Piezoelectric Accelerometers
`and Vibration Preamplifiers
`
`Theory and Application Handbook
`
`
`
`APPLE 1036
`
`APPLE 1036
`
`1
`
`

`

`PIEZOELECTRIC ACCELEROMETER
`AND
`VIBRATION PREAMPLIFIER
`HANDBOOK
`
`by
`
`Mark Serridge, BSc
`
`and
`
`Torben R. Licht, MSc
`
`Revision November 1987
`
`Printed in Denmark: K Larsen & Sen A/S - DK-2600 Glostrup
`
`2
`
`

`

`CONTENTS
`
`VIBRATION MEASUREMENT....................::ccccccecsecseeceeseeeeserseeseseeseesssssenssensensess 1
`
`1
`1.1. INTRODUCTION ooo. csessccsseseseeesseeseceecensessensseeaecorsesorseonenseeaseaseestennennens
`1
`1.2. WHY MEASURE VIBRATION? ..00.0.......:ce:ceecceeceeceeeeeceececeeeeeeeresaneonssneeaneees
`1.3. WHAT IS VIBRATION? 000... eeeeeseececceececsceeeceecesecneceseeenseessenseatesnssanesneseas 5
`1.4. VIBRATION PARAMETERS.......0.o.....eeeesceeseesseessesseeaeeeceeeneceeceaeeneeeaeeetesenss 6
`1.5. THE QUANTIFICATION OF VIBRATION LEVELS.....0...... cc eeseseeeeereeees 7
`Linear amplitude and frequency scales.................-:.-::scssessseseeeeseeneeees 9
`
`Logarithmic amplitude and frequency scales .................::eeeeeee 9
`1.6. ANALYSIS OF VIBRATION MEASUREMENTS..................:-0oe 11
`
`THE PIEZOELECTRIC ACCELEROMETER..................00.0-eee 12
`
`2.1.
`2.2.
`
`2.3.
`
`2.4.
`2.5.
`
`2.6.
`
`2.7.
`2.8.
`
` ...0........:c-csccceeceeceeseceeeeansccececansececeaescecaceeeceeaseaesseeueaesensaees 12
`INTRODUCTION.
`OPERATION OF AN ACCELEROMETER ...............:.ccesceccceseeeceeseeseeeeeees 13
`Analytical treatment of accelerometer operation ...............:.ccceecees 14
`FREQUENCY RANGE....0000.:....:c.eccccsccecescecsescssesseeececstareatiteterssestessessereenes 18
`Upper frequency Jirmit: «2.2... cece eeeeceeseeeceesececeneeneceeeseeseaseeneenteneeetes 19
`Lower frequency JiMit «00... ecceesceeseeesersessceesersnsensensansessaenseesaneesnens 20
`PIEZOELECTRIC MATERIALS...............::ssscecsecsscceeseenereceessenesceeeessecensees 20
`PRACTICAL ACCELEROMETER DESIGNG ...............cscseesseereeeeeeeereteeees 22
`Line-drive accelerometers. ...........2.c:cccccccecseceesessesceteensesestereeneterseesseesnsens, 24
`
`Other GOSIQMS ....... ccc ececee ce ecereoeseeteceteneeseeseessenssensesonnensensensenseasseaseasesaees 25
`ACCELEROMETER SENSITIVITY ou... eeeseesecsesoneeseesoesetsneasensneseenees 25
`Charge and voltage Sensitivity .................c:cssscesssssessssrsseessssessassestsasees 26
`Uni-Gain® sensitivity ...........cccsscesssssessssesscessscscessessssecsereceseveesetesecreersenes 28
`Linearity and dynamic range...........
`28
`
`Transverse SONSItivity ............sccscsscsscsscesresscserssrcsseseeserscesscssnssenssnseatssnees 29
`PHASE RESPONSE uu... cccscsssescssssessccssscsscenersecsesssoseossncessanenesesseesorssesees 30
`TRANSIENT RESPONSE. 00.0... ccescccsseseeessesessscescerenecsecssesersenssnasensentnensens 33
`Leakage CFFCCHS on. ccssessessessessecstecessssessecrsscsteorsssssessscateesseensceseesteteetees 33
`
`ZOO: Shaft
`
`ye cececceccs cunesctertecnswestac sweet asa sosvThac oc. See eeteeae Eesescsnscoussonscdbessnartacs 37
`
`3
`
`

