Elec467 Power Machines &
Transformers
Electric Machines by Hubert, Chapter 1
Topics: Magnetics, electromagnetic
forces, generated voltage and energy
conversion
Magnetic Fields
Right hand rule: current
generated fields have the
flux in the same direction as
your fingers with the thumb
of your right-hand pointed in
the direction of current flow.
Current flow is for
conventions current flow
with the positive source
supplying the current.
Group fields are the combined effect
of individual wires with the flux lines
emanating from the north pole and
entering the south pole.
Magnetic Circuits
l
(a) Transformer action captures magnetic flux within the
circular path of the metallic core over length l passing totally
within the cross-sectional area A.
(b) Application of transformer application combined
with motor action.
Magnetic formulas
Magnetomotive force (mmf)
F = N*I N is # of turns, I is current in amps. units: ampere-turns
Magnetic Field Intensity
H = F/l l is magnetic length in meters. units: A-t/m
Magnetic Flux
Reluctance
Φ = F /R in Webers
R = l/µA in A-t/Wb
Flux Density
Permeability
B = Φ/A in teslas
µ = B/H
A is square meters
µ = µ r µo
in Wb/A-t m
µo= 4π·10-7 Wb/A-t m
Magnetic Flux Density vs.
Magnetic Field Intensity
Labeling realms
Saturation occurs when all the magnetic domains in a material
are aligned together. Since you are changing the material on the
molecular level by reorienting the domains, this absorbs energy
heating up the material.
Magnetization & the
relative permeability curves
The magnetization is H, the magnetic field intensity…given that N and l are
constant for any one electromagnet, it’s directly related to the current flow.
Magnetic flux: parallel paths/gap
Hystersis occurs when a material
is driven by an AC current
b-O is the
residual
magnetism
c-O is the
coercive
force
needed to
remove the
residual
magnetism
Hysteresis Power Loss calculation: Ph = kh·f·Bnmax
Ph is Hysteresis Power loss
Kn is a constant
f is frequency
n is Steinmetz exponent
Bmax is maximum value of the flux density wave in Teslas
Flux bunching
Flux polarity rule: flux flowing in the same direction are the same polarity and repel each
other, flux flowing in opposite direction are of opposite polarity and attract each other.
Application of flux bunching:
motor action
Counterclockwise rotational movement is
generated from flux bunching with the
application of current in the rotor winding.
Calculating the mechanical force: BlI
Fmechanical = B · leff · I (Newtons)
where leff is l·sin α or l·cos β
B is flux density and I is current
Voltage driven motor action
Torque using a simplified diagram
Distance d is the moment arm measured from the center of the shaft to the center of the conductor.
The force F is the mechanical force calculated using the BLI formula from the previous slide.
TORQUE (TD) is the product of the mechanical force times the radius d (measured in meters) times
the number of conductors: TD = 2 · Fmech · d (N·m)
Generator Action
Lenz’s Law is a special case of Newton’s 3rd law of physics: for every action
there is an equal and opposite reaction. In this case the action is the
movement of conductor X to the right thru the flux. The movement in this
direction if caused by motor action would have current flowing from X to X’ and
flux bunching occurring on the left side of the conductor. Assume there is zero
current flow at the start. Since the movement source was mechanical, the
reaction of the conductor is opposite and seeks to oppose the movement to the
right. The conductor’s flux field appears as seen in (b) and the current is drawn
from the conductor when previously there was none. The load the mechanical
source (aka prime mover) feels is the opposing force created by the movement.
Generator Action
• Speed voltage and BLV rule follow Faraday’s Law: the
voltage induced is proportional to the number of
turns and rate of change of flux.
• The direction that the voltage is induced is in a
direction to oppose the action that caused it
according to Lenz’s Law.
• The potential voltage e induced by a conductor
moving through a magnetic field is:
e = B leff v
where B is flux density in Teslas and v is the velocity of the conductor in meters/second.
Sinusoidal current flow from motion
When a closed coil as seen to
the left in a magnetic field is
driven continuously, the current
is created by generator action
and for every 360º of rotation,
the current changes direction
twice. The flux field seen by the
conductors varies in a
sinusoidal fashion from zero
when moving horizontally to
maximum Φ.
Φ = Φmax sin(wt)
The rate of rotation is w in radians
The voltage created is
Emax = 2πf NΦmax
and is a sinusoidal waveform.
Erms = 4.44f NΦmax
Flux power losses
While a coil generates flux flowing through an iron core, it also creates
circular currents flowing in the material in the same pattern as the winding.
These are called eddy currents. Naturally, a flowing current uses power. A
solution to reduce eddy losses is to used insulated sheet metal for the core.
This power loss is calculated using
Pe = kef2B2max (Watts/unit mass)
ke = constant
f = frequency of flux wave in Hertz
Bmax= maximum value of flux density wave in Teslas
Force multiplier: multiple poles
With multiple poles additional
cycles are created by generator
action provided the windings
are properly positioned. The
frequency created in one
rotation is ½ the number of
poles.
cycles = Pn/2
Multiply this value by the
number of rotations in a second
to get the frequency generated
in Hertz.
The position of the poles
around the rotor are known as
space degrees. The cycles are
known as electrical degrees
and can exceed 360º.
Chapter formula summary part a
Chapter formula summary part b