MECH 4010 & 4015
Design Project I
Fall 2013
CONCEPTUAL DESIGN REPORT
Magnetic Levitation Demonstration Apparatus
Team # 11
Ajay Puppala
Fuyuan Lin
Marlon McCombie
Xiaodong Wang
Submitted: November 8, 2013
Team #11
Conceptual Design Report
Table of Contents
List of Figures................................................................................................................................................................ 3
List of Tables ................................................................................................................................................................. 3
1.
Project Information............................................................................................................................................. 4
1.1.
1.2.
1.3.
1.4.
Project Title................................................................................................................................................ 4
Project Customer(s) ................................................................................................................................... 4
Group Members ......................................................................................................................................... 4
Useful Definitions and Acronyms .............................................................................................................. 4
2.
Conceptual Design Summary ............................................................................................................................. 5
3.
Background and Context .................................................................................................................................... 6
4.
Requirements ...................................................................................................................................................... 7
5.
Functional Overview .......................................................................................................................................... 8
6.
Component Review ............................................................................................................................................ 9
6.1.
6.2.
6.3.
6.4.
7.
Magnetic Levitation ................................................................................................................................... 9
Levitated Object ....................................................................................................................................... 12
Sensors ..................................................................................................................................................... 13
Microcontroller ........................................................................................................................................ 16
Overview of Conceptual Solution Alternatives ................................................................................................ 18
7.1.
Concept 1 ................................................................................................................................................. 18
7.1.1. Electromagnetic Suspension ............................................................................................................. 18
7.2.
Concept 2 ................................................................................................................................................. 21
7.2.1. Electrodynamics Repulsion .............................................................................................................. 21
7.3.
Concept 3 ................................................................................................................................................. 22
7.3.1. Vertical MagLev Track .................................................................................................................... 22
7.4.
Concept 4 ................................................................................................................................................. 23
7.4.1. Toroidal Electromagnetic Track ....................................................................................................... 23
8.
Feasibility ......................................................................................................................................................... 25
9.
Testing and Verification ................................................................................................................................... 26
10.
Required Engineering Expertise ....................................................................................................................... 27
11.
Resources ......................................................................................................................................................... 28
11.1.
11.2.
12.
Facilities ................................................................................................................................................... 28
Additional Advisors ................................................................................................................................. 28
References ........................................................................................................................................................ 29
Appendix A
Concept Sketches ............................................................................................................................. 30
Appendix B
Concept Evaluation Rubric .............................................................................................................. 34
Appendix C
Sample Calculations for designing an Electromagnet ...................................................................... 37
Appendix D
Supporting Literature ....................................................................................................................... 38
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 2 of 39
Team #11
Conceptual Design Report
List of Figures
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13
Figure 14
Figure 15
Figure 16
Figure 17
Figure 18
Figure 19
Figure 20
Figure 21
Figure 22
Figure 23
Figure 24
Figure 25
Figure 26
General Schematic of demonstration device ........................................................................................... 8
Functional block diagram for the magnetic levitation apparatus............................................................. 8
Levitation of model car based on rotational stabilization (courtesy of futuristicnews.com) ................. 10
Transrapid monorail system using electromagnetic levitation (Picture courtesy
www.maglev.net) .................................................................................................................................. 10
Eddy currents induced magnetic field (Diagram courtesy of www.microwavesoft.com) ..................... 11
Classification tree of four viable types of sensors for the magnetic levitation apparatus ...................... 13
Picture of Hall Effect sensor (courtesy: www.micropac.com) .............................................................. 14
Inductive proximity sensor (left, courtesy of www.asi-ez.com) and capacitive displacement
sensor (right, courtesy of www.pepperl-fuchs.us) ................................................................................. 14
Photoelectric sensor (left, courtesy of www.directindustry.com), optical proximity sensor
(center, courtesy: www.setsensing.com), and reflective sensor (right, www.indiamart.com) .............. 14
Ultrasonic sensor (courtesy of letsmakerobots.com) ............................................................................. 15
LEGA Mindsdtorms NXT 2.0 (left) and Arduino UNO (right) ............................................................ 16
Single electromagnet design with Hall Effect sensor ............................................................................ 19
single electromagnet design with photoelectric sensor ......................................................................... 19
Multiple electromagnet series arrangement........................................................................................... 20
Double electromagnet suspension design .............................................................................................. 21
Single coil suspension design ................................................................................................................ 22
Multiple coil parallel arrangement design ............................................................................................. 22
Vertical Maglev design ......................................................................................................................... 23
Toroidal electromagnet design .............................................................................................................. 24
Magnetic Levitation Track design ......................................................................................................... 30
Single electromagnetic suspension design with photoelectric sensor ................................................... 31
Single electromagnetic suspension design with Hall Effect sensor....................................................... 31
Double electromagnet design with Hall Effect sensor for suspension and/or repulsion ....................... 32
Single multiple coil electromagnetic suspension design with Hall Effect sensor ................................. 32
Vertical ring electromagnetic track design ............................................................................................ 33
Toroidal electromagnet design .............................................................................................................. 33
List of Tables
Table 1
Table 2
Table 3
Table 4
Table 5
Table 6
All options available in each category .................................................................................................... 9
Comparison of sensors based on detection range and cost .................................................................... 15
Evaluation Matrix for Sensors............................................................................................................... 15
Comparison of Microcontroller cost ..................................................................................................... 17
Highlights selected options from each category .................................................................................... 18
Required engineering expertise ............................................................................................................. 27
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 3 of 39
Team #11
1.
Conceptual Design Report
Project Information
1.1.
Project Title
Magnetic Levitation Demonstration Apparatus
1.2.
Project Customer(s)
Dr Robert Bauer
Professor
Mechanical Engineering Department
Dalhousie University
1.3.
Group Members
Ajay Puppala
Fuyuan Lin
Marlon McCombie
Xiaodong Wang
1.4.
Tel: 1-902-999-4414
Tel: 1-902-488-6688
Tel: 1-902-489-6655
Tel: 1-902-488-8556
email: aj874646@dal.ca
email: fy330663@dal.ca
email:mr587226@dal.ca
email: xd367973@dal.ca
Useful Definitions and Acronyms
AWG
EOPD
EM
GUI
I/O
MagLev
MCU
P
PC
PCB
PI
PID
PPE
PWM
MECH4010/4015
-
American Wire Gage
Electro-Optical Proximity Detector
Electromagnet
Graphical User Interface
Input/output
Magnetic Levitation
Microcontroller Unit
Proportional Control
Personal Computer
Printed Circuit Board
Proportional Integra Control
Proportional Integral Derivative Control
Personal Protective Equipment
Pulse Width Modulation
Magnetic Levitation Demonstration Apparatus
Page 4 of 39
Team #11
2.
