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 (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)

round rotor salient pole rotor

Electrical vs Mechanical Frequency

At steady state f_e P f_m 2  N N N N S S S S m n

mechanical speed _{revolution/minute (rpm)} 60 60 1 _m m m n n f   rev/second

Slots and Coils (1)

tooth slot top top bottom bottom

Slots and Coils (2)

coil side _{coil side} coil end

coil end coil leads

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 S_ph : phase per coils of Number  c

Number of turns per phase: N_ph S N_{ph c} S N m



 

c 2

Number of conductors per phase: C_ph 2N _ph= S N m

 



On armature

Note: The above three equations are independent of the

number of poles (P). For balanced m-phase design, S_ph

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, 8N_c turns, 16N_c conductors per phase

1 2 3 45 6 7 8 9 10 11 12 13 turns 8N_c N _ph  turns 4 2 / Nc 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 34 56 7 8 9 10 11 12 13 m  D

3 phase, 24 slots, 2 pole Phase A, full-pitch

Pole Pitch

P P P    360o  2

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 S_P  P D P 

  _{(in meter or inch)}

36s8p

Note: S_P may not be an integer.

5 . 4 8 36_  P S

Coil Pitch

Let S_c 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 S_P

slots, if S_P 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 S_P slots.

.

m

 _m  S_c

Fractional Pitch Coil (1)

Phase A, full-pitch _{Phase A, (11/12)-pitch}

1 2 3 45 6 7 8 9 10 11 12

24 slots, 2 pole, 3 phase P  2₂  

o 180       _{m o} 165 12 11 _      _m m  1 2 3 45 6 7 8 9 10 11 12 13 m  12 24 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

2 4 2  _P   12 24 2  _m   6 2 4_    _m  o 150 6 5 _    o 180     m  o 90 2    _{m 75}o 12 5 2 6 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: q _{Number of}Number _phasesof_{( m}Stator _{) Number} Slots ( _ofS)_{poles( P)}

 

Number of groups = Number of poles (P) for double layer winding

P S q

3

 for 3 phase machine

Group (2)

5 . 1 4 3 18 _   q

q can take fractional number

5 . 1 2 3 9 _   q

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.

F

R

T





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 B_loop

B

B

T



k

_loop



d

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 dm  IdS dT  dm  B

UCF

Torque Property of a Machine (1)



sin

S R S R

B

kB

T

k







B

B

T

Since

B

_net



B

_R



B

_S



sin

)

(

net R net R R net R

B

kB

T

k

k













B

B

B

B

B

T

UCF

Torque Property of a Machine (2)

B_R

B_net

UCF

Torque Property of a Machine (3)

motor generator   S R kB B T  