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- 1. Chapter-1 Magnetic Circuits Dr. AtifIqbal Dept. of Electrical Engineering Qatar University 8/10/2021 ELEC 312-Electric Machines 1
- 2. Content of Chapter-1 1 •Introduction • Magnetic Circuit 2 • Hysteresis Properties • Inductance • Hysteresis Losses 3 • Eddy Current Losses • Permanent Magnets 8/10/2021 ELEC 312-Electric Machines 2
- 3. 1. Introduction • Materialsthat can be magnetized, which are also the ones that are strongly attracted to a magnet, are called magnetic/ferromagnetic. • In all electrical machines, magnetic materials are used to enhance magnetic field for better energy conversion. • High flux density can be obtained in the machine by using magnetic material which results in high torque or high machine output per unit machine volume. • In other words, the size of the machine is greatly reduced by the use of magnetic materials. 8/10/2021 ELEC 312-Electric Machines 3
- 4. • Magnetic fieldsare the fundamental mechanism by which energy is converted from one form to other form in motors, generators and transformers. • Magnetic materials are classified in terms of their magnetic properties and their uses. If a material is easily magnetized and demagnetized then it is referred to as a soft magnetic material, whereas if it is difficult to demagnetize then it is referred to as a hard (or permanent) magnetic material. • E.g. Iron, Nickle, Cobalt and their Alloys 8/10/2021 ELEC 312-Electric Machines 4
- 5. • A currentcarrying conductor produces a magnetic field around it. • A time varying magnetic field induces a voltage in a coil of wire if it passes through that coil (Transformer action) • A current carrying wire in the presence of a magnetic field has a force induced in it (Motor action) • A moving conductor in the presence of a magnetic field has a voltage induced in it. (Generator action) 8/10/2021 ELEC 312-Electric Machines 5
- 6. Right Hand Rule •The magnetic field lines around a long wire which carries an electric current form concentric circles around the wire. • The direction of the magnetic field is perpendicular to the wire and is in the direction the fingers of your right hand would curl if you wrapped them around the wire with your thumb in the direction of the current. 8/10/2021 ELEC 312-Electric Machines 6
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- 8. Electric Field andMagnetic Field • A static charge produces electric field around its vicinity • A magnet produces magnetic field around it • A moving charge produces both electric and magnetic fields. The electric and magnetic field are perpendicular to each other. The resultant field is the vector sum of the two fields. • The electric field lines originate from positive charges and sinks into negative charges. • The magnetic field lines originate from North Pole and sink into South Pole (outside the magnet) and reverse inside the magnet body. 8/10/2021 ELEC 312-Electric Machines 8
- 9. Magnetic Circuits • Inelectric machines, the magnetic circuits is formed by ferromagnetic materials only (as in transformers) • In rotating machine magnetic circuit is formed by ferromagnetic materials in conjunction with an air gap. • The magnetic field (or flux) is produced by passing an electrical current through coils wound on ferromagnetic materials. • In permanent magnet machines magnetic flux is produced by PM. 8/10/2021 ELEC 312-Electric Machines 9
- 10. Examples of MagneticCircuit 8/10/2021 ELEC 312-Electric Machines 10 Magnetic Circuit without Air-gap Magnetic Circuit with Air-gap
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- 12. Magnetic Circuits 8/10/2021 ELEC 312-Electric Machines 12 Fig. 1.A simple magnetic core
- 13. Terms related tothe magnetism • Magnetic Field or flux (Wb) • Magnetic flux density B (Wb/sq m) or Tesla • Magnetic field Intensity H Amp/m, Am-turn/m or AT/m • Magnetomotive Force mmf F Amp-turn, or AT • Reluctance R Amp-turn/wb • Permeance P wb/AT • Permeability µ henery/m • Absolute Permeability • Core length, Core Cross sectional area 8/10/2021 ELEC 312-Electric Machines 13 7 10 4 X o
- 14. 8/10/2021 ELEC 312-Electric Machines 14 H is Magneticfield intensity that represents the effort made by current to establish the flux. It is independent of the medium.
