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Lecture Set 1

# Lecture Set 1 - Lecture Set 1 Introduction to Magnetic...

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Lecture Set 1 Introduction to Magnetic Circuits S.D. Sudhoff Spring 2012 1

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Reading Techniques for Analysis of Electromechanical Systems Ø Sections 1.1-1.5 2
Goals Review physical laws pertaining to analysis of magnetic systems Introduce concept of magnetic circuit as means to obtain an electric circuit Learn how to determine the flux-linkage versus current characteristic because it will be key to understanding electromechanical energy conversion 3

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Review of Symbols Flux Density in Tesla: B (T) Flux in Webers: Φ (Wb) Flux Linkage in Volt-seconds: λ (Vs,Wb-t) Current in Amperes: i (A) Field Intensity in Ampere-meters: H (Am) Permeability in Henries/meter: μ (Η/ m 29 Magneto-Motive Force: F (A,A-t) Permeance in Henries: P (H) Reluctance in inverse Henries: R (1/H) Inductance in Henries: L (H) Current (fields) into page: Current (fields) out of page: 4
1.1 MMF and Kirchoff’s Voltage Law for Magnetic Circuits By Ampere’s Law Magneto Motive Force (MMF) 5 x x i F = x x i d = l H H l d start end x i

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1.1 MMF and Kirchoff’s Voltage Law for Magnetic Circuits Breaking Up the Current 6
1.1 MMF and Kirchoff’s Voltage Law for Magnetic Circuits Breaking up the path 7 H l d start end x i 1 l 3 l 4 l 2 l

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1.1 MMF and Kirchoff’s Voltage Law for Magnetic Circuits Breaking up the integral 8 H l d start end x i 1 l 3 l 4 l 2 l
1.1 MMF and Kirchoff’s Voltage Law for Magnetic Circuits Kirchoff’s MagnetoMotive Force Law: The Sum of the MMF Drops Around a Closed Loop is Equal to the Sum of the MMF Sources for That Loop 9

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1.1 MMF and Kirchoff’s Voltage Law for Magnetic Circuits A quick example on MMF sources (going CCW): 10 10 conductors, 3 A = 5 conductors, 2 A =
1.1 MMF and Kirchoff’s Voltage Law for Magnetic Circuits A quick example on MMF drop: 11

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1.1 MMF and Kirchoff’s Voltage Law for Magnetic Circuits How about Fca ? 12
1.2 Flux and Kirchoff’s Current Law for Magnetic Circuits A node in a magnetic circuit 13 Node 1 Node 2 Node 3 Node 4 Depth into page = g d i r o r ε

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1.2 Flux and Kirchoff’s Current Law for Magnetic Circuits Gauss’ Law Separating the Surface Into Regions Flux through m’th surface 14 = 0 S B d 0 1 = = S B d m S M m = m d m S S B Φ
1.2 Flux and Kirchoff’s Current Law for Magnetic Circuits Examples of Flux 15 B = 1 T S = 8 m2 B = 1 T S = 8 m2

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1.2 Flux and Kirchoff’s Current Law for Magnetic Circuits Recall And Thus 16 0 = = M m j m Φ 0 1 = = S B d m S M m = m d m S S B Φ
1.2 Flux and Kirchoff’s Current Law for Magnetic Circuits Kirchoff’s Flux Law: The Sum of the Flux Leaving A Node of a Magnetic Circuit is Zero 17

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1.2 Flux and Kirchoff’s Current Law for Magnetic Circuits A quick example on Kirchoff’s Flux Law 18
1.3 Material Characteristics and Ohm’s

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