11 basic concepts of a machine
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Transcript of 11 basic concepts of a machine
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 onAir gap (Gap): between stator and rotor
Basic Concepts of A Machine (1)
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)
Basic Concepts of A Machine (3)
round rotor salient pole rotor
Basic Concepts of A Machine (4)
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
Slots and Coils (1)
toothslot
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: 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.
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
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
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
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
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
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
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
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
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
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
UCF Torque Property of a Machine (1)
sin SR
SR
BkBTk
BBT
Since SRnet BBB
sin
)(
netR
netR
RnetR
BkBTkk
BB
BBBT
UCF Torque Property of a Machine (2)
BR
Bnet
6 pole synchronous machine
UCF Torque Property of a Machine (3)
motor generator
SRk BBT