Magnetic Circuits. Fig. 1 The right hand rule for magnetic flux. The unit for the flux Φ is (weber) and the magnetic flux density B is given as:

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1 Maneti Ciruits MTE 30 Sprin 006 E.F. EL-Saadany Maneti Ciruits Eetri mahines and transformers have eetri iruits and maneti iruits interinked throuh the medium of maneti fux. Eetri urrent fow throuh the eetri iruits, whih are made up of windins. On the other hand, maneti fuxes fow throuh the maneti iruits, whih are made up of iron ores. The interation between the urrents and the fuxes is the basi of the eetromehania enery onversion proess that takes pae in enerators and motors. However, in transformers it is more feasibe to think about the proess in terms of an enery transfer. In transformers, the enery transfer is normay assoiated with hane in votae and urrent eves. Thus, maneti iruits pay an essentia roe. 1. Basis The maneti fux is produed due to the fow of a urrent in a wire (eetri manet). The diretion of the produed maneti fux is determined by the riht-hand rue as shown in Fi. 1. Fi. 1 The riht hand rue for maneti fux The unit for the fux Φ is (weber) and the maneti fux density B is iven as: B Wb/m (Tesa) The maneto-motive fore mmf is the abiity of a oi to produe maneti fux. The mmf unit is mp-turn and is iven by: mmf I (T ). The maneti fux intensity H is the mmf

2 Maneti Ciruits MTE 30 Sprin 006 E.F. EL-Saadany mmf per unit enth aon the path of the fux and is iven by: H ( T / m), where is the mean or averae path enth of the maneti fux in meters. The reation between the mmf and the fux is overned by the system reutane, suh that mmf, where the reutane is iven by μ, where The averae enth of the maneti ore (m) The ross setion area (m ) μ The permeabiity of the materia (T/m ) The permeabiity of the materia is iven by μ μ0μ r where: μ 0 is the permeabiity of air and μr is the reative permeabiity. From the above reationships, we an onude that: B mmf ( H) ( μ) μh The reation B-H is known as the manetization harateristis of the materia and is broken to three different reions: Linear, knee and saturation as shown in Fi.. Fi. Manetization Curve

3 Maneti Ciruits MTE 30 Sprin 006 E.F. EL-Saadany. naoy between maneti and eetri iruits ELECTIC CICUIT MGETIC CICUIT E EMF F MMF esistane eutane I Current Fux σ Condutivity μ Permeabiity E I mmf ρ σ μ series 1 series parae parae 1 3. Maneti Ciruit naysis In order to anayze any maneti iruit, two steps are mandatory as iustrated by Fi. 3: Step #1: Find the eetri equivaent iruit that represents the maneti iruit. Step #: nayze the eetri iruit to sove for the maneti iruit quantities. 1 1 μ 1 F F F [ 1 ] + Fi. 3 Maneti iruit anaysis

4 Maneti Ciruits MTE 30 Sprin 006 E.F. EL-Saadany Exampe The maneti iruit shown beow has the foowin dimensions: 16 m, 40m, 0.5mm and 350 turns. The ore is made of a materia with the B-H reationship iven beow. For B 1.0 T in the ore, find: a) The fux and the tota fux inkae λ, where λ. b) The required urrent to set this fux if there is no air ap. ) The required urrent with the presene of an air ap. B (Tesa) H (.T) Fi. 4 Maneti iruit for the exampe Soution a) B mWb λ Wb. t b) With no air-ap F I I, μ

5 Maneti Ciruits MTE 30 Sprin 006 E.F. EL-Saadany B μ H t / wb I. 86 m 350 ) With air-ap F I ( + ) μ 5000, I 7 μ ( 4π ) ( + ) ,679.6 In this exampe, it is ear that the urrent needed to set the same fux in ase of maneti iruits with air ap ompared to those iruits without air-ap is muh hiher. 4. Frinin Effet The frinin effet resuts from the presene of the air ap in the maneti iruit. The main onsequene of the frinin effet is to make the maneti fux density of the air ap different from the fux density of the ore due to the path of the fux., but B B Some times air aps are introdued in the maneti iruits to inearize the B-H urve. For a iven urrent, the fux density wi be smaer due to the air ap presene and saturation is not reahed.

6 Maneti Ciruits MTE 30 Sprin 006 E.F. EL-Saadany 5. Leakae Fux In order to set up a speifi fux in the ore, more MMF is needed due to the fux eakae phenomenon. OTE In most maneti iruit anaysis, both eakae fux and frinin effet are neeted. Fi. 5 Frinin effet and eakae fux 6. Core Losses (Iron Losses) There are two types of osses that are present in the iron ore of any transformer or rotatin mahine, namey hysteresis and eddy urrent osses. 6.1 Hysteresis Losses Transformers and most rotatin mahines operate on aternatin urrents. In suh devies, the fux in the iron hanes ontinuousy both in vaue and diretion. The maneti domains are therefore, oriented first in one diretion, then the other, at a rate that depends upon the frequeny. If we pot the fux density B as a funtion of the fied intensity H, we obtain a osed urve aed hysteresis oop as shown in Fi. 6. In desribin a hysteresis oop, the fux moves suessivey from +B m, +B r, 0, -B m, -B r, 0, and +B m, orrespondin respetivey to points a, b,, d, e, f, and a in the fiure beow. The maneti materia absorbs enery durin eah ye and this enery is dissipated as heat. The amount of heat reeased per ye is equa to the area of the hysteresis oop. To redue the hysteresis osses, a maneti materia that have narrow hysteresis oop is normay seeted.

7 Maneti Ciruits MTE 30 Sprin 006 E.F. EL-Saadany Fi. 6 Hysteresis oop Fi. 7 Hysteresis oop for different materias The hysteresis osses an be auated usin an empiria formua iven as: P h k h V f B n max Where: P h The hysteresis osses (Watt) k Hysteresis onstant h V The materia voume f The exitation frequeny B The maximum fux density max n Materia onstant (1.5-.5)

Eddy urrents (resut due to the indued emf "Faraday's aw") are set up as shown and they fow throuhout the entire enth of the ore. The resut of eddy urrents is to heat up the ore resutin in I osses. Fi.

8 Maneti Ciruits MTE 30 Sprin 006 E.F. EL-Saadany 6. Eddy Current Losses The Eddy urrent probem arises when iron has to arry an a fux. Fi. 8 shows a oi arryin an a urrent that produes an a fux in a soid iron ore. Eddy urrents (resut due to the indued emf "Faraday's aw") are set up as shown and they fow throuhout the entire enth of the ore. The resut of eddy urrents is to heat up the ore resutin in I osses. Fi. 8 Coi arryin an a urrent Eddy urrents an be redued by spittin the ore in two aon its enth as shown in Fi. 9, takin are to insuate the two setions from eah other. The votae indued in eah setion is one haf of what it was before, with the resut of the Eddy urrent, and the orrespondin osses are onsideraby redued. If the ore is further subdivided as shown in Fi., the osses derease proressivey. In pratie, the ore is omposed of amination of mm in thikness. Fi. 9 Eddy urrents in two setion ore The Eddy urrent osses an be auated usin an empiria formua iven as: P ( f t ) e ke V B max

9 Maneti Ciruits MTE 30 Sprin 006 E.F. EL-Saadany Fi. Eddy urrent redution when usin aminated ore where: P e The Eddy urrent osses (Watt) k Materia dependent onstant e V The materia voume f The exitation frequeny B The maximum fux density max t Lamination thikness 7. Indutanes The indutane (in Henry) is iven by λ L I I Sine: and F I, μ Therefore, λ L I I Iμ I L L 11 1 λ 11 sef indutane I 1 λ 1 mutua indutane I 1

10 Maneti Ciruits MTE 30 Sprin 006 E.F. EL-Saadany where: λ 11 is the tota fux inkin oi 1 due to I 1 when I 0, and λ 1 is the tota fux inkin oi due to I 1 when I 0 1 L 11, L, L 1 1 L1 8. Faraday's Law When a iruit is inked by a maneti fux that is varyin with time due to: 1. eative motion of the maneti fied and the iruit. Time varyin nature of the maneti fied. d n emf wi be indued in the iruit and is iven by: E, whih is known as Faraday's ow for dt indution. The emf indued in the iruit an drive a urrent if this iruit is osed via a oad. The diretion of the indued urrent is suh that the maneti fied enerated by the urrent OPPOSES the maneti fied that aused the emf and the urrent. This is known as Lenz's aw, whih states that: d E dt

The Calculation of Inductor Sizes, for Heat Treatment of Aluminum Wires

The Calculation of Inductor Sizes, for Heat Treatment of Aluminum Wires IO Journa of Engineering (IOJEN) IN (e): 5-, IN (p): 78-879 Vo 6, Issue 8 (ug 6), V PP -7 wwwiosrjenorg The Cauation of Indutor izes, for Heat Treatent of uinu Wires yan Y -awashdeh -Baqa`a ppied University