Vibration Handbook - Tinex Diagnostika
Vibration HandbookFundamentals – Transducers – Measurement methods PRÜFTECHNIK AG Vibration Handbook1
ForewordMaintenance plays an increasingly important economic role inmodern industry, as managers realize that the key to retaininglong-term investment capital value lies in regular service andinspection. In addition, conscientious maintenance practiceshelp avoid unplanned machine stoppage and the resulting production downtime while improving production quality andplant safety.The German DIN Standard 31 051 defines maintenance as ‘allmeasures for retention and re-creation of the specification condition as well as for determining and evaluating the actual condition of technical aspects of a system.’ Vibration measurementis one of the primary measurement methods for determiningactual machine condition and allows a comprehensive evaluation through the potential of Fourier transformation.PRÜFTECHNIK has a long history of putting innovative technological ideas into industrial maintenance practice - with thepractical advantage for the user always foremost in mind. Thisguiding principle was first confirmed by OPTALIGN, theworld's first laser shaft alignment system.This handbook is intended to provide you, the user, with a solid basis of vibration knowledge and a useful reference for putting this knowledge into practice. We wish you much enjoyment and success in doing so.PRÜFTECHNIK AGVibration HandbookOrder number VIB 9.433G PRÜFTECHNIK AGAll rights reserved.
Table of contentsTable of roduction to vibration measurement . 3Periodic vibration in the time domain . 4Composite vibrations . 6Vibration parameters . 7Conversion factors . 9Periodic vibration in the frequency domain . 10Fourier transformation . 10Frequency analysis . 11Rigidity, mass, damping . 13Summary . 162.Vibration transducers for differentmeasurement problems. 17Piezo transducers . 17Induction transducers (velocity probes) . 19Eddy current transducers (proximity probes) . 20Transducer mounting . 212.12.22.32.43.3.43.4.13.4.23.4.3Evaluating machine conditionthrough vibration analysis . 25Vibration severity according to ISO 2372 . 25Definition . 26Classification . 27Frequency analysis . 29Fundamentals . 29Terminology . 30Spectra of standard vibration forms . 37Notes on successful vibration analysis . 39Vibration causes andtheir characteristic frequencies . 40Case histories of machine damage . 41Radial compressor coupling damage . 41Chiller misalignment . 43Summary . 444.Index . 455.Bibliography . 473.13.1.13.1.23.23.2.13.2.23.2.33.2.43.3 PRÜFTECHNIK AG Vibration Handbook3
Introduction to vibration measurement1. Introduction to vibration measurementVibration can occur in a multitude of forms. Whether they bedesirable (in the form of a tone emitted by a tuning fork) orundesirable (such as the noise and vibration of a jackhammeror the characteristic jolt made by a refrigerator starting up),vibrations are a part of everyday life.VIB 8. 51 5 / M 5RPR ÜFTHECExamples of vibrationIn industrial environments, the study of vibrations and theircauses and remedies is very important to ensure the smoothoperation and long operating life of critical production aggregates. Mechanical vibration serves as an excellent indicator ofmachine condition, because it includes the influences of dynamic loading, foundation behavior and all external influences. Most rotating equipment vibration occurs due to rotor imbalance or insufficient shaft alignment.The following pages offer a brief introduction to appropriatetheoretical fundamentals, which aid in understanding the subsequent discussion of measurement processes and analysis.This introduction has purposely been kept simple for the novice to the field of vibration measurement; the bibliography listssources for more in-depth study of these topics. PRÜFTECHNIK AG Vibration Handbook3
Introduction to vibration measurement1.1 Periodic vibration in the time domainVibration is generally considered to be the movement of a massor a body about its position at rest. Periodic vibration occurswhen the vibration repeats itself at regular intervals of time(e.g. tuning fork).x(t) x sin (ωωt φ )XtTf 1/TFig. 1 Periodic vibrationThe time length of a single vibration cycle is known as the vibration period T. The reciprocal 1/T is known as the vibrationfrequency and is expressed in cycles per second, or Hertz (Hz).The following sine function describes the undamped periodicvibration shown above:x(t) x sin (ωt φ);x(t): Displacement, instantaneous vibration valuex:Amplitude, maximum instantaneous valueω:Angular frequency; ω 2 π/T 2 π fφ:Phase angle, initial position of the oscillation att 0.The equation indicates the displacement - the vibration - as afunction of time.4 PRÜFTECHNIK AG Vibration Handbook
