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Unformatted text preview: Lecture 8 Transformations of Torque Equations Newton’s Law of Motion governing the rotational motion is: L e m T T dt d J − = ω (1) where m m dt d ω θ = 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 ω m0 , yields ) ( ) ( ) ( L L e e m m T T T T dt d J Δ + − Δ + = Δ + ω ω (2) m m m m dt d ω ω θ θ Δ + = Δ + ) ( The equilibrium operating speed ω m0 is satisfied by L e m T T dt d J − = ) ( ω (3) m m dt d ω θ = leaving the small perturbation terms L e m T T dt d J Δ − Δ = Δ ω (4) m m dt d ω θ Δ = Δ Information regarding the mathematical model of Δ T L will have to be obtained from supplier of the load. For the moment, it is assumed that Δ T L =0. Attention is focussed on what Δ T e can be. Assuming that T e is a function of θ m and ω m , then m m e m m e e T T T ω ω θ θ Δ ∂ ∂ + Δ ∂ ∂ = Δ ] [ ] [ (5) Substituting (5) and Δ T L =0 in (4) m m m dt d b k...
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 Spring '09
 BonTekOoi
 Moment Of Inertia, Rotation, dt dt, TL dt

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