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MECE E3430 Engineering Design

Spring 2013

Group 2

Ivett Ortega

Wole Oyelola

Claudia Vargas

Columbia University

Department of Mechanical Engineering

February 21, 2013

Executive Summary

In this paper the analysis and design of a magnetic bearing system consisting of both a passive

axial magnetic bearing and an active two-axis radial magnetic bearing is presented. The passive

magnetic bearing employs a set of permanent magnets to supply an axial position stiffness to

stabilize the rotor. The active two-axis radial magnetic bearing uses four electromagnets to

stabilize the rotor on the axes perpendicular to the rotation axis. The analysis of both bearings

used in this system was performed using Finite Element Method Magnetics. Furthermore, several

testing methods are described in order to validate the stability of the system, as well as assess the

response of the control system.

MECE E3430 Engineering Design i 2/21/2013

TABLE OF CONTENTS

1. CONCEPT SELECTION ............................................................................................................................. 1

2. FINAL CONCEPT DESCRIPTION ........................................................................................................... 1

3. LITERATURE SEARCH RESULTS .......................................................................................................... 1

4. SPECIFICATIONS AND PARAMETER ANALYSIS .............................................................................. 3

4.1 Shaft Specifications .................................................................................................................................... 3

4.2 Shaft Analysis ............................................................................................................................................. 3

4.3 Active Magnetic Bearing Specifications .................................................................................................... 3

4.4 Passive Magnetic Bearing Specifications ................................................................................................... 6

4.5 Active and Passive Magnetic Bearing Analysis ......................................................................................... 6

5. FINAL DESIGN ............................................................................................................................................ 8

6. PLAN .............................................................................................................................................................. 9

7. PROBLEM ANALYSIS................................................................................................................................ 9

8. CONCLUSION ............................................................................................................................................ 10

9. REFERENCE LIST .................................................................................................................................... 11

1. APPENDICIES ............................................................................................................................................ 13

1.1 Appendix A: Creo Models & Dimensions ................................................................................................ 13

1.2 Appendix B: Calculations ......................................................................................................................... 34

1.3 Appendix C: FEMM and Creo Analysis .................................................................................................. 35

1.4 Appendix D: Manufacturer Specifications ............................................................................................... 37

1.5 Appendix E: Circuit Diagrams ................................................................................................................. 41

1.6 Appendix F: Budget ................................................................................................................................. 42

1.7 Appendix G: Gantt Chart .......................................................................................................................... 43

MECE E3430 Engineering Design ii 2/21/2013

LIST OF FIGURES

FIGURE 1: STATOR CROSS SECTION (ELECTROMAGNET SIDE) ......................................................... 4

FIGURE 2: STATOR CROSS SECTION (SENSOR SIDE) ......................................................................... 5

FIGURE 3: STATOR EXPLODED VIEW ............................................................................................... 5

FIGURE 4: PERMANENT MAGNETIC BEARING .................................................................................. 6

FIGURE 5: FEMM ANALYSIS, ACTIVE MAGNETIC BEARING ........................................................... 7

FIGURE 6: FEMM ANALYSIS, PERMANENT MAGNETIC BEARING .................................................... 8

FIGURE 7: COMPLETE ASSEMBLY .................................................................................................... 8

Appendix A

FIGURE A- 1: AMB STATOR FRONT VIEW WITH ELECTROMAGNET ............................................... 13

FIGURE A- 2: AMB STATOR BACK VIEW WITH PHOTOTRANSISTORS (NO BACK PLATE) .............. 13

FIGURE A- 3: AMB EXPLODED VIEW WITH FRONT AND BACK PLATES ......................................... 14

FIGURE A- 4: AMB CROSS-SECTIONAL VIEW WITH ELECTROMAGNET ......................................... 14

FIGURE A- 5: COMPLETE ASSEMBLY WITH TWO AMBS, PMB AND WATER WHEEL ...................... 15

FIGURE A- 6: SIDE VIEW OF COMPLETE ASSEMBLY ....................................................................... 15

FIGURE A- 7: WATER WHEEL ........................................................................................................ 16