- 15. 1.1 i−H RELATION •The relationship between current (i) and field intensity (H) can be obtained by using Ampère’s circuit law. • Which states that the line integral of the magnetic field intensity H around a closed path is equal to the total current enclosed by the contour. Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 15 Ampère’s circuit law 3 2 1 i i i i l d H i dl H cos
- 16. 1.1 i−H RELATION •For the circular path case, at each point on this circular contour, H and dl are in the same direction, that is, θ=0. • Because of symmetry, H will be the same at all points on this contour. Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 16 i dl H Hdl i r H 2 r i H 2
- 17. 1.2 B−H RELATION •The magnetic field intensity H produces a magnetic flux density B everywhere it exists. • These quantities are functionally related by: Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 17 Tesla or m Weber/ 2 H B T or Wb/m2 0 H B r μ is a characteristic of the medium and is called the permeability of the medium. μ0 is the permeability of free space and is 4π10−7 henry/meter. μr is the relative permeability of the medium.
- 18. 1.2 B−H RELATION •For free space or electrical conductors (such as aluminum or copper) or insulators, the value of μr is unity. • However, for ferromagnetic materials such as iron, cobalt, and nickel, the value of μr varies from several hundred to several thousand. • For materials used in electrical machines, μr varies in the range of 2000 to 6000. • A large value of μr implies that a small current can produce a large flux density in the machine. Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 18 H B r 0
- 19. 1.3 MAGNETIC EQUIVALENTCIRCUIT • Example: Toroid Magnetic Circuit. • Assumptions: • When current i flows through the coil of N turns, magnetic flux is mostly confined in the core material. • The flux outside the toroid, called leakage flux, is so small that for all practical purposes it can be neglected. Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 19 Toroid magnetic circuit
- 20. 1.3 MAGNETIC EQUIVALENTCIRCUIT • Consider a path at a radius r. • The magnetic field intensity on this path is H and, from Ampère’s circuit law: Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 20 Ni l d H Ni Hl F Ni r H 2 The quantity Ni is called the magnetomotive force (mmf ) F, and its unit is ampere‐turn. Ni Hl (At/m) l Ni H (T) l Ni B
- 21. 1.3 MAGNETIC EQUIVALENTCIRCUIT • Magnetic Flux: • If no leakage flux: Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 21 dA B (Web) BA where B is the average flux density in the core and A is the area of cross section of the toroid. R F R Ni A l Ni A l Ni / P A l R 1 R is called reluctance of the magnetic path, and P is called the permeance of the magnetic path.
- 22. 1.3 MAGNETIC EQUIVALENTCIRCUIT • Previous equations suggest that the driving force in the magnetic circuit is the magnetomotive force F =Ni, which produces a flux against a magnetic reluctance R. • The magnetic circuit of the toroid can therefore be represented by a magnetic equivalent circuit as shown below: Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 22
- 23. 1.1.3 MAGNETIC EQUIVALENTCIRCUIT Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 23
- 24. • In Fig.1 the source of magnetic field is the ampre turn or mmf Ni acting on the circuit. The mmf is given as (Ampere’s law); • 8/10/2021 ELEC 312-Electric Machines 24 etc N Hl i l Ni H l R H R Hl Ni F dl H Ni F c c c c ; ; .
- 25. 8/10/2021 ELEC 312-Electric Machines 25 Note: Inverse ofReluctance is permeance
- 26. 8/10/2021 ELEC 312-Electric Machines 26 The elementof R in the magnetic circuit analogy is similar in concept to the electrical resistance. It is basically the measure of material resistance to the flow of magnetic flux. Reluctance in this analogy obeys the rule of electrical resistance (Series and Parallel Rules). Reluctance is measured in Ampere-turns per weber. Series Reluctance Req = R1 + R2 + R3 + …. Parallel Reluctance, 1 2 3 1 1 1 1 ... eq R R R R
- 27. 8/10/2021 ELEC 312-Electric Machines 27 Magnetic circuitapproach simplifies the calculations related to the magnetic field in a ferromagnetic material, however, this approach has inaccuracy embedded into it due to assumptions made in creating this approach (within 5% of the real answer). Possible reason of inaccuracy is due to: 1. The magnetic circuit assumes that all flux are confined within the core, but in reality a small fraction of the flux escapes from the core into the surrounding low- permeability air, and this flux is called leakage flux. 2. The reluctance calculation assumes a certain mean path length and cross sectional area (csa) of the core. This is correct if the core is just one block of ferromagnetic material with no corners, for practical ferromagnetic cores which have corners due to its design, this assumption is not accurate.