Conceptual Design Report
Conceptual Design Summary
The objective of this project is to discuss the various concepts of a Magnetic Levitation Demonstration
Apparatus for MECH 4900(4905) Control Systems II course. The scope and requirements for the project are briefly
outlined and an overview of the functional components is given. There are various components in building the
device including the physical levitation, sensors, circuitry, microcontroller, and MATLAB/Simulink. Vast arrays of
options are available for each of these components; the most viable ones are considered in the document.
Consequently, several concepts were proposed and filtered down to one or two based on the degree of fulfillment of
basic requirements, cost assessment, design compatibility, and overall feasibility.
Concepts for levitation are generated based on the selected components and general design approach. These
concepts are examined for advantages and disadvantages to find better alternatives. To find the best solution for the
design and alternatives the requirement criteria is revoked and a rubric is built for comparison. Feasibility of the
design is considered and possible challenges are encapsulated. The future course of action for successful completion
of the project is enumerated in the feasibility section of the document. A method of testing the device components is
provided for validation. Additionally, the progress level of the group in the different areas related to the group is
laid out in the required expertise section. Finally, supporting calculations, literature review, and design sketches
were presented.
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 5 of 39
Team #11
3.
Conceptual Design Report
Background and Context
Demonstrations provide the opportunity for students to predict theoretical outcomes of real life
applications of course material which in turn allow them to confirm their initial understanding of those same
concepts. By making a prediction, students develop an expectation based on their initial understanding of the
concept. As they observe the demonstration they find out whether their prediction is accurate. If not, the
instructor can discuss any differences between their initial understanding and what the demonstration
actually shows.
Visual demonstrations help to bridge the gap between visual and verbal communication of course
material. Although diagrams may be a step further to having a better visual understanding of a concept, a
demonstration that produces live feedback vastly improves the delivery of course material. This concept is
similar to a salesman increasing the appeal of a product by showing its many uses through infomercials; i.e.
demonstrations of the basic use of a known concept (e.g. blending with the Magic Bullet). The only difference
for course material from this analogy is that the concepts being taught are new to students and may not be
initially understood from course lectures. Consequently, demonstrations allow students an extra chance to
try out their own theories on a subject to confirm their understanding.
Thus, the scope of our project is to design and build a portable and compact device that magnetically
levitates an object to demonstrate the different design theories presented in MECH4900 Systems II.
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 6 of 39
Team #11
4.
Conceptual Design Report
Requirements




Purpose
o
Build portable demonstration device
o
Levitate object magnetically
o
Educational tool
o
Demonstrate theories presented in MECH4900(4905) Control Systems II
Visual Requirements
o
Shall be viewable from a back of the classroom and/or using cameras
o
Levitate object for range of 5 cm
User Convenience & Safety
o
Easy to carry; i.e. lightweight
o
Easy to store
o
No potential electrical risk to user
o
No potential projectile risk to user
o
No PPE required for operation
Power Requirements
o



Conventional 120 VAC input
User Interactive Requirements
o
Simulate a wide variety of control methods available in MATLAB/Simulink
o
User shall interact with the device using a graphical user interface (GUI)
o
Device shall be ready to operate once plugged into PC
o
No additional programming shall be required
Demonstrative Requirements
o
Comparison of desired, simulated, manipulated, and measured controller variables
o
Nyquist plots
o
Bode diagrams
o
Lag, lead, lag-lead compensation techniques
o
P, PI, PID control
Miscellaneous
o
Shall be an active controller
o
Budget $1,500
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 7 of 39
Team #11
5.
Conceptual Design Report
Functional Overview
Figure 1 below shows a general schematic of the components needed to build a functional magnetic levitation
demonstration apparatus based on the specified requirements mentioned. For magnetic levitation to be
achieved for the purpose of demonstrating various design techniques presented in Control Systems II, a user
would need to be able to vary the outcome of levitation; i.e. the levitated object must be manipulated in some
manner. The manipulation of a levitated object could only be achieved by some form of motion of the
levitated object as indicated by the very definition of levitation; “the phenomenon of a person or thing rising
into the air ...” (Wordnet Web, Princeston University). Consequently, it is anticipated that the levitating
magnetic field must be varied to achieve positional manipulation of the levitating object.
Figure 1
General Schematic of demonstration device
The next figure outlines the required functionality of the operating device. The final design should
meet this functionality.
INPUT
PROCESS
OUTPUT
Control method generated in
MATLAB/Simulink
Execute the control method from
MATLAB/Simulink through
microcontroller
Graphical display of recorded data
Current supplied to the magnetic
coil
Maintain the position of the
levitated object using system
feedback
Position feedback of object from
sensor
Record data from sensor over
specified duration of demostration
Figure 2
Functional block diagram for the magnetic levitation apparatus
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 8 of 39
Team #11
6.
Conceptual Design Report
Component Review
A list of component options was obtained from general research in each category. They are presented in the table below:
Table 1
All options available in each category
Levitation
Technique
Permanent
Magnets
Material
Chrome Steel
Object
Shape
Rectangular
prism
Sensor
Microcontroller
Horizontal
Hall Effect
Arduino
Motion
Electromagnetic
Regular Steel
Circular disk
Vertical
Reflective
Electrodynamics
Superconducting
Neodymium
Composite
Solid sphere
Hollow sphere
Angled
Optical Proximity
Photoelectric
Capacitive
Displacement
Inductive
Proximity
Ultrasonic
Diamagnetic
LEGO Mindstorm
NXT 2.0
BeagleBoard
Altera DE2
The following sections go through the selection process for each device. Best two or one are selected from each
category. Concepts are generated based on the selections
6.1.
Magnetic Levitation
There are different to ways to levitate an object magnetically. The four major techniques consider in
the project are shown in the chart below. Quantum theory is intentionally ignored because the effect is so
small that it is certainly cannot meet the range of levitation required in the project (Lance 2005).