Appendix C

FIGURE C- 1: CREO ANALYSIS FOR MATERIAL STRENGTH OF ROTOR AT 2000 RPM .................... 35

FIGURE C- 2: FEMM ANALYSIS OF AMB WITH MAGNETIC FIELD DENSITY ................................. 36

FIGURE C- 3: FEMM ANALYSIS OF PMB WITH MAGNETIC FIELD DENSITY .................................. 36

Appendix D

FIGURE D- 1: B666 PULL FORCE BETWEEN TWO MAGNETS AS A FUNCTION OF DISTANCE BETWEEN

MAGNETS (COURTESY OF K&J MAGNETICS, INC.) ................................................................. 38

MECE E3430 Engineering Design iii 2/21/2013

FIGURE D- 2: FEMM ANALYSIS OF B666 MAGNETIC FIELD DENSITY (COURTESY OF K&J

MAGNETICS, INC.) ................................................................................................................. 39

FIGURE D- 3: APW ELECTROMAGNET, GAUSSES AS A FUNCTION OF DISTANCE ........................... 40

Appendix E

FIGURE E- 1: QRD1114 SENSOR CIRCUIT ..................................................................................... 41

FIGURE E- 2: CONTROL COMPENSATOR CIRCUIT FOR ONE ELECTROMAGNET ............................... 41

Appendix G

FIGURE G- 1: GANTT CHART.......................................................................................................... 43

LIST OF TABLES

Appendix F

TABLE F- 1: BUDGET ..................................................................................................................... 42

MECE E3430 Engineering Design 1 2/21/2013

1. CONCEPT SELECTION

Initially, the focus was to design a single AMB using four electromagnets. One of the major

limitations to this design was the original $500 budget. Feedback from Design Review I

expressed concerns with axial movement of the shaft as well as inducing a rotation on the shaft

for testing. Based on this feedback the subsequent version of the design intended to use an axial

PMB and two AMBs, each containing three electromagnets. The decision to use three

electromagnets in each AMB was a result of the fact that more using more than six

electromagnets would have increased the project cost by requiring an Arduino with 8 PWM

inputs. One downside to this new design was that the control system for a three pole AMB

quickly becomes very complex, based on information from various journal articles. Ultimately,

the leading factor in the final design decision explained below was the increase in the budget to

$1,125.

2. FINAL CONCEPT DESCRIPTION

The final design employs two AMBs to stabilize the shaft in the z-direction along the entire

length of the shaft. A PMB is used to maintain a position in the axial direction, as little instability

will be present in this direction. Each AMB will contain four electromagnets and will be used to

control the x and y-axis, which are more prone to instability. All electromagnets will be

purchased in order to guarantee their functionality. Furthermore, the decision to purchase

electromagnets with north and south poles on the same face was made in order to provide a

substantial attractive force.

3. LITERATURE SEARCH RESULTS

Information collected from the literature review assisted in the decision to pursue the design of a

hybrid magnetic bearing. The advantage of a hybrid bearing to this project is that it has been

tested by many different people and groups before; therefore many journal articles and patents

related to the topic are available. Many of the journals deal with complex issues that stem from

magnetic bearing designs; however, they provide a substantial amount of information helpful to

this project.

Several articles showed that the majority of radial magnetic bearings utilize an eight-magnet, or

eight-pole, design. Due to budget constraints, this design employs a lesser number of poles. In

order to obtain an understanding of the physics behind a system utilizing fewer poles, “Optimal

design of a three-pole active magnetic bearing” by Chen and Chan-Tang was reviewed. This

paper outlines the importance of the orientation of the poles with respect to the center, the bias

current required to support the force balance condition between the rotor and the stator, and

helpful information regarding the calculation of the magnetic circuit and flux.

The text Magnetic Circuit: Electromagnetic Engineering by Karapetoff allowed for further

understanding of the concepts of magnetic circuits. The text “Introduction to Electrodynamics”

by Griffith was also consulted to review some necessary topics regarding electromagnetism. In

order to examine a more complete picture of the possible body friction losses due to eddy


currents and hysteresis, the paper “Design and analysis of a novel low loss homopolar

electrodynamic bearing” by Lembke as also referenced.

The poles are each at a 90⁰ with respect to each other in our design. We made this decision after

reviewing the considerations in the paper by Chen. In this paper, the magnetic bearing analyzed

utilized three poles and had them in a “Y” orientation. This orientation minimized the hysteresis

losses by giving the two upper poles the same bias current. For our four pole design, rather than

modeling an analogous “X” orientation, we decided that a cross orientation. This way the rotor

will be aligned directly with the top pole, and the two horizontal poles will have the same bias

current. This will greatly simplify the control system.