- 28. 8/10/2021 ELEC 312-Electric Machines 28 3. In ferromagneticmaterials, the permeability varies with the amount of flux already in the material. The material permeability is not constant hence there is an existence of non-linearity of permeability. 4. For ferromagnetic core which has air gaps, there are fringing effects that should be taken into account as shown: c g A A If fringing is neglected then the area of core and area of airgap is same If fringing is considered then the area of airgap will be about 2% to 5% higher ) 1.05( to 02 . 1 c g A A
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- 33. 8/10/2021 ELEC 312-Electric Machines 33 Example 2 A ferromagneticcore is shown. Three sides of this core are of uniform width, while the fourth side is somewhat thinner. The depth of the core is 10cm, and the other dimensions are shown in the figure. There is a 200 turn coil wrapped around the left side of the core. Assuming relative permeability µr of 2500, how much flux will be produced by a 1A input current? Solution: 3 sides of the core have the same cross sectional area, while the 4th side has a different area. Thus the core can be divided into 2 regions: (1) the single thinner side (2) the other 3 sides taken together
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- 35. 8/10/2021 ELEC 312-Electric Machines 35 The magnetic circuitcorresponding to this core:
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- 38. 1.5 MAGNETIC CIRCUITWITH AIR GAP • In electric machines, the rotor is physically isolated from the stator by the air gap. • Practically the same flux is present in the poles (made of magnetic core) and the air gap. Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 38 To maintain the same flux density, the air gap will require much more mmf than the core. If the flux density is high, the core portion of the magnetic circuit may exhibit a saturation effect. However, the air gap remains unsaturated, since the B−H curve for the air medium is linear (μ is constant).
- 39. 1.5 MAGNETIC CIRCUITWITH AIR GAP • A magnetic circuit having two or more media is known as a composite structure. • For the purpose of analysis, a magnetic equivalent circuit can be derived for the composite structure. • Let us consider the following simple composite structure with its equivalent electric circuit: Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 39
- 40. 1.5 MAGNETIC CIRCUITWITH AIR GAP • The driving force in this magnetic circuit is the mmf, F=Ni, and the core medium and the air gap medium can be represented by their corresponding reluctances: Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 40 c c c c A l R g g g A l R 0
- 41. 1.5 MAGNETIC CIRCUITWITH AIR GAP Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 41 g c R R Ni g g c c l H l H Ni c C A B g g A B
- 42. 8/10/2021 ELEC 312-Electric Machines 42 Example 2 Figure showsa ferromagnetic core whose mean path length is 40cm. There is a small gap of 0.05cm in the structure of the otherwise whole core. The csa of the core is 12cm2, the relative permeability of the core is 4000, and the coil of wire on the core has 400 turns. Assume that fringing in the air gap increases the effective csa of the gap by 5%. Given this information, find 1.the total reluctance of the flux path (iron plus air gap) 2.the current required to produce a flux density of 0.5T in the air gap.
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- 44. 8/10/2021 ELEC 312-Electric Machines 44 Solution: The magnetic circuitcorresponding to this core is shown below:
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- 47. 8/10/2021 ELEC 312-Electric Machines 47 Example 3 Figure showsa simplified rotor and stator for a dc motor. The mean path length of the stator is 50cm, and its csa is 12cm2. The mean path length of the rotor is 5 cm, and its csa also may be assumed to be 12cm2. Each air gap between the rotor and the stator is 0.05cm wide, and the csa of each air gap (including fringing) is 14cm2. The iron of the core has a relative permeability of 2000, and there are 200 turns of wire on the core. If the current in the wire is adjusted to be 1A, what will the resulting flux density in the air gaps be?
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- 49. 8/10/2021 ELEC 312-Electric Machines 49 Solution: To determine theflux density in the air gap, it is necessary to first calculate the mmf applied to the core and the total reluctance of the flux path. With this information, the total flux in the core can be found. Finally, knowing the csa of the air gaps enables the flux density to be calculated. The magnetic ckt corresponding to this machine is shown below.
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- 57. 1.6 INDUCTANCE • Acoil wound on a magnetic core, such as that shown below, is frequently used in electric circuits. • This coil may be represented by an ideal electric circuit element, called inductance, which is defined as the flux linkage of the coil per ampere of its current. Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 57 Inductance of a coil–core assembly. (a) Coil–core assembly. (b) Equivalent inductance. =N i
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- 63. Magnetic property ofFerromagnetic material-Magnetization Curve 8/10/2021 ELEC 312-Electric Machines 63
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- 65. Magnetization Curve • Smallincrease in the mmf produces large increase in the flux‐Linear region • After a certain point further increase in mmf does not change the flux‐saturation region • Transition point between saturation and unsaturated region is called Knee point. • All Electric machine core is designed to operate at knee point. 8/10/2021 ELEC 312-Electric Machines 65
- 66. 8/10/2021 ELEC 312-Electric Machines 66 Hysteresis Loss Consider ACcurrent, there will be residual flux when moving from the positive half cycle to the negative cycle of the ac current flow and vice versa. Energy Losses in a Ferromagnetic Core • Hysteresis Losses • Eddy current losses
- 67. 8/10/2021 ELEC 312-Electric Machines 67 Explanation of HysteresisLoop Apply AC current. Assume flux in the core is initially zero. As current increases, the flux traces the path ab. (saturation curve) When the current decreases, the flux traces out a different path from the one when the current increases (path bcd). When the current increases again, it traces out path deb. HYSTERESIS is the dependence on the preceding flux history and the resulting failure to retrace flux paths. When a large mmf is first applied to the core and then removed, the flux path in the core will be abc. When mmf is removed, the flux does not go to zero – residual flux. This is how permanent magnets are produced. To force the flux to zero, an amount of mmf known as coercive mmf must be applied in the opposite direction.
- 68. 8/10/2021 ELEC 312-Electric Machines 68 Why does hysteresisoccur? To understand hysteresis in a ferromagnetic core, we have to look into the behaviour of its atomic structure before, during, and after the presence of a magnetic field. The atoms of iron and similar metals (cobalt, nickel, and some of their alloys) tend to have their magnetic fields closely aligned with each other. Within the metal, there is an existence of small regions known as domains where in each domain there is a presence of a small magnetic field which randomly aligned through the metal structure. This as shown below:
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- 70. Hysteresis Loss • Thehysteresis loops are obtained by slowly varying the current i of the coil over a cycle. • When i is varied through a cycle, during some interval of time, energy flows from the source to the coil–core assembly, and during some other interval of time, energy returns to the source. • However, the energy flowing in is greater than the energy returned back. 8/10/2021 ELEC 312-Electric Machines 70
- 71. • Therefore, duringa cycle of variation of i (hence H), there is a net energy flow from the source to the coil–core assembly. • This energy loss heat the core. • The loss of power in the core due to the hysteresis effect is called hysteresis loss. • The amount of the hysteresis loss is proportional to the hysteresis loop size (or the area of loop). 8/10/2021 ELEC 312-Electric Machines 71
- 72. 2.1 HYSTERESIS LOSS •Assume that the coil has no resistance and the flux in the core is Φ. • The voltage e across the coil, according to Faraday’s law, is: Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 72 dt d N e The energy transfer during an interval of time t1 to t2 is: 2 1 2 1 2 1 2 1 Nid idt dt d N eidt pdt W t t t t t t
- 73. 2.1 HYSTERESIS LOSS •where Vcore =Al represents the volume of the core. • The integral term in this equation represents the hatched area. • The energy transfer over one cycle of variation is: Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 73 BA N Hl i 2 1 2 1 B B B B HdB lA AdB N Hl N W 2 1 B B core HdB V W h core core core cycle W V B-H V HdB V W loop of area
- 74. 2.1 HYSTERESIS LOSS •The power loss in the core due to the hysteresis effect is: Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 74 f W V P h core h HdB Wh is the energy density in the core (= area of the B−H loop). Frequency of variation of the current i. Note: It is difficult to evaluate the area of the hysteresis loop, because the B−H characteristic is nonlinear and multivalued, and no simple mathematical expression can describe the loop.
