Magnetic circuit

1. 03/08/11 Dr Awang Jusoh/Dr Makbul Chapter 1 Introduction to Electromechanical Energy Conversion

2. 1.1 Magnetic Circuits 03/08/11 Dr Awang Jusoh/Dr Makbul

6. Magnetic Field Concept 03/08/11 Dr Awang Jusoh/Dr Makbul

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. Magnetic Equivalent Circuit 03/08/11 Dr Awang Jusoh/Dr Makbul Analogy between magnetic circuit and electric circuit

20. Magnetic Circuit with Air Gap 03/08/11 Dr Awang Jusoh/Dr Makbul

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

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.

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.

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. Mutual Inductance where is the self-inductance of coil 2. Similarly, the flux linkage of coil 2 is is the mutual inductance and

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. 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. 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: