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# Chapter1 part1

Magnetic circuit

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### Chapter1 part1

1. 1. 03/08/11 Dr Awang Jusoh/Dr Makbul Chapter 1 Introduction to Electromechanical Energy Conversion
2. 2. 1.1 Magnetic Circuits 03/08/11 Dr Awang Jusoh/Dr Makbul
3. 3. Magnetic Field Concept <ul><li>Magnetic Fields: </li></ul><ul><li>Magnetic fields are the fundamental mechanism by which energy is converted (transferred) from one form to another in electrical machines. </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul <ul><li>Magnetic Material </li></ul><ul><li>Definition : A material that has potential to attract other materials toward it, materials such as iron, cobalt, nickel </li></ul><ul><li>Function: Act as a medium to shape and direct the magnetic field in the energy conversion process </li></ul>
4. 4. Magnetic Field Concept <ul><li>Magnetic field around a bar magnet </li></ul><ul><li>Two “poles” dictated by direction of the field </li></ul><ul><li>Opposite poles attract (aligned magnetic field) </li></ul><ul><li>Same poles repel (opposing magnetic field) </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul
5. 5. Magnetic Field Concept <ul><li>Magnetic Flux/ Flux Line Characteristic </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul 1. Outside - Leaves the north pole (N) and enters the south pole (S) of a magnet. Inside - Leaves the south pole (S) and enters the north pole (N) of a magnet. 2. Like (NN, SS) magnetic poles repel each other. 3. Unlike (NS) magnetic poles attracts each other. 4. Magnetic lines of force (flux) are always continuous (closed) loops, and try to make as shortest distance loop. 5. Flux line never cross each others
6. 6. Magnetic Field Concept 03/08/11 Dr Awang Jusoh/Dr Makbul
7. 7. Machines Basic Requirements <ul><li>Presence of a “magnetic fields” can be produced by: </li></ul><ul><ul><li>Use of permanent magnets </li></ul></ul><ul><ul><li>Use of electromagnets </li></ul></ul><ul><li>Then one of the following method is needed: </li></ul><ul><ul><li>Motion to produce electric current (generator) </li></ul></ul><ul><ul><li>Electric current to produce motion (motor) </li></ul></ul>03/08/11 Dr Awang Jusoh/Dr Makbul
8. 8. Ampere’s Law <ul><li>Any current carrying wire will produce magnetic field around itself. </li></ul><ul><li>Magnetic field around a wire: </li></ul><ul><li>Thumb indicates direction of current flow </li></ul><ul><li>Finger curl indicates the direction of field </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul
9. 9. Ampere’s Law <ul><li>Ampere’s law: the line integral of magnetic field intensity around a closed path is equal to the sum of the currents flowing through the surface bounded by the path </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul Recall that the vector dot product is given by  dl H I 1 I 2 in which  is the angle between H and d l .
