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Unformatted text preview: Lecture 8 Transformations of Torque Equations Newtons Law of Motion governing the rotational motion is: L e m T T dt d J = (1) where m m dt d = and where J is the moment of inertia of the shaft system, T e is the electromechanical torque and T L is the load torque. Small signal perturbation around the equilibrium operating speed m0 , yields ) ( ) ( ) ( L L e e m m T T T T dt d J + + = + (2) m m m m dt d + = + ) ( The equilibrium operating speed m0 is satisfied by L e m T T dt d J = ) ( (3) m m dt d = leaving the small perturbation terms L e m T T dt d J = (4) m m dt d = Information regarding the mathematical model of T L will have to be obtained from supplier of the load. For the moment, it is assumed that T L =0. Attention is focussed on what T e can be. Assuming that T e is a function of m and m , then m m e m m e e T T T + = ] [ ] [ (5) Substituting (5) and T L =0 in (4) m m m dt d b k...
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- Spring '09