`

`3. VIBRATION PREAMPLIFIERS uu... ce csseseseeseeesesecseesaeseneeeeneneaseesees 38
`
`............:c:csesssesssesseeseeeens 39
`3.1. PREAMPLIFIER DESIGN AND OPERATION.
`3.2. CHARGE AMPLIFIERS.
`....0....2.2:.ccccccccccseceesecsceseesseessessnesseeseecseesnesensetserennens 39
`Charge Sensitivity ec ecensensesssessseseensestecsseceseesesseeetenteetsessepateeeeeatees 40
`Lower Limiting FreQuency ou... see eceeeereeeeeeeteeeeeneentoeteneeneenenee 44
`Capacitive loading of input by accelerometercables...............00 48
`Charge attenuation .......0.0....
`es
`See 49
`
`
`Noise in charge amplifiers ......
`castenseseceaececeeneeenseensenssaneaeesaneens 50
`3.3. VOLTAGE PREAMPLIFIERS .......
`WiicessaesStessenesseassanesenessceesesseeed 54
`
`
`Voltage SOMSITIVITY 20... eeeeeeeeceeceeeceeeeeetensenseseeeseescetaaenaceaseuneeaneseesanss 55
`
`Lower Limiting Frequency ou...
`eecesesenseesecnseeneeeeseneseseeessenssesssneesetane 56
`Noise in voltage preamplifiers 2.2.0.2... cecseseseesecsensseesenssnsseeenesanes 57
`3.4, PREAMPLIFIER OUTPUT CABLES. 000... ecceseessessecceenseenesneeneeeteneceesees 57
`3.5. LINE-DRIVE SYSTEMS. ou... eeeeeeseeeseeseeceecteeseeseesssesnensecseessessensseesetaneess 58
`Briel & Kjzer line-drive accelerometer and line-drive supply ........... 61
`Brdel & Kjzer line-drive amplifier and line-drive supply................00 61
`3.6. COMPARISON OF THE SENSITIVITY OF DIFFERENT
`VIBRATION PREAMPLIFIER SYSTEMS TO
`EXTERNAL NOISE SOURCES.
`........ccccccccccscenecseceecsecsesssessessessnessneseeens 61
`Grounded accelerometer and charge preamplifier OE
`64
`Grounded accelerometer with charge preamplifier
`(“floating” fpUut) oo. ec eeeseeteceeeseaeeeessaeneaseaseaeesaataatsaesasesetsansenseaneaes 65
`Bruel & Kjzer line-drive amplifier and power supply
`(QroUNdE” INPUt) uu... ee eee eceeeecenceeetecseneecceseteceeaneeeeaneseessesenesnessenseeees 66
`Bruel & Kjaer line-drive amplifier and power supply
`(“floating” iMDUt) 0... eee eeeseeeseeeeeeeeeseeeceeeeeeceseececeseecetearesnenessatesessessanss 68
`Line-drive system based on constant current
`POWEP SUPPLY ou... ec cetccetccseesseeeenereneeeseeeseessaeessneesseesenssensensenseessenessnenseaseenes 70
`Balanced accelerometer and differential charge
`AMPNFISL oo. eee csecsseneeeessceessenssecneaeseneensseesaeeseenseeseaeseaneesaeennesssuetensensiannes 69
`Insulated mounting of the accelerometer .Q...........:::ccccssseceeneeceeneeeees 71
`...........eceseseeseeserseesseeseeseeteentens 71
`3.7. SPECIAL PREAMPLIFIER FEATURES.
`
`Integration N@tWOrkS oo... ecesssscssesseeessseerenseasensensessensesescensensesenssasereetaes 72
`FiOS oo... cece esses neeneseneeesaters i rs sors Sere «Renee tne ee tne eet TeneenTic eaten Teast 76
`..........
`.. 78
`Overload Indicator.
`
`Reference Oscillator oo. eceeecesscsseeeseeseeeeeeeeeeeeeeeeneasseneensenessesensesnseates 78
`Power SUPpPlie@s
`..........ccscccssccssrsesecesnseesecsseessesaeeceseeseareuseessaesesnessuersenstansene 78
`
`4. ACCELEROMETER PERFORMANCE IN PRACTICE ...........00.0.ee 79
`
`A.A. INTRODUCTION oo ceesesseeeeeeeseseeseesensseaeeoesanseeseeensessensausaeseeaeanessensanes 79
`4.2. ENVIRONMENTAL EFFECTS.
`............cseccsesssesesccsscesnccaessscsrsssesenssansseeseees 80
`TEMPeratuUre FANGE cece scseeesesetsennenseesneeeetnneesensees
`. 80
`
`
`Temperature transient ..........cccessseessecerenseensenees
`. 82
`
`4
`
`