Using the patent search engine available to the United States Patent and Trademark Office

website, www.uspto.gov, we were able to find the patent US6664680, by searching the

keywords, “Active Magnetic Bearing Flywheel”. This patent is entitled Flywheel Device with

Active Magnetic Bearings. Upon reviewing the patent, we learned more about using flywheels as

a practical application of magnetic bearings. This patent argues the use of permanent magnets

rather than electromagnets to decrease power consumption, reduce cost, and increase reliability.

This patent also provides an inclusive control system block diagram.

From this patent we were able to obtain the following parameter to be used for a category search

in the USPTO databases.

310/90.5

o This subclass is indented under subclass 90. Subject matter wherein the bearing

has an induction field.

Because this category is so specific, we were able to find several patents that addressed our exact

project.

The first most relevant patent is titled “Magnetic bearing control device having a three-phase

converter, and use of a three-phase converter for controlling a magnetic bearing” (US8294314)

and provides an in-depth discussion on the control system used for the magnetic bearings. More

specifically, it addresses the hardware components needed to complete the task.

“Magnetic axial bearing and a spindle motor having this kind of magnetic axial bearing”

(US8212444) also provides a substantial amount of information related to our project. Although

it is important to note that this patent focuses on a rotating axial bearing, the methods of

employing permanent magnets and flux guide elements are still applicable to our project.

“Method and systems for operating magnetic bearings and bearingless drives” (US8115358)

focuses on the circuitry used to generate a signal for energizing the windings of the magnetic

bearing element. This addresses the issues of detecting the radial position of the element within

the bearing. According to this patent, this is a low-cost and efficient means for dynamically

suspending the rotor of the rotary device.

“Large gap horizontal field magnetic levitator” (US8169114) this last patent addresses magnetic

levitation conducted over large gaps. It is important to note that this patent discusses cases with


two types of magnets, permanent magnets and electromagnets. In order to control the levitating

object the employment of a servomechanism is discussed.

All the patent searches provided very in-depth information on the details of magnetic bearings,

such as part arrangements, control system options, and control system components.

4. SPECIFICATIONS AND PARAMETER ANALYSIS

The specifications of this design are based on the optimal distance at which the electromagnets,

permanent magnet, and proximity sensors can function to levitate the intended mass.

4.1 Shaft Specifications

The design began with the selection of the shaft and shaft mass. A ¾ inch shaft was selected as

the levitation mass to present a reasonable distance between electromagnets in order to avoid any

interference between them. Unhardened steel was chosen as the shaft material for its strength,

machinability, and ferromagnetic properties. These ferromagnetic properties allow the shaft to be

levitated by the electromagnets; therefore the shaft will serve as the rotor for the AMB. A key

slot will be machined into the shaft for a key size of 0.1875 inches by 0.1875 inches, in order to

attach rotating parts.

In order to address the issue of rotating the shaft during testing as well as adding a rotating mass,

a water wheel has been added to the shaft. The water wheel will be secured using a key a ¾ inch

collar, acquired through Stock Drive, on either side. By applying compressed air to the water

wheel, rotation will be induced, and the effect on the control system will be tested. The speed of

the water wheel will be monitored using a tachometer to measure the RPM. Due to the shape, the

water wheel will be manufactured using the 3D printer.

4.2 Shaft Analysis

Using finite element method analysis on Creo, the strength of the shaft was tested to ensure the

material would not deform at high rotational speeds. Speeds of up to 2000 RPM were tested, and

it was found the shaft saw a maximum shear stress of 55,000 lbm/(in·s2). Unhardened steel can

withstand stresses up to approximately 13,000,000 lbm/(in·s2), thus material shearing is not a

concern.

4.3 Active Magnetic Bearing Specifications

The most critical portion of this design is that of the AMB stator. Each stator will include four

electromagnets, each at 90 degrees from each other, in order to fully constrain the x and y-axis.

The stator will also house the proximity sensors that detect the position of the shaft.

