Torque of Induction Motor under Running Condition (T r )

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Alvin Davidson
5 years ago
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1 Torque of Induction Motor under unning Condition T r It i the torque developed by the motor under running condition i.e., at lip. From figure, the rotor circuit/phae at lip. Let, E =E : rotor e.m.f/phae under running condition volt X = : rotor reactance/phae under running condition : rotor reitance/phae under running condition Z : rotor impedance/phae under running condition otor current/phae, I co E Z E otor p.f, Z under running condition under running condition

2 Torque of Induction Motor under unning Condition T r Since, the motor torque/phae at lip or under running condition i: condition running under torque motor E N T N if phae per torque E N T N if rp peed ynch i N Z E E T E E E E Z Z E I T r r r r co

3 Torque of Induction Motor under unning Condition T r If the tator or upply voltage V i contant, then tator flux and hence E will be contant. T r E Where: the contant not equal to = E It may be een that the running torque i: i- Directly proportional to the lip. If the lip increae i.e., motor peed decreae, the torque will increae and vice-vera. ii- Directly proportional to quare of upply voltage, becaue E V 3

4 Example 5: A Y-connected rotor of an induction motor ha tandtill impedance of 0.4+j4 ohm per phae and the rheotat impedance per phae i 6+j ohm. The motor ha an induced emf of 80V between lip-ring at tandtill when connected to it normal upply voltage. Find: i rotor current at tandtill when the rheotat i in the circuit. ii rotor current at lip 3% when the lip-ring are hort-circuited. Anwer [An.: 5.65A - 3.3A] 4

5 5 Maximum Torque under unning Condition T rmax Auming the upply voltage i contant, to get the maximum value of the running torque, take a derivative for it w.r.t the contant and equating the reult with zero a follow: condition running under X e i d dt T r r.,. 0 0 Hence, the running torque will be maximum when: otor reitance/phae = lip * Standtill rotor reactance/phae max X T r

6 Maximum Torque under unning Condition T rmax Alo: E 3 E Tr max Max. X X N X motor torque under running condition Note: - The maximum running torque i independent on the rotor reitance becaue the rotor reitance i contant for the motor. - The maximum running torque varie inverely with the tandtill reactance. Hence, it hould be kept a mall a poible. - The maximum running torque varie directly with the quare of the applied voltage. 6

7 Example 6: 3-ph, lip-ring, induction motor with Y-connected rotor ha an induced emf of 0V between lip-ring at tandtill with normal voltage applied to the tator. The rotor winding ha a reitance per phae 0.3 ohm and tandtill leakage reactance per phae i.5 ohm. calculate: i ii rotor current/phae when running hort-circuited with 4% lip. Slip and rotor current/phae when the rotor i developing maximum torque. Anwer [An.: 9A A] 7

8 Example 7: A 3-ph, induction motor having 6-pole, Y-connected tator winding run on 40V, 50Hz upply. The rotor i connected a Y-connection. The rotor reitance and tandtill reactance are 0. ohm and 0.85 ohm per phae. The ratio of tator to rotor turn i.8. Full-load lip i 4%. calculate: i ii Developed torque at full-load. Maximum torque and peed at that maximum torque. Anwer [An.: 5.4Nm - 99Nm - 860rpm] 8

9 Torque-Slip Characteritic The motor torque under running condition i given by: T r If a curve i drawn between the torque and lip for a particular value of rotor reitance ; the graph thu obtained i called torque-lip characteritic. Fig. how a family of torque-lip characteritic for a lip-range from = 0 to = for variou value of rotor reitance. 9

10 Torque-Slip Characteritic The following point may be noted carefully: T r i At = 0, T r = 0 o that torque-lip curve tart from the origin. ii A lip incree beyond zero value i.e., lip i mall but larger than zero the cae of normal peed that cloe to ynchronim o that i negligible a compared to. Tr Tr linear relation between T r & Hence torque-lip curve i a traight line from zero lip to a lip that correpond to full-load the haded region at uing the urve of 0

11 T r Torque-Slip Characteritic iii A lip increae beyond full-load lip for increaing load of the motor, the torque increae and become maximum at = /X. Thi maximum torque in an induction motor i called pull-out or breakdown torque. It value i at leat twice the full-load value when the motor i operated at rated voltage and frequency. iv A the lip further incree i.e., motor peed fall with further increae in motor load, then become neglegible compared to. Therfore, the motor low down and eventually top. Tr T r In fact, the table operation of the motor lie between the value of = 0 and that correponding to maximum torque. i operating range hown haded in the figure

12 Torque-Slip Characteritic v Becaue the maximum running torque i independent of the value of rotor reitance, o, it i remain the ame. Therefore, the addition of reitance to the rotor circuit doe not change the value of maximum running torque but it i only change the value of lip at which maximum torque occur.

Torque-Speed Characteritic The torque developed by a 3-ph induction motor depend on it peed but the relation cannot be repreented by a imple equation.

13 Torque-Speed Characteritic The torque developed by a 3-ph induction motor depend on it peed but the relation cannot be repreented by a imple equation. A hown in figure, T : repreent nominal full-load torque at full-load peed N..5T : repreent tarting or locked rotor torque at N= 0 at =..5T : repreent the maximum or breakdown torque at = /X. If the load torque exceed breakdown torque, the motor will uddenly top. 3

14 Speed egulation of Induction Motor It i the difference between no-load peed and full-load peed. It i an indication for motor performance, a the value of peed regulation decreae, the motor will have a bad performance Where; N nl N fl N nl N fl % Speed regulation 00 N : no-load peed of the motor. : full-load peed of the motor. If the no-load peed of the motor i 800r.p.m. and it full-load peed i 780r.p.m, then change in peed i =0r.p.m. and %peed regulation =0 00/780 =.56%. The peed regulation of an induction motor i 3% to 5%. Thi value i low enough. So, the induction motor i claed a a contant-peed motor. fl 4

Speed Control of 3-Phae Induction Motor 0 f N N P The peed of induction motor N can be varied by changing: i Supply frequency, f. ii No. of tator pole, P. iii The lip,.

15 Speed Control of 3-Phae Induction Motor 0 f N N P The peed of induction motor N can be varied by changing: i Supply frequency, f. ii No. of tator pole, P. iii The lip,. The change of f i generally not poible becaue the commercial upplie have contant frequency. Therefore, the practical method of peed control are either to change P or. 5

16 Speed Control of 3-Phae Induction Motor. Squirrel Cage Motor It peed changed by changing number of tator pole only two or four peed are poible by thi method. Two-peed motor ha one tator winding provide two peed For intance, the winding may be connected for either 4 or 8 pole, giving N of 500 or 750r.p.m. Four-peed motor are equipped with two eparate tator winding each of which provide two peed.. Wound rotor motor The peed of wound rotor motor i changed by changing the motor lip. Thi can be achieved by; Varying the tator line voltage. Varying the reitance of the rotor circuit. 6

Comparison between Induction Motor and Transformer An induction motor is considered as a transformer with a rotating short-circuited secondary.

Comparison between Induction Motor and Transformer An induction motor is considered as a transformer with a rotating short-circuited secondary. Comparion between Induction Motor and Tranformer An induction motor i conidered a a tranformer with a rotating hort-circuited econdary. The tator winding correpond to tranformer primary and the rotor winding