Induced emf Developed torque Magnetization curve SEE 3433 ELECTRICAL MACHINES

Induced emf Regardless of operation, emf is always induced in armature circuit when there is rotation Induced emf e a = B  v l For a conductor of length l, moving at a speed v in magnetic field intensity B, the induced voltage is given by: e a = B v l X X X X v +ea+ea

Induced emf

l

e a = 2 B  m r l + e a  In terms of flux per pole, where  = B A and l + + _ _ + e a 

Induced emf where  = B A and which gives This is an induced voltage for a single turn. If there are N turns with a parallel path,

Developed torque Force produced, F = B  l i For a conductor of length l, carrying current i in magnetic field intensity B, the torque developed is given by: F c = B i l X X X X F i

Developed torque

x l i i

x l IaIa IaIa T = F r T c = B l I a r T 2c = 2 B l I a r In terms of flux per pole, where  = B A and

Developed torque This is torque for a single turn. If there are N turns with a parallel path, Similar to the constant obtained in induced emf !

Magnetization curve Is a plot of the induced emf vs I f on an open armature circuit, at a given rotor speed +Ea+Ea I f Field current Induced emf E a = K    (flux per pole) depends on field (stator) current and hence MMF of the stator circuit K is a constant – depends on physical construction of the machine  - angular speed of the rotor At a given speed and K, the emf induced depends on  Field circuit Armature circuit

How does  vary with the field current? Flux path produced by field: stator core  air gap  rotor core  airgap  stator core At low , core reluctance is small – most of MMF drop appear across air gap – consequently relation between  and field current is almost linear (due to the airgap)  IfIf Flux will increase with field current - but not necessarily linear! Magnetization curve

How does  vary with the field current? As field current increases, so too  - some part of the core (especially the rotor teeth) will saturate  Relation between  and I field is no longer linear  IfIf Magnetization curve

Since for constant speed Ea   the curve can be represented by E a vs I f EaEa I field Magnetization curve 11 Reduced speed 22 33  1 >  2 >  3