Introduction to vibration measurementThe fundamental physical source of this vibration and of therecorded signal could be thought of, for example, as follows:Fig. 2 Mass on spring pendulumThe vibration velocity v is the change in displacement x over aperiod of time. Its waveform is shifted by 90 from the positionof the displacement, i.e. velocity reaches its minimum (v 0)when amplitude is greatest. The velocity attains its maximumwhen the system oscillates through its zero level:v(t) x ω cos (ωt φ);The vibration acceleration a is the change in velocity over time.From a mathematical point of view, it is the second derivativeof displacement with respect to time. The acceleration waveform is shifted by 90 from the corresponding velocity wave(and therefore by 180 from the displacement curve). Thismeans that acceleration reaches its maximum when displacement is at its minimum; both pass the zero point at the sametime.a(t) -x ω2 sin (ωt φ);The displacement amplitude alone may be considered as follows:Vibration displacementx in mmVibration velocityv x ω in mm/sVibration accelerationa x ω2 in mm/s2At mid-range frequencies, vibration is normally measured interms of velocity; high frequencies call for acceleration mea- PRÜFTECHNIK AG Vibration Handbook5
Introduction to vibration measurementsurement. These deliver the best possible dynamic performance.1.1.1 Composite vibrationsWhen several periodic vibrations occur simultaneously, a com-S1XftXTS2f 2tXf S12 fS2tFig. 3 Superimposed sine wavesposite vibration results which is also periodic. This type of complex vibration is quite normal for practically all machinery.When vibrations overlap, the time domain depiction (with am-6 PRÜFTECHNIK AG Vibration Handbook
Introduction to vibration measurementplitude plotted along the time axis) cannot show individualwave components of the composite signal.1.1.2 Vibration parametersxx(t) x cos (ωω t φ ); xt 0φtfT 1/TFig. 4 Parameters of a sine waveAmplitude, frequency and phase angle determine the exactshape of a sine wave.The vibration frequency is important information for machinediagnosis, because certain causes of vibration - for example,rotor imbalance - occur at fixed multiples of the speed (frequency) at which massive components rotate.The phase angle φ describes the starting position of the oscillating point at time t 0. This phase angle and the phase difference between two measurement locations is extremely important for balancing and vibration diagnosis. PRÜFTECHNIK AG Vibration Handbook7
Introduction to vibration measurementStandard vibration parametersPeak-to-peak valuevalue::Difference between the largest and smallest vibration value,abbreviated as xppPeak valuevalue::Maximum vibration (also known as amplitude), abbreviated asxm.Median value:Quantifies the vibration strength over time:Definition: xMed 1x dt;TFor a sine wave: xMed 2 xmπEffective value:Quantifies the energy of vibration over time (also known as:RMS root-mean-square).Definition: xeff 1Tx2 dtFor a sine wave: xeff 12xmSxxMedxefft 0xmxmxppttt 0Fig. 5 Parameters of vibration strength measurementThe peak-to-peak value of a vibration is preferable when themaximum displacement is of interest, e.g. for problems relatedto machine component loading or internal separation distances.The peak value is best for examination of short-lived phenomena or transient signals.The effective value (RMS) shows most clearly the energy content of the vibration.8 PRÜFTECHNIK AG Vibration Handbook
Introduction to vibration measurement1.1.3 Conversion factorstoConversion ectivevaluePeak-to-peakvalue10.50.320.35Peak value210.640.71Median value3.141.5711.11Effective value2.831.410.901Fig. 6 Conversion factors PRÜFTECHNIK AG Vibration Handbook9
Introduction to vibration measurement1.2 Periodic vibration in the frequency domainAs mentioned earlier, when the vibration signal is composed ofseveral waves occurring simultaneously, the time signal alonedoes not show much information regarding its individual components. The frequency diagram obtained from the same timesignal, however, is generally much more useful because itclearly shows the individual vibrations (frequency components) which make up the complex signal.1.2.1 Fourier transformationThe French mathematician Jean Baptiste Fourier devised amethod for breaking down any waveform into a series of sinewave components, and conversely.In other words, everyday machine vibrations can be analyzedto determine which frequencies account for what portion ofthe overall measured vibration. Fourier's formulae supply themathematical basis for transforming the time signal into thefrequency spectrum.AmplitudeFrequencyTimeFig. 710Vibration in time and frequency domains PRÜFTECHNIK AG Vibration Handbook
Introduction to vibration measurementThe great advantage of displaying the frequency spectrum isthat all the individual components of vibration are readily recognizable.Time signalFrequency spectrumXt fXt fX tfFig. 8 Time signals and their corresponding frequency spectra1.2.2 Frequency analysisThe objective of frequency spectrum analysis is to break downa complex vibration signal into its individual frequency components according to their respective power. Experience hasshown that the operating condition can be observed very closely, since a machine in good condition exhibits a stable spectrum over extended periods of FrequencyFig. 9 Comparison of time domain vs. frequency domain PRÜFTECHNIK AG Vibration Handbook11
