IRON LOSSES EVALUATION IN HIGH SPEED DRIVES. G. D. Kalokiris 1, P. S. Georgilakis 2 and A. G. Kladas 1. (
|
|
- Phillip Dean
- 5 years ago
- Views:
Transcription
1 IRON LOSSES EVALUATION IN HIGH SPEED DRIVES G. D. Klokiris 1, P. S. Georgilkis 2 nd A. G. Klds 1 1 Ntionl Technicl University of Athens, GR-1578, Greece (e-mil: kldsel@centrl.ntu.gr) 2 Technicl University of Crete, GR-731, Chni, Greece (e-mil: pgeorg@dpem.tuc.gr) ABSTRACT The pper presents electricl mchine design considertions introduced y exploiting new mgnetic mteril chrcteristics. The mterils considered re morphous lloy rions s well s Neodymium lloy permnent mgnets involving very low eddy current losses. Such dvnce mterils enle electric mchine opertion t higher frequencies compred with the stndrd iron lmintions used in the trditionl mgnetic circuit construction nd provide etter efficiently. Keywords: Finite element method, permnent mgnets, rotor skew, design methodology. 1. INTRODUCTION A methodology for electricl mchine modeling enling to exploit new mgnetic mteril chrcteristics re presented y the uthors. The mterils considered re thin mgnetic lmintions, morphous lloy rions s well s Neodymium lloy permnent mgnets involving very low eddy current losses s mentioned in (1)-(3). Such mterils enle electric mchine opertion t high frequencies compred with the stndrd iron lmintions used in the trditionl mgnetic circuit construction. Moreover, simpler winding configurtions re dopted, tking into considertion tht there will e power electronics converter ensuring the connection of the mchine to the electric grid (4)-(6). The study of synchronous nd permnent mgnet mchines sed on such mterils is undertken in three steps. In first step the typicl design procedure is conveniently dpted in order to include the new mgnetic mteril properties. In second the designed mchine chrcteristics re checked y mens of detiled field clcultion through finite element modeling ssocited to sensitivity nlysis techniques. In third step prototype is constructed in order to vlidte the mchine performnce. Low losses nd high volumic power ssocited with high speed nd converter mchine opertion re the min dvntges of such pplictions (7)-(1). 2. CALCULATION METHODOLOGY The proposed mchine design procedure involves two steps. In first step stndrd design methodology is used for preliminry design. In second step the method of finite elements is implemented to clculte the mchine efficiency nd performnce. Finlly, prototypes re constructed in order to vlidte nd compre the simulted mchine chrcteristics to the corresponding experimentl results (11)-(12). In cse of vrile reluctnce mchines, the electromechnicl conversion is sed on the mgnetic energy exchnges in the mgnetic circuit with the vrition of reluctnce with rotor position nd of excittion. In generl, the stored energy in the mgnetic circuit is mximized when the reluctnce is minimum (conjunction) nd is minimized when the reluctnce is mximum (opposition), while the pproprite current vrition ensures pproprite torque. The studied structure of mchines is multidiscoidl (Fig. 1) with discs composed from non-mgnetic resins where convenient ferromgnetic prts re emedded (1). The method of finite elements, is sed on discretistion of the solution domin into smll regions. In mgnetosttic prolems the unknown quntity is usully the mgnetic vector potentil A, nd is pproximted y mens of polynomil shpe functions. In two dimensionl cses tringulr elements cn esily e dpted to complex configurtions nd first order elements exhiit dvntges in iron sturtion representtion (13). The size of elements must e smll enough to provide sufficient ccurcy. In this wy the differentil equtions of the continuous prolem cn e trnsformed into system of lgeric equtions for the discrete prolem. The prcticl prolems necessitte usully severl tenths of thousnds of unknowns. However, pproprite numericl techniques hve een developed, enling to otin the solution of such systems within resonle time, even when personl computers re used. It should e mentioned tht the 3D prolems require considerly higher computtionl resources thn the 2D ones. In the present pper the 2D finite element model dopted, involves vector potentil formultion, while the mgnetic flux Φ m per pole cn e clculted s follows:
2 Figure 1. Multidiscoidl Vrile Reluctnce Mchine structure studied. : sttor prt : rotor prt ( 2 A ) Φ = B ds = A dl L (1) m S 1 C 1 where L is the length of the mgnetic circuit in m, A is the mgnetic vector potentil, A gp is the vector potentil vlue in the middle of the ir-gp, B is the flux density in Tesl, S 1 is the cross-sectionl re norml to the direction of flux in m 2 nd C 1 is the contour surrounding the surfce S 1 in m. The electromotive force t no lod cn e clculted s follows: d Φ m E = - (2) dt The vlue of the voltge of the mchine operted s genertor under lod conditions cn e clculted y reltion (3): V = E - RI - jl ω Ι (3) where V is the voltge on sttor windings in V, E is the electromotive force t no lod in V, R is the sttor resistnce in Ω, L σ is the sttor lekge inductnce in H, ω is the rotor ngulr velocity in rd/sec nd I is the sttor current in A. Then the mgnetic flux nd electromotive forces cn e derived y using equtions (1) nd (2). Finlly, we clculte the iron losses for this mchine t the low nd high frequency opertion y the eqution: σ gp c Figure 2. Flux distriution in the two dimensionl vrile reluctnce mchine configurtion for low excittion. : Conjunction : Intermedite position c: Opposition P =P -P iron totl Cu where P =P +P Cu Cu rotor Cu sttor 3. RESULTS AND DISCUSSION A. Vrile Reluctnce Mchines (4) The vrile reluctnce mchine considered is three phse comprising three sttor discs nd two rotor discs for ech phse mounted on the sme trnsxle, s shown in Fig. 1. Ech disc comprises 24 ferromgnetic teeth while ech phse hs pproprite flux return core prts. The mgnetic field nlysis hs een performed in two dimensionl Crtesin pproximtion y considering peripherl cutwy of the ctive prt of the mchine s shown in Fig.2. This figure shows the mgnetic field density distriution for different rotor
3 conjunction opposition Figure 4. Reduced torque per excittion in the vrile reluctnce mchine with rotor position. c Figure 3. Flux distriution in the two dimensionl vrile reluctnce mchine configurtion for high excittion. : Conjunction : Intermedite position c: Opposition positions in cse of low excittion current. The mgnetic circuit in this cse is unsturted. The sme results for high excittion current re shown in Fig. 3. It my e noted tht the teeth re highly sturted in this cse, especilly in the corners for intermedite positions (Fig. 3). The reduced torque per excittion cn e clculted y convenient rdil extrpoltion of the two dimensionl results nd the otined results re shown in Fig. 4. This figure compres the numericl (continuous line) results with the mesured ones (dshed line). The two curves vritions with rotor position re similr ut the mesured results re somewht smller due to the fct the return flux circuits (3D feture) hs een neglected in the two dimensionl representtion. An importnt prt of losses in vrile reluctnce mchines is due to hysterisis effect nd in order to ccount for this n pproprite Preisch-Neel model hs een developed for the iron lmintions used (14). In order to ssocite pproprite weights to this model the experimentl hysterisis curves otined for the iron lmintions used hve een considered, shown in Fig. 5. In vrious points of the ferromgnetic teeth of the vrile reluctnce mchine different hysterisis curves re otined, which vry lso with the excittion imposed. One chrcteristic of the mchine tested, involving unidirectionl excittion, is tht minor hysterisis curves re otined s shown in Figs. 6 nd 7. The clculted curves in these figures hve een otined y mking two importnt ssumptions: the field density vlues re computed through the two dimensionl nlysis presented (end mgnetic circuit effects s well s return flux pths re neglected) while eddy currents in iron lmintions ws supposed to hve negligile effects on locl field vlue vritions (sttic field nlysis). Moreover, the Preisch-Neel model dopted ignores frequency vrition effects nd ssumes unidirectionl flux density vritions (rottionl field effects re not ccounted). Figure 5. Experimentl hysterisis curves otined with direct current excittion for the.35 mm width iron lmintions used.
4 Figure 8. No lod voltge wveform of permnent mgnet mchine (simultion) Figure 6. Unidirectionl excittion of the vrile reluctnce mchine nd minor hysterisis curves clculted. Figure 9. No lod voltge wveform of permnent mgnet mchine (mesurement) 3 2 Figure 7. Minor hysterisis curves clculted in vrious points of the teeth of the vrile reluctnce mchine. Phse Voltge (V) B. Permnent Mgnet Mchines The cse of permnent mgnet mchine hs een considered. The mchine designed hs een checked through 2.5 kw prototype which hs een connected to n pproprite power electronics converter. The irgp width hs een chosen 1 mm while multipole peri-pherl mchine structure hs een dopted. The geometry of the permnent mgnet mchine is given in (6) providing lso the mesh employed for the two dimensionl finite element progrm of the mchine involving, pproximtely 21 nodes 4 tringulr elements. In first step the no lod operting conditions hve een exmined. The corresponding simulted voltge wveform is shown in Fig. 8 while the mesured one is given in Fig. 9, respectively. In these figures good greement etween the simulted nd mesured results cn e oserved. The simultion results concerning full lod voltge of synchronous genertor re presented in Fig Angle (degrees) Figure 1. Full lod voltge wveform of permnent mgnet mchine (simultion) Figure 11. Full lod voltge wveform of permnent mgnet mchine (mesurement) Figure 11 gives the mesured results under the sme operting conditions. A good greement cn e oserved in these figures etween the simulted nd mesured results lso in the cse of full lod.
5 C. Asynchronous Mchines where F t is the totl circumferentil tngentil force in Newton nd r g is the middle ir-gp rdius in meters. The Mxwell s stress tensor is clculted y reltion (6): Moreover, mesurements were relized for n synchronous motor, which ws supplied y n inverter with vrile frequency. The motor is three phse, 4-pole, mchine supplied t frequency of 4 Hz, t voltge of 28 V while the nominl, speed is 1.8 rpm. The motor ws tested under no lod nd low lod operting conditions, for vrious frequencies. Fig. 12 shows the field distriution in the mchine supplied t fundmentl frequency of 3 Hz, while Fig. 12 gives the field distriution t the switching frequency of 1 khz. 1 Ft = B n Β t dl L µ C where B n nd B t re the norml nd tngentil mgnetic flux density components, respectively, to the integrtion surfce of ir-gp C in Tesl, µ is the permeility of ir nd L is the ctive prt of the mchine. 4 voltge (V) f = 3 Hz (6) 2 15 f=3 Hz current (A) Figure 12. Simulted field distriution in the mchine under low lod conditions : fundmentl supply frequency of 3Hz : switching frequency of 1 khz Fig. 13 presents the respective mesured phse voltge nd current time vritions. Fig. 14 shows the field distriution in the mchine supplied t fundmentl frequency of 1 Hz, while Fig. 15 presents the respective mesured phse voltge nd current time vritions t the switching frequency of 1 khz. Tle I presents the mesured nd simultion results under no lod conditions with switching frequency of 1 khz. Tle II presents the sme results under low lod conditions. Tle III presents the results relted to switching frequency of 1 khz. The simulted torque T s is clculted y the reltion: T = F r (5) s t g Figure 13. Mesured supply quntities in the mchine for supply frequency of 3 Hz, under low lod conditions : phse voltge time vrition : phse current time vrition Figure 14. Simulted field distriution in the mchine, fundmentl supply frequency of 1 Hz under low-lod conditions
6 In Tles I, II nd III good greement etween the mesured nd simulted results for oth voltge nd torque vlues cn e oserved. voltge (V) (A) current Tle I. Mesured nd simultion results under no lod conditions nd f s = 1 khz f = 1 Hz f = 1 Hz Figure 15. Mesured supply quntities in the mchine for supply frequency of 1 Hz under low lod conditions : phse voltge time vrition : phse current time vrition Tle II. Mesured nd simultion results under low lod conditions nd f s = 1 khz Tle III. Mesured nd simultion results under low lod conditions nd f s = 1 khz 1 4. CONCLUSIONS In this pper, methodologies re proposed in order to evlute the iron losses in vrious types of electricl mchines fvored for high speed drive pplictions. Electricl mchine opertion hs een investigted y using the finite element method for the mchine nlysis nd verified y mesurements. Moreover, the low cost involved mkes such drives ttrctive rivls of the conventionl ones. 5. REFERENCES 1. A. Klds, Etude du couple et des pertes fer d une mchine reluctnce vrile, report DEA, Universites Pris VI nd Pris XI, C. Mrchnd, Z. Ren, Z. nd A. Rzek, Torque optimiztion of uried permnent mgnet synchronous mchine y geometric modifiction using FEM, in Proceedings EMF 94, Leuven, pp , A. To, T. Lipo, "Generic torque mximizing design methodology of surfce permnent mgnet Vernier mchine", IEEE Trns. on Ind. Appl., Vol. 36, no 6, pp , G. Tsekours, S. Kirtzis, A. Klds, J. Tegopoulos, "Neurl Network Approch compred to Sensitivity Anlysis sed on Finite Element Technique for Optimiztion of Permnent Mgnet Genertors", IEEE Trns. Mgn., Vol. 37, no 5/1, pp , M. A. Alhmdi, N. Demerdsh "Modeling nd experimentl verifiction of the performnce of skew mounted permnent mgnet rushless dc motor drive with prmeters computed from 3D FE mgnetic field solutions", IEEE Trns. on Energy Conversion, Vol. 9, no 1, pp. 1-35, G. D. Klokiris, A. G. Klds: "New mgnetic mteril impct in electric mchine design: high speed opertion nd reduction of losses", Journl of Sensors nd Actutors A: Physicl (Elsevier), vol.16, no 1/3, pp G. D. Klokiris, A. G. Klds, J. A. Tegopoulos: "Permnent Mgnet Mchine Optimiztion y using FEM nd Sensitivity Anlysis Techniques", Optimistion nd Inverse Prolems in Electromgnetism, Kluwer Acdemic Pulishers, pp , ISBN G. D. Klokiris, A. G. Klds, J. A. Tegopoulos: 2D nd 3D finite element design of skewed mounted permnent mgnet synchronous genertors, Proceedings of the 3 rd Jpnese-Mediterrnen Workshop on Applied Electromgnetic Engineering for Mgnetic nd Superconducting Mterils, ccepted for puliction in the Journl of Mteril Processing Technology, Elsevier. 9. M.R. Duois, H. Polinder, nd J.A. Ferreir, "Contriution of Permnent-Mgnet Volume Elements to No-Lod Voltge in Mchines", IEEE Trnsctions on Mgnetics, vol. 39/3, 23, pp P. Dziwniel, B. Boulem, F. Piriou, J.P. Ducreux, nd P. Thoms "Comprison etween two Approches to Model Induction Mchines with Skewed Slots", IEEE Trnsctions on Mgnetics, vol. 36/4, 2, pp G. D. Klokiris, Th. Kefls, A. G. Klds: Specil ir-gp element for 2D FEM nlysis of electricl mchines ccounting for rotor skew, Eleventh Biennil IEEE Conference on Electromgnetic Field Computtion (CEFC 24), Seoul, Kore, June 6-9, 24, pp G.D. Klokiris, A.G. Klds: High speed mchines using dvnced mgnetic mterils nlyzed y pproprite finite element models, IASME Trnsctions, Vol. 1, no 2, April 24, pp H. De Gersem, K. Hmeyer, T. Weilnd, "Skew interfce conditions in 2-D finite-element mchine models", IEEE Trnsctions on Mgnetics, vol.39/3, 23, pp G. Friedmn, I.D. Myergoyz, Hysteretic energy losses in medi descried y vector Preisch model, IEEE Trnsctions on Mgnetics, Vol. 34, no 4, pp , July 1998.
High speed machines using advanced magnetic materials analyzed by appropriate finite element models
High speed mchines using dvnced mgnetic mterils nlyzed y pproprite finite element models G. D. KALOKIRIS, A. G. KLADAS Lortory of Electricl Mchines nd Power Electronics, Electric Power Division Fculty
More informationELE B7 Power Systems Engineering. Power System Components Modeling
Power Systems Engineering Power System Components Modeling Section III : Trnsformer Model Power Trnsformers- CONSTRUCTION Primry windings, connected to the lternting voltge source; Secondry windings, connected
More informationFEM ANALYSIS OF ROGOWSKI COILS COUPLED WITH BAR CONDUCTORS
XIX IMEKO orld Congress Fundmentl nd Applied Metrology September 6 11, 2009, Lisbon, Portugl FEM ANALYSIS OF ROGOSKI COILS COUPLED ITH BAR CONDUCTORS Mirko Mrrcci, Bernrdo Tellini, Crmine Zppcost University
More informationOn the Uncertainty of Sensors Based on Magnetic Effects. E. Hristoforou, E. Kayafas, A. Ktena, DM Kepaptsoglou
On the Uncertinty of Sensors Bsed on Mgnetic Effects E. ristoforou, E. Kyfs, A. Kten, DM Kepptsoglou Ntionl Technicl University of Athens, Zogrfou Cmpus, Athens 1578, Greece Tel: +3177178, Fx: +3177119,
More informationIndustrial Electrical Engineering and Automation
CODEN:LUTEDX/(TEIE-719)/1-7/(7) Industril Electricl Engineering nd Automtion Estimtion of the Zero Sequence oltge on the D- side of Dy Trnsformer y Using One oltge Trnsformer on the D-side Frncesco Sull
More informationA New Method for Estimating Permanent Magnet Synchronous Machine Parameters
J. Bsic. Appl. Sci. Res., (9)9145-9151, 01 01, TextRod Publiction ISSN 090-4304 Journl o Bsic nd Applied Scientiic Reserch www.textrod.com A New Method or Estimting Permnent Mgnet Synchronous Mchine Prmeters
More informationADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS
ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct:
More information#6A&B Magnetic Field Mapping
#6A& Mgnetic Field Mpping Gol y performing this lb experiment, you will: 1. use mgnetic field mesurement technique bsed on Frdy s Lw (see the previous experiment),. study the mgnetic fields generted by
More informationQUADRATURE is an old-fashioned word that refers to
World Acdemy of Science Engineering nd Technology Interntionl Journl of Mthemticl nd Computtionl Sciences Vol:5 No:7 011 A New Qudrture Rule Derived from Spline Interpoltion with Error Anlysis Hdi Tghvfrd
More informationLec 3: Power System Components
Lec 3: Power System Components Dr. Mlbik Bsu 8/0/2009 Lesson pln 3 nd L.O. Sequence nlysis exmple ( detil fult nlysis next sem) Trnsformer model recp, tp chnge nd phse chnge, 3-phse Modeling of Synchronous
More informationReview of Calculus, cont d
Jim Lmbers MAT 460 Fll Semester 2009-10 Lecture 3 Notes These notes correspond to Section 1.1 in the text. Review of Clculus, cont d Riemnn Sums nd the Definite Integrl There re mny cses in which some
More informationANALYTICAL CALCULATION OF PARALLEL DOU- BLE EXCITATION AND SPOKE-TYPE PERMANENT- MAGNET MOTORS; SIMPLIFIED VERSUS EXACT MODEL
Progress In Electromgnetics Reserch B, Vol. 47, 145 178, 13 ANALYTICAL CALCULATION OF PARALLEL DOU- BLE EXCITATION AND SPOKE-TYPE PERMANENT- MAGNET MOTORS; SIMPLIFIED VERSUS EXACT MODEL Kmel Boughrr 1,
More informationApplication Chebyshev Polynomials for Determining the Eigenvalues of Sturm-Liouville Problem
Applied nd Computtionl Mthemtics 5; 4(5): 369-373 Pulished online Septemer, 5 (http://www.sciencepulishinggroup.com//cm) doi:.648/.cm.545.6 ISSN: 38-565 (Print); ISSN: 38-563 (Online) Appliction Cheyshev
More informationA ROTATING DISC IN CONSTANT PURE SHEAR BY S. KUMAR AND C. V. JOGA RAO
A ROTATING DISC IN CONSTANT PURE SHEAR BY S. KUMAR AND C. V. JOGA RAO (Deprtment of Aeronuticl Engineering, Indin Institute of Science, Bnglore-3) Received April 25, 1954 SUMMARY The disc of constnt pure
More informationCross-section section of DC motor. How does a DC Motor work? 2 Commutator Bars N X. DC Motors 26.1
DC Motors 26.1 How does DC Motor work? Crosssection section of DC motor Mgnetic field vector, B oft Iron Core (otor) Wire length vector, dl Force vector, df Current, i Permnent Mgnet (ttor) Crosssection
More informationDesigning Information Devices and Systems I Anant Sahai, Ali Niknejad. This homework is due October 19, 2015, at Noon.
EECS 16A Designing Informtion Devices nd Systems I Fll 2015 Annt Shi, Ali Niknejd Homework 7 This homework is due Octoer 19, 2015, t Noon. 1. Circuits with cpcitors nd resistors () Find the voltges cross
More informationWELCOME TO THE LECTURE
WELCOME TO THE LECTURE ON DC MOTOR Force on conductor If conductor is plced in mgnetic field nd current is llowed to flow through the conductor, the conductor will experience mechnicl force. N S Electric
More informationReview of Gaussian Quadrature method
Review of Gussin Qudrture method Nsser M. Asi Spring 006 compiled on Sundy Decemer 1, 017 t 09:1 PM 1 The prolem To find numericl vlue for the integrl of rel vlued function of rel vrile over specific rnge
More informationSummary of equations chapters 7. To make current flow you have to push on the charges. For most materials:
Summry of equtions chpters 7. To mke current flow you hve to push on the chrges. For most mterils: J E E [] The resistivity is prmeter tht vries more thn 4 orders of mgnitude between silver (.6E-8 Ohm.m)
More informationSome basic concepts of fluid dynamics derived from ECE theory
Some sic concepts of fluid dynmics 363 Journl of Foundtions of Physics nd Chemistry, 2, vol. (4) 363 374 Some sic concepts of fluid dynmics derived from ECE theory M.W. Evns Alph Institute for Advnced
More information2. VECTORS AND MATRICES IN 3 DIMENSIONS
2 VECTORS AND MATRICES IN 3 DIMENSIONS 21 Extending the Theory of 2-dimensionl Vectors x A point in 3-dimensionl spce cn e represented y column vector of the form y z z-xis y-xis z x y x-xis Most of the
More informationReversible magnetization processes in scalar Preisachtype models of hysteresis
JOURNAL O OPTOELECTRONIC AND ADVANCED ATERIAL Vol. 8, No. 5, Octoer 26, p. 171-1714 Reversile mgnetiztion processes in sclr Preischtype models of hysteresis L. TOLERIU *, A. TANCU Deprtment of olid tte
More informationDESIGN OF FERRITE MAGNET CFSM TO IMPROVE SPEED RESPONSE OF EPS SYSTEM
Interntionl Journl of Automotive Technology, Vol. 18, No. 3, pp. 499 504 (2017) DOI 10.1007/s12239 017 0049 x Copyright 2017 KSAE/ 096 13 pissn 1229 9138/ eissn 1976 3832 DESIGN OF FERRITE MAGNET CFSM
More informationAbstract. Keywords. 1. Introduction. Eric S. Sanches, José A. Santisteban
Engineering, 2014, 6, 655-669 Published Online October 2014 in SciRes. http://www.scirp.org/journl/eng http://dx.doi.org/10.4236/eng.2014.611065 Comprtive Study of Conventionl, Fuzzy Logic nd Neurl PID
More informationLazhar Roubache 1, *, Kamel Boughrara 1,Frédéric Dubas 2,andRachidIbtiouen 1
Progress In Electromgnetics Reserch B, Vol. 77, 85 11, 17 Semi-Anlyticl Modeling of Spoke-Type Permnent-Mgnet Mchines Considering the Iron Core Reltive Permebility: Subdomin Technique nd Tylor Polynomil
More informationENERGY-BASED METHOD FOR GAS TURBINE ENGINE DISK BURST SPEED CALCULATION
28 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES ENERGY-BASED METHOD FOR GAS TURBINE ENGINE DISK BURST SPEED CALCULATION Anton N. Servetnik Centrl Institute of Avition Motors, Moscow, Russi servetnik@cim.ru
More informationThe Influence of Interface and Semiconductor Bulk Traps Generated Under HEFS on MOSFET`s Electrical Characteristics
Proceedings of the 5th Smll Systems Simultion Symposium 2014, Niš, Seri, 12th-14th Ferury 2014 The Influence of Interfce nd Semiconductor Bulk Trps Generted Under HEFS on MOSFET`s Electricl Chrcteristics
More informationFig. 1. Open-Loop and Closed-Loop Systems with Plant Variations
ME 3600 Control ystems Chrcteristics of Open-Loop nd Closed-Loop ystems Importnt Control ystem Chrcteristics o ensitivity of system response to prmetric vritions cn be reduced o rnsient nd stedy-stte responses
More informationAdomian Decomposition Method with Green s. Function for Solving Twelfth-Order Boundary. Value Problems
Applied Mthemticl Sciences, Vol. 9, 25, no. 8, 353-368 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/.2988/ms.25.486 Adomin Decomposition Method with Green s Function for Solving Twelfth-Order Boundry
More information332:221 Principles of Electrical Engineering I Fall Hourly Exam 2 November 6, 2006
2:221 Principles of Electricl Engineering I Fll 2006 Nme of the student nd ID numer: Hourly Exm 2 Novemer 6, 2006 This is closed-ook closed-notes exm. Do ll your work on these sheets. If more spce is required,
More informationKINEMATICS OF RIGID BODIES
KINEMTICS OF RIGID ODIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. Description
More informationBend Forms of Circular Saws and Evaluation of their Mechanical Properties
ISSN 139 13 MATERIALS SCIENCE (MEDŽIAGOTYRA). Vol. 11, No. 1. 5 Bend Forms of Circulr s nd Evlution of their Mechnicl Properties Kristin UKVALBERGIENĖ, Jons VOBOLIS Deprtment of Mechnicl Wood Technology,
More informationGenetic Programming. Outline. Evolutionary Strategies. Evolutionary strategies Genetic programming Summary
Outline Genetic Progrmming Evolutionry strtegies Genetic progrmming Summry Bsed on the mteril provided y Professor Michel Negnevitsky Evolutionry Strtegies An pproch simulting nturl evolution ws proposed
More informationAMPERE CONGRESS AMPERE on Magnetic Resonance and Related Phenomena. Under the auspices of The GROUPEMENT AMPERE
AMPERE 2000 th 30 CONGRESS AMPERE on Mgnetic Resonnce nd Relted Phenomen Lison, Portugl, 23-2 July 2000 Under the uspices of The GROUPEMENT AMPERE Edited y: A.F. MARTINS, A.G. FEIO nd J.G. MOURA Sponsoring
More information1B40 Practical Skills
B40 Prcticl Skills Comining uncertinties from severl quntities error propgtion We usully encounter situtions where the result of n experiment is given in terms of two (or more) quntities. We then need
More information10 Vector Integral Calculus
Vector Integrl lculus Vector integrl clculus extends integrls s known from clculus to integrls over curves ("line integrls"), surfces ("surfce integrls") nd solids ("volume integrls"). These integrls hve
More informationENERGY LOSSES PREDICTION IN NON-ORIENTED SILICON IRON SHEETS
ENERGY LOSSES PREDICTION IN NON-ORIENTED SILICON IRON SHEETS GHEORGHE PĂLTÂNEA, VERONICA PĂLTÂNEA *1, HORIA GAVRILĂ Key words: Non-oriented silicon iron, Energy losses, Mgnetic ojects, Energy losses prediction,
More informationNew Expansion and Infinite Series
Interntionl Mthemticl Forum, Vol. 9, 204, no. 22, 06-073 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.2988/imf.204.4502 New Expnsion nd Infinite Series Diyun Zhng College of Computer Nnjing University
More informationMethods of Analysis and Selected Topics (dc)
Methods of Anlysis nd Selected Topics (dc) 8 Ojectives Become fmilir with the terminl chrcteristics of current source nd how to solve for the voltges nd currents of network using current sources nd/or
More informationDesigning Information Devices and Systems I Spring 2018 Homework 7
EECS 16A Designing Informtion Devices nd Systems I Spring 2018 omework 7 This homework is due Mrch 12, 2018, t 23:59. Self-grdes re due Mrch 15, 2018, t 23:59. Sumission Formt Your homework sumission should
More informationANALYSIS OF MECHANICAL PROPERTIES OF COMPOSITE SANDWICH PANELS WITH FILLERS
ANALYSIS OF MECHANICAL PROPERTIES OF COMPOSITE SANDWICH PANELS WITH FILLERS A. N. Anoshkin *, V. Yu. Zuiko, A.V.Glezmn Perm Ntionl Reserch Polytechnic University, 29, Komsomolski Ave., Perm, 614990, Russi
More informationSection 4: Integration ECO4112F 2011
Reding: Ching Chpter Section : Integrtion ECOF Note: These notes do not fully cover the mteril in Ching, ut re ment to supplement your reding in Ching. Thus fr the optimistion you hve covered hs een sttic
More informationGoals: Determine how to calculate the area described by a function. Define the definite integral. Explore the relationship between the definite
Unit #8 : The Integrl Gols: Determine how to clculte the re described by function. Define the definite integrl. Eplore the reltionship between the definite integrl nd re. Eplore wys to estimte the definite
More informationELECTRODYNAMIC FORCES BETWEEN TWO DC BUSBARS DISTRIBUTION SYSTEMS CONDUCTORS
U.P.B. Sci. Bull., Series C, Vol. 78, Iss., 16 ISSN 86-354 ELECTRODYNAMIC FORCES BETWEEN TWO DC BUSBARS DISTRIBUTION SYSTEMS CONDUCTORS Mri-Ctlin PETRESCU 1, Lucin PETRESCU This pper nlzes DC usr sstem
More informationu( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 2-18, pp 44-48): Determine the equation of the following graph.
nlyzing Dmped Oscilltions Prolem (Medor, exmple 2-18, pp 44-48): Determine the eqution of the following grph. The eqution is ssumed to e of the following form f ( t) = K 1 u( t) + K 2 e!"t sin (#t + $
More informationSOUND INTENSITY PROBE CALIBRATOR FOR FIELD USE: CALCULATING THE SOUND FIELD IN THE CALIBRATOR USING BOUNDARY ELEMENT MODELLING
Pge 1 of 1 SOUND INTENSITY PROBE CALIBRATOR FOR FIELD USE: CALCULATING THE SOUND FIELD IN THE CALIBRATOR USING BOUNDARY ELEMENT MODELLING PACS REFERENCE: 43.58 Fm Ginn, Bernrd; Olsen,Erling; Cutnd,Vicente;
More informationORDER REDUCTION USING POLE CLUSTERING AND FACTOR DIVISION METHOD
Author Nme et. l. / Interntionl Journl of New Technologies in Science nd Engineering Vol., Issue., 7, ISSN 9-78 ORDER REDUCTION USING POLE CLUSTERING AND FACTOR DIVISION METHOD A Chinn Nidu* G Dileep**
More informationMagnetic forces on a moving charge. EE Lecture 26. Lorentz Force Law and forces on currents. Laws of magnetostatics
Mgnetic forces on moving chrge o fr we ve studied electric forces between chrges t rest, nd the currents tht cn result in conducting medium 1. Mgnetic forces on chrge 2. Lws of mgnetosttics 3. Mgnetic
More informationI1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3
2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is
More informationIn the diagram below, the rotation continues until N-S alignment, resulting in lock-up that is, if nothing is done to prevent it.
25-1 DC motors DC motors re importnt in mny pplictions. In portble pplictions using bttery power, DC motors re nturl choice. DC mchines re lso used in pplictions where high strting torque nd ccurte speed
More informationStudy on the Calculation of Magnetic Force Based on the Equivalent Magnetic Charge Method
Avilble online t www.sciencedirect.com Physics Procedi 4 () 9 97 Interntionl Conference on Applied Physics nd Industril Engineering Study on the Clcultion of Mgnetic Force Bsed on the Equivlent Mgnetic
More informationCMDA 4604: Intermediate Topics in Mathematical Modeling Lecture 19: Interpolation and Quadrature
CMDA 4604: Intermedite Topics in Mthemticl Modeling Lecture 19: Interpoltion nd Qudrture In this lecture we mke brief diversion into the res of interpoltion nd qudrture. Given function f C[, b], we sy
More informationResistors. Consider a uniform cylinder of material with mediocre to poor to pathetic conductivity ( )
10/25/2005 Resistors.doc 1/7 Resistors Consider uniform cylinder of mteril with mediocre to poor to r. pthetic conductivity ( ) ˆ This cylinder is centered on the -xis, nd hs length. The surfce re of the
More informationChapter 9 Definite Integrals
Chpter 9 Definite Integrls In the previous chpter we found how to tke n ntiderivtive nd investigted the indefinite integrl. In this chpter the connection etween ntiderivtives nd definite integrls is estlished
More information1. a) Describe the principle characteristics and uses of the following types of PV cell: Single Crystal Silicon Poly Crystal Silicon
2001 1. ) Describe the principle chrcteristics nd uses of the following types of PV cell: Single Crystl Silicon Poly Crystl Silicon Amorphous Silicon CIS/CIGS Gllium Arsenide Multijunction (12 mrks) b)
More informationLecture 20: Numerical Integration III
cs4: introduction to numericl nlysis /8/0 Lecture 0: Numericl Integrtion III Instructor: Professor Amos Ron Scribes: Mrk Cowlishw, Yunpeng Li, Nthnel Fillmore For the lst few lectures we hve discussed
More informationELE B7 Power System Engineering. Unbalanced Fault Analysis
Power System Engineering Unblnced Fult Anlysis Anlysis of Unblnced Systems Except for the blnced three-phse fult, fults result in n unblnced system. The most common types of fults re single lineground
More informationLABYRINTH SEALS DYNAMIC COEFFICIENTS AND CRITICAL SPEED RESEARCH BASED ON CHILDS MODEL
Abstrct LABYINTH SALS DYNAMIC COFFICINTS AND CITICAL SPD SACH BASD ON CHILDS MODL M Wensheng, Hung Hi, Feng Guoqun AVIC Shenyng Aeroengine eserch Institute, Shenyng, Chin Keywords:lbyrinth sels, dynmics
More informationCONTRIBUTIONS TO THE STUDY OF TUBULAR
TECHNICAL UNIVERSITY OF CLUJ-NAPOCA IOANA-CORNELIA VESE CONTRIBUTIONS TO THE STUDY OF TUBULAR LINEAR ELECTRIC ACTUATORS PH.D. THESIS Ph.D. Supervisor: Prof.Dr.ing. Mirce M. RADULESCU ABSTRACT OCTOBER 2010
More information13: Diffusion in 2 Energy Groups
3: Diffusion in Energy Groups B. Rouben McMster University Course EP 4D3/6D3 Nucler Rector Anlysis (Rector Physics) 5 Sept.-Dec. 5 September Contents We study the diffusion eqution in two energy groups
More informationMeasuring Electron Work Function in Metal
n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd
More informationCOUPLING OF DAMAGE MECHANICS AND PROBABILISTIC APPROACH FOR LIFE-TIME PREDICTION OF COMPOSITE STRUCTURES
ORAL/POSTER REFERENCE : COUPLING OF DAMAGE MECHANICS AND PROBABILISTIC APPROACH FOR LIFE-TIME PREDICTION OF COMPOSITE STRUCTURES Y. Bruner, J. Renrd, D. Jeulin nd A. Thionnet Centre des Mtériux Pierre-Mrie
More informationProperties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives
Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn
More informationNUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by.