10. 10. Ampere’s Law <ul><li>If the magnetic intensity has constant magnitude and points in the same direction as the incremental length d l everywhere along the path, Ampere’s law reduces to </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul in which l is the length of the path. Examples of such cases: (i) Magnetic field around a long straight wire, (ii) Solenoid
11. 11. <ul><li>Example 1: </li></ul><ul><li>( a long straight </li></ul><ul><li>Wire) </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul Example 2: (Solenoid)
12. 12. Flux Density <ul><li>Number of lines of magnetic force (flux) passing through unit area </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul or Wb/m 2
13. 13. Field Intensity <ul><li>The effort made by the current in the wire to setup a magnetic field. </li></ul><ul><li>Magnetomotive force (mmf) per unit length is known as the “magnetizing force” H </li></ul><ul><li>Magnetizing force and flux density related by: </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul
14. 14. Permeability <ul><li>Permeability  is a measure of the ease by which a magnetic flux can pass through a material (Wb/Am). The higher the better flux can flow in the magnetic materials. </li></ul><ul><li>Permeability of free space  o = 4  x 10 -7 (Wb/Am) </li></ul><ul><li>Relative permeability,  r : </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul
15. 15. Reluctance <ul><li>Reluctance, which is similar to resistance, is the opposition to the establishment of a magnetic field, i.e.&quot; resistance ” to flow of magnetic flux. Depends on length of magnetic path  , cross-section area A and permeability of material  . </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul
16. 16. Magnetomotive Force <ul><li>The product of the number of turns and the current in the wire wrapped around the core’s arm. ( The ability of a coil to produce flux ) </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul N
17. 17. Magnetomotive Force <ul><li>The MMF is generated by the coil </li></ul><ul><li>Strength related to number of turns and current, Symbol F, measured in Ampere turns (At) </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul
18. 18. Magnetization Curve 03/08/11 Dr Awang Jusoh/Dr Makbul Behavior of flux density compared with magnetic field strength, if magnetic intensity H increases by increase of current I, the flux density B in the core changes as shown.  flux (  )  current (I) linear Near saturation
19. 19. Magnetic Equivalent Circuit 03/08/11 Dr Awang Jusoh/Dr Makbul Analogy between magnetic circuit and electric circuit
20. 20. Magnetic Circuit with Air Gap 03/08/11 Dr Awang Jusoh/Dr Makbul
21. 21. Parallel Magnetic Circuit 03/08/11 Dr Awang Jusoh/Dr Makbul l 2 l 1 l 3 I N S 1 S 2 S 3 + - NI  1  3  2 I II <ul><ul><li>Loop I </li></ul></ul><ul><ul><ul><li>NI = S 3  3 + S 1  1 </li></ul></ul></ul><ul><ul><ul><li>= H 3 l 3 + H 1 l 1 </li></ul></ul></ul><ul><ul><li>Loop II </li></ul></ul><ul><ul><ul><li>NI = S 3  3 + S 2  2 </li></ul></ul></ul><ul><ul><ul><li>= H 3 l 3 + H 2 l 2 </li></ul></ul></ul><ul><ul><li>Loop III </li></ul></ul><ul><ul><ul><li>0 = S 1  1 + S 2  2 </li></ul></ul></ul><ul><ul><ul><li>= H 1 l 1 + H 2 l 2 </li></ul></ul></ul>
22. 22. Electric vs Magnetic Circuit 03/08/11 Dr Awang Jusoh/Dr Makbul Magnetic circuit Electric circuit Term Symbol Term Symbol Magnetic flux  Electric current I Flux density B Current density J Magnetomotive force F Electromotive force E Permeability  Permitivity  Reluctance Resistance R
23. 23. Leakage Flux <ul><li>Part of the flux generated by a current-carrying coil wrapped around a leg of a magnetic core stays outside the core. This flux is called leakage flux. </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul Useful flux
24. 24. Fringing Effect <ul><li>The effective area provided for the flow of lines of magnetic force (flux) in an air gap is larger than the cross-sectional area of the core. This is due to a phenomenon known as fringing effect. </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul Air gap – to avoid flux saturation when too much current flows - To increase reluctance
25. 25. Example 1 03/08/11 Dr Awang Jusoh/Dr Makbul Refer to Figure below, calculate:- 1) Flux 2) Flux density 3) Magnetic intensity Given  r = 1,000; no of turn, N = 500; current, i = 0.1 A. cross sectional area, A = 0.0001m 2 , and means length core l C = 0.36 m. <ul><li>1.75x10 -5 Wb </li></ul><ul><li>0.175 Wb/m 2 </li></ul><ul><li>139 AT/Wb </li></ul>
