In-situ calibration of rotating coil magnetic measurement systems: a case study on Linac4 magnets at CERN
|
|
- Cuthbert Poole
- 5 years ago
- Views:
Transcription
1 7 th Symposium IMEKO T 4, 3 rd Symposium IMEKO T 9 ad 5 th IWAD Workshop Istrumetatio for the IT Era Sept. 8-,, Kosice, Slovakia I-situ calibratio of rotatig coil magetic measuremet systems: a case study o Liac4 magets at EN Pasquale Arpaia,, Marco Buzio, Giacarlo Golluccio,, Ferado Mateo Departmet of Egieerig, Uiversity of Saio, orso Garibaldi 7, 8 Beeveto, Italy. Ph : , Fax: , arpaia@uisaio.it EN, Europea Orgaizatio for Nuclear esearch Geeva 3, Switzerlad Ph: , giacarlo.golluccio@cer.ch; marco.buzio@cer.ch Abstract- A i-situ procedure for calibratig the equivalet radius ad width of the coil trasducer i rotatig mode measuremets for magetic field quality aalysis is proposed. The stadard calibratio procedure is ot suitable whe the coil is loger tha the maget uder test, because a average value of the radius ad of the width alog the legth as a whole is obtaied. This problem icreases for small coils used i small-aperture magets, such as quadrupoles of ew-geeratio liear accelerators. I the paper, the problem of the coil parameter calibratio is highlighted ad the the proposed calibratio method ad the correspodig measuremet statio are illustrated. Experimetal results of a case study o the maget series of the ew liear particle accelerator LINA4, desiged to itesify the proto flux curretly available i the accelerator chai at the Europea Orgaizatio for Nuclear esearch (EN), are reported. I. Itroductio The most accurate techique of field quality measuremet for particle accelerator magets is based o a trasducer coil rotatig ito the maget apertures []. A measuremet of the magetic flux liked to the rotatig coil as a fuctio of the agular positio is delivered. The mai quatities of iterest for field quality characterizatio are the harmoic coiciets of the D field expasio []. Those coiciets deped essetially o the legth, the width ad the rotatio radius of the coils. By meas of mechaical measuremets practically oly the legth ca be obtaied accurately eough (+ -3 ~ -4 ). Magetic measuremets are the best optio because all o-idealities are automatically icluded i the results [3]. The equivalet width ad radius have to be determied by rotatig the coil i a kow uiform dipole field ad i a uiform quadrupolar magetic field respectively. The classical approach to the coil calibratio [4], usig a uiform magetic field over the whole coil legth, gives a average value for the radius ad width which is suitable whe the coil is shorter tha the maget uder test or i the ideal case of perfectly costat width. This procedure fails whe the coil geometry is ot regular, ad the mechaical errors become more ifluet whe the coil size is reduced. At EN, a ew liear accelerator Liac4 is curretly beig built to replace the old Liac. The trasverse focusig to the beam is give by several Permaet Maget Quadrupoles (PMQ) [5] with a aperture mm ad 45 mm legth. The small dimesios of the support used to build up the coil (i this case mm of legth, less tha mm i width ad mm thickess) make the widig process more difficult. Low rigidity i the widig ca easily occur at the ed side ad i the middle of the coil. I this paper, first the theoretical backgroud of the rotatig coil magetic measuremet is illustrated, focusig o the coil sesitivity parameter calculatio. I sectio II, the proposed coil calibratio method is show i the specific case of a quadrupole maget. The last sectio will report about the measuremet statio ad the experimetal results o Liac4 PMQs. II. otatig coil backgroud I the classical D harmoic aalysis, the field harmoic cotet is proportioal to the DFT coiciets Ψ of the flux samples Φ k as a fuctio of the agular positio: Ψ N k Φ k e ( k ) πi( ) From eq. (), the magetic field harmoic coiciets are derived []: ()
2 7 th Symposium IMEKO T 4, 3 rd Symposium IMEKO T 9 ad 5 th IWAD Workshop Istrumetatio for the IT Era Sept. 8-,, Kosice, Slovakia N κ where is the erece radius (typically the trasverse size of the particle beam), N is the umber of agular poits per tur ad κ are complex geometric calibratio coiciets or coil sesitivity factors. These represet the coil geometry completely, ad they are idepedet of the measured magetic field. For a perfect radial coil, iitially o the horizotal plae (zero iitial phase), with a ifiitesimally thi widig cross-sectio, the factors reduce to a real umber [3]: NT Lc κ W + Ψ + W where is the average radius, L c is the legth of the coil, is the harmoic order, N T is the umber of coil turs ad W is the width of the coil. I other words, the coil sesitivity factors for a radial coil ca be computed from the total equivalet area A c of the coil (give by the legth, the width ad the umber of turs) ad the equivalet radius (average betwee the two coil eds). All κ are proportioal to total coil area A c ad icrease like radius - ad icrease with W. I the stadard case A c is estimated magetically rotatig the coil i a uiform kow erece dipole ad i a erece quadrupole oce fixed the legth of the coil by meas of geometrical measuremets [3]. The harmoic coiciets of eq. (3) are erred to the coil erece axes defied by the zero erece of the agular ecoder []. A traslatio ad a rotatio i the -D complex plae are ecessary to er the harmoic coiciets to the maget erece frame [6]. The distace vector z x + i y betwee the coil erece frame ad the maget erece frame (figure ), which for a quadrupole maget is cetred o the magetic axis where B, ca be calculated from []: () (3) Y z (4) Y z We X X a) b) Figure : a) radial coil rotatig i a quadrupole field. Y-X is the maget frame, Y -X is the coil frame. b) details of the compesatio scheme with two ested radial coils, the ier coil has half of the width W but has the double the umber of turs.
3 7 th Symposium IMEKO T 4, 3 rd Symposium IMEKO T 9 ad 5 th IWAD Workshop Istrumetatio for the IT Era Sept. 8-,, Kosice, Slovakia II. I-situ coil calibratio method A. alibratio Method Whe the coil width irregularities are importat ad oly a part of the coil is immersed i the magetic field, the geeral method described above must be completed maget uder test istead of the stadard ereces ( isitu calibratio). I priciple, if the maget is moved trasversally by a give distace ad the quadrupole compoet is kow, the radius ad the equivalet width W of the coil ca be recostructed directly. I other words, the two parameters ca be computed by calculatig κ ad κ from eq. (3) ad substitutig them i eq. (): Ψ NNT LcW Ψ3 NN L W T c (5) Assumig for istace a purely horizotal movemet x, from (4) ad (5), if the phase error betwee the coil frame ad the maget frame is egligible, ca be derived: Ψ 3 x e (6) Ψ The maget stregth, correspodig to the itegrated quadrupole gradiet (GdL), is used to calibrate the W : (7) ad: GdL w L c { ψ } e 3 GdL The erece value of the gradiet GdL must be obtaied i this method by a idepedet measuremet. (8) III. Experimetal esults () The coil used to measure this maget is mm log with a exteral diameter of 9 mm. It presets two ested radial widigs o the same plae (figure b). The exteral oe geerates the absolute sigal relative to the mai field of the quadrupole. The ier oe is coected i series oppositio to the exteral coil, i order to geerate a sigal more sesitive to the high order harmoics []. Whe the two coils are coected i electrical oppositio the κ of the series, as well the κ, are zero. This relatio ca be obtaied oly if the two coils have the same equivalet surface, thus the iteral widig, sice it has half of the W, it has twice the umber of turs. A. Measuremet statio architecture I Figure, the equipmet used to calibrate the coil directly o the measuremet system is depicted. The agular erece of the ecoder is prelimiarily aliged to the gravity by meas of a sesor tilt o the shaft. A -D traslatio stage, equipped by a liear ecoder of.3 μm resolutio ad μm repeatability, allows the permaet quadrupole to be moved i the x-y directio. The agular error ad the offset of the axes origis betwee the maget erece frame ad the -D stage were foud by movig the maget first alog the x, the i y directio [7] ad measurig the displacemet z from eq.(4). The agular error of.5 ad the origi displacemet of 3 μm i the x directio ad of 6 μm i y will ot affect the calibratio procedure. The measuremet system is a ew rotatig bech aimed at testig the PMQ magets of the Liac4 drift tube [5].
4 7 th Symposium IMEKO T 4, 3 rd Symposium IMEKO T 9 ad 5 th IWAD Workshop Istrumetatio for the IT Era Sept. 8-,, Kosice, Slovakia Figure : the rotatig coil ad the calibratio system. B. Measuremet procedure With the help of the D stage, the maget is first cetred with respect to the rotatig coil by miimizig iteratively eq. (5). The coil radius ad the equivalet width ca be measured i 4 steps: i) move the maget alog the x axis to a give positio; ii) make a cotiuous rotatio measuremet of the flux as a fuctio of the agular positio; iii) calculate the FFT obtaiig the d ad the 3 rd harmoic of the measured flux (from (5), a movemet i the x axis correspods to a variatio i the real part of the, ad a movemet i the coordiate y affects the imagiary part of the d harmoic coiciet); iv) calculate the from eq. (7) ad W from eq. (9).. esults The procedure was applied to the Liac4 shaft usig a prototype permaet quadrupole measured with the stretched wire system. The SSW [8] measured a itegrated gradiet of.435 Tm/m for this maget. The logitudial positio was fixed at mm from the left coil edge, where the width variatio is liear ad is far from the coil ed side. The repeatability of the radius ad of the coil area is better tha + µm. The ucertaity of the two parameters calculated propagatig the error from eq. (6) ad (8) is + μm for the radius ad + 6 µm for the equivalet width. The exteral coil is affected i the cetral part by a strog variatio i the width profile. The iteral coil is ested i the exteral oe, thus its width is more uiform. Nevertheless, the radius variatio with respect to the axis rotatio reduces the uiformity of the measuremet (the variatio i the measuremet is about +5 % alog the mm of the exteral coil legth ad of +3 % for iteral coil). The accuracy of the gradiet measuremet is withi the specificatios oly for the calibrated coil regios (better tha.3 %, with respect to the required %). Oce the coils are calibrated i a specific logitudial positio usig the erece maget, the calculated κ are exploited to evaluate the magetic stregth ad harmoic quality of several quadrupoles of the Liac4 drift tube tak. The quadrupole stregth measured is withi the toleraces of +.5% required from the beam optic specificatio, eve if the ucertaity of the rotatig coil measuremet (+.8 Tm/m) is higher tha the oe of the stretched wire (+. Tm/m). II. oclusios I this paper, a ovel procedure to calibrate directly i situ the coil sesitivity geometry parameter is proposed. This procedure represets a improvemet with respect to the stadard oe, which returs a average value of the coil radius ad width alog the whole legth of the coil, is ot accurate eough whe the magetic legth is shorter tha the coil legth ad the coil surface geometry is poor. The ew procedure is applied to the prototype coils developed to measure the field quality of six permaet quadrupoles of the Liac4 drift tube. The MS error of the magetic stregth measuremet, compared to the stretched wire system take as the erece, is improved from 6 % to.%. Sice the tolerace required for the accelerator is %, the ew procedure ca be used with cofidece to avoid systematic measuremets with the stretched wire system. efereces [] A. Jai, Harmoic coils, AS o measuremet ad aligmet of accelerator ad detector magets, EN 3
5 7 th Symposium IMEKO T 4, 3 rd Symposium IMEKO T 9 ad 5 th IWAD Workshop Istrumetatio for the IT Era Sept. 8-,, Kosice, Slovakia 98-5, August 998. [] L. Bottura, Stadard aalysis procedures for field quality measuremet of the LH magets part I: Harmoics, EN-iteral ote, February. [3] M. Buzio, Maifacturig ad calibratio of search coils, EN Accelerator school, Jue 9, Bruges, Belgium. [4] O. Dukel, oil Maufacture, Assembly ad Magetic alibratio Facility for Warm ad old Magetic Measuremets of LH Supercoductig Magets, 4 th Iteratioal Magetic Measuremet Workshop IMMW4, September 5, Geeva, Switzerlad. [5]. Garoby, G. Bellodi, F. Gerigk, K. Hake, A.M. Lombardi, M. Pasii,. ossi, E.Z. Sargsya, M. Vretear, Liac4, a ew ijector for the EN PS Booster, Proceedigs of Europea Particle Accelerator oferece 6, Ediburgh [6] L. Walckiers, Harmoic oils, EN Accelerator school, Jue 9, Bruges, Belgium. [7] S.. Gottschalk, K. Kagas, D. J. Taylor, W. Thayer, a Air Bearig otatig oil Magetic Measuremet System, Proceedigs of Europea Particle Accelerator oferece 5, Koxville. [8] L. Walckiers, Magetic measuremet with coils ad wires, EN Accelerator school, Jue 9, Bruges, Belgium. 4
OFFSET CORRECTION IN A DIGITAL INTEGRATOR FOR ROTATING COIL MEASUREMENTS
XX IMEKO World Cogress Metrology for Gree Growth September 9 4, 0, Busa, Republic of Korea OFFSET CORRECTION IN A DIGITAL INTEGRATOR FOR ROTATING COIL MEASUREMENTS P. Arpaia,, P. Cimmio,, L. De Vito, ad
More informationRecent Magnetic Measurement Activities at BNL
Recet Magetic Measuremet Activities at BNL Aimesh Jai (O behalf of the Maget Test Group) Supercoductig Maget Divisio Brookhave Natioal Laboratory Upto, New York 11973-5000, USA 1 Itroductio Magetic measuremet
More informationProbability, Expectation Value and Uncertainty
Chapter 1 Probability, Expectatio Value ad Ucertaity We have see that the physically observable properties of a quatum system are represeted by Hermitea operators (also referred to as observables ) such
More information17 Phonons and conduction electrons in solids (Hiroshi Matsuoka)
7 Phoos ad coductio electros i solids Hiroshi Matsuoa I this chapter we will discuss a miimal microscopic model for phoos i a solid ad a miimal microscopic model for coductio electros i a simple metal.
More information577. Estimation of surface roughness using high frequency vibrations
577. Estimatio of surface roughess usig high frequecy vibratios V. Augutis, M. Sauoris, Kauas Uiversity of Techology Electroics ad Measuremets Systems Departmet Studetu str. 5-443, LT-5368 Kauas, Lithuaia
More informationMeasurement uncertainty of the sound absorption
Measuremet ucertaity of the soud absorptio coefficiet Aa Izewska Buildig Research Istitute, Filtrowa Str., 00-6 Warsaw, Polad a.izewska@itb.pl 6887 The stadard ISO/IEC 705:005 o the competece of testig
More informationA statistical method to determine sample size to estimate characteristic value of soil parameters
A statistical method to determie sample size to estimate characteristic value of soil parameters Y. Hojo, B. Setiawa 2 ad M. Suzuki 3 Abstract Sample size is a importat factor to be cosidered i determiig
More informationFluid Physics 8.292J/12.330J % (1)
Fluid Physics 89J/133J Problem Set 5 Solutios 1 Cosider the flow of a Euler fluid i the x directio give by for y > d U = U y 1 d for y d U + y 1 d for y < This flow does ot vary i x or i z Determie the
More informationAnalytic Continuation
Aalytic Cotiuatio The stadard example of this is give by Example Let h (z) = 1 + z + z 2 + z 3 +... kow to coverge oly for z < 1. I fact h (z) = 1/ (1 z) for such z. Yet H (z) = 1/ (1 z) is defied for
More informationProvläsningsexemplar / Preview TECHNICAL REPORT INTERNATIONAL SPECIAL COMMITTEE ON RADIO INTERFERENCE
TECHNICAL REPORT CISPR 16-4-3 2004 AMENDMENT 1 2006-10 INTERNATIONAL SPECIAL COMMITTEE ON RADIO INTERFERENCE Amedmet 1 Specificatio for radio disturbace ad immuity measurig apparatus ad methods Part 4-3:
More informationPrinciple Of Superposition
ecture 5: PREIMINRY CONCEP O RUCUR NYI Priciple Of uperpositio Mathematically, the priciple of superpositio is stated as ( a ) G( a ) G( ) G a a or for a liear structural system, the respose at a give
More informationDISTRIBUTION LAW Okunev I.V.
1 DISTRIBUTION LAW Okuev I.V. Distributio law belogs to a umber of the most complicated theoretical laws of mathematics. But it is also a very importat practical law. Nothig ca help uderstad complicated
More informationCHAPTER 8 SYSTEMS OF PARTICLES
CHAPTER 8 SYSTES OF PARTICLES CHAPTER 8 COLLISIONS 45 8. CENTER OF ASS The ceter of mass of a system of particles or a rigid body is the poit at which all of the mass are cosidered to be cocetrated there
More informationPILOT STUDY ON THE HORIZONTAL SHEAR BEHAVIOUR OF FRP RUBBER ISOLATORS
Asia-Pacific Coferece o FRP i Structures (APFIS 2007) S.T. Smith (ed) 2007 Iteratioal Istitute for FRP i Costructio PILOT STUDY ON THE HORIZONTAL SHEAR BEHAVIOUR OF FRP RUBBER ISOLATORS T.B. Peg *, J.Z.
More informationCEE 522 Autumn Uncertainty Concepts for Geotechnical Engineering
CEE 5 Autum 005 Ucertaity Cocepts for Geotechical Egieerig Basic Termiology Set A set is a collectio of (mutually exclusive) objects or evets. The sample space is the (collectively exhaustive) collectio
More information6 Sample Size Calculations
6 Sample Size Calculatios Oe of the major resposibilities of a cliical trial statisticia is to aid the ivestigators i determiig the sample size required to coduct a study The most commo procedure for determiig
More informationFAILURE CRITERIA: MOHR S CIRCLE AND PRINCIPAL STRESSES
LECTURE Third Editio FAILURE CRITERIA: MOHR S CIRCLE AND PRINCIPAL STRESSES A. J. Clark School of Egieerig Departmet of Civil ad Evirometal Egieerig Chapter 7.4 b Dr. Ibrahim A. Assakkaf SPRING 3 ENES
More informationProblem Cosider the curve give parametrically as x = si t ad y = + cos t for» t» ß: (a) Describe the path this traverses: Where does it start (whe t =
Mathematics Summer Wilso Fial Exam August 8, ANSWERS Problem 1 (a) Fid the solutio to y +x y = e x x that satisfies y() = 5 : This is already i the form we used for a first order liear differetial equatio,
More informationTwo or more points can be used to describe a rigid body. This will eliminate the need to define rotational coordinates for the body!
OINTCOORDINATE FORMULATION Two or more poits ca be used to describe a rigid body. This will elimiate the eed to defie rotatioal coordiates for the body i z r i i, j r j j rimary oits: The coordiates of
More informationHydrogen (atoms, molecules) in external fields. Static electric and magnetic fields Oscyllating electromagnetic fields
Hydroge (atoms, molecules) i exteral fields Static electric ad magetic fields Oscyllatig electromagetic fields Everythig said up to ow has to be modified more or less strogly if we cosider atoms (ad ios)
More informationDamped Vibration of a Non-prismatic Beam with a Rotational Spring
Vibratios i Physical Systems Vol.6 (0) Damped Vibratio of a No-prismatic Beam with a Rotatioal Sprig Wojciech SOCHACK stitute of Mechaics ad Fudametals of Machiery Desig Uiversity of Techology, Czestochowa,
More informationWe will conclude the chapter with the study a few methods and techniques which are useful
Chapter : Coordiate geometry: I this chapter we will lear about the mai priciples of graphig i a dimesioal (D) Cartesia system of coordiates. We will focus o drawig lies ad the characteristics of the graphs
More informationSPEC/4/PHYSI/SPM/ENG/TZ0/XX PHYSICS PAPER 1 SPECIMEN PAPER. 45 minutes INSTRUCTIONS TO CANDIDATES
SPEC/4/PHYSI/SPM/ENG/TZ0/XX PHYSICS STANDARD LEVEL PAPER 1 SPECIMEN PAPER 45 miutes INSTRUCTIONS TO CANDIDATES Do ot ope this examiatio paper util istructed to do so. Aswer all the questios. For each questio,
More informationSECTION 2 Electrostatics
SECTION Electrostatics This sectio, based o Chapter of Griffiths, covers effects of electric fields ad forces i static (timeidepedet) situatios. The topics are: Electric field Gauss s Law Electric potetial
More informationThe standard deviation of the mean
Physics 6C Fall 20 The stadard deviatio of the mea These otes provide some clarificatio o the distictio betwee the stadard deviatio ad the stadard deviatio of the mea.. The sample mea ad variace Cosider
More informationPhysics Supplement to my class. Kinetic Theory
Physics Supplemet to my class Leaers should ote that I have used symbols for geometrical figures ad abbreviatios through out the documet. Kietic Theory 1 Most Probable, Mea ad RMS Speed of Gas Molecules
More informationTRACEABILITY SYSTEM OF ROCKWELL HARDNESS C SCALE IN JAPAN
HARDMEKO 004 Hardess Measuremets Theory ad Applicatio i Laboratories ad Idustries - November, 004, Washigto, D.C., USA TRACEABILITY SYSTEM OF ROCKWELL HARDNESS C SCALE IN JAPAN Koichiro HATTORI, Satoshi
More informationFundamental Concepts: Surfaces and Curves
UNDAMENTAL CONCEPTS: SURACES AND CURVES CHAPTER udametal Cocepts: Surfaces ad Curves. INTRODUCTION This chapter describes two geometrical objects, vi., surfaces ad curves because the pla a ver importat
More informationWHAT IS THE PROBABILITY FUNCTION FOR LARGE TSUNAMI WAVES? ABSTRACT
WHAT IS THE PROBABILITY FUNCTION FOR LARGE TSUNAMI WAVES? Harold G. Loomis Hoolulu, HI ABSTRACT Most coastal locatios have few if ay records of tsuami wave heights obtaied over various time periods. Still
More informationOBJECTIVES. Chapter 1 INTRODUCTION TO INSTRUMENTATION FUNCTION AND ADVANTAGES INTRODUCTION. At the end of this chapter, students should be able to:
OBJECTIVES Chapter 1 INTRODUCTION TO INSTRUMENTATION At the ed of this chapter, studets should be able to: 1. Explai the static ad dyamic characteristics of a istrumet. 2. Calculate ad aalyze the measuremet
More informationTopic 9: Sampling Distributions of Estimators
Topic 9: Samplig Distributios of Estimators Course 003, 2016 Page 0 Samplig distributios of estimators Sice our estimators are statistics (particular fuctios of radom variables), their distributio ca be
More informationLECTURE 14. Non-linear transverse motion. Non-linear transverse motion
LETURE 4 No-liear trasverse motio Floquet trasformatio Harmoic aalysis-oe dimesioal resoaces Two-dimesioal resoaces No-liear trasverse motio No-liear field terms i the trajectory equatio: Trajectory equatio
More informationREGRESSION (Physics 1210 Notes, Partial Modified Appendix A)
REGRESSION (Physics 0 Notes, Partial Modified Appedix A) HOW TO PERFORM A LINEAR REGRESSION Cosider the followig data poits ad their graph (Table I ad Figure ): X Y 0 3 5 3 7 4 9 5 Table : Example Data
More informationVibratory Motion. Prof. Zheng-yi Feng NCHU SWC. National CHung Hsing University, Department of Soil and Water Conservation
Vibratory Motio Prof. Zheg-yi Feg NCHU SWC 1 Types of vibratory motio Periodic motio Noperiodic motio See Fig. A1, p.58 Harmoic motio Periodic motio Trasiet motio impact Trasiet motio earthquake A powerful
More informationFrequency Domain Filtering
Frequecy Domai Filterig Raga Rodrigo October 19, 2010 Outlie Cotets 1 Itroductio 1 2 Fourier Represetatio of Fiite-Duratio Sequeces: The Discrete Fourier Trasform 1 3 The 2-D Discrete Fourier Trasform
More informationR is a scalar defined as follows:
Math 8. Notes o Dot Product, Cross Product, Plaes, Area, ad Volumes This lecture focuses primarily o the dot product ad its may applicatios, especially i the measuremet of agles ad scalar projectio ad
More informationStatistics 511 Additional Materials
Cofidece Itervals o mu Statistics 511 Additioal Materials This topic officially moves us from probability to statistics. We begi to discuss makig ifereces about the populatio. Oe way to differetiate probability
More informationFACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING. Lectures
FACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING Lectures MODULE 5 STATISTICS II. Mea ad stadard error of sample data. Biomial distributio. Normal distributio 4. Samplig 5. Cofidece itervals
More informationThe Michelson Interferometer
The Michelso Iterferometer Ady Chmileko, 0310799 Istructor: Jeff Gardier Sectio 1 (Dated: :30 pm Tuesday October, 013) I. PURPOSE The purpose of the experimet is to use the Michelso Iterferometer, oce
More informationDETERMINATION OF MECHANICAL PROPERTIES OF A NON- UNIFORM BEAM USING THE MEASUREMENT OF THE EXCITED LONGITUDINAL ELASTIC VIBRATIONS.
ICSV4 Cairs Australia 9- July 7 DTRMINATION OF MCHANICAL PROPRTIS OF A NON- UNIFORM BAM USING TH MASURMNT OF TH XCITD LONGITUDINAL LASTIC VIBRATIONS Pavel Aokhi ad Vladimir Gordo Departmet of the mathematics
More informationFilter banks. Separately, the lowpass and highpass filters are not invertible. removes the highest frequency 1/ 2and
Filter bas Separately, the lowpass ad highpass filters are ot ivertible T removes the highest frequecy / ad removes the lowest frequecy Together these filters separate the sigal ito low-frequecy ad high-frequecy
More information2C09 Design for seismic and climate changes
2C09 Desig for seismic ad climate chages Lecture 02: Dyamic respose of sigle-degree-of-freedom systems I Daiel Grecea, Politehica Uiversity of Timisoara 10/03/2014 Europea Erasmus Mudus Master Course Sustaiable
More informationTopic 9: Sampling Distributions of Estimators
Topic 9: Samplig Distributios of Estimators Course 003, 2018 Page 0 Samplig distributios of estimators Sice our estimators are statistics (particular fuctios of radom variables), their distributio ca be
More informationCHAPTER 10 INFINITE SEQUENCES AND SERIES
CHAPTER 10 INFINITE SEQUENCES AND SERIES 10.1 Sequeces 10.2 Ifiite Series 10.3 The Itegral Tests 10.4 Compariso Tests 10.5 The Ratio ad Root Tests 10.6 Alteratig Series: Absolute ad Coditioal Covergece
More informationSalmon: Lectures on partial differential equations. 3. First-order linear equations as the limiting case of second-order equations
3. First-order liear equatios as the limitig case of secod-order equatios We cosider the advectio-diffusio equatio (1) v = 2 o a bouded domai, with boudary coditios of prescribed. The coefficiets ( ) (2)
More informationThe axial dispersion model for tubular reactors at steady state can be described by the following equations: dc dz R n cn = 0 (1) (2) 1 d 2 c.
