Lecture 4RELUCTANCE MACHINES The inductances in the 2x2 inductance matrix are: )](2cos[xdBAxxLLLθθ−+=)](2cos[ydBAyyLLLθθ−+=)]2cos()(cos([yxdByxAyxxyLLLLθθθθθ−−+−==Single-Phase Reluctance MachineConsider the x-winding as the a-phase with θx=0. Then, ]2cos[dBAaLLLθ+=. If the a-phase current is ia, the magnetic co-energy is: Wm1=0.5Laia2. The torque is 25.0adaeiLTθ∂∂=which is (1) 2]2sin2[5.0adBeiLTθ−=How does one make this machine produce a non-zero time invariant torque, so that as a motor it can drive a constant load torque TL? Newton’s Law of Motion governing the rotational motion is: LemTTdtdJ−=ω(2) where Jis the moment of inertia of the shaft system and TLis the load torque. So far, most of the class notes are on analysis. Answering the above question requires synthesis, which is an art. Trial and error is applied most of the time. Often, we use results from known experience. For example, one can propose using the ac mains where cos()aiItωδ=+and assume thatdtθω=. Substituting in (1) 20.5[ 2sin(2)][0.5(1cos(22 )]eBTLtItωωδ=−++Therefore 20.5[sin(2)0.5sin(42 )0.5sin 2 ]eBTI Lttωωδδ= −+++(3) Substituting (3) in (2)
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