NUMERICAL INTEGRATION 1 Introduction The inverse process to differentition in clculus is integrtion. Mthemticlly, integrtion is represented by f(x) dx which stnds for the integrl of the function f(x) with
More informationChapter 6 Electrostatic Boundary Value Problems. Dr. Talal Skaik
Chpter 6 Electrosttic Boundry lue Problems Dr. Tll Skik 1 1 Introduction In previous chpters, E ws determined by coulombs lw or Guss lw when chrge distribution is known, or potentil is known throughout
More informationHomework Assignment #1 Solutions
Physics 56 Winter 8 Textook prolems: h. 8: 8., 8.4 Homework Assignment # Solutions 8. A trnsmission line consisting of two concentric circulr cylinders of metl with conductivity σ nd skin depth δ, s shown,
More information5.7 Improper Integrals
458 pplictions of definite integrls 5.7 Improper Integrls In Section 5.4, we computed the work required to lift pylod of mss m from the surfce of moon of mss nd rdius R to height H bove the surfce of the
More informationCS12N: The Coming Revolution in Computer Architecture Laboratory 2 Preparation
CS2N: The Coming Revolution in Computer Architecture Lortory 2 Preprtion Ojectives:. Understnd the principle of sttic CMOS gte circuits 2. Build simple logic gtes from MOS trnsistors 3. Evlute these gtes
More informationWeek 10: Line Integrals
Week 10: Line Integrls Introduction In this finl week we return to prmetrised curves nd consider integrtion long such curves. We lredy sw this in Week 2 when we integrted long curve to find its length.
More informationTHERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION
XX IMEKO World Congress Metrology for Green Growth September 9,, Busn, Republic of Kore THERMAL EXPANSION COEFFICIENT OF WATER FOR OLUMETRIC CALIBRATION Nieves Medin Hed of Mss Division, CEM, Spin, mnmedin@mityc.es
More informationPlates on elastic foundation
Pltes on elstic foundtion Circulr elstic plte, xil-symmetric lod, Winkler soil (fter Timoshenko & Woinowsky-Krieger (1959) - Chpter 8) Prepred by Enzo Mrtinelli Drft version ( April 016) Introduction Winkler
More informationPotential Changes Around a Circuit. You must be able to calculate potential changes around a closed loop.
Tody s gend: Potentil Chnges Around Circuit. You must e le to clculte potentil chnges round closed loop. Electromotive force (EMF), Terminl Voltge, nd Internl Resistnce. You must e le to incorporte ll
More informationEffects of peripheral drilling moment on delamination using special drill bits
journl of mterils processing technology 01 (008 471 476 journl homepge: www.elsevier.com/locte/jmtprotec Effects of peripherl illing moment on delmintion using specil ill bits C.C. Tso,, H. Hocheng b Deprtment
More informationPhysics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018
Physics 201 Lb 3: Mesurement of Erth s locl grvittionl field I Dt Acquisition nd Preliminry Anlysis Dr. Timothy C. Blck Summer I, 2018 Theoreticl Discussion Grvity is one of the four known fundmentl forces.
More informationChapter 6 Techniques of Integration
MA Techniques of Integrtion Asst.Prof.Dr.Suprnee Liswdi Chpter 6 Techniques of Integrtion Recll: Some importnt integrls tht we hve lernt so fr. Tle of Integrls n+ n d = + C n + e d = e + C ( n ) d = ln
More informationFully Kinetic Simulations of Ion Beam Neutralization
Fully Kinetic Simultions of Ion Bem Neutrliztion Joseph Wng University of Southern Cliforni Hideyuki Usui Kyoto University E-mil: josephjw@usc.edu; usui@rish.kyoto-u.c.jp 1. Introduction Ion em emission/neutrliztion
More informationChapter 4: Techniques of Circuit Analysis. Chapter 4: Techniques of Circuit Analysis
Chpter 4: Techniques of Circuit Anlysis Terminology Node-Voltge Method Introduction Dependent Sources Specil Cses Mesh-Current Method Introduction Dependent Sources Specil Cses Comprison of Methods Source
More informationSection 6.1 INTRO to LAPLACE TRANSFORMS
Section 6. INTRO to LAPLACE TRANSFORMS Key terms: Improper Integrl; diverge, converge A A f(t)dt lim f(t)dt Piecewise Continuous Function; jump discontinuity Function of Exponentil Order Lplce Trnsform
More informationBoolean algebra.