Pseudo levitation primarily consists of two magnets constrained vertically. They would distance
themselves apart causing levitation. This type of levitation can be immediately ruled out because it is passive.
However, it can be used in other techniques to improve the design. Also, this system can be slightly altered to
achieve stability and active control. According to Earnshaw’s theorem, permanent magnets cannot be
levitated in static configuration (Lance 2005). However, if one of them were to spin continuously with a drive
coil, levitation above a toroidal magnet arrangement is possible. The drive coil can be controlled to gain active
control. This type of levitation is employed in the Levitron toys shown below:
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 9 of 39
Team #11
Conceptual Design Report
Levitation of model car based on rotational stabilization (courtesy of futuristicnews.com)
Figure 3
Electromagnetic levitation consists of one or more magnetic coils that are exposed to time- varying
current to create electromagnetic field to hold an object in place. This system by itself is quite unstable
because the strength of the magnetic field is high when the object is closer and low when it is further apart.
However, the field strength can be controlled through a feedback loop which is also required in the project
(Brandt 1989). The feedback loop would control the position of the levitating object based on the current that
flows through the electromagnets to adjust its field strength. This type of levitation is used in high speed
monorails.
Figure 4
Transrapid monorail system using electromagnetic levitation (Picture courtesy
www.maglev.net)
Electrodynamic levitation consists of conductors that are exposed to time-varying magnetic field to
induce eddy currents in the conductive material. It creates a repulsive magnetic field around the conductor
holding the magnet coil without any support (Thompson 2000).
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 10 of 39
Team #11
Figure 5
Conceptual Design Report
Eddy currents induced magnetic field (Diagram courtesy of www.microwavesoft.com)
This type of design puts restrictions on the type of object that can be levitated. Certainly it has to be always a
coil. Levitation can mostly be in vertical direction with the coil on top of the conductive material. This places
another major restriction on the type of motion for object to be levitated.
The stability achieved through electrodynamic levitation is considerably greater than the
electromagnetic type of levitation. This is mainly because the levitating object is pushed against gravity as
supposed to holding it. However, the levitation Is stable vertically, it may not be stable horizontally. Some sort
of support may be required to arrest the motion on the horizontal plane. Further research and advise from
the review panel member Dr. Little is needed.
Diamagnetism is a material property to repel any applied magnetic flux. A permanent magnet can be
stabilized with a di-magnet like pyrolytic graphite (Lance 2005). This technique has to be ruled out because
of the same reason for pseudo levitation, it is passive. Meissner effect which is a special case of diamagnetism
has to be ruled out due to the same reason.
The major requirements for the selection of a technique are active control of the device, stability of levitation,
ease of to build, availability of materials, and the range of levitation. These are used as the parameters for
evaluation of each technique. Table shows a comparison of the levitation techniques mentioned using the
following evaluation criteria:
1.
2.
3.
4.
5.
Unacceptable
Below Average
Acceptable
Good
Best
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 11 of 39
Team #11
Table 2
Conceptual Design Report
Evaluation Matrix for Levitation Techniques
Active
or
Passive
Passive
Stability of
Levitation
Availability
of Materials
Range of
Levitation
Ease to
Build
Total
N/A
N/A
N/A
N/A
-
Rotational Stabilization
Active
2
3
5
3
13
Electromagnetic
Active
3
5
4
5
17
Electrodynamic
Active
5
4
4
3
16
Diamagnetic
Passive
N/A
N/A
N/A
N/A
-
Pseudo Levitation
From the evaluation matrix, electromagnetic and electrodynamic types were chosen as the most suitable for
the experiment. This selection leads to a final but important factor of the project to be considered, direction of
motion. Three type of motion can be considered; vertical, horizontal, or a combination of the two. However,
for the sake of simplicity and designing an apparatus that can capture the attention of users, vertical motion
was considered to be the best option. This decision was made as vertical motion is easier to see from a
distance in comparison to horizontal motion and a combination of the two would require a more
cumbersome apparatus design that may take away from the ergonomic requirements of the project.
Additionally, it is impressive to see an object move against gravity without any visible aids.
6.2. Levitated Object
For magnetic levitation to be demonstrated, a suitable object must first be selected. Magnetic levitation
can only be performed on an object that can be affected by an external magnetic field. Objects that are
attracted to magnets and not able to independently sustain a magnetic field are not suitable for magnetic
levitation. These objects are attracted to magnets through magnetic induction and thus, will change magnetic
polarity in bias to magnetic attraction (CyberPhysics.co.uk). Although, magnetic attraction can be used for
levitation, these materials are still not suitable for the project as their magnetic strength varies with distance
from a magnetic source. Consequently, the most suitable object for this project is a magnet because of its
ability to maintain its magnetic poles and, most importantly, field strength in the presence of an external
magnetic field. Magnets are distinguished as strong or weak in comparison to each other based on their
permeability. Consequently, the primary criterion for selecting a suitable object material for the project is
magnetic permeability. The higher an object’s permeability the better its suitability for levitation as this also
results in an increase in sensitivity to an external magnetic field. For successful controlled levitation to occur,
the levitated objected must be able to respond to a varying magnetic field strength of an external force.
The secondary criterion of the object is its shape and size. The object should be suitably large for the
levitation to be viewable from a distance. For flat shapes, visibility may be hindered based on the objects
orientation. Consequently, the object’s shape must be one of either uniform uniaxial cross-section or visibly
well-proportioned in size. In addition, for an object with a non-uniform proportion of width and height, an
external magnetic field may cause the object to levitate horizontally away from the vertical axis of levitation.
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 12 of 39
Team #11
Conceptual Design Report
Consequently, an object with uniform uniaxial cross-section is a better option for the levitating object. The
object can be either solid or hollow; however, a hollow sphere may require a denser material than a solid one
for the same size in order to maintain a suitable weight for levitation. Additionally, it would be difficult to
make or buy a hollow sphere as compared to a solid sphere especially for a permanent magnet. The following
table shows an evaluation matrix for object selection.
6.3. Sensors
There are various types of sensors that can measure the linear displacement of the levitating object
without touching it. It is important to determine the best type of sensor because the range and sensitivity
determines the range of the levitating object. The following diagram the categories and sensors that can be
used from each category.