The selected electromagnets are designed with the north and south poles both present on the top

face. Note that as a result each electromagnet provides an attractive magnetic force. The

maximum holding force specified by the manufacturer is 25 lbf. (See Appendix A, APW

Company Drawing) The relationship between distance and electromagnetic gauss are also given


by the manufacturer (see Appendix D, Figure D-3). This relationship was used to determine the

intended gap between the electromagnet and the shaft.

The electromagnets must be close enough to the rotor to induce a magnetic field strong enough

to levitate the shaft weight. The shaft and waterwheel have a combined weight of only 1.90 lbs.

The design will be capable of levitating 5 lbs, thus ensuring a 2.5 factor of safety. Based on these

parameters, the design allows for a 0.3 inch gap when the system is active and a 0.6 inch gap

when the system is inactive (see Appendix B).

In order to provide stability, each electromagnet will sit on a flat base within the stator which

includes a tapped hole to secure the electromagnet using a screw supplied by the manufacturer. A

channel will be machined from the electromagnet to the bottom of the stator in order to lead the

wiring to the control system without interfering with the other magnets, as shown in Figure 1.

Figure 1: Stator Cross Section (Electromagnet Side)

The housing for the proximity sensors must somewhat mirror that of the electromagnetic stator in

order to provide an appropriate measuring point to be fed back through the control system. To

avoid the need for two stators, the sensor housing is designed to sit on the other side of a thin

wall within the same stator as the electromagnet, see Figure 2. A sensor will be located next to

each of the electromagnets used such that each magnet can be independently and simultaneously

controlled based on the position of the shaft.


Figure 2: Stator Cross Section (Sensor Side)

Each sensor is designed to detect distances between 0 and 0.78 inches (0 cm to 2 cm) (See

Appendix A). As a safety measure the sensor is designed to detect the shaft at a maximum

distance of 0.689 inches (1.75 cm), which occurs when the electromagnets are turned off and the

shaft is as far away from the top sensor as possible. When the AMB is active, the sensor will be

about 0.425 inches (~1 cm) from the shaft.

Each sensor includes four electrical leads; therefore this side of the stator also includes a channel

to lead the wiring out of the stator. One area of concern regarding the phototransistors is the

effect of light interference from the environment. In order to address this each sensor will sit

within a second wall in order to create a dark trench (See Appendix A, Figure A-4). Due to this

layout, the sensors will be secured to each wall using epoxy.

Figure 3: Stator Exploded View


Based on these parameters, the final stator design is about 2.5 inches wide, 4.75 inches tall and

1.25 inches thick (See Appendix A, Drawing 4). Aluminum was selected as the material of the

stator and its plates due to its ease of machinability and ability to withstand a sudden drop of the

stator. The stator will be machined in three parts, as shown in Figure 3. The central portion of the

stator will be machined on both sides: one containing the electromagnet housing and the other

containing the proximity sensor housing. Two plates, each with a different interior diameter, will

be machined and secured to each side of the stator using four screws. It is important to note that

at no point in time will the rotor be sitting on an electromagnet. Due to the size of the inner

diameter of the sensor side plate, the shaft will sit on the sensor side of the stator when the

electromagnets are not active.

4.4 Passive Magnetic Bearing Specifications

In order to account for axial instability, a PMB is placed toward the end of the shaft. A set of

neodymium magnets are oriented with poles opposing each other to provide repulsive forces that

prevent axial movement. An acrylic ring mounted with eight neodymium magnets is attached to

the shaft via a key, and two stands each containing four appropriately oriented magnets are used

to repel these magnets from each side. The north poles of the magnets face each other on one

side, and the south sides of the magnets face each other on the other, as seen in Figure 4. At a

distance of 0.2 inches the magnets create a repulsion force of approximately 2 lbf – higher than

any axial force expected to be exerted on the shaft. See Appendix D for the pull force and

illustration of the magnetic field of the B666 neodymium magnet used.

Figure 4: Permanent Magnetic Bearing

4.5 Active and Passive Magnetic Bearing Analysis

The magnetic fields induced by the AMB and PMB were modeled using Finite Element Method

Magnetics or FEMM software. FEMM is a freeware package that utilizes finite element analysis

to solve electrodynamic problems. This program features meshing applications that operate

quickly in comparison to other programs of its kind. Unfortunately, FEMM has the drawback of

having only 2D capabilities and relatively weak drafting dexterity.


The AMB was modeled as a frontal cross-section, showing effects in the x and y-axis. Each

electromagnet was assigned aluminum casing, coils of 26 AWG wire and 260 coil loops each, as

specified by the manufacturer. The cross section of the electromagnetic side of the stator

required that two rectangles be the model for the electromagnetic coils; one denoting current

entering the page, the other denoting current exiting the page. By the right-hand rule, the

magnetic field points either upward or downward in the y-direction, based on the direction of the

current loops.

The PMB was modeled including all three components (two stands and the ring on the stator)

from the side view, as it is designed to control the z-axis. The stands contained three squares

each, and the rotor contained six squares, each square representing a permanent magnet. Each

permanent magnet was assigned the material NdFeB, grade N42, as specified by the

manufacturer. The location of the north and south poles were then assigned for each magnet such

that they would have a repulsive alignment with respect to each of the three components.

Based on the design of the stator, the magnetization vector M is related to the vector potential, A.

By taking the integral twice, two boundary conditions were determined. These were used by the

program to map out finite element method meshes for both cases. These meshes were then used

to plot the magnetic field density for both the AMB and PMB.

Figure 5: FEMM Analysis, Active Magnetic Bearing

From the magnetic field density plot it is shown that the majority of the current must go through

the electromagnet at the top of the bearing. By integrating the area of the rotor, pictured in the

center, the magnetic flux through the rotor can be determined. The force applied on the rotor is

proportional to the magnetic flux squared. Using this information, the current required to lift the

rotor can be calculated.


Figure 6: FEMM Analysis, Permanent Magnetic Bearing

As shown in the magnetic field density plot of the PMB, it is evident that the magnetic field lines

are less dense in between each cube magnet. This shows that the attractive magnetic forces will

not only be weak between each component, but in fact, the components will repel each other. As

the components get closer to each other the repulsive forces will increase, thus negating axial

fluctuations in the rotor.

5. FINAL DESIGN

The complete design of the system is shown in Figure 7. It consists of a 16 inch long ¾ inch steel

shaft that functions as the electromagnet bearing rotor, with active magnetic bearings as

stabilizers in the x and y-direction, permanent magnets for axial stability and a wheel that will be

used to rotate the shaft with compressed air. The complete assembly is 16 inches by 4 inches and

4.75 inches high. The wheel measures 4 inches in diameter and is 1 inch wide, and has angled

slots to allow air flow into it and induce a rotation.

Figure 7: Complete Assembly


A QRD1114 sensor, which combines an infrared emitted diode with an infrared phototransistor

to detect the reflected infrared signal will be used to detect the distance from the sensor to the

shaft. The sensor will provide the circuit the information needed to determine how much current

to draw through each magnet, and therefore how much pulling force each magnet will exert. A

sensor will be located next to each of the electromagnets such that each magnet can be

independently and simultaneously controlled based on the position of the shaft. See Appendix E

for the sensor circuit diagram.

The current running through each magnet will be controlled using an Arduino Mega 2560 R3,

which has a clock speed fast enough to quickly adjust for the position of the shaft based on the

data obtained by the sensor. A preliminary circuit diagram for the AMB controller can be found

in Appendix E.

Appendix A contains dimensioned drawings of major components of the assembly, including

holes for screws and keys. Finally, a complete list of parts with vendors, part numbers, and costs

can be found in the budget in Appendix F.

6. PLAN

The next step in the project process is to complete a prototype using one electromagnet.

Prototyping is set to begin after receiving feedback from Design Review II. The Arduino,

proximity sensors and one electromagnet have been purchased and received. In addition, a

prototype stator has been 3D printed. This first test will consist of one magnet levitating a ¼ inch

steel rod. This will test the sensitivity of the phototransistor to light, the accuracy of our FEMM

analysis, and will help complete the final circuit used in the control system. In addition the shaft

will be spun manually to determine whether the control system can compensate for stability

induced by rotation.

Once the control system is working properly and the magnet and sensors have been tested, the

remaining parts will be ordered and assembly will begin. Manufacturing will begin the first week

of March, and all parts are to be completed by the end of that week. The complete assembly is

expected to be completed by April 1st (see Gantt chart in Appendix G for a complete schedule).

Future tests on the complete system will include spinning the shaft at several RPM and adding

additional weight to test the response of the control system.

