IEC 61212-3-3/FRAGf
(Main)IEC 60994
IEC 60994
This guide applies to any type of reaction or impulse turbine, as well as to any type of pump-turbine and storage pump, coupled to an electric generator or motor. It covers the field of vibration and pulsation tests referred to as standard tests.[
]The contents of the corrigendum of April 1997 have been included in this copy.
Matériaux isolants - Tubes et barres industriels rigides, ronds, stratifiés, à base de résines thermodurcissables, à usages électriques - Partie 3: Spécifications pour matériaux particuliers - Feuille 3: Barres rondes, stratifiées, moulées
La CEI 61212-3-3:2006 donne les exigences relatives aux barres industrielles rigides rondes, stratifiées, moulées, à usages électriques, à base de différentes résines et de différents matériaux de renfort. Les modifications principales apportées par rapport à l'édition précédente sont les suivantes: instructions supplémentaires relatives à l'utilisation et à la sécurité de l'application. Reformatage du document pour correspondre au format de document actuel de la CEI. Ajout du Type EP GC 43.
Guide for field measurement of vibrations and pulsations in hydraulic machines (turbines, storage pumps and pump-turbines)
General Information
Relations
Standards Content (Sample)
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Guide for field measurement of vibrations and pulsations in hydraulic machines (turbines, storage pumps and pump-turbines)Guide pour la mesure in situ des vibrations et fluctuations sur machines hydrauliques (turbines, pompes d'accumulation et pompes-turbines)Guide for field measurement of vibrations and pulsations in hydraulic machines (turbines, storage pumps and pump-turbines)27.140Vodna energijaHydraulic energy engineering17.160Vibracije, meritve udarcev in vibracijVibrations, shock and vibration measurementsICS:Ta slovenski standard je istoveten z:IEC 60994SIST IEC 60994:1999en01-april-1999SIST IEC 60994:1999SLOVENSKI
STANDARD
SIST IEC 60994:1999
NORMEINTERNATIONALEINTERNATIONALSTAN DARDCEIIEC994Première éditionFirst edition1991-01Guide pour la mesure in situ des vibrationset fluctuations sur machines hydrauliques(turbines, pompes d'accumulationet pompes-turbines)Guide for field measurement of vibrationsand pulsations in hydraulic machines (turbines,storage pumps and pump-turbines)© IEC 1991 Droits de reproduction réservés — Copyright - all rights reservedAucune partie de cette publication ne peut être reproduite niNo part of this publication may be reproduced or utilized inutilisée sous quelque forme que ce soit et par aucunany form or by any means, electronic or mechanical,procédé, électronique ou mécanique, y compris la photo-including photocopying and microfilm, without permission incopie et les microfilms, sans l'accord écrit de l'éditeurwriting from the publisher.International Electrotechnical Commission3, rue de Varembé Geneva, SwitzerlandTelefax: +41 22 919 0300e-mail: inmail@iec.chIEC web site http: //www.iec.chIEC•Commission Electrotechnique InternationaleInternational Electrotechnical CommissionMe1+wyHapo Haa 3neMTpoTexHH4ecKae HOMuccua•CODE PRIXXBPRICE CODEPour prix, voir catalogue en vigueurFor price, see current catalogueSIST IEC 60994:1999
Publication 60994 de la CEI(Première édition - 1991)Guide pour la mesure in situdes vibrations et fluctuations surmachines hydrauliques (turbines,pompes d'accumulationet pompes-turbines)IEC Publication 60994(First edition - 1991)Guide for field measurement ofvibrations and pulsations in hydraulicmachines (turbines, storage pumps andpump-turbines)CORRIGENDUM 1Page 6 - AVANT-PROPOSDans la liste des publications citées de la CEI,à la cinquième ligne, au lieu de*** Actuellement document 4(Bureau Central)48lire:CEI 41 (1991): Essais de réception sur place desturbines hydrauliques, pompes d'accumulation etpompes-turbines en vue de la détermination de leursperformances (troisième édition)Corrections en anglais uniquementPage 7 - PREFACEIn the list of other IEC publications quoted, fifth line,instead of***At present Document 4(Central Office)48read:IEC 41 (1991): Field acceptance tests to deter- minethe hydraulic performance of hydraulic turbines,storage pumps and pump-turbines (third edition)Page 17 – Subclause 2.3.2.7In the definitions column, third line, instead of.quantity. A is. read .quantity, A is. (comma insteadof full stop) *Page 19In the footnote, at end of first line, instead of .N inthe denomination. read .N in the denominator.Page 21In the definitions column, fifth line, instead of.function, X(t) over. read .function X(t) over.(no comma)Page 25 – 2.3.4.11In the definitions column, first and second line,instead of .length of the connecting pipe connectingthe pressure transducer. read .length of the pipeconnecting the pressure transducer.Page 41 – 4.1.1In item d), second and third line, instead of.unbalance; also and if. read .unbalance andalso if.4.1.3 - In the first line, instead of .to the machinewater passages. read .to the water passages.* Bold types are for clarity onlySIST IEC 60994:1999
