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