7. PROBLEM ANALYSIS

In performing the material strength analysis of the shaft on Creo, the calculations were limited by

the types of analysis available on Creo. The structural integrity of the shaft was tested assuming

the ends were constrained, so there was no displacement in the z-direction, because there is no

option available for the centrifugal effects of rotation on a free-floating shaft. The results showed

that the maximum shear stress on the shaft was approximately 55,000 lbm/( in·s2) and steel can

withstand stresses of up to 13,000,000 lbm/( in·s2) . Therefore the analysis proves that even with

constraints at the ends of the shaft the maximum shear stress will not be reached. One of the risks

of using the FEMM software is that is only capable of models in two dimensions.


8. CONCLUSION

The hybrid magnetic bearing design uses a combination of active magnetic bearings and a

passive magnetic bearing to levitate and stabilize a steel shaft while it rotates. A controller using

a phototransistor as a proximity sensor will adjust the amount of current going through each

electromagnet as needed to provide the correct amount of magnetic force needed to maintain

levitation of the shaft. A passive magnetic bearing at the end of the shaft will provide axial

stability to prevent the shaft from moving in the z-direction. Using a water wheel in the center,

compressed air will be used to rotate the shaft in order to show that the control compensator can

account for instability induced by shaft rotation.


9. REFERENCE LIST

B. Shafai, S. Beale, P. LaRocca, and E Cusson, "Magnetic bearing control systems and adaptive

forced balancing," IEEE Contr. Syst. Mug., vol. 14, no. 2, pp. 4-13, Apr. 1994

Budig, P.-K.; , "On the theory and application of magnetic bearings," Systems, Signals and

Devices (SSD), 2012 9th International Multi-Conference on , vol., no., pp.1-9, 20-23

March 2012 doi: 10.1109/SSD.2012.6198013

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6198013&isnumber=6197898

B. V. Jayawant, Electromagnetic Levitation and Suspension Techniques. UK: Edward Arnold,

1981.

Chen, Shyh-Leh, and Chan-Tang Hsu. "Optimal design of a three-pole active magnetic bearing."

Magnetics, IEEE Transactions on 38.5 (2002): 3458-3466.

Denk, Kopken, Stoiber, Wedel (2007) US8294314 Magnetic bearing control device having a

three-phase converter, and use of a three-phase converter for controlling a magnetic

bearing

F. Matsumura et al., “Fundamental equation of horizontal shaft magnetic bearing and its control

system,” Trans. JIEE, vol. 101-C, pp.

Gabrys (2001) US6664680 Flywheel Device with Active Magnetic Bearings

Griffiths, David J. Introduction to Electrodynamics. 3rd ed. Upper Saddle River, NJ: Prentice

Hall, 1999. Print.

Karapetoff, Vladimir. Magnetic Circuit: Electromagnetic Engineering. Palm Springs: Wexford

College, 2003. Print.

Lembke, Torbjörn A. Design and analysis of a novel low loss homopolar electrodynamic

bearing. Diss. KTH, 2005.


M. S. de Queiroz and D. M. Dawson. Nonlinear control of active magnetic bearings: A

backstepping approach. IEEE Transactions on Control System Technology, 4(5):545-

552,

1996.

Popov, Bauer, Schmid, Schwamberger (2008) US8212444 Magnetic axial bearing and a spindle

motor having this kind of magnetic axial bearing

Rakov (2009) US8115358 Method and systems for operating magnetic bearings and bearingless

drives

Samanta, P.; Hirani, H.; , "Magnetic Bearing Configurations: Theoretical and Experimental

Studies," Magnetics, IEEE Transactions on , vol.44, no.2, pp.292-300, Feb. 2008 doi:

10.1109/TMAG.2007.912854

URL:

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4432699&isnumber=4432685

Schweitzer, G. "Active Magnetic Bearings - Chances and Limitations." International Centre for

Magnetic Bearings, n.d. Web. 11 Nov. 2012. http://www.mcgs.ch/web-content/AMB-

chances_and_limit.pdf

Setiawan, Joga D., Ranjan Mukherjee, and Eric H. Maslen. "Adaptive Compensation of Sensor

Runout for Magnetic Bearings With Uncertain Parameters: Theory and Experiments."

Journal of Dynamic Systems, Measurement, and Control 123.2 (2001): 211. Print.