Corrections en anglais uniquementPage 49 — 5.2.3In the eighth line, instead of .in the draft tube ata distance of 0.5 D5 to 1.0 D5 from. read .0.5to 1.0 times the suction diameter of the runner(Ds) from.Tenth line, instead of .0.2 D5 - 0.8 D5 from.read .0.2 Ds — 0.8 Ds from.Eleventh line, instead of .D5 being. read.Ds being.Twelfth line, instead of .outer contour of theelbow, read .outer side of the elbow.Page 51 — 5.2.10Item b), instead of .thrust bearing loadpulsations, by means of strain measurements onevery bearing element; read .thrust bearingload pulsations, on every bearing element bymeans of strain measurements;Page 53 — 5.6.1In item b), first line, instead of .and runner bladeangle. read .and runner/impeller bladeangle.Page 55 — 5.7.4In the second line, instead of .position of arunner vane or nozzle and/or guide blade.read .position of a guide vane or nozzleand/or runner blades.Page 59 — 6.1.1In item b), instead of Upper frequency**:— for Pelton turbines:readUpper frequency:— for Pelton turbines**In the first footnote (*), end of first line, insteadof .lower than the vortex rope. read .lowerthan the suction vortex.Page 65 — 6.3.5In the second line, instead of .any measuringpoint. read .any measuring operatingcondition.Page 71 — Clause 6.8In the seventh line (second dash), remove thewords .(see Figure 7). and place them innext line so as to obtain .are eliminated (seeFigure 7).Page 85 — 8.3In the seventh line, instead of .A/D conversion.read .A/D (analog to digital) conversion.Page 58 — 6.1.1Au point b), au lieu deLimite supérieure de fréquence**:— turbines Pelton:lire Limite supérieure de fréquence:— turbines Pelton**Corrections en anglais uniquementSIST IEC 60994:1999
Page 108 — Article B2.Dans la dernière formule de la page, ajouterun signe moins à la suite du second signeégale (= -)Corrections en anglais uniquementPage 95 - 9.2.4Ninth line, instead of Only in the last case isphase information preserved, read: Only inthe last case phase information ispreserved.Page 99 -10.3In the second line, instead of .should beagreed with the concerned parties,. read.should be agreed between the concernedparties,.Page 103 - Clause A2.In the last but one line, instead of .conversionof the signals from the three signals. read.conversion of the three signals.Page 118 — Figure C2.Sous le tableau, à la cinquième ligne (4èmetiret), au lieu de-rendement de la pompe ou de la turbine,lire—rendement de la pompe ou de la turbine, etc.Page 109 - B2.In the last formula of the page, add a minus signjust after the second equal sign (= -)Page 115 - C7.In the fifth line (third dash), instead of (.recorderor plotter, output). read(.recorder orplotter output). (no comma)Page 117 - Figure Cl.In the heading of the table, last column, instead ofConditions test/. read Test conditions/.Page 119 — Figure C2.Below the table, fifth line (4th dash),instead of-turbine or pump efficiency,read—turbine or pump efficiency, etc.Page 132 — Figure Dl.Page 133 — Figure Dl.Dans le schéma, au lieu de HB lire IIIn the diagram, instead of //B read 11Avril 1997April 1997SIST IEC 60994:1999
SIST IEC 60994:1999
994 ©IEC- 3 -CONTENTSPageFOREWORD 7PREFACE
7INTRODUCTION
9SECTION ONE - GENERALClause1.Scope and object 111.1Scope 111.2Object 111.3Excluded topics 132.Terms, definitions, symbols and units 132.1Units 132.2 Terms
132.3List of terms specific to this guide 152.4 Classification of hydraulic machines
273.Guarantees
41SECTION TWO - EXECUTION OF TESTS4.Test conditions to be fulfilled
414.1 Operating conditions under which measurements are performed
414.2 Checks on the machine before the beginning of tests
435.Test procedure
435.1Parameters determining the operating point
435.2 Vibration and pulsation quantities to be measured and locations of measuringpoints
475.3Personnel 515.4 Agreement of test procedure
515.5 Test programme
535.6Preparations for tests 535.7 Observations
555.8Repetition of tests 57SECTION THREE - METHODS OF MEASUREMENT, DATA ACQUISITION AND PROCESSING6.Considerations relating to the methods of measurement
596.1Vibrations 596.2Radial vibrations of the shaft relative to the bearings
656.3Pressure pulsations
656.4Stresses 676.5Shaft torque pulsations
676.6Rotational speed pulsations
716.7Power pulsations
716.8 Guide vane torque pulsations
716.9Radial thrust pulsations measured at the guide bearings
716.10 Axial thrust pulsations measured at the thrust bearing
756.11 Measured quantities defining the machine operating point
75SIST IEC 60994:1999
994 OO I EC— 5 —7.Calibration
757.1General
757.2Direct calibration 777.3Calibration by electrical reference signals 818.Recording
838.1Graphical recorders
838.2 Magnetic tape recorders
858.3Digital recording 859.Data acquisition and processing 879.1General
879.2 Selection of data processing methods
8910.Measurement uncertainties
9711.Final report 99APPENDIX A — Formulae for calculating principal stresses and signal processing fordynamic strain measurements with rosettes
101APPENDIX B — Formulae for calculating the torque on a cylindrical solid shaft and theaxial load on a rectangular or circular section link using the strain gaugetechnique
109APPENDIX C - Example of final report
113APPENDIX D — Distortion of pressure pulsation measurements for transducers mountedwith connecting pipe
131SIST IEC 60994:1999
Six Months' RuleReport on Voting4(CO)454(CO)50Publication Nos.184 (1965):222 (1966):***Other publications quoted:ISO standards2041 (1975):3945 (1985):5347-0 (1987):5348 (1987):7919-1 (1986):8042 (1988):994 © IEC— 7 —INTERNATIONAL ELECTROTECHNICAL COMMISSIONGUIDE FOR FIELD MEASUREMENT OF VIBRATIONSAND PULSATIONS IN HYDRAULIC MACHINES(TURBINES, STORAGE PUMPS AND PUMP-TURBINES)FOREWORD1)The formal decisions or agreements of the IEC on technical matters, prepared by Technical Committees on which all theNational Committees having a special interest therein are represented, express, as nearly as possible, an internationalconsensus of opinion on the subjects dealt with.2)They have the form of recommendations for international use and they are accepted by the National Committees in thatsense.3)In order to promote international unification, the IEC expresses the wish that all National Committees should adopt thetext of the IEC recommendation for their national rules in so far as national conditions will permit. Any divergencebetween the IEC recommendation and the corresponding national rules should, as far as posssible, be clearly indicated inthe latter.PREFACEThis standard has been prepared by IEC Technical Committee No. 4: Hydraulic turbines.The text of this standard is based on the following documents:Full information on the voting for the approval of this standard can be found in the VotingReport indicated in the above table.Other IEC Publications quoted in this standard:Methods for specifying the characteristics of electro-mechanical transducers forshock and vibration measurements.Methods for specifying the characteristics of auxiliary equipment for shock andvibration measurement.At present Document 4(Central Office)48.Vibration and shock — Vocabulary. Bilingual edition.Mechanical vibration of large rotating machines with speed range from 10 to 200 tr/s— Measurement and evaluation of vibration severity in situ.Methods for the calibration of vibration and shock pick-ups — Part 0: Basic concepts.Mechanical vibration and shock — Mechanical mounting of accelerometers.Mechanical vibration of non-reciprocating machines — Measurements on rotatingshafts and evaluation — Part 1: General guidelines.Shock and vibration measurements — Characteristics to be specified for seismicpick-ups.SIST IEC 60994:1999