Sensors
Magnetic Sensor
Hall Effect Sensor
Electric Sensor
Optical Sensor
Inductive Proximity
Sensor
Photoelectric
Sensor
Capacitive
Displacement
Sensor
Optical Proximity
Sensor
Frequency based
Sensor
Ultrasonic Sensor
Reflective Sensor
Figure 6
Classification tree of four viable types of sensors for the magnetic levitation apparatus
From the diagram it is evident that there are four major categories of sensors. They are divided primarily
based on the method of operation. Magnetic sensor would measure the magnetic field strength generated
from the coil and the permanent magnet that is levitated. If the distance of the levitating magnet increased or
decreased relative to the coil, the field through the sensor would change correspondingly. Using a predetermined field strength and distance table, position of the object can be determined. The only type of
magnetic sensor considered for the project is the Hall Effect sensor.
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 13 of 39
Team #11
Figure 7
Conceptual Design Report
Picture of Hall Effect sensor (courtesy: www.micropac.com)
Electric sensors works similar to a magnetic sensor, however, the magnet part is replaced either with a
capacitor or inductor that is looped around. When the object enters the sensing field, Eddy currents flow
through the object which reduces the signal amplitude and triggers a change of state in the sensor output
(DigiKey Corp.).
Figure 8
Inductive proximity sensor (left, courtesy of www.asi-ez.com) and capacitive displacement sensor
(right, courtesy of www.pepperl-fuchs.us)
Optical sensors used light as a medium to detect the presence and movement of target. They are
various techniques that can be used to send and/or receive light signals from the object. Based on the
techniques optical sensors are further divided into photoelectric sensor, optical proximity sensor and
reflective sensor. EOPD is one example of the optical proximity sensor.
Figure 9
Photoelectric sensor (left, courtesy of www.directindustry.com), optical proximity sensor (center,
courtesy: www.setsensing.com), and reflective sensor (right, www.indiamart.com)
Finally, the frequency based sensors are extremely powerful and useful for high detection distances.
Ultrasonic sensor is one type of frequency based sensor that can be used in the project. Basically, it emits high
frequency sound energy. Waves reflect of levitating object and are detected by the sensor. The sensor
measures the total time required for the pulse to return and calculate the distance (DigiKey Corp.).
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 14 of 39
Team #11
Figure 10
Conceptual Design Report
Ultrasonic sensor (courtesy of letsmakerobots.com)
The major requirements for the selection of the sensor are the range of detection of the sensor, its
compatibility with the microcontroller, and extent of effect of unwanted inputs in the measurement. Other
factors which are important to consider during the selection is the size of the sensor and ease of
configuration. Cost per unit to purchase the sensor is also important consider in the selection process. The
following table shows a list of sensors and corresponding costs based on the range of detection:
Table 2
Comparison of sensors based on detection range and cost
Type of Sensor
Detection Range (cm)
Price per unit (USD)
Hall effect sensor
N/A
1.00
Ultrasonic sensor
N/A
400+
Inductive proximity sensor
0.2
1.0
2.0
1.0
2.5
1.0
15.0
35.00
50.00
115.00
100.00
200.00
66.00
7.50
*EOPD - 55.00
2.50
Capacitive displacement sensor
Photoelectric sensor
Optical proximity sensor
Reflective sensor
5.0
*All the prices are obtained from the Digi-Key website except for the EOPD which is taken from the Robotshop website.
Table 3
Evaluation Matrix for Sensors
4
Testing
&
Configuration
5
25
3
3
3
16
2
3
3
3
15
2
2
3
3
3
14
3
3
4
4
3
5
22
Optical proximity
4
3
3
3
3
3
22
Reflective
4
4
3
3
3
3
20
Range of
Detection
Unit
Cost
Resistance to
Interference
Microcontroller
Compatibility
Size
Hall effect
4
4
4
4
Ultrasonic
4
1
2
Inductive proximity
Capacitive
displacement
Photoelectric
1
3
1
Sensor
∑
The evaluation for each of the sensor type for requirements is based on the same criteria used for the levitation
techniques.
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 15 of 39
Team #11
Conceptual Design Report
From the evaluation matrix it is clearly evident that Hall Effect sensor, photoelectric sensor, and optical
proximity sensor distinguish compared to other type of sensors. If the selection has to be further narrowed
down to two sensors, definitely one of them would be Hall Effect sensor. Between the photoelectric and
optical proximity sensor is hard choose because they both have an equal score of 22. However, based on past
research, most models are build using the photoelectric sensor rather than optical proximity sensor. It is
convenient to choose photoelectric but further research and comparison is required.
6.4. Microcontroller
A microcontroller (MCU) is a small, self-contained computer on a single integrated circuit (IC) containing
a processor core, memory, and programmable input/output peripherals. Microcontrollers are used in many
automatically controlled devices. The MCU can be described as the hub of the magnetic levitation device; it
will be responsible for controlling the power input of the electromagnet, retrieving data from the device’s
sensor, and for returning the retrieved data back to MATLAB/Simulink to be plotted and displayed on a PC.
Consequently, the MCU will be responsible for executing the function of controllers designed in
MATLAB/Simulink. There are several MCUs available from different manufacturers. However, the main
criterion to be met for the project by the MCUs is to be compatible with Matlab/Simulink via available
programming toolboxes. The MATLAB/Simulink toolboxes are separate toolkits that allow users to interface
with and command the MCU using MATLAB syntax or by uploading controllers through Simulink. The
following are some supported MCUs according to the MATLAB/Simulink website:

LEGO Mindstorms NXT 2.0

Arduino

Altera DE2

BeagleBoard
Figure 11
LEGA Mindsdtorms NXT 2.0 (left) and Arduino UNO (right)
Given that the scope and requirements of the project do not exceed the specifications of any of the
aforementioned MCUs, they were all deemed viable for the project’s application. Out of the four MCUs
mentioned, the LEGO Mindstorms NXT 2.0 and Arduino were readily available for testing, free of charge, from
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 16 of 39
Team #11
Conceptual Design Report
the University. Consequently, there is on-campus support available from the lab technicians and graduate
students in the Mechanical Engineering department of the University. However, a decision was made to go
with the Arduino; specifically the Arduino UNO. The decision to choose the Arduino was made primarily
because it was cheaper than the NXT. Additionally, it has been the choice for most Mechanical engineering
senior year projects that required some form of controlling unit. The following is a comparison of the unit
cost of the MCUs mentioned above:
Table 4
Comparison of Microcontroller cost
Microcontroller
LEGO Mindstorms NXT 2.0
Arduino
Altera DE2
BeagleBoard
MECH4010/4015
Unit Cost (CAD)
349.99
28.95
269.00
45.00
Magnetic Levitation Demonstration Apparatus
Page 17 of 39
Team #11
7.
