ENGG 225 Fall 2025
of
Overview
Week 13 notes
motors
Textbook Sections 15.4-15.6
Motors
generators)
(and
comprised
are
of
two
components
main
8
8
(stationary part)
DC
many
wired
coils
in
The
interactive
thereby
·
stator
·
Overview
DC
of
Efficiency
instead
could
is
a
by the stator's
permanent magnets.
important
motor
a
DC
machine
,
electrical
input
power
Pin
m
as
Pin
9
Motor
=
"eta"
Port
Pin
For
windings
&
~
defined
field
parameter
vI
is
(wires)
characteristics
operating
?
Efficiency
conductors
field
magnetic
use
motor
very
have
torque
often
most
produced
·
stator
and
part)
fields
magnetic
stationary
a
rotor
physical
producing
produces
the
,
Crotating
:
vi
(Watts)
x
100%
(connects
mechanical
windings) .
(called
produces
·
types
machine
shaft
rotor
stator
For
&
mechanical
output power Post
to
load)
Mechanical
output
power
Pout
:
where
Toot
:
com
and
=
where
Newton-metres
output
torque ,
in
angular
shaft
speed
Wm
(796 Watts
TortWm(Watts)
:
1HP]
(Nm)
rads/sec .
in
,
=
Mmx
=
60
Inm
Speed
in
speed
shaft
revolutions
rpm)
per minute ,
regulation
Depending
the
on
mechanical
load
type
motor
speed
,
regulation
Speed
.
SR
Mno-load
=
Equivalent
circuit
motors
for
defined
increased
as
100
x
%
-
the
(and
full-load
smaller the better
can
be
)
100 %
>
machines
modeled
be
can
DC
is
with
decrease
may
"full-load
-
↑
DC
is
with
simple circuits
two
Ra Carmature resistance)
t
&
↑
t
-
-
Rf
↓
(field resistance)
FA
V+
Vf
3 Le (field windings)
speed
torque Tm
,
-
-
⑧
-
ARMATURE
FIELD
For
Since
rotating
a
we
are
DC
machine ,
Wa
rotational
speed ,
Tm
torque
Nm
(Newton-metres)
the
field
operating
with
DC
,
,
wi
,
rads/ses
circuit
reduces
to
t
If
&
Chf
8
VF
= RF
acts
short
like
circuit
a
DC)
at
-
The
armature
induced
EA
voltage
Ea
t
9
EA
Wm
And
the
developed
total
the
with
three
In
are
=
magnetic flux
K
=
machine
constant
motor/generator
circuits.
:
mechanical
for
equation
equations
torque
o
K If
=
Pder
These
To
=
mechanical
Tder
Together,
,
Tder
-
KQWm
=
power
:
Tder Wm
=
the
to
key
analyzing
DC
↳
t
9
EA
Telev
,
com
EA
=
Tdev
=
p
=
KOWm
MACHINE
KO IA
EQUATIONS
Tum
-
electrical
mechanical
side
side
Normally
,
Power
and
At
the
we
lump
torque
K
:
mechanical
and
o
together
"developed"
output
of
us
.
the
Ka
:
"Output
"
motor :
MACHINE
CONSTANT
In
&
↓
g
Ea
Tder
-
,
wa
-
-
electrical
developed
power
power
mechanical
Pdev
Tdev
and
Developed
such
as
·
a
do
KPIA
=
rotational
account
into
take
not
Pdev/wm
=
losses
:
friction
(bearings)
windage
(wind resistance (
·
In
torque
and
power
FAEA
=
practical
motor ,
Plev
have
we
Pout,
Pout
Tout
,
Tout
Tdev
rotational
Pder-Prof
=
:
Tder-Trot
losses
Prot , Trot
If
there
Shunt-connected
In
this
rotational
no
are
in
=
Pder ,
Tout
=
Idev-
motors
DC
configuration
connected
Port
then
losses ,
,
parallel
the
field
and
armature
circuits
are
:
RA
&
Im
VT
A
*
If
↓
W
·
ERf
FA
+
g
EA
Br-
-
Tdev
,
Wm
·
The
total
input
power
is
Pin
=
V+ F
S
,
total
"line" current
Some
is
this
of
the
creates
dissipated
field .
Power
absorbed
field
the
by
windings
heat.
as
PF
IfRp
=
VI
=
RF
Armature
similarly
resistance
dissipates
Pa
FERA
=
power
heat
as
(V-Eal
=
RA
The
remaining
developed
is
power
Pder
power
and
Separately
This
excited
DC
motors
configuration
is
similar
have
separate
armature
to
short-connected ,
In Ea
*
Tder
except
=
the
Pder/Wm
field
and
sources .
Ra
W
*
JA
~
=
↳
+
If
& RF
0
v
·
+
S
EA
Tdev
-
field
armature
motors
-Termanent
magnet DC
Similar
to
permanent
Useful
in
separately
excited,
except
field
the
magnets
.
fractional-horsepower applications
·
servos
·
small
·
power windows
:
fans
,
windshield
wipers
is
produced
by
,
Wm
Series-connected
DC
motors
T
If
-
A
↳
#
Field
in
and
armature
connected
RA
m
LF
series .
W
W
RF
+
field
where
If
:
VT
In
*
S
↓
EA
-
-
armature
series
many
-
connected
applications
·
·
·
motors
have
high torque
at
:
electric
automotive
electric
drills
household
,
starter
screwdrivers
mixers
motors
low
speeds
,
suitable
for
Tdev
,
Wm