Download - 11 basic concepts of a machine
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Basic Concepts of A Machine
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Stator: stationary portion of the machine Rotor: rotating portion of the machine Shaft: the stiff rod that the rotor is mounted onAir gap (Gap): between stator and rotor
Basic Concepts of A Machine (1)
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Basic Concepts of A Machine (2)
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)
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Basic Concepts of A Machine (3)
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round rotor salient pole rotor
Basic Concepts of A Machine (4)
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Electrical vs Mechanical Frequency
At steady state me fPf2
N
N
N
N
S
S S
S
mnmechanical speed revolution/minute (rpm)
60601 m
mmn
nf rev/second
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Slots and Coils (1)
toothslot
top
top
bottom
bottom
Double Layer Lap Winding
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Slots and Coils (2)
coil side coil side
coil end
coil endcoil leads
Nc turns, 2Nc conductors
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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: mSS ph :phaseper coils ofNumber
cNumber of turns per phase: ph ph cS NN S N
m
c 2Number of conductors per phase: 2 =ph phS NC N
m
On armature
Note: The above three equations are independent of the number of poles (P). For balanced m-phase design, Sphshould be an integer.
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1 2 34
567
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
12
3456
78
910111213
turns8 cNN ph turns4 2/ cN
PN ph
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Slot Pitch Slot pitch in electrical angle is defined by m
P 2
where m is the mechanical angle between two adjacent slots:
Sm 2
SP
The slot pitch is also defined as the arc length between two slots on stator inner circle (with diameter D):
SD
s
1 23
456
78
910111213m
D
3 phase, 24 slots, 2 polePhase A, full-pitch
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Pole Pitch
PPP 2360 o
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:
PSSP
PD
P (in meter or inch)
36s8pNote: SP may not be an integer.5.4
836
PS
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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
SS
2 mP
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 SPslots, 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
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Fractional Pitch Coil (1)
Phase A, full-pitch Phase A, (11/12)-pitch
12
3456
78
9101112
24 slots, 2 pole, 3 phase 2
2P
o180 m o1651211
m
m
12
3456
78
910111213
m
12242 m
12 m
m
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1 2 34
567
Fractional Pitch Coil (2)
Phase A, full-pitch Phase A, (5/6)-pitch
456
1 23
m
24 slots, 4 pole, 3 phase24
2 P
12242 m
624 m
o15065
o180
m
o902
mo75
125
265
m
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Group (1)
4 pole, 3 phase, 24 slot machinePhase A, (5/6)-pitch
This group consists of 2 coils.
Number of coils per group: )( poles ofNumber )( phases ofNumber )( SlotsStator ofNumber
PmSq
Number of groups = Number of poles (P) for double layer winding
PSq
3 for 3 phase machine
Number of coils = Number of slots for double layer winding
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Group (2)
5.143
18
q
q can take fractional number
5.123
9
q
4 pole, 3 phase, 18 slot 2 pole, 3 phase, 9 slot
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UCFTorque
0
RF
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
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UCFTorque 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
( )
12
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 dxdyIBIdxdy Id
T T aa B S B
d Idm S d d T m B
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UCF Torque Property of a Machine (1)
sin SR
SR
BkBTk
BBT
Since SRnet BBB
sin
)(
netR
netR
RnetR
BkBTkk
BB
BBBT
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UCF Torque Property of a Machine (2)
BR
Bnet
6 pole synchronous machine
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UCF Torque Property of a Machine (3)
motor generator
SRk BBT