Conceptual Design Report
Overview of Conceptual Solution Alternatives
Based on the component selection criteria discussed in the previous section, the following table was
generated to display the selected component considerations.
Table 5
Highlights selected options from each category
Levitation
Technique
Permanent
Magnets
Material
Chrome Steel
Object
Shape
Rectangular
prism
Motion
Horizontal
Electromagnetic
Regular Steel
Circular disk
Vertical
Electrodynamics
Superconducting
Neodymium
Composite
Solid sphere
Hollow sphere
Angled
Microcontroller
Sensor
Arduino
Hall Effect
LEGO Mindstorm
NXT 2.0
BeagleBoard
Altera DE2
Diamagnetic
Reflective
Optical Proximity
Photoelectric
Capacitive
Displacement
Inductive
Proximity
Ultrasonic
Consequently, the following concept design solutions were generated based on selection considerations for
levitation technique, object motion, and sensor. The circuitry and microcontroller were excluded as these
components do not affect the physical design of the apparatus. The following preliminary designs were
developed from hand sketches included in Appendix A.
7.1.
7.1.1.
Concept 1
Electromagnetic Suspension
The first concept that is generated based on the components that were chosen is the simple
electromagnetic suspension shown in the figure next page. The design uses an electromagnet to generate
magnetic field when power an external source. The linear position of the levitating object is determined using
a Hall Effect sensor. One sensor is enough to get the position and it is placed right under the electromagnet.
The stand to hold the device and clamp to mount the electromagnet are kept simple to avoid complications.
The major advantages with this design are simplicity of design and easiness to build. The stand and
other parts can be enhanced if this concept is chosen for reliability and portability. A major disadvantage with
this design are only small variations in position of levitating object is possible. Also, the use of Hall Effect
sensor requires a table of comparison for the field strength
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 18 of 39
Team #11
Figure 12
Conceptual Design Report
Single electromagnet design with Hall Effect sensor
An alternative for the single electromagnet design concept is the use of photoelectric sensor. This
requires changing the design of the stand and holding method for the electromagnetic coil. This is illustrated
in figure given below:
Figure 13
single electromagnet design with photoelectric sensor
A major advantage with this type of design it is extremely accurate but the range of the sensor is quite
small. The bulbs and the sensor have to be place very close to each other. It is not very difficult to build and
appropriate level of complexity for the project. The light from the LED would help to display the object much
better than the other two designs.
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 19 of 39
Team #11
Conceptual Design Report
The problem with the low strength of the magnetic field still persists with the design. An alternative to
the single coil design is having multiple coil electromagnets as shown in figure 14. This design might address
the problem with the range of distance for the levitating object. Presumably, adding more electromagnets
may increase the magnetic field in turn gives extra range for the levitating object. The only complication with
this design is the integration of electromagnets to produce a combined magnetic field. It requires clear
understanding of functionality of electromagnets.
Figure 14
Multiple electromagnet series arrangement
The best possible way to overcome the problem is to use two electromagnets to extend the range of
magnetic field (Please see figure 16 on the next page). There would be severe problems in terms of stability
and obtaining levitation. The levitating permanent magnet can snap to either one of electromagnet if the
current flow and direction is not properly monitored. This design might need careful attention while building
and testing for functionality.
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 20 of 39
Team #11
Conceptual Design Report
Figure 15
7.2.
7.2.1.
Double electromagnet suspension design
Concept 2
Electrodynamics Repulsion
The second major concept generated from the levitation technique is the electromagnetic repulsion.
Figure 18 shows a simple arrangement based on the concept. A magnetic coil is levitated on top of a
conductor plate that is induced with eddy currents and field around it. It is easy to build and test. Attaining
vertical stability with repulsion is easier compared to electromagnetic suspension. However stability on
horizontal plane is difficult without constraining the magnetic coil. This might pose problems with the
display, may not seem free levitation. Either Hall Effect sensor or the photoelectric sensor can be used for the
measurement of distance of the magnetic coil from the conductor plate. Current has to be supplied to the
moving magnetic coil which may be difficult with the wiring and other connections.
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 21 of 39
Team #11
Conceptual Design Report
Figure 16
Single coil suspension design
The concept of using multiple electromagnets can be extended to suspension. Figure 17 shows an
example of three coils in parallel configuration. This might cause problem of stability but increases the range
of levitation which is better for classroom display. Another problem with this design is trying to achieve the
functionality and testing the device.
Figure 17
7.3.
7.3.1.
Multiple coil parallel arrangement design
Concept 3
Vertical MagLev Track
The following design is consider as a different approach from the general evaluation. The idea is
motivated from the Maglev trains discussed in the levitation techniques. It gives an opportunity to
approach the design problem in a different perspective. It is uncertain whether this design may be
feasible but it was considered during evaluation. The major advantage of this model is the motion of
a levitating disk is properly constrained; thus, there is proper stability for motion. The levitation
can be seen through the gaps between the electromagnets. The major disadvantage with this
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 22 of 39
Team #11
Conceptual Design Report
approach is that it looks like the disk is supported by the electromagnet tracks. Also, the cost to
build the physical model may be quite expensive compared to others consider primarily due to the
extra material needed to build the electromagnet tracks and the levitating disk.
Figure 18
7.4.
7.4.1.
Vertical Maglev design
Concept 4
Toroidal Electromagnetic Track
Another concept consider apart from the evaluation of components is the toroidal electromagnetic track.
An object is levitated inside a torus shape core where magnetic wire coil is place around in equidistance. Few
advantages with this type of system is amount of magnetic flux that escapes outside the coke is minimum due
to symmetry. Also, it gives higher efficiency required for the sensitive circuitry. The major disadvantage is
visibility requires molding transparent plastic and also there is only limited power capacity to pass it on to
four coils.
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 23 of 39
Team #11
Figure 19
Conceptual Design Report
Toroidal electromagnet design
All solution design alternatives are considered and briefly explained with advantages and disadvantages.