Introduction to vibration measurementReliable machine diagnosis is possible when the individualpeak frequencies in the vibration spectrum can be traced backto their corresponding machine parts.TransmissiongearsAnti-friction bearingUnbalanceFig. 10Machine vibrationsWhen measuring vibration, you should also consider that thesignal measured on the outer surface of the machine housingmay not coincide with the original 'inner' signal. The reason forthis lies in the transmission path.Example:If the inner ring of a bearing is damaged, the vibration must betransmitted from the inner ring via the rolling elements. thenthe signal is transferred from the outer ring outward via thebearing race and corresponding load-bearing housing portionto the measurement location. Here is where the vibrationtransducer converts the vibration into a measurable quantity e.g. voltage. Factors such as mass or rigidity of machine partsand the damping caused by individual parts - and, of course, atcomponent interfaces - can affect the output signal. This meansthat two identical machines mounted on different foundationsunder otherwise identical conditions can emit different vibration signals. These conditions must be considered when evaluating measurements.12 PRÜFTECHNIK AG Vibration Handbook
Introduction to vibration measurement1.3 Rigidity, mass and dampingA turbocompressor, for example, contains a vast number of thecomponents and interfaces just mentioned. Each of these components can in turn be seen as a separate vibration system untoitself. Detailed information on these components (mass-springsystems) and their vibration behavior is extremely beneficialtoward accurate machine vibration analysis - and nearly crucial to explaining and understanding phenomena such as resonance. Machines possess three qualities which determine theirvibration behavior - that is, their reaction to excitation forcesRigidity ("K" in kg/m),Mass ("m" in kg),Damping ("c" in kg s/m).cKmFFig. 11Mass-spring systemRigidity is a measure of force needed to bend or to stretch astructure by a certain amount (spring constant). Damping is ameasure of the force that works to counteract this.The relationship can be simplified as follows:Excitation force Rigidity ‘force’ Mass ‘force’ Damping ‘force’In other words: equilibrium always exists between the excitation force and the reaction forces (rigidity, mass and damping). PRÜFTECHNIK AG Vibration Handbook13
Introduction to vibration measurementIf any one of the reaction forces is increased, then the vibrationamplitude changes accordingly. The value of vibration amplitude is generally dependent on the total influence of the threereaction forces. In practice, however, these do not combine in alinear fashion.Example: Mass (weight) force is proportional to acceleration.Rigidity, in turn, is proportional to displacement. As a result,these two reaction forces tend to counteract each other, sincetheir phases differ by 180 (just like those of displacement andacceleration.)The third factor, damping, is proportional to vibration velocity,and its phase is 90 away from those of mass and rigidity.The vibration frequency must also be considered relative tothese opposing forces. While the rigidity remains constant overthe entire frequency range, the mass forces increase proportionally to the square of the frequency. At a certain frequency,the mass and rigidity forces are in equilibrium and effectivelycancel each other due to their 180 phase difference. The onlyresistant force remaining is that of damping, and as a result,the entire system vibrates at considerably higher amplitude.Displacementlow dampinghigh dampingFrequencyFig. 12 Resonance behaviorThis point is known as the resonance frequency. Here the amplitude can be held low with appropriately high damping.14 PRÜFTECHNIK AG Vibration Handbook
Introduction to vibration measurementAnother interesting resonance-related phenomenon is thephase shift that occurs between the excitation force and its resultant vibration. The circumstances previously mentionedlead to the conclusion that for frequencies below resonance, rigidity plays the dominant opposing role in phase with the vibration. At higher frequencies, the mass forces take over, with180 phase difference between the excitation force and the vibration. This means that a 180 phase shift between excitationand vibration takes place as the resonance frequency is passed.Phase shift(Angle change)180 180 high damping90 90 low damping0 0 FrequencyFig. 13 Phase shift as a function of rotation frequencyThe operator or measurement technician must realize that every system - including his favorite vibration transducer,mounting bracket or magnetic fixture - has its own resonancefrequency. The resonance characteristics of a vibration transducer mounted with a magnetic fixture can influence high-frequency readings considerably, and the transducer's own resonance frequencies can limit its applicability.Machines mounted on their foundations must be seen as complex systems composed of many mass-spring units. Each ofthese individual systems, in turn, has several degrees of freedom and its own resonance frequencies. This means that thesame aggregate can exhibit quite different vibration behaviorin different operating locations, since the foundation, pipingetc. all exert their influence on each individual oscillator.For example, it is nearly impossible to balance a rotor whichoperates near its resonance frequency, because then even minor speed deviations cause a phase shift of 50 or 60 . Thismultitude of potential oscillators, combined with a wide rangeof possible excitation sources, is quite a common situation inrotating equipment maintenance. PRÜFTECHNIK AG Vibration Handbook15