`

`Acoustic SENSITIVITY 2... eel cee cee cee eneeeeeneereneseenenenecneneeseaenannenenetanes 84
`BaSe StFAINS 0... cee ceseeeessteseeceeecctscetenessessesuecsecescsesseeaneussseneeseanesssseenenens 85
`HUMIGItY oo... cece ceeeeseeeteesessesesrseeessesesensesesecessensseensaeteeansenerseenensdenensonsen 85
`we 86
`Magnetic sensitivity 00.0.0...ccs eeeeceeeeeneeeeeceeenenees
`
`Radiation ....ccccccccccesesscsssseneeeecsecececsesenscoeeeseeaseeesenenscanenesenerseussensenenenieenens 86
`4.3. MASS LOADING EFFECTS OF ACCELEROMETERS. .........:eceeee 86
`4.4. MOUNTING THE ACCELEROMETER ........... ccc ececeseeeeeeeeeeneenenententenees 88
`Vibration test surface finish requireMeNts 0.2.00... cesses seteeeseeeteeeees 89
`Mounting loCation 20.0... cece eecenesseneenesseeeeeeneceneenstenseaeanensessenensenecneseeees 89
`Determination of the frequency response of accelerometers
`using different Mounting teCHMiquess .......... cece rerstststetseaenenens 90
`Stud MOUNTING 00...eeecceeeceseeeeesneenrssesseeeesrsnessesececsesescetesestensensersensesesens 90
`
`WAX MOUMRING 00.0... eeeeeccteerseeneseseceneceseeeessecsessesssnssncsssssseeseeseeessoasvassaeans 93
`Magnetic Mounting ............csceeseeeeseeeseeeneseneesceseeecaeaeseneneressssnsnstavavaenannas 95
`Self-adhesive MOUNtINg GiISCS 0.0... ec eee seeeteeneeeeeeeeneennesnenensensenes 97
`
`ACNeSIVES ........ccceccsccessersseseesscensetsnnensesnsaaescetseesesssacsassensensessesseeeansensneenaeenee 98
`
`PROBES) ecco sr. oces aeaewed aac sem erosisevecsresgpeesesssscessevscroggersecstecesdbasenseneereg 102
`.........-. eee eee eee esecesenseneneesneeesseseesaenenevenessenanenee 105
`4.5. MECHANICAL FILTERS.
`DOSCTIPtiON oo...eseesscssessesensssssorseonsnseaeseseceeneatsecsesenserenensearaaeasensoooantens 105
`Operation oo... ce eeseeesssssssssscssseenesesesssansessssasseseneenstsenseniansensenneaneenensannis 106
`4.6. ACCELEROMETER CABLES. uuu... cecccscsssesseneseeeeeneereeneneeeeaenenenesanones 107
`4.7. GROUNDING PRECAUTIONS. ou... ..ccesetcccsssscneceneeresseseeseesesesensnenestenses 109
`
`ACCELEROMETER CALIBRATION AND TESTING...}................ccseeeeee 111
`
`5.1. INTRODUCTION o....cccececsseescnsterecseeesereeraanasecusenenecseecaeseesarestesatentaennees 111
`Why calibrate an accelerometer? .........cecseseccseseeserseesesseeeseereerereeses 113
`5.2. THE HIERARCHY OF CALIBRATION STANDARDS)
`............0ceeee 114
`
`The general hierarchy 00... ccesesccessssesesssesscesesseneeeterseeseaeseanennsenenees 114
`
`The hierarchy at B&K weeseceteneseesenteeeesssesessesersteseeseensonsersaseaees 115
`The accuracy of calibration techniques.
`............cccssseceeeeteereeeeeeees 118
`5.3. CALIBRATION METHODS. uu... icc ecesssessscnsetsscsseesseseesessensensnseneenteeneeae 119
`Laser InterferomMetery 20.0... ccsessccseeceessseneceseresssenscnestsenseessesnensneneesees 119
`Other absolute Methods ......... cece eeecceeeeereeeeesssssassecereeeneneetanenteenesseeses 121
`Comparison calibration by the
`“back-to-back” Method ...........ccceeecsceeceeseeeerssenseeseeveuseeceeeeansententeseesanes 121
`FFT-based back-to-back Calibration ......... cece eceeeeteereeereeeennetee 123
`The use of calibrated vibration exciters
`for SeNSitivity CHECKING ..........ccsssessssseseeseesseesesecessenetenteneeeeenseeanoes 124
`5.4. MEASUREMENT OF OTHER ACCELEROMETER PARAMETERS .. 125
`Transverse SENSITIVItY .....-.. eect see stscneneensenseesnssnseasesnereeteseanennenenes 125
`FrEQUENCY ESPONSE .........esseseescesseessescsrssecssesrensneseensetonsesssessnateneseesauanes 126
`Undamped natural frequency.............ccscsseccsseesetetesereeeneteentenneessneenans 128
`Capacitance oo...esessscssessssssssssssensestecenenenensersnensecesseaeseneeetensesrstiesesaeeness 129
`
`5
`
`

`

`5.5. DETERMINATION OF THE EFFECTS OF THE ENVIRONMENT
`
`
`
`....0.....eee 129
`ON THE ACCELEROMETER SPECIRICATIONS.
`Temperature transient sensitivity 0.0... eee ee cee cence seeseneneeneee 129
`Temperature Sensitivity 0.0...eee seeeteeeeneeteetceteceteetees
`te
`Base strain Sensitivity ............. ce ecceecceececeeeeeceeeceeeeeeeeeseeseteeeeeeseeteneeee 130
`ACOUSTIC SONSITIVILY oon. ee eee eeeereeeeeeeeteeeteeeeeeseeeeeeteereeereeraeeceasaeens 130
`Magnetic Sensitivity 0. ccc csscesssensenssesseessesssssasereserssiessensseasecneee 131
`Temperature lIMits .2...... eee eee eeeseeseeecee tee eceeseesseeseeseeeseeseeesteneeeareneenaes 131
`SHOCK VWMits oe ee ee eeeeeeseeeeeeeeeeeeeaceseeseesseeescasesassaseuneseessensenseseneseeses 132
`5.6. FACTORY TESTING OF ACCELEROMETER CABLES..............0000 132
`5.7. CALIBRATION EQUIPMENT uu... eeeecsesereeessensensssesecseceenseesesesseeesnes 133
`Calibration System Type 9559 ooo... cece eeeeeeeeceeseeeeeeneenersenssesseesseses 133
`Individual calibration CQUuIPMENt ........ ccc est ceeeeeeseeeneenseenesateeee 133
`5.8. STANDARDS RELATING TO THE CALIBRATION
`OF ACCELEROMETERS. ou... cesses eeeeecesceeseeseeeeeseeeneccersoeseesetseeereneers 134
`
`APPENDICES oun... cecccecscccccsseeseceeceeeseenecerenesenseseesanersassneaaseasensnaseesneasansenenes 137
`
`APPENDIX A. Conversion Charts .0..0...0.....esesscessesseeeeeseteeeeereeseseneseesenaeans 138
`APPENDIX B. Vibration NOMOGrFAM ou... eee esse cseeneerseseesceereneseneorserseeaes 141
`APPENDIX C. Vibration standards .0..0..... ec eseeseecesceseeesersaesasesessenseesseoes 142
`APPENDIX D. Briel & Kjzer Vibration Literature 0... cee seeenreeenesen 142
`APPENDIX E. Summary of Briel & Kjaer Preamplifiers ...0...0. cece 144
`APPENDIX F. Summary of Brie! & Kjzer instruments
`with built-in preamplifiers 0.0... ee cece ccceeeeseeseesestenstenteee 146
`APPENDIX G. Briel & Kjzer accelerometer frequency and dynamic
`FANGS CHAPS ooo. eee ceeeeseteeeseeeeeeseeeesssaeeessensasesseeseneesseseeees 148
`APPENDIX H. Summary of Briel & Kjzer accelerometers ............. eee 150
`
`6
`
`

`

`t
`
`= Time
`
`= Frequency
`f
`= Angular frequency
`w
`jo =
`
`Xs
`
`of
`
`seismic
`
`e
`
`= Baseto the Natural Logarithm
`
`General Dynamics
`
`4hn®<&
`
`= Velocity
`
`= Acceleration
`u
`Force
`= Peri
`eriod
`ul
`Time constant
`
`@m
`
`A
`
`Z;
`
`2,
`
`
`SYMBOL NOTATION
`
`
`
`
`General Quantities
`Accelerometer Dynamics
`
`
`Seismic mass
`
`Mass of base
`= Displacement
`mass
`
`Displacement of base
`Excitation force
`
`
`
`Natural resonance frequen-
`cy (rads/sec)
`
`
`= Mounted
`resonance
`
`quency (rads/sec)
`
`Mounted resonance_fre-
`
`quency (Hz)
`= Displacement
`
`
`
`
`
`= Mechanical
`r
`structure
`
`Impedance of
`= Mechanical
`accelerometer
`
`
`
`
`General Electrical Quantities
`
`Current
`
`
` Voltage
`= Charge
`I
`
`
`Capacitance
`= Resistance
`
`
`N2OO<
`
`
`fre-
`
`= Amplification factor
`
`Impedance of
`
`Impedance
`
`7
`
`