Appendix B contains the rubric for evaluation of the all the design alternatives for the 4 concepts. The basic
requirements are weighted the most compared to the parts, design, and cost assessment. The general
evaluation criterion, in page 12 is used for the assessment. This assessment does not consider the cost to
build the circuitry mainly because it is almost the same for all the concepts.
From the assessment it is evident that single electromagnet design with Hall Effect sensor is the best
solution followed by single coil suspension design. They were the top scoring concepts mainly because they
were consider a good design for the basic requirements which was weighted most in the assessment, as much
as 60%. Certainly if design assessment that evaluates for complexity and ease to build other concepts like the
single electromagnet design with photoelectric sensor and double electromagnet suspension design would be
considered. It is not surprising that their scores follow very close to the first two designs.
If other designs have to consider apart from the single electromagnet design with Hall Effect sensor for
magnetic strength it would be double electromagnet suspension design and for better design as a whole
single electromagnet design with photoelectric sensor would be considered.
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 24 of 39
Team #11
8.
Conceptual Design Report
Feasibility
The concept design, single electromagnet design with the Hall Effect sensor, was selected after
evaluating all concepts. The major components of the design include the single electromagnet levitation,
spherical permanent magnet made of Neodymium, Hall Effect sensor, and Arduino microcontroller. Almost
all of the components are available in retail stores in Halifax, N.S. except for the electromagnet which may
have to be ordered custom-made or hand built according to the magnetic field strength requirement. This
concept design has the option of conducting ether repulsion or attraction levitation depending on its
position/orientation on the apparatus. Consequently, this design provides the option of testing out both
methods of electromagnetic levitation. Testing of the device and the operating circuitry can also be a cause for
concern in the project as these components determine the feasibility of the design to meet the project’s
requirements.
In terms of availability of materials, the Hall Effect sensor and Arduino microcontroller can be
obtained from a local electronics store in Halifax called Jentronics. Permanent magnets made of Neodymium
are available at Princess Auto; however, these are disk shaped. Initial prototype and testing phase can be
carried out with the available magnet size but further research is needed to find a spherical neodymium
magnet locally; these can be purchased online. The circuit needed for the system can be built with a
prototype board, wires, and electrical components that can be bought at Jentronics. Putting them together
according to the requirement may require research into electric circuits and guidance from Electrical
advisors. Once the layout for the circuitry is determined it can be printed at a local PCB contract
manufacturer, Sunsel Systems.
There are multiple options for the electromagnet design. Calculations in Appendix C indicate the
initial approach towards building the electromagnet. There are various limitations and parameters that need
to be determined. Off the shelf electromagnets are available; however, testing is required to determine
whether this is suitable or needs to be built based on specified calculations for the apparatus (please see
Appendix D). A major challenge anticipated for the project is the integration of the components to achieve
functionality through input methods from MATLAB/Simulink. The group has so far successful interfaced the
microcontroller with MATLAB and Simulink. Other challenges include building a block diagram, executing
control methods from Control Systems II course syllabus, retrieving data from the sensor, and adhering to the
project requirements.
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 25 of 39
Team #11
9.
Conceptual Design Report
Testing and Verification
There are a variety of different shapes of magnets that can be tested to confirm the concerns of shape
on object levitation. As mentioned above in the Feasibility section, different materials and shapes of magnets
are available for purchase; thus, tests will be conducted on as many different shapes before making a final
decision. In addition, it is possible to purchase electromagnets at local hardware stores for testing, as opposed
to purchasing wires and electromagnet core materials separately without certainty of success. The
electromagnets available for purchase come in the form of pneumatic switches and igniters; these can be
taken apart to retrieve the electromagnet solenoid.
Given that the MCU must act as an input/output (I/O) hub, it is important to test out this basic
functionality in the simplest manner possible to verify its usefulness to the project. A common means of
testing out I/O applications is by toggling LEDs on and off to determine whether signal transmission is
possible. However, this may not be the most effective means of confirming data retrieval from the MCU.
Consequently, a viable alternative to testing data retrieval would be to connect a simple sensor to be powered
and read by the MCU; for example, a temperature sensor. Successful execution of basic I/O tests, as
mentioned, will prove that the necessary control of a magnetic levitating device can be achieved. Toggling the
on/off state of an LED is proof of concept that the required external supply to the electromagnet can be
regulated as needed. Retrieving data from a sensor will be proof of concept that it is possible to retrieve data
from a sensor. The next step in testing and verification would be to attempt the same test mentioned above,
but this time using the MATLAB/Simulink toolboxes. Successfully accomplishing communication or control of
the MCU using MATLAB/Simulink would prove that it is possible to control the magnetic levitation device
using the chosen MCU and MATLAB/Simulink. In other words, this would fulfill part of the necessary
functional requirements of the project.
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 26 of 39
Team #11
Conceptual Design Report
10. Required Engineering Expertise
The following table presents a list of anticipated engineering expertise required for successful project
completion.
Table 6
Required engineering expertise
Technical Area
Technical
Communication
Research &
Development
Team Member Responsible
Ajay Puppala
Fuyuan Lin
Xiadong Wang
Marlon McCombie
Ajay Puppala
Fuyuan Lin
Xiadong Wang
Level of Expertise Required
Expert
This skill is important for the necessary
documentation and communication required
for the duration of the project
Intermediate
Detail research must be carried out. This will
help to determine the parameters necessary
for levitation and component selection and
testing. This expertise is important to the
overall success of the project
Intermediate
A clear understanding of the function of circuit
components is required for reliable and effective
transfer of power and data among the
components.
Amateur
A basic understanding of microcontrollers and
programming is required to be able to test and
communicate with the system components and
the required GUI.
Intermediate
An intermediate level of understanding for this
technical area is required for successful
communication and testing between the
microcontroller and the required GUI and
simulation and testing of the apparatus’ ability
to meet the projects main requirement for
demonstration.
Circuit Analysis
Marlon McCombie
Fuyuan Lin
Microcontrollers
Marlon McCombie
MATLAB/Simulink
Controller Design
Ajay Puppala
Xiadong Wang
Marlon McCombie
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 27 of 39
Team #11
Conceptual Design Report
11. Resources
11.1.
Facilities
The following is a list of facilities that are required for the project duration and a short description
for their necessity:
 Design workbench
o For testing prototype apparatus and for storing materials and components to allow
easy access by team members
 Measurements Laboratory (C255)
o For testing EM with varying current input using an bench power supply; especially
in the unlikely case that the currents needed for levitation are potentially dangerous
 Machine Shop/Carpentry Shop
o For fabricating a suitable chassis for the final apparatus
11.2.