994 ©IEC— 9 —GUIDE FOR FIELD MEASUREMENT OF VIBRATIONSAND PULSATIONS IN HYDRAULIC MACHINES(TURBINES, STORAGE PUMPS AND PUMP-TURBINES)INTRODUCTIONOn a machine in service, pulsations and vibrations which cannot be avoided and which do notaffect by themselves the service life of the plant where they occur, can always be observed. Theirvalues depend on many factors, among which are the flow pattern in the water passages underdifferent operating conditions of the unit, peculiarities of the design as well as the thoroughness ofmanufacture, erection and maintenance. Such pulsations and vibrations can be considered asdetrimental only when certain parts of the machine or of the plant are subject to forces that mayimpair its resistance or when unacceptable disturbances are carried to its environment.In extreme cases, vibrations in hydraulic machines can result in the formation of cracks and evenin fracture of components due to fatigue*.Excessive vibration in hydraulic machines not only can reduce their trouble-free service life butcan also affect operation of governing systems and instruments, the behaviour of the attachedstructures and the health of personnel.Measurement of pulsation and vibration characteristics or, preferably, of their effects is to becarried out in accordance with this guide which also gives the information necessary to derive thevalue of the physical quantities from the readings of the measuring instruments.Given the present state of knowledge, it can only be hoped that measurements made incompliance with this guide will reveal a basic characteristic making it possible to relate pulsationsand vibrations to their effects statistically, with an acceptable confidence level.Vibration studies of a hydraulic machine represent a long and difficult operation and hence areexpensive (particularly as regards the non-availability of the machine) and therefore should beundertaken only if a limited number of measurements of stresses or movements indicates thepossibility of a real danger. The purpose of such work is, if possible, to eliminate the source ofdetrimental loadings after having identified it or, should this not be practicable, to define anoperating procedure reducing such loadings to an acceptable level. There are many sources ofdisturbances but a very small number of them, and even one only, may create a real problem on agiven machine.As a rule, the vibrational state of a hydraulic machine is assessed from tests in which the vibrationis measured at individual characteristic points of the structure. A standard experimental set-up,designed on the basis of good practice and experience, should already yield sufficient indicationsabout the general vibrational conditions of the machine. However, examination of results thusacquired can sometimes point to strong local amplification (resonance) in some vital parts of themachine; if such is the case, the affected part(s) should be more closely investigated by meansof an appropriate experimental arrangement. Flow pattern in the water passages may have* In previous years fatigue failures in hydraulic machines were few in number. However, the current tendency to increasespecific loads and to save material in the design of hydraulic machines can lead to lowering of dynamic rigidity of thestructure, which may increase the risk of vibration in newly designed machines. Also the increase in geometricaldimensions stemming from increasing unit capacity can lead to a lowering of characteristic vibration frequencies of themachine or of some parts thereof (guide vanes, etc.). Thus the frequencies in question could more easily interact with thefrequencies of hydraulic and/or electrical oscillations in the system (or harmonics thereof).SIST IEC 60994:1999
994©IEC— 11 —important effects on the vibrations of hydraulic machines. In order to obtain an accurate vibrationanalysis, it is common practice to relate appropriately located measurements of vibrations (see 5.2.1and 5.2.2) with appropriately located measurements of pulsations* of other important quantities,such as:pressure pulsations (see 5.2.3);—pulsations of local strains and corresponding stresses (see 5.2.4);shaft torque pulsations (see 5.2.5);—rotation speed pulsation (see 5.2.6);—power pulsations (see 5.2.7);—guide vane torque pulsations (see 5.2.8);—radial thrust pulsations measured at guide bearings (see 5.2.9);axial thrust pulsations measured at thrust bearing (see 5.2.10);and, if need be, also other quantities.It is in no way intended that all the measurements listed in this guide should be carried out inevery case.SECTION ONE — GENERAL1. Scope and object1.1 Scope1.1.1 This guide applies to any type of reaction or impulse turbine, as well to any type ofpump-turbine and storage pump, coupled to an electric generator or motor.1.1.2 The guide covers the field of vibration and pulsation tests referred to as standard tests.The objectives of the tests are as follows:Assessment of hydraulic machine design, manufacture and quality of erection from theviewpoint of vibration**.—Assessment of the changes of vibration behaviour during the machine life.—Provision of recommendations applying to operation of unit (for instance, choice of themost appropriate transient sequences).—Aid in analysing faults and break downs.1 1.3 If it is not possible to apply the recommendations of the guide because of the construction ofthe hydraulic machine, or if it is not necessary to conduct some of the measurements, suchitems may be omitted on prior agreement between the manufacturer and the user.1.2 Object1.2.1 To establish uniform rules to be applied when carrying out vibration and pulsation tests. Toestablish methods of measuring and of test data processing.* In this guide, the term `pulsation" is understood to mean any periodic (or quasi-periodic) fluctuation, irrespectiveof its frequency.** Recommendations on assessment of the vibrational and pulsatory state of the machine will not be prepared untilsystematic data have been accumulated in accordance with this guide and have been properly interpreted.SIST IEC 60994:1999
994 0C IEC— 13 —1.2.2 To indicate criteria for a unified approach to the comparison of vibrations and pulsations ofdifferent hydraulic machines of the same class (see 2.4).1.2.3 To ensure the possibility of accumulating actual data of sufficient homogeneity on differenthydraulic machines.1.3 Excluded topics1.3.1 The guide excludes all matters of purely commercial interest.1.3.2 The guide is not concerned with special vibration and pulsation tests for research purposes,although it is recommended that the methods described in the guide be applied to usualvibration and pulsation tests.1.3.3 Laboratory model vibration and pulsation tests and tests of separate full-sized parts in theworkshop are not dealt with in this guide.However, if pulsation tests on a model are available, they should be taken into con-sideration.1.3.4 The problems related to the vibrations of civil engineering works and of parts of theelectrical machine other than bearing(s) or the shaft, as well as the pressure pulsations in thewaterways external to the machine*, are not dealt with in the guide.However, in specific cases, when the causes of excessive vibration of a hydraulic machineare uncertain or might be influencing other parts of the plant, it may be appropriate to inspectthe civil engineering work structures and/or the electrical machine as well as the waterwaysexternal to the machine.1.3.5 The guide excludes recommendations on identifying and eliminating causes of vibrations.1.3.6 Although quite often noise measurements and noise analysis, if adequately performed, canbe a useful diagnostic tool to assess vibratory troubles of a hydraulic machine, this guideconsiders only mechanical vibrations to the exclusion of acoustical effects (noise).1.3.7 Regulation systems may interact with phenomena of "pulsations" of hydraulic, mechanicaland electrical quantities in a hydroelectric power plant. However, treatment of such interac-tions or guidelines for conducting artificial-excitation test by injecting a sine signal in thegovernor loop (as is often done e.g. to determine the frequency response of the system) areoutside the scope of this guide.2. Terms, definitions, symbols and units2.1 UnitsThe International System (SI) is used throughout this guide.2.2 TermsThe terms, definitions and symbols relating to hydraulic turbines, storage pumps andpump-turbines are in compliance with the IEC Publication 000***. The terms not defined in2.3 can be found in the publication just mentioned.* In the case of absence of valves and/or gates, the machine is understood to include waterways between highpressure/low pressure reference sections, as specified for guarantees (see IEC Publication 000***).*** At present Document 4(Central Office)48.SIST IEC 60994:1999
994 © IEC— 15 —The terms, definitions and symbols relating to vibrations and pulsations as well asmathematical terms are in compliance with ISO Standard 2041 and IEC Publications 184 and222.2.3 List of terms specific to this guideTabulated below are the terms, symbols and units relating to vibrations and pulsationsadopted throughout this guide.TermsDefinitionsSymbolsUnits2.3.1Terms relating to descriptionof vibrations and pulsationsas functions of time*2.3.1.1Dynamic absolute displace-ment(see IEC 184)u (t)m2.3.1.2Dynamic absolute velocity(see IEC 184)v (t)m/s2.3.1.3Dynamic absolute accelera-tion(see IEC 184)w (t)m/s22.3.1.4Dynamic relative displace-ment between two parts e.g.the shaft and the part onwhich the proximity trans-ducer is fixed (d = 0 when theshaft touches the transducer)d(t)m2.3.1.5Pressure pulsationOscillatory variation of the pressure of the li-quid referred to its mean value during a timeinterval At previously selected13(t)Pa2.3.1.6Strain pulsationOscillatory variation of the strain referred to itsmean value during a time interval At previouslyselected-t(t)m/m2.3.1.7Stress pulsationOscillatory variation of the stress referred to itsmean value during a time interval At previouslyselectedr(t)N/m22.3.1.8Shaft torque pulsationOscillatory variation of the shaft torque refer-red to its mean value during a time interval Atpreviously selectedM(t)N • m2.3.1.9Rotational speed pulsationOscillatory variation of the rotational speed re-ferred to its mean value during a time interval140rev/sAt previously selected2.3.1.10Power pulsationOscillatory variation of the power referred to itsmean value during a time interval At previouslyselectedP(t)W2.3.1.11Guide vane torque pulsationOscillatory variation of the guide vane torquereferred to its mean value during a time intervalII-1-Gv (t)N • mAt previously selected2.3.1.12Radial pulsation measuredat guide bearingOscillatory variation of the radial load on theguide bearing referred to its mean value duringa time interval At previously selectedR(t)N2.3.1.13Axial pulsation measured atthrust bearingOscillatory variation of the axial load on thethrust bearing referred to its mean value duringa time interval At previously selectedt(t)N* For the definitions of vibrations and pulsations see 2.3.2.SIST IEC 60994:1999
994 © IEC- 17 -TermsDefinitionsSymbolsUnits2.3.2General terms relating to par-ameters used to describe vi-brations and pulsations*2.3.2.1VibrationThe variation with time of a quantity, which isdescriptive of the motion or position of amechanical system, when the magnitude isalternatelygreaterandsmaller thansomeaverage value of reference2.3.2.2Periodic vibration or pulsa-tionA quantity whose values recur at equal intervalsof the independent variable (time)Note. — A periodic quantity X (t) which is afunction of time t, and can be expressed as X = f(t) = f (t+ nT) where n is an integer, T is aconstant interval of time and t is the runningtime2.3.2.3Fundamental period(period)The smallest interval of time for which a per-iodic function of time repeats itself (see 2.3.2.2)TsNote. — If there is no ambiguity, the funda-mental period is called the period2.3.2.4FrequencyThe reciprocal of periodfHz2.3.2.5Harmonic(ofaperiodicquantity)A sinusoidal component (of a composite per-iodic function of time) whose frequency is aninteger multiple of the fundamental frequency2.3.2.6Angular frequency (circularfrequency)The product of the frequency of a sinusoidalphenomenon by the factor 27rwrad/s2.3.2.7Simple harmonic quantity;sinusoidal quantityA periodic quantity that is a sinusoidal functionof time. Thus X = A sin (cot + (p) where X (t) isthesimpleharmonicquantity.Aistheamplitude, m is the angular frequency (see2.3.2.6), t is the running time, cp is the phaseangle of the oscillation (radians)2.3.2.8Simple harmonic motion orpulsationA motion or pulsation that is a sinusoidalfunction of time2.3.2.9Phaseangle;Phase(of asinusoidal quantity)If a sinusoidal quantity has advanced throughmT units of time (T being the period) asmeasured from a value of time taken asreference, the phase angle is m2 itgorad2.3.2.10AmplitudeThe maximum value of a sinusoidal quantityX(t)A[X](differentunits accordingto the physicalnature of X)2.3.2.11Peak-to-peakvalueof anoscillating quantity**The algebraic difference between the extremevalues of the quantity. In the case of a sinus-oidal quantity the peak-to-peak value is twicethe amplitude, i.e. 2AAXPP[X] 2.3.2.12CompoundvibrationorpulsationVibration or pulsation consisting of the super-position (sum) of several simple harmonicvibrations or pulsationsNote. — In cases when the ratio of each of thefrequencies of simple harmonic vibrations tofundamental frequency is aninteger, com-pound vibration is called polyharmonic vibra-tion* The definition of "pulsation" is the same as that of "vibration", with the difference that the quantity involved is notdescriptive of the motion or position of a mechanical system.** Peak value (AX, [X]) of an oscillating quantity (as opposed to peak-to-peak value) is the maximum absolute value of thedeviation from the mean value (see 2.3.3.1) of the oscillating quantity.SIST IEC 60994:1999