5.4 Applicatio of Perturbatio Methods to the Dispersio Model for Tubular Reactors The axial dispersio model for tubular reactors at steady state ca be described by the followig equatios: d c Pe dz z =
More informationLecture 1 Probability and Statistics
Wikipedia: Lecture 1 Probability ad Statistics Bejami Disraeli, British statesma ad literary figure (1804 1881): There are three kids of lies: lies, damed lies, ad statistics. popularized i US by Mark
More informationFormation of A Supergain Array and Its Application in Radar
Formatio of A Supergai Array ad ts Applicatio i Radar Tra Cao Quye, Do Trug Kie ad Bach Gia Duog. Research Ceter for Electroic ad Telecommuicatios, College of Techology (Coltech, Vietam atioal Uiversity,
More information4. Hypothesis testing (Hotelling s T 2 -statistic)
4. Hypothesis testig (Hotellig s T -statistic) Cosider the test of hypothesis H 0 : = 0 H A = 6= 0 4. The Uio-Itersectio Priciple W accept the hypothesis H 0 as valid if ad oly if H 0 (a) : a T = a T 0
More informationMark Lundstrom Spring SOLUTIONS: ECE 305 Homework: Week 5. Mark Lundstrom Purdue University
Mark udstrom Sprig 2015 SOUTIONS: ECE 305 Homework: Week 5 Mark udstrom Purdue Uiversity The followig problems cocer the Miority Carrier Diffusio Equatio (MCDE) for electros: Δ t = D Δ + G For all the
More informationKMXP Linear Position Sensor
Liear Positio Sesor SPECIFICATIONS AMR liear positio sesor DFN x6 package, very compact Small wall thickess for large air gaps High operatig temperature of 50 C O the edge solderig possible Movig a KMXP
More informationEXPERIMENT OF SIMPLE VIBRATION
EXPERIMENT OF SIMPLE VIBRATION. PURPOSE The purpose of the experimet is to show free vibratio ad damped vibratio o a system havig oe degree of freedom ad to ivestigate the relatioship betwee the basic
More informationSpectral Analysis. This week in lab. Next classes: 3/26 and 3/28. Your next experiment Homework is to prepare
Spectral Aalysis This week i lab Your ext experimet Homework is to prepare Next classes: 3/26 ad 3/28 Aero Testig, Fracture Toughess Testig Read the Experimets 5 ad 7 sectios of the course maual Spectral
More informationOffice: JILA A709; Phone ;
Office: JILA A709; Phoe 303-49-7841; email: weberjm@jila.colorado.edu Problem Set 5 To be retured before the ed of class o Wedesday, September 3, 015 (give to me i perso or slide uder office door). 1.
More informationMCT242: Electronic Instrumentation Lecture 2: Instrumentation Definitions
Faculty of Egieerig MCT242: Electroic Istrumetatio Lecture 2: Istrumetatio Defiitios Overview Measuremet Error Accuracy Precisio ad Mea Resolutio Mea Variace ad Stadard deviatio Fiesse Sesitivity Rage
More informationNotes The Incremental Motion Model:
The Icremetal Motio Model: The Jacobia Matrix I the forward kiematics model, we saw that it was possible to relate joit agles θ, to the cofiguratio of the robot ed effector T I this sectio, we will see
More informationAnalysis of Experimental Measurements
Aalysis of Experimetal Measuremets Thik carefully about the process of makig a measuremet. A measuremet is a compariso betwee some ukow physical quatity ad a stadard of that physical quatity. As a example,
More informationMechatronics. Time Response & Frequency Response 2 nd -Order Dynamic System 2-Pole, Low-Pass, Active Filter
Time Respose & Frequecy Respose d -Order Dyamic System -Pole, Low-Pass, Active Filter R 4 R 7 C 5 e i R 1 C R 3 - + R 6 - + e out Assigmet: Perform a Complete Dyamic System Ivestigatio of the Two-Pole,
More informationES.182A Topic 40 Notes Jeremy Orloff
ES.182A opic 4 Notes Jeremy Orloff 4 Flux: ormal form of Gree s theorem Gree s theorem i flux form is formally equivalet to our previous versio where the lie itegral was iterpreted as work. Here we will
More informationInfinite Sequences and Series
Chapter 6 Ifiite Sequeces ad Series 6.1 Ifiite Sequeces 6.1.1 Elemetary Cocepts Simply speakig, a sequece is a ordered list of umbers writte: {a 1, a 2, a 3,...a, a +1,...} where the elemets a i represet
More informationTime-Domain Representations of LTI Systems
2.1 Itroductio Objectives: 1. Impulse resposes of LTI systems 2. Liear costat-coefficiets differetial or differece equatios of LTI systems 3. Bloc diagram represetatios of LTI systems 4. State-variable
More informationACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH00030 SEMESTER / Statistics
ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH00030 SEMESTER 1 018/019 DR. ANTHONY BROWN 8. Statistics 8.1. Measures of Cetre: Mea, Media ad Mode. If we have a series of umbers the
More informationx a x a Lecture 2 Series (See Chapter 1 in Boas)
Lecture Series (See Chapter i Boas) A basic ad very powerful (if pedestria, recall we are lazy AD smart) way to solve ay differetial (or itegral) equatio is via a series expasio of the correspodig solutio
More informationProblem 1. Problem Engineering Dynamics Problem Set 9--Solution. Find the equation of motion for the system shown with respect to:
2.003 Egieerig Dyamics Problem Set 9--Solutio Problem 1 Fid the equatio of motio for the system show with respect to: a) Zero sprig force positio. Draw the appropriate free body diagram. b) Static equilibrium
More informationWe are mainly going to be concerned with power series in x, such as. (x)} converges - that is, lims N n
Review of Power Series, Power Series Solutios A power series i x - a is a ifiite series of the form c (x a) =c +c (x a)+(x a) +... We also call this a power series cetered at a. Ex. (x+) is cetered at
More informationMONITORING THE STABILITY OF SLOPES BY GPS
MONITORING THE STABILITY OF SLOPES BY GPS Prof. S. Sakurai Costructio Egieerig Research Istitute Foudatio, Japa Prof. N. Shimizu Dept. of Civil Egieerig, Yamaguchi Uiversity, Japa ABSTRACT The stability
More informationANALYSIS OF EXPERIMENTAL ERRORS
ANALYSIS OF EXPERIMENTAL ERRORS All physical measuremets ecoutered i the verificatio of physics theories ad cocepts are subject to ucertaities that deped o the measurig istrumets used ad the coditios uder
More informationStreamfunction-Vorticity Formulation
Streamfuctio-Vorticity Formulatio A. Salih Departmet of Aerospace Egieerig Idia Istitute of Space Sciece ad Techology, Thiruvaathapuram March 2013 The streamfuctio-vorticity formulatio was amog the first
More informationAnalysis of composites with multiple rigid-line reinforcements by the BEM
Aalysis of composites with multiple rigid-lie reiforcemets by the BEM Piotr Fedeliski* Departmet of Stregth of Materials ad Computatioal Mechaics, Silesia Uiversity of Techology ul. Koarskiego 18A, 44-100
More informationMath 116 Second Exam
Math 6 Secod Exam November, 6 Name: Exam Solutios Istructor: Sectio:. Do ot ope this exam util you are told to do so.. This exam has 9 pages icludig this cover. There are 8 problems. Note that the problems
More informationSimilarity Solutions to Unsteady Pseudoplastic. Flow Near a Moving Wall
Iteratioal Mathematical Forum, Vol. 9, 04, o. 3, 465-475 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/imf.04.48 Similarity Solutios to Usteady Pseudoplastic Flow Near a Movig Wall W. Robi Egieerig
More informationNumerical Simulation of Thermomechanical Problems in Applied Mechanics: Application to Solidification Problem
Leoardo Joural of Scieces ISSN 1583-0233 Issue 9, July-December 2006 p. 25-32 Numerical Simulatio of Thermomechaical Problems i Applied Mechaics: Applicatio to Solidificatio Problem Vicet Obiajulu OGWUAGWU
More informationLecture 1 Probability and Statistics
Wikipedia: Lecture 1 Probability ad Statistics Bejami Disraeli, British statesma ad literary figure (1804 1881): There are three kids of lies: lies, damed lies, ad statistics. popularized i US by Mark
More informationChapter 9: Numerical Differentiation
178 Chapter 9: Numerical Differetiatio Numerical Differetiatio Formulatio of equatios for physical problems ofte ivolve derivatives (rate-of-chage quatities, such as velocity ad acceleratio). Numerical
More information[ ] sin ( ) ( ) = 2 2 ( ) ( ) ( ) ˆ Mechanical Spectroscopy II
Solid State Pheomea Vol. 89 (003) pp 343-348 (003) Tras Tech Publicatios, Switzerlad doi:0.408/www.scietific.et/ssp.89.343 A New Impulse Mechaical Spectrometer to Study the Dyamic Mechaical Properties
More informationTopic 9: Sampling Distributions of Estimators
Topic 9: Samplig Distributios of Estimators Course 003, 2018 Page 0 Samplig distributios of estimators Sice our estimators are statistics (particular fuctios of radom variables), their distributio ca be
More informationPreliminary Examination - Day 1 Thursday, May 12, 2016
UNL - Departmet of Physics ad Astroomy Prelimiary Examiatio - Day Thursday, May, 6 This test covers the topics of Quatum Mechaics (Topic ) ad Electrodyamics (Topic ). Each topic has 4 A questios ad 4 B
More informationNotes on iteration and Newton s method. Iteration
Notes o iteratio ad Newto s method Iteratio Iteratio meas doig somethig over ad over. I our cotet, a iteratio is a sequece of umbers, vectors, fuctios, etc. geerated by a iteratio rule of the type 1 f
More informationINF-GEO Solutions, Geometrical Optics, Part 1
INF-GEO430 20 Solutios, Geometrical Optics, Part Reflectio by a symmetric triagular prism Let be the agle betwee the two faces of a symmetric triagular prism. Let the edge A where the two faces meet be
More informationFree Space Optical Wireless Communications under Turbulence Channel Effect
IOSR Joural of Electroics ad Commuicatio Egieerig (IOSR-JECE) e-issn: 78-834,p- ISSN: 78-8735.Volume 9, Issue 3, Ver. III (May - Ju. 014), PP 01-08 Free Space Optical Wireless Commuicatios uder Turbulece
More informationMarkov Decision Processes
Markov Decisio Processes Defiitios; Statioary policies; Value improvemet algorithm, Policy improvemet algorithm, ad liear programmig for discouted cost ad average cost criteria. Markov Decisio Processes
More informationa. For each block, draw a free body diagram. Identify the source of each force in each free body diagram.