Additional Advisors
Name:
Position:
Telephone:
Email:
Dr. Ya-Jun Pan
Professor, Mechanical Dept.
1-902-494-6788
yajun.pan@dal.ca
Name:
Position:
Telephone:
Email:
Dr. Timothy Little
Professor, Electrical Dept.
1-902-494-3988
timothy.little@dal.ca
Name:
Position:
Telephone:
Email:
Jonathan MacDonald
Electrical Technician, Mechanical Dept.
1-902-494-6557
jon.macdonald@dal.ca
Name:
Position:
Telephone:
Email:
Angus MacPherson
Mechanical Technician, Mechanical Dept.
1-902-494-3238
angus.macpherson@dal.ca
Name:
Position:
Telephone:
Email:
Corey MacNeil
Automation Specialist, Jentronics Ltd.
1-902-468-7987
corey@jentronics.ca
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 28 of 39
Team #11
Conceptual Design Report
12. References
Brandt, E. H. "Levitation in Physics." N.p., 20 Jan. 1989. Web. 28 Oct. 2013.]\
“Definition of Levitation.” http://wordnetweb.princeton.edu/perl/webwn?s=levitation. Retrieved
November 6, 2013
“Electromagnetic Induction.” http://www.cyberphysics.co.uk/topics/magnetsm/electro/EMI.htm.
Retrieved November 7, 2013
"Electronic Components Distributor | DigiKey Corp. | CA Home Page. N.p., n.d. Sat. 03 Nov. 2013
“LEGO Mindstorms Online Store.” http://shop.lego.com/en-CA/LEGO-MINDSTORMS-NXT-2-0-8547.
Retrieved November 6, 2013
“Liquidware Online Store” http://www.liquidware.com/shop/show/ARD-UNO/. Retrieved November 6,
2013
"RobotShop : The World's Leading Robot Store." RobotShop. N.p., n.d. Sat. 03 Nov. 2013
Thompson, Marc T. "Eddy Current Magnetic Levitation: Models and Experiments." IEEE. N.p., 200. Web.
28 Oct. 2013.
Williams, Lance. "Electromagnetic Levitation Thesis." N.p., 2005. Web. 28 Oct. 2013.
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 29 of 39
Team #11
Conceptual Design Report
Appendix A Concept Sketches
Figure 20
Magnetic Levitation Track design
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 30 of 39
Team #11
Conceptual Design Report
Figure 21
Single electromagnetic suspension design with photoelectric sensor
Figure 22
Single electromagnetic suspension design with Hall Effect sensor
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 31 of 39
Team #11
Conceptual Design Report
Figure 23
Double electromagnet design with Hall Effect sensor for suspension and/or repulsion
Figure 24
Single multiple coil electromagnetic suspension design with Hall Effect sensor
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 32 of 39
Team #11
Conceptual Design Report
Figure 25
Vertical ring electromagnetic track design
Figure 26
Toroidal electromagnet design
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 33 of 39
Team #11
Conceptual Design Report
Appendix B Concept Evaluation Rubric
Rubric for Design Assessment
Single
electromagnet
design with Hall
Effect Sensor
Single
electromagnet
design with
Photoelectric
sensor
Multiple
electromagnet
series arrang.
Basic Requirements (60% weightage)
1
Viewablility & Stability of the levitating object
3
3
3
2
Implement control design theories
4
4
4
3
Portable
4
4
4
4
Power input: Household Outlet
4
4
4
5
Total weight: Easy to carry
5
4
3
6
Safe in class environment
4
4
4
7
Graphical User Interface (GUI) for interaction
4
4
4
8
Simulation: MATLAB
4
4
4
9
All plots are shown in the GUI window
4
4
4
Strength of the magnetic field
3
3
4
Wiring
5
5
3
2
Sensor effectiveness in detection of the object
3
4
3
3
Microprocessor
5
5
5
4
Total displacement levitating object
3
2
3
5
Frame support
5
5
5
Parts Requirements (20% weightage)
1
Electromagnet
Design Assessment (10% weightage)
1
Design complexity
3
4
4
2
Ease to build
4
3
2
3
Holistic Judgement
5
4
3
Cost Assessment (10% weightage)
1
Cost of wiring for electromagnet
4
4
3
2
Cost of sensor
4
2
4
3
Cost of microprocessor
4
4
4
4
Cost of building the frame
4
3
3
29.2
28.2
27.3
Total Score
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 34 of 39
Team #11
Conceptual Design Report
Rubric for Design Assessment
Double
electromagnet
suspension
design
Single coil
suspension
design
Multiple coil
parallel
arrangement
design
Basic Requirements (60% weightage)
1
View ability & Stability of the levitating object
5
4
3
2
Implement control design theories
4
4
4
3
Portable
3
4
3
4
Power input: Household Outlet
4
4
4
5
Total weight: Easy to carry
3
5
3
6
Safe in class environment
4
4
4
7
Graphical User Interface (GUI) for interaction
4
4
4
8
Simulation: MATLAB
4
4
4
9
All plots are shown in the GUI window
4
4
4
Strength of the magnetic field
5
4
5
Wiring
3
3
3
2
Sensor effectiveness in detection of the object
3
3
3
3
Microprocessor
5
5
5
4
Total displacement levitating object
4
3
4
5
Frame support
5
3
4
Parts Requirements (20% weightage)
1
Electromagnet
Design Assessment (10% weightage)
1
Design complexity
4
3
4
2
Ease to build
3
4
3
3
Holistic Judgment
5
4
2
Cost Assessment (10% weightage)
1
Cost of wiring for electromagnet
4
3
2
2
Cost of sensor
4
4
4
3
Cost of microprocessor
4
4
4
4
Cost of building the frame
3
4
2
28.7
29
26.7
Total Score
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 35 of 39
Team #11
Conceptual Design Report
Rubric for Design Assessment
Vertical Maglev
Track
Toroidal
Electromagnetic
Track
Basic Requirements (60% weightage)
1
View ability & Stability of the levitating object
3
3
2
Implement control design theories
4
4
3
Portable
4
4
4
Power input: Household Outlet
4
4
5
Total weight: Easy to carry
3
3
6
Safe in class environment
4
3
7
Graphical User Interface (GUI) for interaction
4
4
8
Simulation: MATLAB
4
4
9
All plots are shown in the GUI window
4
4
Strength of the magnetic field
4
4
Wiring
2
2
2
Sensor effectiveness in detection of the object
3
3
3
Microprocessor
5
5
4
Total displacement levitating object
4
3
5
Frame support
4
2
Parts Requirements (20% weightage)
1
Electromagnet
Design Assessment (10% weightage)
1
Design complexity
4
5
2
Ease to build
2
2
3
Holistic Judgment
4
3
Cost Assessment (10% weightage)
