Chapter 1 MAGNETIC CIRCUIT
MAGNETIC CIRCUIT It is the path which is followed by magnetic flux. It is basically ferromagnetic with coil wound around them
Why MAGNETIC CIRCUIT? It is an important component in the design of electrical machines.
Examples of Magnetic Circuits
The object of today lecture It is required to understand the concepts of magnetic circuits By making Analogy between Electric circuit and magnetic circuit
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 =
Permeability It is the degree of magnetization of a material to allow magnetic flux to pass through it. It is analogous to conductivity in an electricalcircuit • relative permeability. • µ permeability of a material • For ferromagnetic materials • For non-ferromagnetic materials o = Permeability of air = 4*10-7 H/m
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 electricalcircuit •The reluctance of a material is given by
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.
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:
Magnetic Circuit Calculations •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 isWhere 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 isAcore= 2cm*3cm = 6*10-4 m2the core permeability is
Continue Solution Example 3 The core reluctance isthe 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 isbased on the given flux density B in the gap, the flux isthus magneto motive force isthus 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