final 2002

final 2002 - DEPARTMENT OF ELECTRICAL AND COMPUTING...

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DEPARTMENT OF ELECTRICAL AND COMPUTING ENGINEERING FINAL EXAMINATION ELECTROMECHANICAL ENERGY CONVERSION 304-462B Examiner: Professor B.T.Ooi Date: December 14,2002 Time : PM (3 hours) INSTRUCTIONS: OPEN BOOK EXAMINATION Answer all six questions. Trigonometric Identities cos(A+B)=cosAcosB-sinAsinB cos(A-B)=cosAcosB+sinAsinB sin(A+B)=sinAcosB+cosAsinB sin(A-B)=sinAcosB-cosAsinB [All dimensions are in meters. Field vectors are represented by bold letters, for example B and K . The directional vectors in cylindrical co-ordinates are: u r , u ϕ and u z . The superscript T denotes “transpose”.] An electric machine consists of a cylindrical rotor inside an annular stator. They are separated by an airgap “g” at a mean radius “R”. The stack length is “L”. The permeability of the iron is infinite and the permeability of the airgap is μ o . Question 1 Two 4 -pole stator windings carrying currents i α and i β produce sheet currents: K α = u z i α B s sin( 2 ϕ ) and K β = u z i β B s sin( 2 ϕ -90 0 ) respectively, where B S is the Fourier coefficient of the fundamental space harmonic. (a) What are their magnetic density distributions B α and B β around the airgap? (b)
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final 2002 - DEPARTMENT OF ELECTRICAL AND COMPUTING...

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