Introduction Chapter 1

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Introduction(Chapter 1)
BEE3163 ELECTROMECHANICAL SYSTEMS
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BASIC FOUNDATION

• ELECTROMAGNETICS

The basic concept of electromagnetic field theory
constitute the foundation of electrical motion
devices (motor, generators, and transducers), as
well as electromechanical analysis and design
ELECTROMAGNETICS CIRCUITS AND DEVICES
Iron or ferromagnetic material as pathway
Magnetic flux as energy carrier Current pass
through turns of wire wrapped around the closed
pathway---- electromagnetic circuit is energized
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BASIC FOUNDATION
ELECTROMAGNETICS CIRCUITS
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BASIC FOUNDATION

• Magnetic Flux

If AC current passes through the coil then flux
alternating back and forth in the core If DC
current passes through the coil then flux moves
in only 1 direction in the core SI units Wb
webers
Flux Density, B
Ability of magnetic core to conduct flux is
limited to cross section of the
pathway Ferromagnetic magnetic material of the
core that conduct magnetic flux is limited in
capacity to carry flux Saturated core is
operating at its maximum capacity and no more
flux can be carried in the core Force of the
magnetic flux is proportional to the flux density
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BASIC FOUNDATION
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BASIC FOUNDATION

• Total magnetic flux through the surface

• Ampere circuit law states that

and
Faradays law of induction states that
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BASIC FOUNDATION

• The current flow in the opposite direction of the
  flux linkages.
• The emf represent the magnitude of the potential
  difference in a circuit carrying current

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BASIC FOUNDATION
magnetomotive force, mmf

• Is the result of the electric current circulating
  in the coil wrapped around the core
• mmf in the magnetic circuit is multivalued,
  because its magnitude (amount) increase with each
  turn of wire added to the coil
• 1-turn coil with 2A of electric current
  circulating in it has mmf of 2 amp-turn

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BASIC FOUNDATION

• 10-turns coil with 2A of electric current
  circulating in it has mmf of 20 amp-turn
• mmf NI

mmf magnetomotive force N number of
turn I electric current, A
mmf is the line integral of the time- varying
magnetic field intensity
Using second Maxwells equation
mmf is the sum of induced current and the rate of
change of the flux penetrating the surface of the
contour
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BASIC FOUNDATION
Example

• Magnetic circuit has a core cross sectional area
  of 24cm2 (ALxW 4cm x 6cm) and flux of 1.80mWb
  circulating in it. The flu result from a 6Hz
  alternating current of 0.75A passing through a
  200 turns coil wrapped around the core of the
  magnetic circuit. Determine
• Flux density in the core
• mmf used to set up the flux in the core

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BASIC FOUNDATION
magnetic field strength, H

• If a circuit is made from the same
• Cross sectional area
• mmf
• Ferromagnetic material
• but different in the average length of the
  magnetic path, therefore the magnetic strength
  (H) is greater in shorter path

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BASIC FOUNDATION
magnetic field strength, H

• Example
• 2 cast iron of magnetic circuits have length of
  31cm and 47cm. Each are magnetized by winding 50
  turns of wire around the core and passing 4A of
  electric current through the turns. Determine
  magnetic field strength, H

• Permeability of a substance is an indication of
  its ability to carry magnetic flux when acted on
  by a magnetomotive force, mmf.
• If H, varies, then B caries

• Example
• Determine of the permeability of mild steel core
  of the series magnetic circuit when the magnetic
  field strength of the circuit is 250A/m. Find the
  permeability using BuH and the B-H curve for the
  mild steel

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BASIC FOUNDATION
Reluctance,

• Is a measure of the opposition the magnetic
  circuit offers to the flux
• Analogies to the resistance in electric circuit

Relative Permeability,
Is the ratio of the permeability of the material
to the permeability of free space
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BASIC FOUNDATION

• Duality of the mmf and emf

Inductance and reluctance
Is the ratio of the total flux linkages to the
current which they link
Is the ratio of the mmf to the flux
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BASIC FOUNDATION

• Self inductance

Inductance and reluctance
If L is constant
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BASIC FOUNDATION
Analogies between Electric and Magnetic Circuit
For magnetic circuit
For electric circuit
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BASIC FOUNDATION
Electrostatic
Electrostatic interaction was investigated by
Charles coulomb For charges q1 and q2 separated
by a distance x in free space, the magnitude of
the electric force is
In vector form
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BASIC FOUNDATION
Electrostatic
Gauss Law states that
Ohms Law states that
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BASIC FOUNDATION
Electrostatic
resistivity
Resistance, resistivity and conductivity
relationship
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BASIC FOUNDATION
Electromagnetic Torque

• Energy

Energy stored in capacitor is stored in the
electric field between plates
For the lossless conservative system, the
differential change of the electrostatic energy
is equal to the differential change of mechanical
energy
For translational motion
In Cartesian coordinates
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BASIC FOUNDATION
Energy
Energy stored in magnetostatic field
Ex Energy stored in inductor is stored in the
magnetic field within the coil
For the lossless conservative system, the
differential change of the mechanical energy is
equal to the differential change of magnetic
energy
For translational motion
In Cartesian coordinates
For rotational motion, Torque
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BASIC FOUNDATION

• Example
• Consider the electromagnet that has N turns. The
  distance between the stationary and moveable
  members is denoted as x (t). The mean length of
  the stationary and moveable members are l1 and l2
  respectively and the cross sectional area is A.
  neglecting the leakage flux, find the force
  exerted on the moveable member if the time
  varying current ia(t) is supplied. The
  permeability of stationary and moveable members
  are µ 1 and µ 2 respectively.