Chapter 1 MAGNETIC CIRCUIT

It is the path which is followed by magnetic flux. MAGNETIC CIRCUIT It is the path which is followed by magnetic flux. It is basically ferromagnetic with coil wound around them

in the design of electrical machines. Why MAGNETIC CIRCUIT? It is an important component in the design of electrical machines. 2

Examples of Magnetic Circuits

Simple magnetic circuit

Magnetic circuit with air gap

Simple machine

The object of today lecture It is required to understand the concepts of magnetic circuits By making Analogy between Electric circuit and magnetic circuit

Analogy between Electric circuit and magnetic circuit

is the number of flux lines crossing a surface area. Definitions Related to Electromagnetic Field (Unit is Weber (Wb)) = Magnetic Flux is the number of flux lines crossing a surface area. B (Unit is Tesla (T)) = Magnetic Flux Density Is the number of flux lines per unit area = /A H (Unit is Amp/m) = Magnetic Field Intensity =

o = Permeability of air = 4*10-7 H/m It is the degree of magnetization of a material to allow magnetic flux to pass through it. It is analogous to conductivity in an electrical circuit relative permeability. µ permeability of a material For ferromagnetic materials For non-ferromagnetic materials o = Permeability of air = 4*10-7 H/m 11

•resistance in an electrical circuit Magnetic Reluctance •It is the property of a material which opposes the creation of magnetic flux in it • It is analogous to  •resistance in an electrical circuit •The reluctance of a material is given by 12

Magneto Motive Force (mmf)F It is the external force required to set up the magnetic flux lines within the magnetic material. The magneto motive force F is equal to the product of the number of turns around the core and the current through the turns of wire. 13

Magnetic Field Intensity (H) It is The magneto motive force per unit length magnetic field intensity (H) produce a magnetic flux density B (Tesla). a magnetic flux density is given by: 15

Magnetization Curves

•In magnetic circuit calculations, • it is required to determine • the excitation mmf (F) needed • to establish • a desired flux or • flux density at a given point.

Magnetic Circuit Calculations The magnetic circuit for the toroidal coil can be analyzed to obtain an expression for flux. Magneto motive force F is Where the reluctance is ` and the magnetic flux is

Magnetic Circuit Calculations obtain an expression for flux for the shown magnetic circuit

Effect of air gap on a magnetic circuit obtain an expression for flux for the shown magnetic circuit

Summary of Effect of air gap on a magnetic circuit Increase the reluctance. Greater values of ampere-turn  are required to obtain the same value of B for circuit without air gap linearize magnetic circuits i.e. no saturation

Effect of air gap on Magnetization Curves Air gap is practically an unavoidable part of any magnetic circuit The B-H loop of a magnetic circuit is affected by the presence of air gap. so greater values of H are required to obtain the same value of B  as compared with magnetically materials.

Effects of air gaps on Magnetization Curves As a result the B-H loop gets  slanted,

Example 1 Find magneto motive force (mmf) F in a coil, if the number of turns is 100, and I=2 A. Find the reluctance if the flux produced is 100mWb. Find the permeability if l=50cm and A=0.5 m2 Find the flux density B Find the magnetic force H

Example 2: Given : i=1 A, N=100, lc=40 cm, A= 100 cm2 r =5000 Calculate : F, H, B, and

Magnetic Circuits (Example 3) In the shown Magnetic circuit relative permeability of the core material is 6000, its rectangular cross section is 2 cm by 3 cm. The coil has 500 turns. Find the current needed to establish a flux density in the gap of Bgap=0.25 T.

Magnetic Circuits (Solution Example 3) The current needed to establish a flux density in the gap of Bgap can be calculated as follow: where

Magnetic Circuits (Solution Example 3) Medium length of the magnetic path in the core is lcore=4*6-0.5=23.5cm, and the cross section area is Acore= 2cm*3cm = 6*10-4 m2 the core permeability is

Continue Solution Example 3 The core reluctance is the gap area is computed by adding the gap length to each dimension of cross-section: thus the gap reluctance is:

Continue Solution Example 3. Total reluctance is based on the given flux density B in the gap, the flux is thus magneto motive force is thus the coil current must be

Magnetic Circuits with AC Excitation AC Excitation will increase core losses It is important for the engineer to understand Why the core losses increase ? Core losses are important in determining heating, temperature rise, rating and efficiency.

CORE LOSSES (iron losses) are 1-Hysteresis Losses: hysteresis loss is proportional to the loop area (shaded). To minimize hysteresis loss use materials with thin hysteresis (Silicon steel)

CORE LOSSES (iron losses) are 2-Eddy Current Losses: Eddy currents are created when a conductor experiences changes in the magnetic field.

CORE LOSSES (iron losses) are These induced currents cause Eddy Current Losses. These losses can be reduced by using thin sheets of laminations of the magnetic material.

Thus, Iron Losses in Magnetic Circuit are: Hysteresis losses Eddy Current Losses The iron loss is the sum of these two losses