Comparison of Main Magnetic Force Computation Methods for Noise and Vibration Assessment in Electrical Machines
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Chapter 3 Dynamics of the Electromagnetic Fields
Chapter 3 Dynamics of the Electromagnetic Fields 3.1 Maxwell Displacement Current In the early 1860s (during the American civil war!) electricity including induction was well established experimentally. A big row was going on about theory. The warring camps were divided into the • Action-at-a-distance advocates and the • Field-theory advocates. James Clerk Maxwell was firmly in the field-theory camp. He invented mechanical analogies for the behavior of the fields locally in space and how the electric and magnetic influences were carried through space by invisible circulating cogs. Being a consumate mathematician he also formulated differential equations to describe the fields. In modern notation, they would (in 1860) have read: ρ �.E = Coulomb’s Law �0 ∂B � ∧ E = − Faraday’s Law (3.1) ∂t �.B = 0 � ∧ B = µ0j Ampere’s Law. (Quasi-static) Maxwell’s stroke of genius was to realize that this set of equations is inconsistent with charge conservation. In particular it is the quasi-static form of Ampere’s law that has a problem. Taking its divergence µ0�.j = �. (� ∧ B) = 0 (3.2) (because divergence of a curl is zero). This is fine for a static situation, but can’t work for a time-varying one. Conservation of charge in time-dependent case is ∂ρ �.j = − not zero. (3.3) ∂t 55 The problem can be fixed by adding an extra term to Ampere’s law because � � ∂ρ ∂ ∂E �.j + = �.j + �0�.E = �. j + �0 (3.4) ∂t ∂t ∂t Therefore Ampere’s law is consistent with charge conservation only if it is really to be written with the quantity (j + �0∂E/∂t) replacing j. -
4 Chapter Four Modelling of Lspmsm Using Jmag ( Fem
© ABDULAZIZ SALEH MILHEM 2017 iii This Thesis is dedicated to The soul of my Father My Dear Mother My Wife My Children Shahd, Omar and Noor My Holy Homeland Palestine iv ACKNOWLEDGMENTS All praise and glory to Allah the most merciful, the most beneficent, who gave me the health, strength, and courage to complete my Master’s degree. I would like to express my deep appreciation to my advisor Prof. Zakariya Al-Hamouz for giving me the opportunity to become one of his students. I thank him for his efficient and constant support, help, motivation, and immense knowledge. His precious advices and thorough guidance played a critical role in completing this thesis. I also would like to extend my appreciation to my dissertation committee members Prof. Mohammed Abido and Prof. Ibrahim El-Amin for their insightful comments, support, and profitable questions which incented me to enhance my work. I would like to thank our research group members supervised by Prof. Zakariya Al- Hamouz, they include Mr. Luqman Marraba for his massive support and help, Mr. Khalid Baradiah and Mr. Ibrahim Hussein. I am very grateful to Mr. Osama Hussain the General Manager and Mr. Samir Al-Hourani the Procurement Manager from Al-Osais Contracting Co. for their continuous support and understanding during the study period. I am thankful to the King Fahd University of Petroleum and Minerals (KFUPM) for providing me with the research facilities, precious resources and an environment conducive to intellectual growth for my master research v TABLE OF CONTENTS ACKNOWLEDGMENTS ........................................................................................................ V TABLE OF CONTENTS ........................................................................................................ VI LIST OF TABLES.................................................................................................................. -
This Chapter Deals with Conservation of Energy, Momentum and Angular Momentum in Electromagnetic Systems
This chapter deals with conservation of energy, momentum and angular momentum in electromagnetic systems. The basic idea is to use Maxwell’s Eqn. to write the charge and currents entirely in terms of the E and B-fields. For example, the current density can be written in terms of the curl of B and the Maxwell Displacement current or the rate of change of the E-field. We could then write the power density which is E dot J entirely in terms of fields and their time derivatives. We begin with a discussion of Poynting’s Theorem which describes the flow of power out of an electromagnetic system using this approach. We turn next to a discussion of the Maxwell stress tensor which is an elegant way of computing electromagnetic forces. For example, we write the charge density which is part of the electrostatic force density (rho times E) in terms of the divergence of the E-field. The magnetic forces involve current densities which can be written as the fields as just described to complete the electromagnetic force description. Since the force is the rate of change of momentum, the Maxwell stress tensor naturally leads to a discussion of electromagnetic momentum density which is similar in spirit to our previous discussion of electromagnetic energy density. In particular, we find that electromagnetic fields contain an angular momentum which accounts for the angular momentum achieved by charge distributions due to the EMF from collapsing magnetic fields according to Faraday’s law. This clears up a mystery from Physics 435. We will frequently re-visit this chapter since it develops many of our crucial tools we need in electrodynamics. -
Magnetohydrodynamics 1 19.1Overview
Contents 19 Magnetohydrodynamics 1 19.1Overview...................................... 1 19.2 BasicEquationsofMHD . 2 19.2.1 Maxwell’s Equations in the MHD Approximation . ..... 4 19.2.2 Momentum and Energy Conservation . .. 8 19.2.3 BoundaryConditions. 10 19.2.4 Magneticfieldandvorticity . .. 12 19.3 MagnetostaticEquilibria . ..... 13 19.3.1 Controlled thermonuclear fusion . ..... 13 19.3.2 Z-Pinch .................................. 15 19.3.3 Θ-Pinch .................................. 17 19.3.4 Tokamak.................................. 17 19.4 HydromagneticFlows. .. 18 19.5 Stability of Hydromagnetic Equilibria . ......... 22 19.5.1 LinearPerturbationTheory . .. 22 19.5.2 Z-Pinch: Sausage and Kink Instabilities . ...... 25 19.5.3 EnergyPrinciple ............................. 28 19.6 Dynamos and Reconnection of Magnetic Field Lines . ......... 29 19.6.1 Cowling’stheorem ............................ 30 19.6.2 Kinematicdynamos............................ 30 19.6.3 MagneticReconnection. 31 19.7 Magnetosonic Waves and the Scattering of Cosmic Rays . ......... 33 19.7.1 CosmicRays ............................... 33 19.7.2 Magnetosonic Dispersion Relation . ..... 34 19.7.3 ScatteringofCosmicRays . 36 0 Chapter 19 Magnetohydrodynamics Version 1219.1.K.pdf, 7 September 2012 Please send comments, suggestions, and errata via email to [email protected] or on paper to Kip Thorne, 350-17 Caltech, Pasadena CA 91125 Box 19.1 Reader’s Guide This chapter relies heavily on Chap. 13 and somewhat on the treatment of vorticity • transport in Sec. 14.2 Part VI, Plasma Physics (Chaps. 20-23) relies heavily on this chapter. • 19.1 Overview In preceding chapters, we have described the consequences of incorporating viscosity and thermal conductivity into the description of a fluid. We now turn to our final embellishment of fluid mechanics, in which the fluid is electrically conducting and moves in a magnetic field. -
Mutual Inductance
Chapter 11 Inductance and Magnetic Energy 11.1 Mutual Inductance ............................................................................................ 11-3 Example 11.1 Mutual Inductance of Two Concentric Coplanar Loops ............... 11-5 11.2 Self-Inductance ................................................................................................. 11-5 Example 11.2 Self-Inductance of a Solenoid........................................................ 11-6 Example 11.3 Self-Inductance of a Toroid........................................................... 11-7 Example 11.4 Mutual Inductance of a Coil Wrapped Around a Solenoid ........... 11-8 11.3 Energy Stored in Magnetic Fields .................................................................. 11-10 Example 11.5 Energy Stored in a Solenoid ........................................................ 11-11 Animation 11.1: Creating and Destroying Magnetic Energy............................ 11-12 Animation 11.2: Magnets and Conducting Rings ............................................. 11-13 11.4 RL Circuits ...................................................................................................... 11-15 11.4.1 Self-Inductance and the Modified Kirchhoff's Loop Rule....................... 11-15 11.4.2 Rising Current.......................................................................................... 11-18 11.4.3 Decaying Current..................................................................................... 11-20 11.5 LC Oscillations .............................................................................................. -
Lecture 4: Magnetohydrodynamics (MHD), MHD Equilibrium, MHD Waves
HSE | Valery Nakariakov | Solar Physics 1 Lecture 4: Magnetohydrodynamics (MHD), MHD Equilibrium, MHD Waves MHD describes large scale, slow dynamics of plasmas. More specifically, we can apply MHD when 1. Characteristic time ion gyroperiod and mean free path time, 2. Characteristic scale ion gyroradius and mean free path length, 3. Plasma velocities are not relativistic. In MHD, the plasma is considered as an electrically conducting fluid. Gov- erning equations are equations of fluid dynamics and Maxwell's equations. A self-consistent set of MHD equations connects the plasma mass density ρ, the plasma velocity V, the thermodynamic (also called gas or kinetic) pressure P and the magnetic field B. In strict derivation of MHD, one should neglect the motion of electrons and consider only heavy ions. The 1-st equation is mass continuity @ρ + r(ρV) = 0; (1) @t and it states that matter is neither created or destroyed. The 2-nd is the equation of motion of an element of the fluid, "@V # ρ + (Vr)V = −∇P + j × B; (2) @t also called the Euler equation. The vector j is the electric current density which can be expressed through the magnetic field B. Mind that on the lefthand side it is the total derivative, d=dt. The 3-rd equation is the energy equation, which in the simplest adiabatic case has the form d P ! = 0; (3) dt ργ where γ is the ratio of specific heats Cp=CV , and is normally taken as 5/3. The temperature T of the plasma can be determined from the density ρ and the thermodynamic pressure P , using the state equation (e.g. -
31295005665780.Pdf
DESIGN AND CONSTRUCTION OF A THREE HUNDRED kA BREECH SIMULATION RAILGUN by BRETT D. SMITH, B.S. in M.E. A THESIS IN -ELECTRICAL ENGINEERING Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE IN ELECTRICAL ENGINEERING Jtpproved Accepted December, 1989 ACKNOWLEDGMENTS I would like to thank Dr. Magne Kristiansen for serving as the advisor for my grad uate work as well as serving as chairman of my thesis committee. I am also appreciative of the excellent working environment provided by Dr. Kristiansen at the laboratory. I would also like to thank my other two thesis committee members, Dr. Lynn Hatfield and Dr. Edgar O'Hair, for their advice on this thesis. I would like to thank Greg Engel for his help and advice in the design and construc tion of the experiment. I am grateful to Lonnie Stephenson for his advice and hard work in the construction of the experiment. I would also like to thank Danny Garcia, Mark Crawford, Ellis Loree, Diana Loree, and Dan Reynolds for their help in various aspects of this work. I owe my deepest appreciation to my parents for their constant support and encour agement. The engineering advice obtained from my father proved to be invaluable. 11 CONTENTS .. ACKNOWLEDGMENTS 11 ABSTRACT lV LIST OF FIGURES v CHAPTER I. INTRODUCTION 1 II. THEORY OF RAILGUN OPERATION 4 III. DESIGN AND CONSTRUCTION OF MAX II 27 Railgun System Design 28 Electrical Design and Construction 42 Mechanical Design and Construction 59 Diagnostics Design and Construction 75 IV. -
Gpu-Accelerated Applications
GPU-ACCELERATED APPLICATIONS Test Drive the World’s Fastest Accelerator – Free! Take the GPU Test Drive, a free and easy way to experience accelerated computing on GPUs. You can run your own application or try one of the preloaded ones, all running on a remote cluster. Try it today. www.nvidia.com/gputestdrive GPU-ACCELERATED APPLICATIONS Accelerated computing has revolutionized a broad range of industries with over five hundred applications optimized for GPUs to help you accelerate your work. CONTENTS 1 Computational Finance 2 Climate, Weather and Ocean Modeling 2 Data Science and Analytics 4 Deep Learning and Machine Learning 7 Federal, Defense and Intelligence 8 Manufacturing/AEC: CAD and CAE COMPUTATIONAL FLUID DYNAMICS COMPUTATIONAL STRUCTURAL MECHANICS DESIGN AND VISUALIZATION ELECTRONIC DESIGN AUTOMATION 15 Media and Entertainment ANIMATION, MODELING AND RENDERING COLOR CORRECTION AND GRAIN MANAGEMENT COMPOSITING, FINISHING AND EFFECTS EDITING ENCODING AND DIGITAL DISTRIBUTION ON-AIR GRAPHICS ON-SET, REVIEW AND STEREO TOOLS WEATHER GRAPHICS 22 Medical Imaging 22 Oil and Gas 23 Research: Higher Education and Supercomputing COMPUTATIONAL CHEMISTRY AND BIOLOGY NUMERICAL ANALYTICS PHYSICS SCIENTIFIC VISUALIZATION 33 Safety & Security 35 Tools and Management Computational Finance APPLICATION NAME COMPANY/DEVELOPER PRODUCT DESCRIPTION SUPPORTED FEATURES GPU SCALING Accelerated Elsen Secure, accessible, and accelerated back- * Web-like API with Native bindings for Multi-GPU Computing Engine testing, scenario analysis, risk analytics Python, R, Scala, C Single Node and real-time trading designed for easy * Custom models and data streams are integration and rapid development. easy to add Adaptiv Analytics SunGard A flexible and extensible engine for fast * Existing models code in C# supported Multi-GPU calculations of a wide variety of pricing transparently, with minimal code Single Node and risk measures on a broad range of changes asset classes and derivatives. -
Loads, Load Factors and Load Combinations
Overall Outline 1000. Introduction 4000. Federal Regulations, Guides, and Reports Training Course on 3000. Site Investigation Civil/Structural Codes and Inspection 4000. Loads, Load Factors, and Load Combinations 5000. Concrete Structures and Construction 6000. Steel Structures and Construction 7000. General Construction Methods BMA Engineering, Inc. 8000. Exams and Course Evaluation 9000. References and Sources BMA Engineering, Inc. – 4000 1 BMA Engineering, Inc. – 4000 2 4000. Loads, Load Factors, and Load Scope: Primary Documents Covered Combinations • Objective and Scope • Minimum Design Loads for Buildings and – Introduce loads, load factors, and load Other Structures [ASCE Standard 7‐05] combinations for nuclear‐related civil & structural •Seismic Analysis of Safety‐Related Nuclear design and construction Structures and Commentary [ASCE – Present and discuss Standard 4‐98] • Types of loads and their computational principles • Load factors •Design Loads on Structures During • Load combinations Construction [ASCE Standard 37‐02] • Focus on seismic loads • Computer aided analysis and design (brief) BMA Engineering, Inc. – 4000 3 BMA Engineering, Inc. – 4000 4 Load Types (ASCE 7‐05) Load Types (ASCE 7‐05) • D = dead load • Lr = roof live load • Di = weight of ice • R = rain load • E = earthquake load • S = snow load • F = load due to fluids with well‐defined pressures and • T = self‐straining force maximum heights • W = wind load • F = flood load a • Wi = wind‐on‐ice loads • H = ldload due to lllateral earth pressure, ground water pressure, -
Polywell – a Path to Electrostatic Fusion
Polywell – A Path to Electrostatic Fusion Jaeyoung Park Energy Matter Conversion Corporation (EMC2) University of Wisconsin, October 1, 2014 1 Fusion vs. Solar Power For a 50 cm radius spherical IEC device - Area projection: πr2 = 7850 cm2 à 160 watt for same size solar panel Pfusion =17.6MeV × ∫ < συ >×(nDnT )dV For D-T: 160 Watt à 5.7x1013 n/s -16 3 <συ>max ~ 8x10 cm /s 11 -3 à <ne>~ 7x10 cm Debye length ~ 0.22 cm (at 60 keV) Radius/λD ~ 220 In comparison, 60 kV well over 50 cm 7 -3 (ne-ni) ~ 4x10 cm 2 200 W/m : available solar panel capacity 0D Analysis - No ion convergence case 2 Outline • Polywell Fusion: - Electrostatic Fusion + Magnetic Confinement • Lessons from WB-8 experiments • Recent Confinement Experiments at EMC2 • Future Work and Summary 3 Electrostatic Fusion Fusor polarity Contributions from Farnsworth, Hirsch, Elmore, Tuck, Watson and others Operating principles (virtual cathode type ) • e-beam (and/or grid) accelerates electrons into center • Injected electrons form a potential well • Potential well accelerates/confines ions Virtual cathode • Energetic ions generate fusion near the center polarity Attributes • No ion grid loss • Good ion confinement & ion acceleration • But loss of high energy electrons is too large 4 Polywell Fusion Combines two good ideas in fusion research: Bussard (1985) a) Electrostatic fusion: High energy electron beams form a potential well, which accelerates and confines ions b) High β magnetic cusp: High energy electron confinement in high β cusp: Bussard termed this as “wiffle-ball” (WB). + + + e- e- e- Potential Well: ion heating &confinement Polyhedral coil cusp: electron confinement 5 Wiffle-Ball (WB) vs. -
MHD Equilibrium and Instabilities
MHD equilibrium and instabilities 5.1 Introduction Magnetohydrodynamics is a branch of plasma physics dealing with dc or low frequency effects in fully ionized magnetized plasma. In this chapter we will study both “ideal” (i.e. zero resistance) and resistive plasma, introducing the concepts of stability and equilibrium, “frozen-in” magnetic fields and resistive diffusion. We will then describe the range of low-frequency plasma waves supported by the single fluid equations. 5.2 Ideal MHD – Force Balance The ideal MHD equations are obtained by setting resistivity to zero: E u B 0 u j B p t In equilibrium, the time derivative is ignored and the force balance equation: j B p describes the balance between plasma pressure force and Lorentz forces. Such a balance is shown schematically in Fig. 6.1. What are the consequences of this simple expression? The current required to balance the plasma pressure is found by taking the cross product with B. Then B p B n j kTe kTi B2 B2 This is simply the diamagnetic current! The force balance says that j and B are perpendicular to p. In other words, j and B must lie on surfaces of constant pressure. This situation is shown for a tokamak in Fig. 6.2. The current density and magnetic lines of force are constrained to lie in surfaces 1 of constant plasma pressure. The angle between the current and field increases as the plama pressure increases. In the direction parallel to B: p 0 z Plasma pressure is constant along a field line. (Why is this?) 5.2.1 Magnetic pressure From Maxwell’s equation j 1 B 0 p 1 B B 1 B B 1 B2 0 0 2 or 2 p B 1 B B 20 0 If the magnetic field lines are straight and parallel, so that the right side vanishes. -
Compact Fusion Reactors
Compact fusion reactors Tomas Lind´en Helsinki Institute of Physics 26.03.2015 Fusion research is currently to a large extent focused on tokamak (ITER) and inertial confinement (NIF) research. In addition to these large international or national efforts there are private companies performing fusion research using much smaller devices than ITER or NIF. The attempt to achieve fusion energy production through relatively small and compact devices compared to tokamaks decreases the costs and building time of the reactors and this has allowed some private companies to enter the field, like EMC2, General Fusion, Helion Energy, Lockheed Martin and LPP Fusion. Some of these companies are trying to demonstrate net energy production within the next few years. If they are successful their next step is to attempt to commercialize their technology. In this presentation an overview of compact fusion reactor concepts is given. CERN Colloquium 26th of March 2015 Tomas Lind´en (HIP) Compact fusion reactors 26.03.2015 1 / 37 Contents Contents 1 Introduction 2 Funding of fusion research 3 Basics of fusion 4 The Polywell reactor 5 Lockheed Martin CFR 6 Dense plasma focus 7 MTF 8 Other fusion concepts or companies 9 Summary Tomas Lind´en (HIP) Compact fusion reactors 26.03.2015 2 / 37 Introduction Introduction Climate disruption ! ! Pollution ! ! ! Extinctions Ecosystem Transformation Population growth and consumption There is no silver bullet to solve these issues, but energy production is "#$%&'$($#!)*&+%&+,+!*&!! central to many of these issues. -.$&'.$&$&/!0,1.&$'23+! Economically practical fusion power 4$(%!",55*6'!"2+'%1+!$&! could contribute significantly to meet +' '7%!89 !)%&',62! the future increased energy :&(*61.'$*&!(*6!;*<$#2!-.=%6+! production demands in a sustainable way.