Pre-Lab 4 Tesio & Newto s Third Law Refereces This lab cocers the properties of forces eerted by strigs or cables, called tesio forces, ad the use of Newto s third law to aalyze forces. Physics 2: Tipler
More information. (24) If we consider the geometry of Figure 13 the signal returned from the n th scatterer located at x, y is
.5 SAR SIGNA CHARACTERIZATION I order to formulate a SAR processor we first eed to characterize the sigal that the SAR processor will operate upo. Although our previous discussios treated SAR cross-rage
More informationStatisticians use the word population to refer the total number of (potential) observations under consideration
6 Samplig Distributios Statisticias use the word populatio to refer the total umber of (potetial) observatios uder cosideratio The populatio is just the set of all possible outcomes i our sample space
More informationAxis Aligned Ellipsoid
Machie Learig for Data Sciece CS 4786) Lecture 6,7 & 8: Ellipsoidal Clusterig, Gaussia Mixture Models ad Geeral Mixture Models The text i black outlies high level ideas. The text i blue provides simple
More information8. СОВЕТУВАЊЕ. Охрид, септември ANALYSIS OF NO LOAD APPARENT POWER AND FREQUENCY SPECTRUM OF MAGNETIZING CURRENT FOR DIFFERENT CORE TYPES
8. СОВЕТУВАЊЕ Охрид, 22 24 септември Leoardo Štrac Frajo Keleme Kočar Power Trasformers Ltd. ANALYSS OF NO LOAD APPARENT POWER AND FREQENCY SPECTRM OF MAGNETZNG CRRENT FOR DFFERENT CORE TYPES ABSTRACT
More informationUpper bound for ropelength of pretzel knots
Upper boud for ropelegth of pretzel kots Safiya Mora August 25, 2006 Abstract A model of the pretzel kot is described. A method for predictig the ropelegth of pretzel kots is give. A upper boud for the
More informationMOST PEOPLE WOULD RATHER LIVE WITH A PROBLEM THEY CAN'T SOLVE, THAN ACCEPT A SOLUTION THEY CAN'T UNDERSTAND.
XI-1 (1074) MOST PEOPLE WOULD RATHER LIVE WITH A PROBLEM THEY CAN'T SOLVE, THAN ACCEPT A SOLUTION THEY CAN'T UNDERSTAND. R. E. D. WOOLSEY AND H. S. SWANSON XI-2 (1075) STATISTICAL DECISION MAKING Advaced
More informationPolynomial Functions and Their Graphs
Polyomial Fuctios ad Their Graphs I this sectio we begi the study of fuctios defied by polyomial expressios. Polyomial ad ratioal fuctios are the most commo fuctios used to model data, ad are used extesively
More information(c) Write, but do not evaluate, an integral expression for the volume of the solid generated when R is
Calculus BC Fial Review Name: Revised 7 EXAM Date: Tuesday, May 9 Remiders:. Put ew batteries i your calculator. Make sure your calculator is i RADIAN mode.. Get a good ight s sleep. Eat breakfast. Brig:
More informationt distribution [34] : used to test a mean against an hypothesized value (H 0 : µ = µ 0 ) or the difference
EXST30 Backgroud material Page From the textbook The Statistical Sleuth Mea [0]: I your text the word mea deotes a populatio mea (µ) while the work average deotes a sample average ( ). Variace [0]: The
More informationWave Motion
Wave Motio Wave ad Wave motio: Wave is a carrier of eergy Wave is a form of disturbace which travels through a material medium due to the repeated periodic motio of the particles of the medium about their
More information62. Power series Definition 16. (Power series) Given a sequence {c n }, the series. c n x n = c 0 + c 1 x + c 2 x 2 + c 3 x 3 +
62. Power series Defiitio 16. (Power series) Give a sequece {c }, the series c x = c 0 + c 1 x + c 2 x 2 + c 3 x 3 + is called a power series i the variable x. The umbers c are called the coefficiets of
More informationMagnetic Length Sensor MLS (Hybrid)
Small Hybride Large Hybride AMR gradiet sesor Liear displacemet, movemets, velocities High precisio Various pole pitches available DESCRIPTION Slidig the MLS-Sesors alog a magetic scale will produce a
More informationApproximating the ruin probability of finite-time surplus process with Adaptive Moving Total Exponential Least Square
WSEAS TRANSACTONS o BUSNESS ad ECONOMCS S. Khotama, S. Boothiem, W. Klogdee Approimatig the rui probability of fiite-time surplus process with Adaptive Movig Total Epoetial Least Square S. KHOTAMA, S.
More informationMATH/STAT 352: Lecture 15
MATH/STAT 352: Lecture 15 Sectios 5.2 ad 5.3. Large sample CI for a proportio ad small sample CI for a mea. 1 5.2: Cofidece Iterval for a Proportio Estimatig proportio of successes i a biomial experimet
More informationTrue Nature of Potential Energy of a Hydrogen Atom
True Nature of Potetial Eergy of a Hydroge Atom Koshu Suto Key words: Bohr Radius, Potetial Eergy, Rest Mass Eergy, Classical Electro Radius PACS codes: 365Sq, 365-w, 33+p Abstract I cosiderig the potetial
More informationAnalysis of the No-Load Characteristic of the Moving Coil Linear Compressor
Purdue Uiversity Purdue e-pubs Iteratioal Compressor Egieerig Coferece School of Mechaical Egieerig 008 Aalysis of the No-Load Characteristic of the Movig Coil Liear Compressor Yigbai Xie North Chia Electric
More informationf(x) dx as we do. 2x dx x also diverges. Solution: We compute 2x dx lim
Math 3, Sectio 2. (25 poits) Why we defie f(x) dx as we do. (a) Show that the improper itegral diverges. Hece the improper itegral x 2 + x 2 + b also diverges. Solutio: We compute x 2 + = lim b x 2 + =
More informationStructuring Element Representation of an Image and Its Applications
Iteratioal Joural of Cotrol Structurig Automatio Elemet ad Represetatio Systems vol. of a o. Image 4 pp. ad 50955 Its Applicatios December 004 509 Structurig Elemet Represetatio of a Image ad Its Applicatios
More information