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Electromagnetic and Electromechanical Engineering Principles Notes 01 Basics Electromagnetic and Electromechanical Engineering Principles Notes 01 Basics Marc T. Thompson, Ph.D. Thompson Consulting, Inc. 9 Jacob Gates Road Harvard, MA 01451 Phone: (978) 456-7722 Email: [email protected] Website: http://www.thompsonrd.com © Marc Thompson, 2006-2008 Portions of these notes reprinted from Fitzgerald, Electric Motors, 6th edition Electromechanics Basics 1-1 Background of Instructor • BSEE (’85), MS (’92), and PhD (’97) from MIT • Doctoral work done in the Laboratory for Electromagnetic and Electronic Systems (L.E.E.S.) at MIT in electrodynamic Maglev • Consultant in analog, magnetics, power electronics, electromagnetics, magnetic braking and failure analysis • Adjunct Professor at Worcester Polytechnic Institute, Worcester MA teaching graduate courses in analog design, power electronics, electromechanics and power distribution • Have also taught for University of Wisconsin since 2006 Electromechanics Basics 1-2 Lens Actuator • For high speed laser printing z Iron r Coil Back iron Permanent Nd-Fe-Bo Lens Magnet Air gap Electromechanics Basics 1-3 High Power Laser Diode Driver Based on Power Converter Technology See: 1. B. Santarelli and M. Thompson, U.S. Patent #5,123,023, "Laser Driver with Plural Feedback Loops," issued June 16, 1992 2. M. Thompson, U.S. Patent #5,444,728, "Laser Driver Circuit," issued August 22, 1995 3. W. T. Plummer, M. Thompson, D. S. Goodman and P. P. Clark, U.S. Patent #6,061,372, “Two-Level Semiconductor Laser Driver,” issued May 9, 2000 4. Marc T. Thompson and Martin F. Schlecht, “Laser Diode Driver Based on Power Converter Technology,” IEEE Transactions on Power Electronics, vol. 12, no. 1, Jan. 1997, pp. 46-52 Electromechanics Basics 1-4 Magnetically-Levitated Flywheel Energy Storage System • For NASA; P = 100W, energy storage = 100 W-hrs Guidance and Suspension S N N S N S Flywheel (Rotating) S N Stator Winding N S S N N S S N z N S S N S N N S r Electromechanics Basics 1-5 Transrapid Maglev • Currently in operation from Pudong (Shanghai), connecting airport to subway line • Operational speed is 431 km/hr Electromechanics Basics 1-6 Japanese EDS Maglev • Slated to run parallel to the high-speed Shinkansen line • On December 2, 2003, this three-car train set attained a maximum speed of 581 km/h in a manned vehicle run Reference: http://www.rtri.or.jp Electromechanics Basics 1-7 Japanese EDS Guideway • This view shows levitation, guidance and propulsion coils Electromechanics Basics 1-8 MIT Maglev Suspension Magnet M. T. Thompson, R. D. Thornton and A. Kondoleon, “Flux-canceling electrodynamic maglev suspension: Part I. Test fixture design and modeling,” IEEE Transactions on Magnetics, vol. 35, no. 3, May 1999 pp. 1956-1963 Electromechanics Basics 1-9 MIT Maglev Test Fixture M. T. Thompson, R. D. Thornton and A. Kondoleon, “Flux- canceling electrodynamic maglev suspension: Part I. Test fixture design and modeling,” IEEE Transactions on Magnetics, vol. 35, no. 3, May 1999 pp. 1956-1963 Electromechanics Basics 1-10 MIT EDS Maglev Test Facility • 2 meter diameter test wheel • Max. speed 1000 RPM (84 m/s) • For testing “flux canceling” HTSC Maglev • Sidewall levitation References: 1. Marc T. Thompson, Richard D. Thornton and Anthony Kondoleon, “Scale Model Flux-Canceling EDS Maglev Suspension --- Part I: Design and Modeling,” IEEE Transactions on Magnetics, vol. 35, no. 3, May 1999, pp. 1956-1963 2. Marc T. Thompson and Richard D. Thornton, “Scale Model Flux-Canceling EDS Maglev Suspension --- Part II: Test Results and Scaling Laws,” IEEE Transactions on Magnetics, vol. 35, no. 3, May 1999, pp. 1964-1975 Electromechanics Basics 1-11 Permanent Magnet Brakes • For roller coasters • Braking force > 10,000 Newtons per meter of brake Reference: http://www.magnetarcorp.com Electromechanics Basics 1-12 Halbach Permanent Magnet Array • Special PM arrangement allows strong side (bottom) and weak side (top) fields • Applicable to magnetic suspensions (Maglev), linear motors, and induction brakes Electromechanics Basics 1-13 Halbach Permanent Magnet Array • 2D FEA modeling Electromechanics Basics 1-14 Photovoltaics S. Druyea, S. Islam and W. Lawrance, “A battery management system for stand-alone photovoltaic energy systems,” IEEE Industry Applications Magazine, vol. 7, no. 3, May-June 2001, pp. 67-72 Electromechanics Basics 1-15 Offline Flyback Power Supply P. Maige, “A universal power supply integrated circuit for TV and monitor applications,” IEEE Transactions on Consumer Electronics, vol. 36, no. 1, Feb. 1990, pp. 10-17 Electromechanics Basics 1-16 Transcutaneous Energy Transmission Reference: H. Matsuki, Y. Yamakata, N. Chubachi, S.-I. Nitta and H. Hashimoto, “Transcutaneous DC-DC converter for totally implantable artificial heart using synchronous rectifier,” IEEE Transactions on Magnetics, vol. 32 , no. 5, Sept. 1996, pp. 5118 - 5120 Electromechanics Basics 1-17 50 KW Inverter Switch Electromechanics Basics 1-18 Transformer Failure Analysis Electromechanics Basics 1-19 Non-Contact Battery Charger • Modeled using PSIM Electromechanics Basics 1-20 High Voltage RF Supply Electromechanics Basics 1-21 60 Hz Transformer Shielding Study • Modeled using Infolytica 2D and 3D Electromechanics Basics 1-22 Course Overview • Day 1 --- Basics of power, 3 phase power, harmonics, etc. • Day 2 --- Magnetics, transformers and energy conversion • Day 3 --- Basic machines • Numerous examples are done throughout the 3 days, some from Fitzgerald, Kingsley and Umans Electromechanics Basics 1-23 Course Overview --- Day 1 Electromechanics Basics 1-24 Course Overview --- Day 2 Electromechanics Basics 1-25 Course Overview --- Day 3 Electromechanics Basics 1-26 Basic Circuit Analysis Concepts • Some background in circuits to get us all on the same page • First-order and second-order systems • Resonant circuits, damping ratio and Q • Reference for this material: M. T. Thompson, Intuitive Analog Circuit Design, Elsevier, 2006 and Kusko/Thompson Power Quality in Electrical Systems, McGraw-Hill, 2007 Electromechanics Basics 1-27 First-Order Systems • system with a single energy-storage element is a “first-A order” system • lowpass filtervoltage driven RC Step −t τ v(o t )= V ( 1 − e ) V −t i() t = e τ r R 1 τ = RC ω = h τ 0 . 35 τ R = ω f τ R =2 .