- 75. 2.1 HYSTERESIS LOSS Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 75 n KB B-Hmax loop of Area Both n and K can be empirically determined. • Charles Steinmetz of the General Electric Company performed a large number of experiments and found that for magnetic materials used in electric machines an approximate relation is: f B K P n h h max where Kh is a constant whose value depends on the ferromagnetic material and the volume of the core. where Bmax is the maximum flux density, n varies in the range 1.5 to 2.5, and K is a constant. Usually it is taken as 1.6 f W V P h core h Higher f higher Ph
- 76. 8/10/2021 ELEC 312-Electric Machines 76 A time-changing fluxinduces voltage within a ferromagnetic core. These voltages cause swirls of current to flow within the core – eddy currents. Energy is dissipated (in the form of heat) because these eddy currents are flowing in a resistive material (iron) The amount of energy lost to eddy currents is proportional to the size of the paths they follow within the core. To reduce energy loss, ferromagnetic core should be broken up into small strips, or laminations, and build the core up out of these strips. An insulating oxide or resin is used between the strips, so that the current paths for eddy currents are limited to small areas. Eddy Current Loss
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- 78. 2.2 EDDY CURRENTLOSS • The eddy current loss in a magnetic core subjected to a time‐varying flux is: Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 78 The lamination thickness varies from 0.5 to 5 mm in electrical machines and from 0.01 to 5 mm in devices used in electronic circuits operating at higher frequencies. where Ke is a constant whose value depends on the type of material and its lamination thickness. 2 2 max f B K P e e
- 79. 2.3 CORE LOSS Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 79 HysteresisLoss Eddy Current Loss Core or iron Loss e h c P P P
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- 84. 1.3 SINUSOIDAL EXCITATION •In ac electric machines as well as many other applications, the voltages and fluxes vary sinusoidally with time. • Consider the following coil–core assembly: Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 84
- 85. • Assume thatthe core flux Φ(t) varies sinusoidally with time. Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 85 t t sin ) ( max max is the magnitude of the core flux =2f is the angular frequency f is the frequency From Faraday’s law, the voltage induced in the N-turn coil is: max max cos sin 2 d e t N N t E t dt Induced voltage lags behind the flux by 90 degree E
- 86. • The root‐mean‐square(rms) value of the induced voltage is: Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 86 max max max 2 2 2 2 Nf N E Erms Note: This is an important equation and will be referred to frequently in the theory of ac machines. max 44 . 4 Nf Erms
- 87. Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 87 Note: Induced emfis considered equal to the applied voltage
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- 89. 1.3.1 EXCITING CURRENT •If a coil is connected to a sinusoidal voltage source, a current flows in the coil to establish a sinusoidal flux in the core. Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 89 This current is called the exciting current, iΦ. If the B−H characteristic of the ferromagnetic core is nonlinear, the exciting current will be nonsinusoidal. Without Hysteresis With Hysteresis Current waveforms differ!
- 90. 3.1 EXCITING CURRENT Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 90 i 1 2 3 4 5 6 71 2 3 4 5 6 7 8 9 11 10 12 13 8 9 11 10 12 , 13 11 12 10 9 8 i 2 3 4 5 6 FIGURE 1.18 Exciting current for no hysteresis: Φ−i characteristic and exciting current. Without Hysteresis Loop:
- 91. • Without HysteresisLoop: • The exciting current iΦ is nonsinusoidal, but it is in phase with the flux wave and is symmetrical with respect to voltage e. • The fundamental component iφ1 of the exciting current lags the voltage e by 90o. Therefore no power loss is involved. Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 91 FIGURE 1.18 Exciting current for no hysteresis. (a) Φ−i characteristic and exciting current. (b) Equivalent circuit. (c) Phasor diagram.