`

`SYMBOL NOTATION
`
`
`
`Accelerometer Electrical
`Quantities
`
`Preamplifier Electrical
`Quantities
`
`Preamplifier
`tance
`
`input
`
`resis-
`
`Preamplifier
`tance
`
`input capaci-
`
`Feedback capacitance
`Feedback resistance
`
`Gain of operational amplifi-
`er
`
`Preamplifier input voltage
`
`Preamplifier output voltage
`
`Feedback impedance
`
`impedance of accel-
`Total
`erometer, cable and pream-
`plifier input
`
`Current from C,
`
`through feedback
`Current
`capacitor
`
`Voltage across
`capacitor
`
`feedback
`
`Opencircuit accelerometer
`voltage
`Charge generated by pi-
`ezoelectric elements
`
`Capacitance of accelerom-
`eter
`
`Resistance of accelerome-
`ter
`
`Chargesensitivity of accel-
`erometer
`
`Voltage sensitivity of accel-
`erometer (loaded)
`
`Sva0
`
`= Voltage sensitivity of accel-
`erometer (open circuit)
`
`Capacitance to the housing
`of a balanced accelerome-
`ter from the output pins
`
`Electrical Quantities
`
`Capacitance of cable
`Series resistance of cable
`
`Resistance between centre
`conductor and screen
`
`between
`Capacitance
`screen and inner conductors
`in balanced accelerometer
`cable
`
`Capacitance of dielectric in
`balanced
`accelerometer
`cable
`
`Triboelectric charge noise
`
`Cy
`
`Qn
`
`=
`
`ES
`
`R,float
`
`CMRR
`
`
`
`|
`
`Total capacitance of accel-
`erometer, cable and pream-
`plifier input
`Total resistance of acceler-
`ometer, cable and pream-
`plifier input
`
`“floating”
`of
`Resistance
`stage of preamplifier
`
`Common Mode Rejection
`Ratio of “floating” opera-
`tional amplifier
`
`Noise voltage
`Noise current
`
`Output resistance of
`drive amplifier
`
`line-
`
`8
`
`

`

`1. VIBRATION MEASUREMENT
`
`1.1. INTRODUCTION
`
`Recent years have seen the rise of vibration problems associated with struc-
`tures which are more delicate and intricate, and machines which are faster and
`more complex. The problems have been coupled with demands for lower
`running costs and increased efficiency. Concern has also arisen about the
`effects of noise and vibration on people and on the working lifetime of manu-
`factured items. Consequently, there has been a requirement for a greater
`understanding of the causes of vibration and the dynamic response of struc-
`tures to vibratory forces. To gain such an understanding an accurate,reliable
`and versatile vibration transducer is required. In addition, advanced measure-
`ment and analysis equipmentis often used. However, both the versatility and
`capability of such equipment would be wasted without an accurate vibration
`signal from a reliable vibration transducer.
`
`The piezoelectric accelerometeris the optimum choice of vibration transduc-
`er. The extensive range of high performance measuring equipment now avail-
`able canfully utilize the very wide frequency range and dynamic range offered
`by this type of vibration transducer.
`
`This handbookis intended primarily as a practical guide to making accurate
`vibration measurements with Briel & Kjzer piezoelectric accelerometers.
`
`1.2. WHY MEASURE VIBRATION?
`
`Vibration is measured for many different reasons. In general all uncontrolled
`vibration is an undesirable phenomenon which gives rise to noise, causes
`mechanical stress and is a possible cause of structural failure. Four broad areas
`of vibration measurement can be defined:
`
`1. Vibration Testing. As part of a general environmental test program or as a
`part of engineering design, vibration testing performs the vital role of
`finding out how well a component can endure the vibration environments
`whichit is likely to encounter in a real-life situation.
`
`9
`
`

`

`During a vibration test, a structure (an aircraft component for example) is
`subjected to high vibration levels with a vibration exciter. The vibration level
`Is held constant in defined frequency regions and the frequency is swept.
`This is achieved with a vibration exciter controller and a feedback acceler-
`ometer which provides data concerning the acceleration to which the struc-
`ture is subjected. With the addition of a second accelerometer attached to
`the structure, frequency response information is obtained.
`ai
`
`ae
`
`Fig. 1.1. Vibration testing of an insulator used in the construction of a high
`voltage electricity pylon
`
`10
`
`10
`
`

`

`|
`
`i ial
`
`2. Machine Health Monitoring and Fault Diagnosis. In its simplest form an
`overall measurement of vibration level on a machine is used to give a
`warning of impending problems. However, more information can be ob-
`tained by frequency analysis. This technique involves measuring the charac-
`teristic frequency spectrum of the vibration of a machine in good condition
`and monitoring any changes of the spectral components using vibration
`measurements over a period of time. Such changesare normally indications
`of impending problems. Fault diagnosis can also be performed using vibra-
`tion measurements.
`
`ed
`
`Fig. 1.2. Vibration measurements are used in a machine-health monitoring and
`fault diagnosis program
`
`11
`
`11
`
`

