0195136047.pdf

514 ELECTROMECHANICS f=m du dt =fe−fd−fk=fe−du−kx=Bli−du−kx wheredrepresents the damping coefficient,krepresents the spring cons ...

12.2 emf PRODUCED BY WINDINGS 515 − + N-turn coil on stator Field winding Magnetic flux path Magnetic axis of stator coil Magnet ...

516 ELECTROMECHANICS e=− dλ dt =ωNφsinωt−N dφ dt cosωt (12.2.5) The minus sign associated with Faraday’s law in Equation (12.2.5 ...

12.2 emf PRODUCED BY WINDINGS 517 and(a 2 ,−a 2 ), connected in series by their end connections. The span of each coil is one-ha ...

518 ELECTROMECHANICS In fact, with very few exceptions, three-phase synchronous machines are most commonly used for power genera ...

12.2 emf PRODUCED BY WINDINGS 519 S N b c −b −c a (a) (b) −a + + b 1 c 1 −b 1 −c 1 a 1 (c) −a 1 b 2 c 2 −b 2 −c 2 a 2 −a 2 + + + ...

520 ELECTROMECHANICS (a) (b) + + + + + + + Field Armature coil Field structure Field Brushes on commutator (not shown) Quadratur ...

12.2 emf PRODUCED BY WINDINGS 521 Instant 1 Instant 1 ωm ωm Instant 2 Instant 2 (a) (b) ωm ωm Figure 12.2.5(a)Slip-ring action.( ...

522 ELECTROMECHANICS EXAMPLE 12.2.2 The armature of a four-pole dc machine has a simplex lap wound commutator winding (which has ...

12.3 ROTATING MAGNETIC FIELDS 523 sinusoidally with time. Hence, the corresponding component mmf waves vary sinusoidally with ti ...

524 ELECTROMECHANICS for that instant when thea-phase current is a positive maximum; Figure 12.3.2(b) refers to that instant whe ...

12.3 ROTATING MAGNETIC FIELDS 525 Phase a Phase a Phase b Phase b Phase c Phase c Total (a) (b) Total θ − 90 ° − 30 ° 0 ° 30 ° 9 ...

526 ELECTROMECHANICS ωt (a) (b) i = I cos ωt B = Bm cos ωt Bm cos ωt ωt ω ω Bm/ 2 Bm/ 2 Figure 12.3.3Single-phase winding carryi ...

12.4 FORCES AND TORQUES IN MAGNETIC-FIELD SYSTEMS 527 properties of the core material. Equations (12.4.1) and (12.4.2) may be in ...

528 ELECTROMECHANICS dW=Tedθm (12.4.7) whereθmis expressed in electrical radians. Neglecting the winding resistances, the termin ...

12.4 FORCES AND TORQUES IN MAGNETIC-FIELD SYSTEMS 529 Depending on the convenience in a given situation, either Equation (12.4.1 ...

530 ELECTROMECHANICS EXAMPLE 12.4.1 Consider an elementary two-pole rotating machine with a uniform (or smooth) air gap, as show ...

12.4 FORCES AND TORQUES IN MAGNETIC-FIELD SYSTEMS 531 δr δs δ + + ++ + +++ + ++ + Magnetic axis of stator Magnetic axis of rotor ...

532 ELECTROMECHANICS (c) (1) The excitations are direct currentsIsandIr. For the given conditions ofωs=ωr= ωm=0 andα=0, Te=−LIsI ...

12.4 FORCES AND TORQUES IN MAGNETIC-FIELD SYSTEMS 533 The machine operates as asingle-phase induction machine,and the instantane ...