26. 26. Example 2 <ul><li>The Figure represents the magnetic circuit of a relay. The coil has 500 turns and the mean core path is l c = 400 mm. When the air-gap lengths are 2 mm each, a flux density of 1.0 Tesla is required to actuate the relay. The core is cast steel. </li></ul><ul><li>a. Find the current in the coil. (6.93 A) </li></ul><ul><li>b. Compute the values of permeability and relative permeability of the core. (1.14 x 10 3 , 1.27) </li></ul><ul><li>c. If the air-gap is zero, find the current in the coil for the same flux density (1 T) in the core. ( 0.6 A) </li></ul>03/08/11 Dr Awang Jusoh/Dr Makbul Pg 8 : SEN Data- 1T – 700 at/m
27. 27. Electromagnetic Induction <ul><li>An emf can be induced in a coil if the magnetic flux through the coil is changed. This phenomenon is known as electromagnetic induction. </li></ul><ul><li>The induced emf is given by </li></ul><ul><li>Faraday’s law: The induced emf is proportional to the rate of change of the magnetic flux. </li></ul><ul><li>This law is a basic law of electromagnetism relating to the operating principles of transformers, inductors, and many types of electrical motors and generators. </li></ul>
28. 28. Electromagnetic Induction <ul><li>Faraday's law is a single equation describing two different phenomena: The motional emf generated by a magnetic force on a moving wire, and the transformer emf generated by an electric force due to a changing magnetic field. </li></ul><ul><li>The negative sign in Faraday's law comes from the fact that the emf induced in the coil acts to oppose any change in the magnetic flux. </li></ul><ul><li>Lenz's law: The induced emf generates a current that sets up a magnetic field which acts to oppose the change in magnetic flux. </li></ul>
29. 29. Lenz’s Law An induced current has a direction such that the magnetic field due to the induced current opposes the change in the magnetic flux that induces the current. As the magnet is moved toward the loop, the  B through the loop increases, therefore a counter-clockwise current is induced in the loop. The current produces its own magnetic field to oppose the motion of the magnet If we pull the magnet away from the loop, the  B through the loop decreases, inducing a current in the loop. In this case, the loop will have a south pole facing the retreating north pole of the magnet as to oppose the retreat. Therefore, the induced current will be clockwise.
30. 30. Self-Inductance <ul><li>From Faraday’s law </li></ul><ul><li>Where  is the flux linkage of the winding is defined as </li></ul><ul><li>For a magnetic circuit composed of constant magnetic permeability, the relationship between  and i will be linear and we can define the inductance L as </li></ul><ul><li>It can be shown later that </li></ul>
31. 31. Self-Inductance <ul><li>For a magnetic circuit having constant magnetic permeability </li></ul><ul><li>So, </li></ul>Henry
32. 32. Mutual Inductance + + - -     i  i  N  N  turns turns g  Magnetic core Permeability  , Mean core length l c , Cross-sectional area A c Notice the current i 1 and i 2 have been chosen to produce the flux in the same direction. It is also assumed that the flux is confined solely to the core and its air gap.
33. 33. Mutual Inductance <ul><li>The total mmf is therefore </li></ul><ul><li>with the reluctance of the core neglected and assuming that A c = A g the core flux is </li></ul>If the equation is broken up into terms attributable to the individual current, the flux linkages of coil 1 can be expressed as
34. 34. Mutual Inductance where is the self-inductance of coil 1 and is the flux linkage of coil 1 due to its own current i 1 . The mutual inductance between coils 1 and 2 is and is the flux linkage of coil 1 due to current i 2 .
35. 35. Mutual Inductance where is the self-inductance of coil 2. Similarly, the flux linkage of coil 2 is is the mutual inductance and
36. 36. Mutual Inductance: Example + + - -     i  i  N  N  turns turns g  Magnetic core Permeability   , Cross-sectional area A c = A g = 1 cm X 1.5916 cm Air gap length, g = 2 mm N 1 = 100 turns, N 2 =200 turns Find L 11 , L 22 , and L 12 = L 21 = M
37. 37. Magnetic Stored Energy We know that for a magnetic circuit with a single winding and For a static magnetic circuit the inductance L is fixed For a electromechanical energy device, L is time varying
38. 38. Magnetic Stored Energy The power p is Thus the change in magnetic stored energy The total stored energy at any  is given by setting  1 = 0: