NOTES 30C PERMANENT - THOMPSON CONSULTING, INC
Transcript of NOTES 30C PERMANENT - THOMPSON CONSULTING, INC
Power Electronics Notes 30CPower Electronics Notes 30CNotes on Permanent Magnets
Marc T. Thompson, Ph.D.Thompson Consulting, Inc.
9 Jacob Gates RoadHarvard, MA 01451
Phone: (978) 456-7722 Fax: (240) 414-2655
Email: marctt@thompsonrd comEmail: [email protected]: http://www.thompsonrd.com
Portions of these notes excerpted from the CD ROM accompanying Fitzgerald Kingsley and Umans Electric Machinery
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Portions of these notes excerpted from the CD ROM accompanying Fitzgerald, Kingsley and Umans, Electric Machinery, 6th edition, McGraw Hill, 2003Other notes © Marc Thompson, 2009
Brief History of Permanent Magnetse sto y o e a e t ag ets• c. 1000 BC: Chinese compasses using lodestone
– Later used to cross the Gobi desert
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Reference: K. Overshott, “Magnetism: it is permanent,” IEE Proceedings-A, vol. 138, no. 1, Jan. 1991, pp. 22-31
Brief History of Permanent Magnets (cont.)
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Reference: R. Parker, Advances in Permanent Magnetism, John Wiley, 1990, pp. 3
Brief History of Permanent Magnets (cont.)• c. 200 BC: Lodestone (magnetite) known to the Greeks
– Touching iron needles to magnetite magnetized them• 1200 AD: French troubadour de Provins describes use of a
primitive compass to magnetize needles• 1600: William Gilbert publishes first journal article on
permanent magnetspermanent magnets• 1819: Oersted reports that an electric current moves compass
needle
R fReferences: 1. K. Overshott, “Magnetism: it is permanent,” IEE Proceedings-A, vol. 138, no. 1, Jan. 1991, pp. 22-312. R. Petrie, “Permanent Magnet Material from Loadstone to Rare Earth Cobalt,” Proc. 1995 Electronics Insulation and Electrical Manufacturing and Coil Winding Conf., pp. 63-643. Rollin Parker, Advances in Permanent Magnetism, John Wiley, 19904 E Hoppe “Geshichte des Physik ” Vieweg Braunshweig 1926 pp 339
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4. E. Hoppe, Geshichte des Physik, Vieweg, Braunshweig, 1926, pp. 3395. W. Gilbert, “De Magnete 1600,” translation by S. P. Thompson, 1900, republished by Basic Books, Inc., New York, 1958
Brief History of Permanent Magnets (cont.)• c 1825: Sturgeon invents• c. 1825: Sturgeon invents
the electromagnet, resulting in a way to artificially magnetize materials
• 7-ounce magnet was able gto lift 9 pounds
References:
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References: 1. W. Sturgeon, Mem. Manchester Lit. Phil. Soc., 1846, vol. 7, pp. 6252. Britannica Online
Brief History of Permanent Magnets (cont.)1830 J h H• c. 1830: Joseph Henry
(U.S.) constructs electromagnetsg
Reference: Smithsonian Institute archives
Joseph Henry
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Brief History of Permanent Magnets (cont.)e sto y o e a e t ag ets (co t )• 1917: Cobalt magnet steels developed by Honda and Takagi
in Japanp• 1940: Alnico --- first “modern” material still in use
– Good for high temperatures• 1960: SmCo (samarium cobalt) rare earth magnets• 1960: SmCo (samarium cobalt) rare earth magnets
– Good thermal stability• 1983: GE (later Magnequench) and Sumitomo develop
d i i b (NdF B) th tneodymium iron boron (NdFeB) rare earth magnet– Highest energy product, but limited temperature range
References: 1. K. Overshott, “Magnetism: it is permanent,” IEE Proceedings-A, vol. 138, no. 1, Jan. 1991, pp. 22-312 R P t i “P t M t M t i l f L d t t R E th C b lt ” P 1995 El t i I l ti d
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2. R. Petrie, “Permanent Magnet Material from Loadstone to Rare Earth Cobalt,” Proc. 1995 Electronics Insulation and Electrical Manufacturing and Coil Winding Conf., pp. 63-64
Brief History of Permanent Magnets (cont.)e sto y o e a e t ag ets (co t )• Late 1990s --- Hybrid car utilizing high strength permanent
magnetsg
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Prius and Next-Generation Hybrid
f “ f f
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Reference: M. Kamiya, “Development of Traction Drive Motors for the Toyota Hybrid System”
Maglev System #1M ti (A t MA)• Magnemotion (Acton, MA)
f C “ S f S ”
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Reference: R. Thornton, T. Clark and B. Perreault, “Linear Synchronous Motor Propulsion of Small Transit Vehicles,” Proceedings of the 2004 ASME/IEEE Joint Rail Conference, April 6-8, 2004, Baltimore MD, pp. 101-107
Maglev System #2G l At i (S Di CA)• General Atomics (San Diego, CA)
f S f ( ) “ S
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Reference: U.S. Department of Transportation (Federal Transit Administration), “Low Speed Maglev Technology Development Program – Final Report,” FTA-CA-26-7025-02.1, March 2002.
Eddy Current BrakeM t C (S l B h CA)• Magnetar Corp. (Seal Beach, CA)
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Magnetizing Permanent MagnetsM t i l i l d i id ti i fi t• Material is placed inside magnetizing fixture
• Magnetizing coil is energized with a current producing sufficient field to magnetize the PM materialg
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Reference: E. Furlani, Permanent Magnet and Electromechanical Devices, Academic Press, 2001, pp. 57
Pictorial View of Magnetization Processcto a e o ag et at o ocess
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Reference: R. Parker, Advances in Permanent Magnetism, John Wiley, 1990, pp. 49
Permanent MagnetsE t l ff t f PM b d l d f t• External effects of PMs can be modeled as surface current
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Reference: P. Campbell, Permanent Magnet Materials and their Applications, Cambridge University Press, 1994, pp. 7
Permanent Magnets• After magnetization magnetization vector M has value ofAfter magnetization, magnetization vector M has value of
either +Msat or –Msat. Hci is the temperature-dependent field strength (A/m) which causes the M vector to flip direction
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Reference: P. Campbell, Permanent Magnet Materials and their Applications, Cambridge University Press, 1994, pp. 14-15
Permanent Magnets with High Hci• Constitutive relationship: B = μ (H+M)Constitutive relationship: B μo(H+M)• Since M has values of either +Msat or -Msat, it follows that
the slope of the BH curve for the permanent magnet is ∼μo; thi h ld f NdF B t d t t tthis holds for NdFeB at moderate temperature
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Reference: P. Campbell, Permanent Magnet Materials and their Applications, Cambridge University Press, 1994, pp. 15, 23
Permanent Magnets with Lower Hci• Note that H i is temperature-dependentNote that Hci is temperature dependent• At higher temperature, the “knee” in the 2nd quadrant
shows up. Operation with H inside the magnet less than H lt i i ibl d ti tiHci results in irreversible demagnetization
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Reference: P. Campbell, Permanent Magnet Materials and their Applications, Cambridge University Press, 1994, pp. 15, 23
Demagnetization Curves of Ceramic 8T i l i t d i t• Typical sintered ceramic magnet
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Reference: P. Campbell, Permanent Magnet Materials and their Applications, Cambridge University Press, 1994, pp. 62
Demagnetization Curves of NdFeB• Strong neodymium-iron-boronStrong neodymium iron boron
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Reference: P. Campbell, Permanent Magnet Materials and their Applications, Cambridge University Press, 1994, pp. 74
Curie Temperature• The “Curie temperature” is the temperature at which theThe Curie temperature is the temperature at which the
magnetization is totally destroyed.• The practical maximum operating temperature for a
t t i ll b l th C i t tpermanent magnet is well below the Curie temperature
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Reference: P. Campbell, Permanent Magnet Materials and their Applications, Cambridge University Press, 1994, pp. 74
Maximum Working Temperature• The practical maximum operating temperature for aThe practical maximum operating temperature for a
permanent magnet is well below the Curie temperature
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Reference: Magcraft, “Permanent Magnet Selection and Design Handbook”
Permanent Magnets vs. SteelN t th t PM h h hi h i f• Note that PM has much higher coercive force
Permanent magnet: Alnico 5 M-5 steel
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B-H Loop for M-5 Grain-Oriented SteelO l th t h lf f th l h f t l 0 012” thi k• Only the top half of the loops shown for steel 0.012” thick
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Hysteresis LoopH t i l ti l t h d d• Hysteresis loss proportional to shaded area
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Permanent Magnets“S ft” ti t i l h ti t l• “Soft” magnetic materials such as magnetic steel can behave as very weak permanent magnets
• Permanent magnets, or “hard” magnetic materials, have a g ghigh coercive force Hc and can produce significant flux in an airgap
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Reference: E. Furlani, Permanent Magnet and Electromechanical Devices, Academic Press, 2001, pp. 39
Cast AlnicoCast co
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Reference: R. Parker, Advances in Permanent Magnetism, John Wiley, 1990, pp. 65
Example 1: Permanent Magnet in a Magnetic CktThi l NdF B hi h h li B/H i• This example uses NdFeB which has linear B/H curve in the 3rd quadrant
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Example 1: Permanent Magnet in a Magnetic CktU i A ’ l ( d i h i i f i fi iUsing Ampere’s law (and noting that our approximation of infinite μassures that H = 0 in the steel) we note:
0=+ gHlH gmm where Hg is the magnetic field in the airgap. Next we use Gauss’ magnetic law which says that flux is continuous around a loop, to get:
ggmm ABAB = gg
where Am is the cross-sectional area of the permanent magnet and Bg is the cross-sectional area of the airgap. Noting that Bg = μoHg, we next solve for Bm, as a function of Hm, resulting in the load line equation:
mm
gmom H
gAAl
B ⎟⎟⎠
⎞⎜⎜⎝
⎛−= μ
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Example 1: Permanent Magnet in a Magnetic Ckt
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Example 2: Permanent Magnet in a Magnetic Ckt
Example:
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Example 2: With Alnico Permanent Magnet
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Example 2: With Alnico Permanent MagnetR lt B 0 3 T l• Result: Bg = 0.3 Tesla
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Reference: P. Campbell, Permanent Magnet Materials and their Applications, Cambridge University Press, 1994, pp. 89
Example 2: Load Line Solution with M-5 Steel U l d li B 0 38 G ( h l th• Use same load line; Bg = 0.38 Gauss (much lower than with Alnico)
• Note: Earth’s magnetic field ~ 0.5 Gaussg
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Some Common Permanent Magnet Materials
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Typical NdFeB B-H Curve• Neodymium-iron-boron (NdFeB) is the highest strengthNeodymium iron boron (NdFeB) is the highest strength
permanent magnet material in common use today• Good material for applications with temperature less than
i t l 80 150Capproximately 80 - 150C• Cost per pound has reduced greatly in the past few years• Curve below for “grade 40” or 40 MGOe material
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Typical NdFeB B-H Curve --- Elevated Temp.• Note that the B/H curve degrades at elevated temperatures• If you operate the magnet below the “knee” irreversible
demagnetization may resultdemagnetization may result
1.2
Grade 40 NdFeB, temp = 25 50 75 100 125 150 degrees C, mu-rel=1.1167 alpha = -0.0012 beta = -0.0065
0.8
1
a150C
0.4
0.6
Bm
, Tes
la
100C
125C
900 800 700 600 500 400 300 200 100 00
0.2
25C50C
75C
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-900 -800 -700 -600 -500 -400 -300 -200 -100 0Hm, kA/m
NdFeB B-H Curves for Different Grades
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Reference: Dexter Magnetics, Inc. http://www.dextermag.com
Example 3: Force Between 2” NdFeB Magnet Cubes vs Airgapvs. Airgap
Force between 2" cubic magnets
Attraction Repulsion
120
140
160
180
200
, [lb
Att
0
20
40
60
80
100
Force, Att
Rep
0
0 0.5 1 1.5 2 2.5
Gap, [in.]
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Example 4: Stray Fields from 2” Grade 40 Magnet CubeCube
• At distances r = 6”, 12” and 24”
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Example 5: Magnetic Circuit With Steel• Estimate airgap field B assuming grade 42 NdFeB• Estimate airgap field Bg assuming grade 42 NdFeB• Airgap g, magnet thickness tm
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Example 5: Magnetic Circuit With Steel• This analysis also ignores leakage• This analysis also ignores leakage
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Example 5: Magnetic CircuitMagnetic Circuit
With Steel ---Operating Point vs. Magnet Thickness
tm
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Example 5: 2D FEA, Magnet Thickness tm = g/2
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Example 5: 2D FEA, Magnet Thickness tm = g
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Example 5: 2D FEA, Magnet Thickness tm = 2g
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Example 5: Comparison of Different Magnet Thicknesses
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Circuit Modeling of Permanent MagnetsPermanent Magnets
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Reference: E. P. Furlani, Permanent Magnet and Electromechanical Devices, Academic Press, 2001
Circuit Modeling of Permanent Magnets
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Circuit Modeling of Permanent Magnets
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Circuit Modeling of Permanent Magnets
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Circuit Modeling of Permanent Magnets
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Example 6: Circuit Modeling of Permanent Magnets
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Example 6: Circuit M d li f P tModeling of Permanent
Magnets
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Example 6: Circuit Modeling of Permanent Magnets---FEA
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Method of Images• These two are equivalent in the upper half-plane
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Another Example: Magnetic Circuit With Steel• Which scenario has the lowest leakage flux?
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Reference: www.mmpa.org
Maximum Energy Product• BH has units of Joules per unit volume• BH has units of Joules per unit volume
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Maximum Energy ProductProduct
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Progress in PM Specs• Maximum (BH) product has gone up a lot in the pastMaximum (BH)max product has gone up a lot in the past
20 years
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Reference: J. Evetts, Concise Encyclopedia of Magnetic and Superconducting Materials, Pergamon Press, Oxford, 1992
Example 7: Use of Maximum Energy Product • Find magnet dimensions for desired B = 0 8 TeslaFind magnet dimensions for desired Bg 0.8 Tesla
operating at (BH)max
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Comparison of Different PM Types
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Reference: www.magnetsales.com
Magnetic Conversion Factors
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Reference: www.magnetsales.com
Magnetic Field Estimates
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Reference: www.magnetsales.com
Magnetic Field Estimates
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Reference: www.magnetsales.com
Open Circuited Permanent Magnet
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Reference: P. Campbell, Permanent Magnet Materials and their Applications, Cambridge University Press, 1994, pp. 89
Short-Circuited Permanent MagnetFi d B i id i i l k d i• Find B inside core, ignoring any leakage and assuming infinite permeability in core
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Short Circuited Permanent MagnetF i fi it bilit l d li i ti l• For infinite permeability, load line is vertical
• Intersection of load lines occurs at B ≈ Br
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Reference: P. Campbell, Permanent Magnet Materials and their Applications, Cambridge University Press, 1994, pp. 89
PM and a WindingM t h t t t l d i di• Many motors have permanent magnets, steel and windings
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PM and a Winding --- Load LineN t th t d ti ti if t i• Note that demagnetization can occur if current is sufficiently high
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PM and a Winding --- Graphical Analysis
• At point (a) steel is initially unmagnetized• At point (a), steel is initially unmagnetized• As current increases, B and H follow the locus from (a) to (b)• From (b) to (c), current reduces to zero, and flux density reduces to Br at i = 0• As current goes negative from (c) to (d), curve traces hysteresis loop. Note that
operating point (d) is the same operating point we’d get if there was zero current and an airgap.
• If current goes further negative, locus traces from (d) to (e)• But if current is reduced to zero at point (d) locus traces minor loop from (d) to
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But, if current is reduced to zero at point (d), locus traces minor loop from (d) to (f). The “recoil line” is an approximation to this minor loop
Another Example --- Excitation and Airgap
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Another Example --- Excitation and Airgap --- Load LineLine
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Another Example• Let’s figure out how to magnetize g g
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Another Example
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Another Example
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What Can You Buy?
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Reference: www.dextermag.com
What Can You Buy?
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Reference: www.dextermag.com
What Can You Buy?
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Reference: www.magnetsales.com
Magnetization Patterns
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Reference: www.magnetsales.com
Comparison
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Reference: www.magnetsales.com
Comparison of Maximum Operating Temperatures
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Reference: http://www.electronenergy.com/media/Magnetics%202005.pdf
Comparison of Maximum Operating Temperatures
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Reference: http://www.electronenergy.com/media/Magnetics%202005.pdf
Quotes
It is well to observe the force and virtue and consequence of discoveries and these are to be seen nowhere morediscoveries, and these are to be seen nowhere more conspicuously than in printing, gunpowder, and the magnet.--- Sir Francis Bacon
The mystery of magnetism, explain that to me! No greaterThe mystery of magnetism, explain that to me! No greater mystery, except love and hate.---John Wolfgang von Goethe
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ReferencesP t C b ll P t M t M t i l d Th i• Peter Campbell, Permanent Magnet Materials and Their Applications, Cambridge University Press, 1994
• Edward Furlani, Permanent Magnet and Electromechanical gDevices, Academic Press, 2001
• Rollin J. Parker, Advances in Permanent Magnetism, John Wiley 1990Wiley, 1990
• Lester Moskowitz, Permanent Magnet Design and Application Handbook, 2nd edition, Krieger, 1995V h l S ft M ti M t i l 1979• Vacuumschmelze, Soft Magnetic Materials, 1979
• Dexter Magnetics, www.dextermag.com• Magnet Sales, Inc., www.magnetsales.comg g• Magnetic Materials Producers Association, Std. PMG-88,
“Permanent Magnet Guidelines”
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