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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 θ θ θ = The coupling between the stator and the rotor depends on the angle θ . The torque can be found by taking the partial derivative of the co-energy with respect to θ at constant current, ' . 1 2 sin T i const sr s r W d L T i i d L i i φ θ θ θ = ∂ = = ∂ = − 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 ω ω θ ω ω θ = − + + + − + Then if ω m = ω s or – ω s the average torque is non zero. The average torque over time is either T max sin θ or –T max sin θ . For asynchronous machines, the characteristics are the following: 1. ( ) 2 cos r r r i I t ω = 2. ( ) 2 cos s s s i I t ω = 3. m t θ ω θ = + 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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This note was uploaded on 01/27/2011 for the course ECSE 361 taught by Professor Franciscodgaliana during the Spring '09 term at McGill.
- Spring '09