BASIC ELECTRICAL TECHNOLOGY DET 2113 Chapter 4 Magnetic

BASIC ELECTRICAL TECHNOLOGY DET 211/3 Chapter 4 – Magnetic Circuits 1

Magnetic Materials and Circuits Introduction ØMagnet contains a north pole and south pole. ØMagnet flux leaves the magnet as the north pole and the place where the flux returns to the magnet as the south pole. Two types of magnet: • Permanent magnet • Electromagnet 2

Right Hand Rule and Ampere’s Law When a conductor carries current a magnetic field is produced around it. Fingers– indicate current direction Thumb – indicate the direction of magnetic flux is wrapping around the wire 3

Right Hand Rule and Ampere’s Law The relationship between current and magnetic field intensity can be obtained by using Ampere’s Law states that the line integral of the magnetic field intensity, H around a closed path is equal to the total current linked by the contour. H: the magnetic field intensity at a point on the contour dl: the incremental length at that point If θ: the angle between vectors H and dl then 4

Right Hand Rule and Ampere’s Law Consider a rectangular core with N winding Therefore 5

Relationship between B-H The magnetic field intensity, H produces a magnetic flux density, B everywhere it exists. - Permeability of the medium - Permeability of free space, - Relative permeability of the medium For free space or electrical conductor (Al or Cu) or insulators, unity is 6

MAGNETIC EQUIVALENT CIRCUIT A simple magnetic circuit having a ring shaped magnetic core (toroid) and a coil that extends around the entire circumference When current i flows through the coil of N turns, a magnetic flux is produced. 7

MAGNETIC EQUIVALENT CIRCUIT Assumption: • All fluxes are confined to the core • The fluxes are uniformly distributed in the core The flux outside the toroid (called leakage flux), is so small (can be neglected) Use Ampere’s Law, F = Magnetomotive force (mmf) 8

MAGNETIC EQUIVALENT CIRCUIT Where; N – no of turns of coil i – current in the coil H – magnetic field intensity l – mean length of the core 9

Magnetic Flux Density (B) and Magnetizing Curve (B-H Curve) Case 1: Non magnetic material core (Cu, Al, air, plastic, wood, . . ) 10

Magnetic Flux Density (B) and Magnetizing Curve (B-H Curve) Case 2: Ferromagnetic material core (iron, steel, ferrite, . . ) The magnetic flux density, B increases almost linear in the region of low values of magnetic intensity, H. At higher value of H, the change of B is nonlinear. 11

MAGNETIC EQUIVALENT CIRCUIT The flux in the coil, Where Ф – flux in the coil (wb) F – magnetomotive force (mmf) R – 1/μA = 1/P , Reluctance P = permeance A – cross sectional area 12

ANALOGY BETWEEN MAGNETIC CIRCUIT AND ELECTRIC CIRCUIT a) Magnetic equivalent circuit b) Electric equivalent circuit To solve magnetic equivalent circuit – Kirchhoff Voltage and Current Laws (KVL & KCL) Electric circuit Magnetic circuit Driving force EMF (E) MMF (F) Produces Current (i) Flux (Ф) Limited by Resistance (R) Reluctance (R) 13

MAGNETIC CIRCUIT WITH 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 by magnetic core) and the air gap. To maintain the same flux density, the air gap will require much more mmf than the core. 14

MAGNETIC CIRCUIT WITH AIR GAP Where lc – mean length of the core lg – the length of the air gap 15

FRINGING EFFECT Fringing Effect: Bulging of the flux lines in the air gap. Effect: The effective cross section area of air gap increase so the reluctance of the air gap decrease. The flux density Bg < Bc, Bc is the flux density in the core. If the air gaps is small, the fringing effect can be neglected. So In practical, large air gap will be divided into several small air gaps to reduce the fringing effect. 16

INDUCTANCE A coil wound on a magnetic core as shown in figure above, is frequently used in electric circuits. This coil may be represented by an ideal circuit element, called inductance, which is defined as the flux linkage of the coil per ampere of its current. Flux linkage Inductance 17

Example 15 cm 30 cm 15 cm i N=200 turns l 1 l 2 15 cm 30 cm 15 cm 10 cm A ferromagnetic core is shown in Figure above. Three sides of this core are of uniform width, while the fourth side is somewhat thinner. The depth of the core (into the page) is 10 cm and the other dimensions are shown in figure. There is 200 turn coil wrapped around the left side of the core. Assuming relative permeability mr of 2500, how much flux will be produce by a 1 A input current? 18

Solution Example The mean path length of region 1 is 45 cm and the cross-sectional area is 10 x 10 cm = 100 cm 2. Therefore, the reluctance in the first region is: The mean path length of region 2 is 130 cm and the cross-sectional area is 15 x 10 cm = 150 cm 2. Therefore, the reluctance in the second region is: 19

Solution Example Therefore, the total reluctance in the core is: The total magnetomotive force (MMF) is: The total flux in the core is given by: 20

Assignment 3 15 cm 30 cm 15 cm i 30 cm N=200 turns lc 15 cm 30 cm 15 cm A ferromagnetic core is shown in Figure above. All side of this core are uniform width. The depth of the core is 10 cm. Assuming relative permeability mr of 2500, how much flux will be produce by a 1 A input current? 21

Bersambung minggu hadapan 1. Hantar assignment 1 2. Tutorial II/III (discuss next week) 3. Mid term test I (26/8/2008) 22