τ 2 f = h h h 2π Electromechanics Basics 1-28 First-Order Systems --- Some Details • Frequency response: • Phase response: • -3 dB bandwidth: Electromechanics Basics 1-29 Step Response 10 - 90% Risetime • Often-measured figure of merit for systems • Defined as the time it takes a step response to transition from 10% of final value to 90% of final value • This plot is for a first-order system with no overshoot or ringing Electromechanics Basics 1-30 Relationship Between Risetime and Bandwidth • Exact for a first-order system (with one pole): • Approximate for higher-order systems Electromechanics Basics 1-31 First-Order Step and Frequency Response • Single pole at -1 rad/sec. Electromechanics Basics 1-32 Second-Order Mechanical System • 2 energy storage modes in mass and spring Spring force: Newton’s law for moving mass: Differential equation for mass motion: Guess a solution of the form: Electromechanics Basics 1-33 Second-Order Mechanical System Put this proposed solution into the differential equation: This solution works if: Electromechanics Basics 1-34 Second-Order Mechanical System • Electromechanical modeling; useful for modeling speakers, motors, acoustics, etc. Reference: Leo Beranek, Acoustics, Acoustical Society of America, 1954 Electromechanics Basics 1-35 Second-Order Electrical System 1 v() s 1 1 ω 2 H()= s o = Cs = = = n v() s 1LCs2+ RCs +1 s2 2ζ s s2+ζω2 s + 2 ω i R+ Ls + n n 2+ +1 Cs ωnω n 1 Natural frequency ωn = LC ω RC 1 R 1 R =ς n = = Damping ratio 2 2 L 2 Zo C Electromechanics Basics 1-36 Second-Order System Frequency Response 1 H()ω j = 2 jςω ⎛ ω 2 ⎞ +⎜1 − ⎟ ⎜ 2 ⎟ ωn ⎝ ωn ⎠ 1 H()ω j = 2 2 ⎛ 2ςω ⎞ ⎛ ω 2 ⎞ ⎜ ⎟+⎜1 − ⎟ ⎜ ⎟ ⎜ 2 ⎟ ⎝ ωn ⎠ ⎝ ωn ⎠ ⎛ 2ςω ⎞ ⎜ ⎟ ⎜ ω ⎟ ⎛ 2ςωω ⎞ ∠(H )ω j = − tan−1 ⎝ n ⎠ = −tan −1 ⎜ n ⎟ ⎛ ω 2 ⎞ ω⎜ 2− ω 2⎟ ⎜1 − ⎟ ⎝ n ⎠ ⎜ 2 ⎟ ⎝ ωn ⎠ Electromechanics Basics 1-37 Second-Order System Frequency Response Electromechanics Basics 1-38 Quality Factor, or “Q” Quality factor is defined as: E ω stored Pdiss where Estored is the peak stored energy in the system and Pdiss is the average power dissipation. Electromechanics Basics 1-39 Q of Series Resonant RLC 1 ω = LC 1 E= LI2 stored 2 pk 1 PIR= 2 diss 2 pk ⎛ 1 ⎞ L ⎜ LI 2 ⎟ ⎛ 1 ⎞ pk C Z Q = ⎜ ⎟⎜ 2 ⎟= = o LC ⎜ 1 2 ⎟ R R ⎝ ⎠⎜ IR⎟ ⎝ 2 pk ⎠ Electromechanics Basics 1-40 Q of Parallel Resonant RLC 1 ω = LC 1 E = CV 2 stored 2 pk 1 V 2 P = pk diss 2 R ⎛ 1 ⎞ ⎜ CV 2 ⎟ ⎛ 1 ⎞ pk R R Q = ⎜ ⎟⎜ 2 ⎟= = ⎜ 2 ⎟ ⎝ LC ⎠ 1 Vpk L Zo ⎜ ⎟ ⎝ 2 R ⎠ C Electromechanics Basics 1-41 Relationship Between Damping Ratio and “Quality Factor” Q • s can also be characterized by it’second order system A “Quality Factor” or Q. 1 H() s = =Q ω= ωn 2ς • in transfer function of series resonant circuit:Use Q 1 1 H() s= = s2 2ζ s s2 s 2+ +1 2+ +1 ωnω n ωn nQ ω Electromechanics Basics 1-42 Second-Order System Step Response • Shown for varying values of damping ratio. Electromechanics Basics 1-43 Undamped Resonant Circuit di v dv − i L = c c = L dt L dt C d2 v 1 di v =c −L =c − dt2 Cdt LC We find the resonant frequency by guessing that the voltage v(t) is sinusoidal with v(t) = Vosinωt. Putting this into the equation for capacitor voltage results in: 1 −ω2sin( ωt= ) − sin(ωt ) LC This means that the resonant frequency is the standard (as expected) resonance: 1 ω 2 = r LC Electromechanics Basics 1-44 Energy Methods Storage Mode Relationship Comments Capacitor/electric field 1 E= CV2 storage elec 2 Inductor/magnetic field 1 B 2 E= LI2 = dV storage mag ∫ 2 2μo Kinetic energy 1 E= Mv2 k 2 Rotary energy 1 2 I ≡ mass moment of inertia EI= ω 2 r 2 (kg- m ) Spring 1 k ≡ spring constant (N/m) E = kx 2 spring 2 Potential energy EΔp = Mg Δ h Δh ≡ height change Thermal energy C ≡ thermal capacitance ΔECT = Δ TH T TH (J/K) Electromechanics Basics 1-45 Energy Methods By using energy methods we can find the ratio of maximum capacitor voltage to maximum inductor current.
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