Introduction to vibration measurement1.4 SummaryBefore vibration readings are taken, the rotation frequencyand the frequency range of expected vibration should be ascertained. Any variable load characteristics such as pressure, flowrate, temperature etc. (all of which lead to different results)must be considered as well.A general evaluation of the vibration level can be made bycomparing the measured level with accepted standards for thesame machine type. ISO Standard 2372 defines these limits forthe measured RMS velocity veff . This value describes only thetotal vibration severity without regarding the actual cause ofvibration at the individual characteristic frequencies.Frequency analysis is the only method of examining a definedsource of vibration: with detailed knowledge of the machinedesign, the individual frequency components of the measuredspectrum can be traced to their respective sources, the offending machine parts. This procedure is especially suitable forcondition-based monitoring of machines, allowing the maintenance specialist to intervene when necessary.Displacement transducers deliver the best results at frequencies below approx. 10 Hz due to the limited dynamics of vibration velocity and acceleration within this range.Accelerometers are recommended for comprehensive examination over a wide frequency range, including high-frequencyvibrations above 1000 Hz (e.g. gears).16 PRÜFTECHNIK AG Vibration Handbook
Introduction to vibration measurement PRÜFTECHNIK AG Vibration Handbook17
Vibration transducers for various measurement problems2.Vibration transducersfor various measurement problemsVibration transducers transform mechanical movements intocorresponding electrical signals. Each type of transducer hasits own advantages and disadvantages depending upon thearea of application. The first step toward successful analysis istherefore selection of the appropriate transducer. This sectionexplains the three most important types of vibration transducers and the application areas in which each delivers the mostaccurate and repeatable measurements possible.2.1Piezoelectric transducer(Accelerometer)Piezoelectric transducers can be used to measure nearly all mechanical vibrations that occur in maintenance applications, because they provide accurate measurements over a very widefrequency range. Their resonance frequencies lie above theworking measurement range, and their desi
PRÜFTECHNIK AG Vibration Handbook 5 Introduction to vibration measurement The fundamental physical source of this vibration and of the recorded signal could be thought of, for example, as follows: The vibration velocity v is the change in displacement x over a period of time. Its waveform is shifted by 90 from the position
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The vibration analysis in Section 5 provides the FE-based vibration analysis procedure based on first principles direct calculations. The FE-based vibration analysis is recommended to evaluate the design during the detail design stage. If found necessary, the local vibration is tobe addressed in the detail vibration analysis. The
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vibration. Today, random vibration is thought of as the random motion of a structure excited by a random input. The mathematical theory of random vibration is essential to the realistic modeling of structural dynamic systems. This article summarizes the work of some key contributors to the theory of random vibration from
The dynamic vibration tests on structures are generally subdivided into two groups: (a) forced vibration test and (b) ambient vibration test. In the forced vibration test, the structure is usually excited by artificial means. The excita
The ISO 2631 suggests vibration measure-ments in the three translational axes on the seat pan, but only the axis with the greatest vibration is used to estimate vibration severity.5 The current trend in vibration research is to use multi-axis val-ues.
1 Fluke Corporation 3562 Screening Vibration Sensor FAQ Fluke 3562 Screening Vibration Sensor Frequently asked questions Q: Why should I use a vibration screening sensor and what is the benefit? A: Vibration anomalies are some of the first indications of misalignment, looseness, bearing wear
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