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Unformatted text preview: Lecture 26 Torque in simple machines We know that the inductance matrix of a simple machine with a round rotor is ( ) cos cos sr ss sr rr L L L L L = The coupling between the stator and the rotor depends on the angle . The torque can be found by taking the partial derivative of the co-energy with respect to at constant current, ' . 1 2 sin T i const sr s r W d L T i i d L i i = = = = We have seen that for the synchronous machine, the torque is given by ( ) ( ) ( ) ( ) ( ) ( ) 2 sin sin 2 sr r s s m s m L I I T t t t = + + + + Then if m = s or s the average torque is non zero. The average torque over time is either T max sin or T max sin . For asynchronous machines, the characteristics are the following: 1. ( ) 2 cos r r r i I t = 2. ( ) 2 cos s s s i I t = 3. m t = + The torque is then ( ) ( ) ( ) ( ) ( ) ( ) sin 2 cos 2 cos sin 2 c o s c o s s i n sr s r sr r r s s m sr r s r s m T L i i...
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- Spring '09