25-1 DC motors DC motors re importnt in mny pplictions. In portble pplictions using bttery power, DC motors re nturl choice. DC mchines re lso used in pplictions where high strting torque nd ccurte speed control over wide rnge re importnt. Mjor pplictions for DC motors re: elevtors, steel mills, rolling mills, locomotives, nd excvtors. Like other rotting mchines, DC motors result from the interction of two mgnets. The interction is best understood s one of like poles repelling (north poles repel north poles, south poles repel south poles). One mgnet is ttched to the frme of the motor nd is produced by the current in the field windings. The other mgnet results from current in the rmture windings. Principle of opertion The field current produces the sttionry mgnet shown. The rmture current I produces the rotting mgnet. Rottion results from the fct tht like poles repel. In the digrm below, the rottion continues until N-S lignment, resulting in lock-up tht is, if nothing is done to prevent it. A commuttor is switch tht prevents N-S lignment by reversing the direction of rmture current t just the right time to keep the torque in the direction of intended rottion.
25-2 The direction of the field current does not chnge chnges to the direction of current is confined to the rmture. The commuttor is rotting switch. The fixed contcts re crbon brushes spring-loded ginst the moving contcts on the shft. The bck EMF on the rmture is produced vi Frdy s lw. dϕ V = - dt If the flux were sinusoidl (which it s not this is DC mchine!), the corresponding phsor eqution would be V = -jωf In DC motors, the bck EMF, denoted E, is proportionl to the flux, times the shft speed. The constnt of proportionlity is K, the rmture constnt. E = Kϕω m The torque developed by the rmture is proportionl to the product of the mgnetic flux nd the rmture current. The constnt of proportionlity is the rmture constnt. T = K ϕ I D The developed power is the product of this torque nd the shft speed. P = T ω = K ϕi ω = K ϕωi D D P = E I D
25-3 We consider two types of DC motors the series motor (I f = I ) nd the shunt motor (where the field current nd the rmture current re different). Series DC motors The equivlent circuit is: (L f is neglected in stedy-stte) ( ) E = V - R+R I f E = K ϕω m T = K ϕ I D (stedy-stte) liner when the mgnetic core of the motor is not sturted If we ssume the mchine is working in its liner region, ϕ = Kff I. This results in the developed torque being proportionl to the squre of the rmture current. T = K ϕ I = KKII = KKII = KKI 2 D ff f f Series motors develop very high strting torque becuse of the lrge strting current in motors.
25-4 This is good thing high strting torque is criticl in mny pplictions. Cre must be tken when using DC motors. This is becuse the shft speed is inversely proportionl to the rmture current just think wht this implies for motor ccidentlly disconnected from its lod (so tht I becomes very smll)! Let s look t this more closely. ( ) ( ) E = V - R+R I = K ϕω f m ω m V = - K ϕ R+R I f K ϕ. Since, I = I f in series mchine, nd since in the liner region, ϕ I f (no mgnetic sturtion), ω K = - K 1 m 2 I When DC series motor is initilly switched on, the lrge surge of current produces high strting torques. Strting currents often hve to be limited to prevent electricl nd mechnicl dmge. If the motor lod is lost, T D will get quite smll, cusing I to become smll which, in turn, results in overspeeding the motor. Series motors must lwys be fitted with overspeed protection.
Shunt DC motors 25-5 R c controls I f ϕ E = V - RI = K ϕω T = K ϕ I I = V m D f. Solving for ω m ω m V = - K ϕ IR K ϕ ( R+R ) V, R, nd K re constnts. If R c is not chnged, ϕ remins constnt s well. ωm = K3-K4 I T D = Kϕ I c f The strting torque is s high s in the series motor. However, the shunt, or seprtely-excited, motor hs sfe no-lod speed, providing tht the field circuit is not de-energized. Loss-of-field protection is usully provided to gurd ginst overspeeding. The control resistor R c enbles speed to be controlled very ccurtely over wide rnge.
Power flow in DC motors 25-6 Exmple A DC series motor is rted t 1200V, 750hp, 2500rpm. It hs n rmture resistnce of 0.14Ω nd field resistnce of 0.06Ω. It drws current of 520A from the supply when delivering rted lod. Find: i) rted output torque. ii) rted developed torque. iii) rted efficiency. iv) rottionl losses t rted speed. v) speed when the lod is chnged, cusing the line current to drop to 260 A. vi) developed torque for the conditions in prt (v). vii) horsepower output for the conditions in (v) if the rottionl losses re proportionl to speed 2.
Solution Under rted conditions the motor is modeled s follows: 25-7
25-8 Exmple A DC shunt motor is rted t 600V, 255hp, 2000rpm. It hs n rmture resistnce of 0.07Ω nd totl field resistnce of 80Ω. It drws current of 353A from the supply when delivering rted lod. Find: i) rted output torque ii) rted developed torque iii) rted efficiency iv) rottionl losses t rted speed v) speed when the lod is chnged, cusing the line current to rise to 500 A.(Field resistnce is unltered.) vi) developed torque for the conditions in prt (v). vii) horsepower output for the conditions in (v) if the rottionl losses re proportionl to speed 2. Solution Under rted conditions the motor is modeled s follows:
25-9 Exmple A DC shunt motor is rted t 500V, 100hp, 3600rpm. It hs n rmture resistnce of 0.1Ω nd totl field resistnce of 100Ω. It drws current of 165A from the supply when delivering rted lod. Find: i) rted output torque. ii) rted developed torque. iii) rted efficiency. iv) rottionl losses t rted speed. v) line current when the totl field resistnce is chnged such tht φ is doubled. (Developed torque is unltered.) vi) speed for the conditions in prt (v). vii) horsepower output for the conditions in (v) if the rottionl losses re proportionl to speed 2. viii) efficiency for the conditions in (v). Solution Under rted conditions the motor is modeled s follows:
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