`

`in Industry vibration measurements also form the basis for correcting shaft
`unbalance in rotating machines. Unbalance is a cause of high vibration
`levels which often lead to fatigue and bearing failures.
`
`3. Structural Analysis. This is a powerful experimental method for determin-
`ing the dynamic behaviour of a structure using vibration measurements.
`Using a force transducer and an accelerometer, the excitation signal and
`vibration response of a structure are measured simultaneously using a dual
`channel analyzer. High speed computation, performed within the analyzer
`and often in conjunction with a desk-top computer, provides essential
`information for the design verification and modification of structures vary-
`
`ing in size from small turbine blades to large bridges.
`
`Fig. 1.3. The structural analysis of a train carriage using vibration measure-
`ments
`
`12
`
`12
`
`

`

`4. Human Vibration Measurement. This area concerns the measurement of
`
`the vibration transmitted to human beings. These vibrations can, for exam-
`ple, originate from passenger vehicles and hand-held power tools. The
`measured vibration levels are then related to human comfort and health
`criteria by International Standards.
`
`ie
`
`i7
`
`Fig. 1.4. Measuring the vibration levels transmitted from the handle of a chain
`saw using an accelerometer and a vibration meter
`
`1.3. WHAT IS VIBRATION?
`
`Vibration is a dynamic phenomenon observed as a to-and-fro motion about
`an equilibrium position. Vibration is-caused by the transfer or storage of energy
`within structures, resulting from the action of one or more forces. Vibration is
`often a by-product of an otherwise useful operation and is very difficult to
`avoid.
`
`13
`
`13
`
`

`

`Vibrations can be observedin the time domain,i.e. the change in the ampli-
`tude of the vibration with time (“time history”). Vibration time histories canfall
`into one of several classes as defined by their mathematical form or by the
`statistical properties of the motions they contain. Vibrations can also be looked
`at In the frequency domain where the vibration is described by its frequency
`spectrum. The two domains are related mathematically via the Fourier Trans-
`form. Consult the Briel & Kjzer book “Frequency Analysis” which deals with this
`topic.
`
`Unlike other vibration transducers, piezoelectric accelerometers are used to
`measure ail types of vibrations regardless of the nature of the vibration in the
`time domain or the frequency domain, as long as the accelerometer has the
`correct frequency and dynamic ranges. Because of the wide frequency and
`dynamic ranges of piezoelectric accelerometers it is always possible to find a
`particular type for any vibration measurement. It is only the analysis techniques
`which must change according to the type of vibration.
`
`1.4. VIBRATION PARAMETERS
`
`The piezoelectric accelerometer measures acceleration and this signal can
`be electronically integrated once to provide the velocity signal and a second
`time to provide the displacementsignal. This is an attractive feature of piezo-
`electric accelerometers.
`
`Fig. 1.5 shows the effect of integrating the acceleration of an electric drill.
`The vibration is displayed in the frequency domain. The integrator acts as a
`low-passfilter and attenuates the high frequency components present before
`the integration. Using an integration network effectively “throws away” infor-
`mation about the vibration. Obviously this is only acceptableif the lost informa-
`tion is not required for the purpose of the measurement.
`
`Acceleration should always be usedif there is no reason for an integration.
`For example, an obvious reason for measuring velocity is to obtain the actual
`vibration velocity magnitude.It is also often desirable to minimize the dynamic
`range requirements of the measuring instruments in the vibration measurement
`set-up and henceincreasethe signal-to-noise ratio of the measurement. This is
`achieved by using the parameter which gives the flattest frequency spectrum
`(see Fig.1.5(b)). Only frequency analysis can reveal the frequency composition
`of a vibration signal. For broad-band (wide frequency content) measurements
`on rotating machines the velocity parameteris found to be the best in 70% ofall
`cases, acceleration in 30% and displacementis hardly ever used. Displacement
`parameters are sometimes used for measurements of low frequency and large
`displacementvibrations often encountered on structures such as ships, build-
`ings and bridges.
`
`14
`
`14
`
`

`

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`Fig. 1.5. Frequency analysis of the vibration of an electric drill using the three
`different measurement parameters-acceleration, velocity and displace-
`ment
`
`When complex signals such as shocks and impulses are measured integra-
`tion networks should not be used becausethey introduce phase errors resulting
`in serious amplitude measurementerrors.
`
`1.5. THE QUANTIFICATION OF VIBRATION LEVELS
`
`There are several ways of quantifying the vibration amplitude of a signal in
`the time domain. The actual measurementunits (for example, in/s?, m/s?, g etc)
`maydiffer although the descriptors described in this section are widely used.
`
`7
`
`
`
`15
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`15
`
`

`

`
`
`
`
`
`
`
`
`
`
`§2
`2>
`
`Fig. 1.6. Simple harmonic vibration. The amplitude referred to can be displace-
`ment, velocity or acceleration
`
`Fig. 1.6 shows the simplest form of vibration time history.It is represented by
`a particle oscillating about a reference position where exactly equal conditions
`of motion are encounteredatfixed time intervals. This time interval is called the
`period,T, of the vibration. The vibration amplitude varies sinusoidaily with time.
`
`It can be shown that the shape and period of the vibration remain the same
`when displacement, velocity or acceleration amplitude is chosen to represent
`the motion. Only the relative phases are different.
`
`The amplitude of the vibration signal shown in Fig. 1.6 can be described by
`using the following descriptors.
`
`1. RMS (Root Mean Square) Level: Provides the most useful description of
`vibration levels. The square root of the integrated time-averaged squared
`function is related to the vibration energy and hence the vibration’s damage
`potential. The RMS value of a sine waveis 1/2 times the value of the peak
`level.
`
`2. Peak Level: Defines the maximum level which is measured and is useful in
`the measurementof short duration shocks. However, no accountis taken of
`the time history of the vibration.
`
`3. Peak-to-peak: Although of some usein describing vibration displacements,
`this descriptor is rarely used.
`
`4. Average Level: Takes the time history of the vibration into account but
`there is no useful relationship between the average level and any physical
`quantity. In Fig. 1.6 the average value of the rectified sine wave is referred
`to.
`
`16
`
`16
`
`

`

`5. Crest Factor: Defines the ratio of the peak value of a signal to the RMS
`value. From the definition of RMS above, the crest factor for the sine wave
`in Fig. 1.6 is V2. As the vibration becomes more impulsive, or more random,
`the crest factor increases. This simple relationship is easily calculated with
`a simple vibration meter equipped with RMS and peak facilities. When
`making wide-band measurements on a machine’s bearing housing, an in-
`crease in a single vibration component caused by a faulty bearing may be
`undetectable in the RMS measurement, but might be indicated by an in-
`crease in the crest factor. Hence by monitoring the growth of the crest
`factor, it is possible to predict a breakdown or element fault.
`
`Another example of the utility of crest factors can be found in structural
`testing techniques. The crest factor of the input signal to the structure can
`reveal important information about the excitation. If the crest factor is very
`high, as can be the case with hammer excitation, the structure may be
`driven into non-linear dynamic behaviour. A high crest factor also indicates
`that the input may not contain sufficient energy to obtain a good signal-to-
`noise ratio. On the other hand, a high crest factor is an indication that the
`input has a wide frequency range.
`
`1.5.1. Linear Amplitude and Frequency Scales
`
`Linear amplitude and frequency scales are used in vibration measurements
`when a high resolution is needed. A linear frequency scale helps to separate
`closely spaced frequency components. The linear frequency scale gives the
`further advantage that equally spaced harmonic components of a vibration
`signal are easily recognized.
`
`1.5.2. Logarithmic Amplitude and Frequency Scales
`
`Piezoelectric accelerometers are capable of accurate vibration measure-
`ments over extremely wide dynamic and frequency ranges. Therefore, to obtain
`convenient interpretation of results the following are often required:
`
`1. An amplitude scale which can accomodate vibration amplitudes from the
`lowest detectable amplitudes up to shock amplitudes, and which can also
`simplify the comparison of vibration amplitudes.
`
`A frequency scale with the same percentage resolution over the whole width
`of the recording chart.
`
`The two objectives can be achieved using the followiig:
`
`17
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`17
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`

