11 basic concepts of a machine

 Stator: stationary portion of the machine
 Rotor: rotating portion of the machine
 Shaft: the stiff rod that the rotor is mounted on
 Air gap (Gap): between stator and rotor
Basic Concepts of A Machine (1)

 Load current: the current that varies with load
 Magnetizing current: provide magnetic field and independent of load
 Armature: the winding that carries only load current
 Field: the winding that carries only magnetizing current
 dc machine: the input/output current is dc
 ac machine: the input/output current is ac;
two categories: synchronous machine
induction machine (no field winding,
similar to transformer)

round rotor salient pole rotor

Electrical vs Mechanical Frequency
At steady state me f
P
f
2

N
N
N
N
S
S S
S
mnmechanical speed revolution/minute (rpm)
6060
1 m
mm
n
nf  rev/second

Slots and Coils (1)
tooth
slot
top
top
bottom
bottom
Double Layer Lap Winding

Slots and Coils (2)
coil side coil side
coil end
coil endcoil leads
Nc turns, 2Nc conductors

Slots and Coils (3)
 Each slot has 2 positions: top and bottom (double layer winding)
 Each coil needs to occupy 2 positions: top position of one slot
and bottom position of another slot
Number of armature coils = Number of armature slots (S)
m phase machine:
m
S
Sph:phasepercoilsofNumber 
c
Number of turns per phase: ph ph c
S N
N S N
m

 
c 2
Number of conductors per phase: 2 =ph ph
S N
C N
m
 

On armature
Note: The above three equations are independent of the
number of poles (P). For balanced m-phase design, Sph
should be an integer.

1
2 3
4
5
6
7
Slots and Coils (4)
3 phase, 24 slots
2 pole, Phase A, full-pitch 4 pole, Phase A, full-pitch
8 coils, 8Nc turns, 16Nc conductors per phase
1
2
3
4
5
6
7
8
910111213
turns8 cNNph 
turns4
2/
cN
P
N ph


Slot Pitch
Slot pitch in electrical angle is defined by m
P

2

where m is the mechanical angle between two adjacent slots:
S
m


2

S
P
 
The slot pitch is also defined as the arc length between two
slots on stator inner circle (with diameter D):
S
D
s

 
1
2
3
4
5
6
7
8
910111213
m
D
3 phase, 24 slots, 2 pole
Phase A, full-pitch

Pole Pitch
PP
P


2360o

Pole Pitch: angular distance between two adjacent poles on a machine.
(in mechanical degree)
Regardless of the number of poles on the machine, a pole pitch is
always 180 o or  in electrical degrees.
The pole pitch is also defined as the arc length between two adjacent
poles on stator inner circle (with diameter D) :
Number of Slots per Pole:
P
S
SP 
P
D
P

  (in meter or inch)
36s8pNote: SP may not be an integer.
5.4
8
36
PS

Coil Pitch
Let Sc be the number of slots that the coil spans.
Let m be the mechanical angle that the coil spans or
Coil pitch in electrical angle is defined by
P
c
P
m
S
S





2
m
P
 
Full-Pitch Coil: If the armature coil stretches across the same angle as
the pole pitch, it is called a full-pitch coil. The coil spans across SP
slots, if SP is an integer.
Fractional-Pitch Coil: If the armature coil stretches across an angle
smaller than a pole pitch, it is called a fractional-pitch coil (or short-
pitched coil, chorded coil) . The coil spans less than SP slots.
.m cm S

Fractional Pitch Coil (1)
Phase A, full-pitch Phase A, (11/12)-pitch
1
2
3
4
5
6
7
8
9101112
24 slots, 2 pole, 3 phase 

 
2
2
P
o
180  m o
165
12
11
  m
m
1
2
3
4
5
6
7
8
910111213
m
1224
2 
 m
12

  m
m

1
2 3
4
5
6
7
Fractional Pitch Coil (2)
Phase A, full-pitch Phase A, (5/6)-pitch
4
5
6
1 2
3
m
24 slots, 4 pole, 3 phase
24
2 
 P
1224
2 
 m
62
4 
  m
o
150
6
5
 o
180 
m
o
90
2


m
o
75
12
5
26
5


m

Group (1)
4 pole, 3 phase, 24 slot machine
Phase A, (5/6)-pitch
This group consists of 2 coils.
Number of coils per group: )(polesofNumber)(phasesofNumber
)(SlotsStatorofNumber
Pm
S
q


Number of groups = Number of poles (P) for double layer winding
P
S
q
3
 for 3 phase machine
Number of coils = Number of slots for double layer winding

Group (2)
5.1
43
18


q
q can take fractional number
5.1
23
9


q
4 pole, 3 phase, 18 slot 2 pole, 3 phase, 9 slot

UCF
Torque
0
R
F
T
How to understand torque:
Put the thumb in the direction of torque.
The other four fingers point to the direction of rotation.
FRT 
wrench on a nut

UCF
Torque from a Current Loop
Likewise
Define

Bloop
Note: dm is in the same direction of Bloop and
both are proportional to I

dm = k Bloop
BBT  loopkd
1
1
1 1 1
3 3 3
1
1 3
( )
1
2
1
( )
2
1
2
1
( )( )
2
1
2
x y z z y
y
y y z z y
y x
y y z z y
y x
y x
d Idx Idx B B
dy
d d dy Idx B B
dxdyIB
d d dy Idx B B
dxdyIB d
d d dxdyIB
   
 
     
 
     
  
  
F a B a a
R a
T R F a a a
a
T R F a a a
a T
T T a
2 4
( )
x y
z
d d dxdyIB
Idxdy Id
  
   
T T a
a B S B
d Idm S d d T m B

UCF
Torque Property of a Machine (1)
sinSR
SR
BkBT
k

 BBT
Since SRnet BBB 
sin
)(
netR
netR
RnetR
BkBT
k
k



BB
BBBT

UCF
BR
Bnet
6 pole synchronous machine

UCF
motor generator
 
SRk BBT 

11 basic concepts of a machine

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