- 92. • With HysteresisLoop: • The exciting current is nonsinusoidal as well as nonsymmetrical with respect to the voltage waveform. • The exciting current can be split into two components, one (ic) in phase with voltage e accounting for the core loss and the other (im) in phase with Φ and symmetrical with respect to e, accounting for the magnetization of the core. Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 92 FIGURE 1.18 Exciting current with hysteresis loop. (a) Φ−i loop and exciting current. (b) Phasor diagram. (c) Equivalent circuit..
- 93. • With HysteresisLoop: • The magnetizing component im is the same as the exciting current if the hysteresis loop is neglected. • The exciting current can therefore be represented by a resistance Rc, to represent core loss, and a magnetizing inductance Lm, to represent the magnetization of the core. • Usually, in the phasor diagram only the fundamental component of the magnetizing current im is considered. Prof. Adel Gastli Electrical Machines Chapter1: Magnetic Circuits 93
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- 97. Permanent Magnets • Apermanent magnet is capable of maintaining a magnetic field without any excitation mmf provided to it. • Permanent magnets are normally alloys of iron, nickel, and cobalt. • They are characterized by a large B−H loop, high retentivity (high value of Br), and high coercive force (high value Hc). • These alloys are subjected to heat treatment, resulting in mechanical hardness of the material. • Permanent magnets are often referred to as hard iron, and other magnetic materials as soft iron. • E.g. of PM materials: Alnico (al‐nickel‐cobalt), Neodymium‐ iron‐cobalt, Samirium‐cobalt etc 8/10/2021 ELEC 312-Electric Machines 97
- 98. • A goodpermanent magnet should produce a high magnetic field with a low mass, and should be stable against the influences which would demagnetize it. The desirable properties of such magnets are typically stated in terms of the remanence and coercivity of the magnet materials. 8/10/2021 ELEC 312-Electric Machines 98
- 99. • 8/10/2021 ELEC 312-Electric Machines 99 Total Amp-turn orMMF is = 0 (Because it is PM) Hc lc –MM of Iron portion Hglg ---MMF of Aig-gap porition ) 1 ( c g g c l l H H ) 2 ( 0 0 0 g c c g g c c g g g g c c g g g c c A A B H A A B H Hence H B A A B B A B A B MMF is same in Iron and Airgap Put Hg in (1)
- 100. • 8/10/2021 ELEC 312-Electric Machines 100 B (T) H (AT/m) Air‐gapline or Permeance line Bc Hc
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- 102. Recoil Line • Ifa current is applied and reduced in the coil, then a small loop is locally formed. • After a few cycle line is stabilized, it is called Recoil line. 8/10/2021 ELEC 312-Electric Machines 102
- 103. PM Material • Alnico(Alnico-5 and Alnico-8)-Alloy of Al+Cobalt+Nickle+Fe---Characterized by High Br and Low Hc • Ferrite (Ceramic) Magnet—Characterized by Low Br and High Hc • Samarium Cobalt (rare earth magnet)—Characterized by High Br and High Hc • Ne-Fe-B (rare earth magnet) )—Characterized by High Br and High Hc 8/10/2021 ELEC 312-Electric Machines 103
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- 105. • B.H =Energy stored per unit volume (Energy Density) • For compact size of a PM machine, BH (product of B and H) should be maximized. • The operating point should be chosen at maximum value of BH (as shown in the next slide). Rare Earth magnet has highest BH but it is costly. • Curie Temperature-is the temperature at which material looses its magnetic property. • Rare earth magnet has lowest Curie temp. 8/10/2021 ELEC 312-Electric Machines 105
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- 107. PM Material CurieTemp (degree celcius) Rare earth (Nieodium (Ne)+Fe+Boron) 350 Samarium Cobalt (rare earth) 700 Ferrite Magnet 450 Alnico 890 8/10/2021 ELEC 312-Electric Machines 107
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