`

`1,
`
`A decibel scale. Although more commonly associated with acoustic mea-
`surements the decibel (dB) is equally useful in vibration measurements.It is
`defined as the ratio of one amplitude to another and it is expressed in a
`logarithmic form. For vibration amplitude ratios the following relationship
`exists:
`
`N(dB) = 10 logo ( —Gret
`
`a?
`
`= 201lo
`
`G10
`
`
`a
`Aret
`
`Where
`
`N
`
`a
`
`= numberof decibels
`
`= measured vibration amplitude
`
`Ares
`
`= reference amplitude
`
`According to ISO 1683 the reference amplitudes are as follows:
`
`Acceleration = 10%ms7?
`
`Velocity
`
`10°°ms"
`
`Displacement = 107'?m
`
`For a sine wave of angular frequency w = 1000radians per second (at
`approximately 159Hz) these amplitudes are numerically equivalent. The
`reference amplitudes must be referred to when vibration levels are stated in
`dBs (e.g. “The vibration level was measured at 110 dBreferred to 10° ms”).
`However, when vibration amplitudes are compared, the difference in the
`decibels can be used providedthat they are referred to the same reference.
`For example,
`it
`is correct to say that one level
`is 20dB above another
`without any further reference.
`
`A logarithmic frequency scale. Frequency is sometimes plotted on a
`logarithmic scale. This type of scale has the effect of expanding the lower
`frequency ranges and compressing the higher frequency ranges. The result
`is equal relative resolution over the frequency axis (on a screen or on
`paper), and the size of the scale is kept to reasonable proportions. Thus a
`logarithmic frequency scale is used to cover a wide frequencyscale.
`
`10
`
`18
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`18
`
`

`

`1.6. ANALYSIS OF VIBRATION MEASUREMENTS
`
`The amountof information that can be obtained from traditional time domain
`analysis is limited although modern time domain analysis techniques are be-
`coming more powerful. However, with the addition of frequency analysis equip-
`ment, such as analogue and digital frequency analyzers, very useful additional
`information is obtained. No in-depth coverage of instruments of this nature is
`given in this handbook. The Briel &Kjaer books “Mechanical Vibration and
`Shock Measurements” and “Frequency Analysis” should be referred to for a
`solid theoretical background in frequency analysis, while the main and short
`catalogues should be consulted for details of the range of instruments available
`from Brdel & Kjzer.
`
`The complexity of the measuring instrumentation and the analysis of results
`may vary widely. But in every case the vibration transduceris the mostcritical
`link in the measurement chain, for without an accurate vibration signal the
`results of further analysis will not be reliable.
`
`The most reliable, versatile and accurate vibration transduceris the piezo-
`electric accelerometer.
`
`11
`
`19
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`19
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`

`

`2. THE PIEZOELECTRIC ACCELEROMETER
`
`2.1. INTRODUCTION
`
`The aim of this chapteris to give a basic, and often theoretical insight into the
`operation andthe characteristics of the piezoelectric accelerometer. Due to the
`nature of its operation the performance of the vibration preamplifier will need to
`be included to a small extent. However for a complete description of the
`operation and characteristics of preamplifiers, Chapter 3 “Vibration Preamplifi-
`ers” should be consulted. A summary of the complete Briel & Kjzer range of
`accelerometers can be found in Appendix H.
`
`The piezoelectric accelerometer is widely accepted as the best available
`transducerfor the absolute measurementof vibration. This is a direct result of
`these properties:
`
`1. Usable over very wide frequency ranges.
`
`2. Excellent linearity over a very wide dynamic range.
`
`3. Acceleration signal can be electronically integrated to provide velocity and
`displacement data.
`
`4. Vibration measurements are possible in a wide range of environmental
`conditions while still maintaining excellent accuracy.
`
`5. Self-generating so no external power supply is required.
`
`6. No moving parts hence extremely durable.
`
`7. Extremely compact plus a high sensitivity to massratio.
`
`In order to appreciate these advantagesit is worth examining the character-
`istics of a few other types of vibration transducer and vibration measurement
`devices.
`
`1. Proximity probe. A device measuring only relative vibration displacement.
`It has a responseto static displacements and also a low electrical imped-
`ance output. However, the device is not self-generating and the high fre-
`quency performance is poor.
`In addition the vibrating surface must be
`electrically conductive.
`
`12
`
`20
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`20
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`

`

`2. Capacitive probe. A small, non-contact, vibration displacement transducer
`with a high sensitivity and a wide frequency range. The disadvantages are,
`however, that the vibrating surface must be electrically conductive, the
`probe’s dynamic rangeis very limited and it is difficult to calibrate.
`
`low impedance device capable of
`3. Position potentiometer. A low cost,
`measuring static displacements. However,
`the dynamic and frequency
`rangesare limited and the device only has a short workinglifetime and low
`resolution.
`
`4. Piezoresistive transducer. A vibration acceleration transducer which is
`capable of measuring static accelerations. The measuring frequency and
`dynamic ranges can be wide. The limited shock handling capacity means
`that this type of transducer is easily damaged. Viscous damping is often
`used to protect the transducer against shocks. However, this leads to a
`reduction in the operating temperature range and alters the phase charac-
`teristics.
`
`5. Moving coil. A self-generating low impedancevibration velocity transducer.
`It is severely limited in its