994 © IEC— 19 —TermsDefinitionsSymbolsUnits2.3.2.13ResonanceResonance of a system in forced oscillationexists when any change, however small, in thefrequency of excitation causes a decrease in theresponse of the system2.3.2.14Random vibration or pulsa-Avibrationorpulsation,ofwhichthetionmagnitude cannot be precisely predicted forany given instant of time2.3.3Mathematical terms2.3.3.1Average value; mean value;a) The average value of a number of homoge-X[X]algebraic mean valueneous discrete quantities is equal to thealgebraic sum of the quantities divided bythe number of quantities. The average valueis equal to:NI Xnn=1X—Nwhere X„ is the value of nth quantity: Nis thetotal number of discrete quantitiesb) The average value of a continuous function,X(t), over a time interval between t1 and t2 isequal to:r_X (t) dtfX–rlt2 – t,2.3.3.2Standard deviationThe root-mean-square (r.m.s.) value of the de-Xeff[X]Effective value referred tothe meanviation of a set of numbers (or a function) fromthe mean valuea) For a set of numbersX1, X2, . XNNE (Xn—X)2n=1Xeff =Nwhere the subscript n refers to the n-th value.Nis the total number of discrete quantities inthe set, X is the mean value of the set (see2.3.3.1)*b) If the quantity X (t) is a continuous functionof t, its effective value over an intervalbetween t, and t2isJr2[X(t)-1]2dtXeff =t2— t12.3.3.3Root-mean-square value:a) The root-mean-square (r.m.s.) value of a setXrms[X]r.m.s. value (effective value)of numbers is the square root of the averageof their squared values. The r.m.s. value ofthe set of numbers canbe represented as:NXrms =E Xnn=1N* Sometimes the standard deviation for the data of a sample is defined with (N-1), replacing N in the denominationbecause the resulting value represents a better estimate of the standard deviation of a population from which the sample istaken. For larger values of N(i.e. N> 30) there is practically no difference.SIST IEC 60994:1999
994 © IEC—21 —TermsDefinitionsSymbolsUnitswhere the subscript n refers to the n-th valueand N is the total number of discrete homo-geneous quantitiesb) The root-mean-square (r.m.s.) value of acontinuous function, X(t) over an intervalbetween ti and t2, is equal to the square rootof the average of the squared values of thefunction over the interval. The r.m.s. valueof a continuous single-valued function, X(t)over an intervalbetween ti and t2 is:J12[XdttiXrms—t2—t1Note. - In vibration theory the average ormean value of the vibration is equal to zero. Inthis case the r.m.s. value Xrms is equal to thestandard deviation Xt.,. (see 2.3.3.2) and themean square value Vms is equal to the varianceX2eff (see 2.3.3.4). In the case of a sinusoidalquantity of amplitude A its effective value isA/11-i2.3.3.4VarianceThe square of the standard deviationNote. — When the mean value of a variable iszero, the variance is the mean square value ofXéff[X2]the variable (see Note 2 under Mean squarevalue, 2.3.3.5)2.3.3.5Mean square valueThe mean square value of a function (or set ofArms[X2]numbers) over a given interval is equal to themean of the squared values of the function (orset of numbers) over that intervalNotes 1. — The mean square value is thesquare of the r.m.s. value2. — When the mean value Xis zero themean square value is equal to thevariance (see 2.3.3.4)3. — If the mean value X is not zerothen:Xef.^ny7Vms =f + X22.3.4Other terms utilized2.3.4.1Number of guide or diffuservanes (reactionmachines),or number of Pelton nozzleszo2.3.4.2Number of runner impellerblades (reaction machines),or number of Pelton bucketsz22.3.4.3Flow velocityThe relative velocity of flow over a part to bevim,m/sinvestigated, at a point P, outside the thicknessof the boundary layer, to be specified (seeFigure 1)2.3.4.4Thickness of trailing edge ofMaximum diameter of a sphere tangent to theSma hydraulic profile (guide va-two opposite surfaces of the profile near thene, runner blade, etc.)trailing edge (see Figure 2)2.3.4.5Limitfrequency(lower,The lower and upper frequency values of thef^,,fuHzupper)frequency range of the process under investiga-tionSIST IEC 60994:1999
994 © IEC— 23 —FIG. 1. — Definition of flow velocity*.c)d)e)FIG. 2. — Definition of thickness of trailing edge of a hydraulic profile*.* These definitions are only a rough suggestion to evaluate the
...
Questions, Comments and Discussion
Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.