http://en.wikipedi.org/wiki/elementry_boolen_lger Boolen lger www.tudorgir.com Computer science is not out computers, it is out computtion nd informtion. computtion informtion computer informtion Turing
More informationEquations of Motion. Figure 1.1.1: a differential element under the action of surface and body forces
Equtions of Motion In Prt I, lnce of forces nd moments cting on n component ws enforced in order to ensure tht the component ws in equilirium. Here, llownce is mde for stresses which vr continuousl throughout
More informationResistive Network Analysis
C H A P T E R 3 Resistive Network Anlysis his chpter will illustrte the fundmentl techniques for the nlysis of resistive circuits. The methods introduced re sed on the circuit lws presented in Chpter 2:
More informationThis chapter will show you. What you should already know. 1 Write down the value of each of the following. a 5 2
1 Direct vrition 2 Inverse vrition This chpter will show you how to solve prolems where two vriles re connected y reltionship tht vries in direct or inverse proportion Direct proportion Inverse proportion
More informationMASKING OF FERROMAGNETIC ELLIPTICAL SHELL IN TRANSVERSE MAGNETIC FIELD
POZNAN UNVE RSTY OF TE HNOLOGY AADE M JOURNALS No 7 Electricl Engineering Kzimierz JAKUUK* Mirosł WOŁOSZYN* Peł ZMNY* MASKNG OF FERROMAGNET ELLPTAL SHELL N TRANSVERSE MAGNET FELD A ferromgnetic oject,
More informationNote 12. Introduction to Digital Control Systems
Note Introduction to Digitl Control Systems Deprtment of Mechnicl Engineering, University Of Ssktchewn, 57 Cmpus Drive, Ssktoon, SK S7N 5A9, Cnd . Introduction A digitl control system is one in which the
More informationINTRODUCTION. The three general approaches to the solution of kinetics problems are:
INTRODUCTION According to Newton s lw, prticle will ccelerte when it is subjected to unblnced forces. Kinetics is the study of the reltions between unblnced forces nd the resulting chnges in motion. The
More informationMath 1B, lecture 4: Error bounds for numerical methods
Mth B, lecture 4: Error bounds for numericl methods Nthn Pflueger 4 September 0 Introduction The five numericl methods descried in the previous lecture ll operte by the sme principle: they pproximte the
More informationELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, OAKLAND UNIVERSITY ECE-2700: Digital Logic Design Fall Notes - Unit 1
INTRODUTION TO LOGI IRUITS Notes - Unit 1 OOLEN LGER This is the oundtion or designing nd nlyzing digitl systems. It dels with the cse where vriles ssume only one o two vlues: TRUE (usully represented
More informationPredict Global Earth Temperature using Linier Regression
Predict Globl Erth Temperture using Linier Regression Edwin Swndi Sijbt (23516012) Progrm Studi Mgister Informtik Sekolh Teknik Elektro dn Informtik ITB Jl. Gnesh 10 Bndung 40132, Indonesi 23516012@std.stei.itb.c.id
More informationJim Lambers MAT 169 Fall Semester Lecture 4 Notes
Jim Lmbers MAT 169 Fll Semester 2009-10 Lecture 4 Notes These notes correspond to Section 8.2 in the text. Series Wht is Series? An infinte series, usully referred to simply s series, is n sum of ll of
More information1 Error Analysis of Simple Rules for Numerical Integration
cs41: introduction to numericl nlysis 11/16/10 Lecture 19: Numericl Integrtion II Instructor: Professor Amos Ron Scries: Mrk Cowlishw, Nthnel Fillmore 1 Error Anlysis of Simple Rules for Numericl Integrtion
More informationIntro to Nuclear and Particle Physics (5110)
Intro to Nucler nd Prticle Physics (5110) Feb, 009 The Nucler Mss Spectrum The Liquid Drop Model //009 1 E(MeV) n n(n-1)/ E/[ n(n-1)/] (MeV/pir) 1 C 16 O 0 Ne 4 Mg 7.7 14.44 19.17 8.48 4 5 6 6 10 15.4.41
More informationChapter E - Problems
Chpter E - Prolems Blinn College - Physics 2426 - Terry Honn Prolem E.1 A wire with dimeter d feeds current to cpcitor. The chrge on the cpcitor vries with time s QHtL = Q 0 sin w t. Wht re the current
More informationExamination Electrical Machines and Drives Et4-117 Thursday, October 30, 2003 from 9.00 to 12.00
Exmintion Electricl Mchine nd Drive Et4-117 Thurdy, Octoer 30, 003 from 900 to 100 Thi exmintion conit of 6 prolem The numer efore prolem indicte how mny point cn e erned with thi prolem 15 Prolem 1 c
More informationProblem Solving 7: Faraday s Law Solution
MASSACHUSETTS NSTTUTE OF TECHNOLOGY Deprtment of Physics: 8.02 Prolem Solving 7: Frdy s Lw Solution Ojectives 1. To explore prticulr sitution tht cn led to chnging mgnetic flux through the open surfce
More information4.1. Probability Density Functions
STT 1 4.1-4. 4.1. Proility Density Functions Ojectives. Continuous rndom vrile - vers - discrete rndom vrile. Proility density function. Uniform distriution nd its properties. Expected vlue nd vrince of
More informationNew data structures to reduce data size and search time
New dt structures to reduce dt size nd serch time Tsuneo Kuwbr Deprtment of Informtion Sciences, Fculty of Science, Kngw University, Hirtsuk-shi, Jpn FIT2018 1D-1, No2, pp1-4 Copyright (c)2018 by The Institute
More information10 D. Chakraborty, D. Guha / IJIM Vol. 2, No. 1 (2010) 9-20
Aville online t http://ijim.sriu.c.ir Int. J. Industril Mthemtics Vol., No. (00) 9-0 Addition of Two Generlized Fuzzy Numers D. Chkrorty, D. Guh Deprtment of Mthemtics, IIT-Khrgpur Khrgpur-730, Indi Received
More informationThis final is a three hour open book, open notes exam. Do all four problems.
Physics 55 Fll 27 Finl Exm Solutions This finl is three hour open book, open notes exm. Do ll four problems. [25 pts] 1. A point electric dipole with dipole moment p is locted in vcuum pointing wy from
More informationAvailable online at ScienceDirect. Procedia Engineering 190 (2017 )
Aville online t www.sciencedirect.com ScienceDirect Procedi Engineering 19 (217 ) 237 242 Structurl nd Physicl Aspects of Construction Engineering Numericl Anlysis of Steel Portl Frme Exposed to Fire Lenk
More informationINEQUALITIES FOR TWO SPECIFIC CLASSES OF FUNCTIONS USING CHEBYSHEV FUNCTIONAL. Mohammad Masjed-Jamei
Fculty of Sciences nd Mthemtics University of Niš Seri Aville t: http://www.pmf.ni.c.rs/filomt Filomt 25:4 20) 53 63 DOI: 0.2298/FIL0453M INEQUALITIES FOR TWO SPECIFIC CLASSES OF FUNCTIONS USING CHEBYSHEV
More information