40

60

80

100

120

0 50 100 150 200 250

Time (s)

Spee

d (r

pm)

a

Figure 9.9: Graph and Schematic diagram for arangement (a)

41

9.3.2 Arrangement (b)

0

20

40

60

80

100

120

0 50 100 150 200 250

Time (s)

Spee

d (r

pm)

b

Figure 9.10: Graph and Schematic diagram for arangement (b)

42

9.3.3 Arrangement (c), (d), (e) and (f)

0

20

40

60

80

100

120

0 20 40 60 80 100 120 140

Time (s)

Spee

d (r

pm)

c

d

e

f

(d) (c)

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)

0

20

40

60

80

100

120

0 20 40 60 80 100 120

Time (s)

Spee

d (r

pm)

g

h

(g) (h)

Figure 9.13: Graph and Schematic diagram for arangement (g) and (h)

45

9.3.5 Arrangement (i) and (j)

0

20

40

60

80

100

120

0 20 40 60 80 100 120

Time (s)

Spee

d (r

pm) i

j

(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