1
Cost of wiring for electromagnet
2
3
2
Cost of sensor
4
4
3
Cost of microprocessor
4
4
4
Cost of building the frame
2
3
27
26
Total Score
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 36 of 39
Team #11
Conceptual Design Report
Appendix C Sample Calculations for designing an Electromagnet
Options
1.000
2.000
3.000
4.000
Limitation
Core Diameter (former) (mm)
30.000
30.000
30.000
30.000
30.000
7850.000
7850.000
7850.000
7850.000
7850.000
Diameter of object (mm)
25.000
25.000
25.000
25.000
25.000
Volume of ball (m^3)
0.000
0.000
0.000
0.000
0.000
Mass of ball (kg)
0.064
0.064
0.064
0.064
0.064
Gravity
9.810
9.810
9.810
9.810
10.810
Pole area
0.001
0.001
0.001
0.001
0.001
B (wb/m^2)
0.059
0.059
0.059
0.059
0.059
Air gap (mm)
100.000
90.000
80.000
0.000
300.000
Turns (n)
1000.000
1000.000
1000.000
1000.000
1000.000
r (half diameter of core) (mm)
15.000
15.000
15.000
15.000
15.000
Length of former (mm)
100.000
100.000
100.000
100.000
100.000
0.011
0.011
0.011
0.011
0.011
H (AT/m)
46997.891
46997.891
46997.891
46997.891
46997.891
Magneto-motive force (mmf)
4699.789
4229.810
3759.831
0.000
14099.367
I (A)
4.700
4.230
3.760
0.000
14.099
F (N)
15.042
15.042
15.042
15.042
15.042
AWG 19 gage() (mm)
0.912
0.912
0.912
0.912
0.912
Maximum number of
wires in the first layer
Stacking factor
109.666
109.666
109.666
109.666
109.666
0.900
0.900
0.900
0.900
0.900
Total # of layers
10.132
10.132
10.132
10.132
10.132
1039.264
1039.264
1039.264
1039.264
1039.264
102574.682
102574.682
102574.682
102574.682
102574.682
102.575
102.575
102.575
102.575
102.575
The unitl Resistor of
chosen wire (Ohms per 1000
ft)
Total Resistor
8.051
8.051
8.051
8.051
8.051
2.709
2.709
2.709
2.709
2.709
Total Voltage
12.734
11.460
10.187
0.000
38.201
Heat produced by wire
34.501
31.051
27.601
0.000
103.502
Density of object (kg/m^3)
Cylinder (total area) (m^2)
Wire chosen
Total length of wire (layers)
Total length of wire
(total cylinder) (mm)
(m)
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 37 of 39
Team #11
Conceptual Design Report
Appendix D Supporting Literature
Document source: Design, Development and Testing of an Electromagnet for magnetic levitation system by Dahiru
Sani Shuaibu and Sanusi Sani Adamu.
Note: The following equations are built based for the single electromagnet design with object levitated vertically
upwards against gravity
In the single electromagnet design, air gap between the electromagnet and levitating object plays a crucial
in determining the current that is required to follow through the electromagnet and thus the overall power required to
levitate the object. This requires analysis of force and magnetic field around the electromagnet and in between the
object. The force required to levitate an object is equal to the force of gravity ignoring air friction:
Fmagnet = Fgravity = mg
where m is the mass of the object (kg), g is the acceleration due to gravity (m/s 2). From this equation the magnetic
force required can be determined. Fundamentally, electromagnets generate magnetic field when current is allowed to
pass through it. The field induces flux on ferromagnetic material that is introduced in the field. The force can be
calculated using the following equation:
Fmagnet =
B2A
2μo
where F is the force (N), B is the magnetic field generated by the electromagnet (T), A is the area of the pole faces
of the electromagnet (m2), and µo is the permeability of free space for air it is always 4π x 10 -7 HM-1.With this
equation the B, magnetic field generated by the electromagnet can be found. It can be used to calculate the flux
density, Ф in the air gap using the equation:
Φ=BA
This value can be used to find the magnetizing force, H in the air gap through the following equation:
H=
B
μo
The magnetizing force in turn can be used to find the magneto- motive force (mmf). It primarily depends on
magnetizing force, H and air gap length, l. The value for l has to be estimated initially later altered based on the
current output. To determine current, estimation for number of turns of coil is required. Thus two variables have to
be altered to optimize the current input. The input should be feasible for the project. The following equation
correlates the variables just discussed:
I=
mmf
H ×l
=
N
N
Other major aspects that need to be determined about the electromagnet include the wire type and shape of the core.
The wire selection is based on the resistance of the wire, inductance of coil and overall weight. The resistance of the
wire can be obtained from the data sheet while inductance of the coil, L has to be calculated using the formula:
L=
MECH4010/4015
NΦ
I
Magnetic Levitation Demonstration Apparatus
Page 38 of 39
Team #11
Conceptual Design Report
Higher value for inductance of coil is better for the design in terms levitation i.e., air gap. It is preferable for the wire
to be light weight because it should be easy to carry. Some options considered in the source document are for
annealed copper wires are 17, 18, & 19 AWG with diameters 0.056, 0.048, and 0.040 inch respectively. Further
research in the materials like circular mil and current of square inch density is required to determine the suitable
wire for the project.
The shape of the electromagnet is substantial in increasing the magnetic field generated by the coil.
Referring back to equation:
Fmagnet =
B2A
2μo
Area of the magnetic poles can be varied to achieve greater magnetic force. Since µo is constant and B, field
strength is determined based on the current, maximizing the area would definitely improve the field strength and
ultimately the design. A possible way to improve the area is by using a U shaped or E shaped electromagnet
Selection of either depends on the ease to build and the cost involved in machining.
MECH4010/4015
Magnetic Levitation Demonstration Apparatus
Page 39 of 39