Simon (2010) US8169114 Large gap horizontal field magnetic levitator

T. Lembke (2005). PhD Thesis "Design and Analysis of a Novel Low Loss Homopolar

Electrodynamic Bearing". Stockholm: Universitetsservice US AB. ISBN 91-7178-032-7

http://ieeexplore.ieee.org.ezproxy.cul.columbia.edu/stamp/stamp.jsp?tp=&arnumber=4432699&isnumber=4432685

http://www.mcgs.ch/web-content/AMB-chances_and_limit.pdf

http://www.mcgs.ch/web-content/AMB-chances_and_limit.pdf

http://www.magnetal.se/Dokument/PhDThesis.pdf

http://www.magnetal.se/Dokument/PhDThesis.pdf

http://en.wikipedia.org/wiki/International_Standard_Book_Number

http://en.wikipedia.org/wiki/Special:BookSources/91-7178-032-7


1. APPENDICIES

1.1 Appendix A: Creo Models & Dimensions

Figure A- 1: AMB Stator Front View with Electromagnet

Figure A- 2: AMB Stator Back View with Phototransistors (No Back Plate)


Figure A- 3: AMB Exploded View with Front and Back Plates

Figure A- 4: AMB Cross-Sectional View with Electromagnet


Figure A- 5: Complete Assembly with Two AMBs, PMB and water wheel

Figure A- 6: Side View of Complete Assembly


Figure A- 7: Water Wheel


1.2 Appendix B: Calculations


1.3 Appendix C: FEMM and Creo Analysis

Figure C- 1: Creo Analysis for Material Strength of Rotor at 2000 RPM


Figure C- 2: FEMM Analysis of AMB with Magnetic Field Density

Figure C- 3: FEMM Analysis of PMB with Magnetic Field Density


1.4 Appendix D: Manufacturer Specifications


Figure D- 1: B666 Pull Force between Two Magnets as a Function of Distance between Magnets

(courtesy of K&J Magnetics, Inc.)


Figure D- 2: FEMM Analysis of B666 Magnetic Field Density (courtesy of K&J Magnetics,

Inc.)


Figure D- 3: APW Electromagnet, Gausses as a Function of Distance


1.5 Appendix E: Circuit Diagrams

Figure E- 1: QRD1114 Sensor Circuit

Figure E- 2: Control Compensator Circuit for One Electromagnet


1.6 Appendix F: Budget

Table F- 1: Budget

Part Supplier Part Number Quantity Cost/Unit Subtotal Free Parts

1.0" Diameter

Round

Electromagnet

APW Company EM100-3H-

222

8 $29.95 $239.60

Phototransistor

QRD1114

SparkFun SEN-00246 10 $1.18 $11.80

Arduino Mega

2560 R3

SparkFun DEV-11061 1 $58.95 $58.95

Permanent Magnets K&J Magnetics,

Inc.

B666 16 $1.78 $28.48

Power Supply Marlin P. Jones

& Assoc.

(13.8V 20A) 1 $20.00 $20.00

Circuit

Components

Digi-Key 1 $10.00 $10.00

Protoboard SparkFun 1 $5.00 $5.00

Waterwheel MECE Lab (3D Print) $0.00 $0.00

Steel Shaft 3/4"

OD, 24" L

McMaster 1346K32 1 $22.91 $22.91

Key Stock Drive A 9C39-0632 1 $0.81 $0.00 $0.81

Collar Stock Drive A 7X 2-14024 2 $0.00 $0.00 $20.58

Race McMaster 8975K324 1 $52.69 $52.69

Race Plates McMaster 8975K425 1 $11.77 $11.77

Angle Plates McMaster 1556A24 12 $0.37 $4.44

JB Weld McMaster 7605A11 1 $6.17 $6.17

Acrylic MECE Lab $0.00 $0.00

Tachometer IR Kit SparkFun KIT-10732 1 $2.95 $2.95

Tachometer

Phototransistor

SparkFun 1 $1.13 $1.13

Display SparkFun COM-11629 1 $12.95 $12.95

Poster 1 $50.00 $50.00

Total: $538.84 $560.23

Budget: $1,125.00 $1,125.00

Money Left: $586.16 $564.77


1.7 Appendix G: Gantt Chart

Figure G- 1: Gantt Chart

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