fundamentals of electrodynamic vibration testing...

Fundamentals ofElectrodynamic Vibration

Testing Handbook

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Introduction................................2

A. Electrodynamic ShakersSize & Force...........................3Displacement, Velocity, & Acceleration........................3Frequency Range....................4Armatures................................4Centering & Support.............. 5Head Expanders & Plates.......5Fixturing..................................6Sliptables.................................6Cooling....................................7Chamber Interface.................. 7Vibration Isolation..................8Noise Levels...........................8

B. Vibration ModesRandom...................................9Real Data Acquisition & Playback (RDAP)...............9Sine with Resonant Search & Dwell................................ 10Classical Shock.....................10Shock ResponseSpectrum (SRS)....................11Sine-on-Random...................11Random-on-Random.............11

C. Amplifier Console.............. 12Inverters................................12Magnetic Field Power Supply...................................12Console Design.....................12

D. Vibration Controllers & Instrumentation..................13Software................................13Dynamic Range.................... 14Spectral Resolution...............14Data Acquisition...................15

E. AccelerometersAdvantages & Size............... 16Mounting..............................16Types & Conditioning..........17Sensitivity & Environments.18

F. Universal Vibration Calculator........................... 19

G. References, Resources & Websites.......................... 19

H. Move-in & Installation Questions& Considerations.............. 20

I. Handy Equations & Engineering Reference.......23

J. Handy Conversion Factors & Materials Properties......24

Written and published byThermotron Industries, Holland, MI Copyright 2006.

1gElectrodynamic Vibration Handbook

Table Of Contents

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Vibration testing is performed fora variety of reasons: to determineif a product can withstand the rig-ors of its intended use environ-ment, to insure the final designwill not fall apart during shipping,for Environmental StressScreening to weed out productiondefects, or even as a form ofAccelerated Stress Testing.Vibration tests are commonly usedto improve the reliability of mili-tary hardware, avionics instrumen-tation, consumer electronics, auto-motive components, and telecom-munications gear.

Electrodynamic vibration systemsare capable of performing manydifferent tests that specify sine,random, shock, sine-on-random,random-on-random and other com-plex waveforms as well as repli-cating data that is collected fromreal world conditions.

Breaking the electrody-namic vibration sys-tem down into its dis-crete components, weare quite simply leftwith something anal-ogous to a stereo sys-tem – a big and pow-erful, industrialstrength stereo sys-tem. Using a vibration

control system (synonymous withthe CD player), a signal is sentthrough an amplifier (similar to theamplifier used for a home stereo),to the shaker (something like aspeaker, but made mostly out ofsteel and weighing several tons),where the armature (comparable tothe stereo speaker’s woofer orvoice coil) moves up & down orback & forth in a magnetic field.An added element to the vibrationsystem is an accelerometer thatsenses the output of the shaker andsends this signal back to the con-troller for fine tuning. The con-troller in turn sends a drive signalback to the amplifier which pro-vides accurate, closed-loop controland spectral shaping of the testbeing performed.

This resource presents fundamen-tal concepts and the basic elementsthat comprise an electrodynamicvibration system.

2g Electrodynamic Vibration Handbook

Introduction


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Size & Force (F=ma)When sizing an electrodynamicshaker for a specific applicationyou need to first take into accounttwo essential factors. What is themoving mass(armature, fixture and product)and what acceleration level needsto be achieved? Multiplying thesetwo factors together provides theforce required to perform the testfunction. In the event that theshaker is attached to a sliptable,the mass of the slip plate and driv-er bar attachment must beaccounted for. When a shakerinterfaces with an environmentaltest chamber, the mass of the ther-mal barrier must be added to thetotal moving mass. Don’t forgetto account for miscellaneous massthat mightotherwise beoverlookedsuch as: headexpanders orplates, bolts &nuts, cables,etc. Force canbe expressedin the Englishunits, lbf orthe metricequivalent,kN. It is notuncommon

for the manufacturer of vibrationsystems to derate actual shakerforce capabilities to 80% of theirtrue value as a measure of conser-vative safety.

Displacement, Velocity &AccelerationThe three functional limits to elec-trodynamic shaker performanceare displacement, velocity andacceleration. Displacement limitsshaker operation at the lowest fre-quencies, and acceleration limitsthe shaker performance at thehighest frequencies. Velocity lim-its shaker performance in a bandbetween the other two limits. Asan example, Thermotron’s DS-2250 vibration system has a dis-placement limit of 2” peak-peak, a

velocitylimit of100 inchesper second,and anaccelera-tion limitof 100 g’s.Each ofthose limitsappliesover a dif-ferent fre-quencyrange.


A. Electrodynamic Shakers

An example of a Force calculationF=ma

Vertical Horizontal

Product Mass 25 lb 25 lb

Fixture Mass 40 lb 40 lb

Cables Mass 2 lb 2 lb

Head ExpanderMass

60 lb NA

Slipplate Mass NA 65 lb

Armature Mass 23 lb 23 lb

Total Mass 150 lb 155 lb

Acceleration Level 10 g 10 g

Force Required 1500 lbf 1550 lbf


Displacement of an electrodynam-ic shaker is a function of how farup and down the armature is capa-ble of traveling. Most shaker sys-tems are limited to 2” (50 mm)peak-to-peak travel. This meansthat an armature can travel up oneinch (25 mm) and down one inch(25 mm) from its center position.It is standard practice to protectthe shaker from overtravel situa-tions by utilizing sensors that shutthe system down before themechanical limits of the shaker areexceeded.

Velocity is the speed at which thearmature can move. Velocity limitsfor electrodynamic shakers canreach 100 inches per second (2.5m/sec). The higher the velocitylimit, the greater the shaker’s capa-bility of attaining a wider range ofshock pulses.

Acceleration is expressed in termsof gravitational units or g’s. A sin-gle g is equal to the accelerationdue to gravity 32 ft/sec2 (9.8m/sec2), 2 g’s is twice the acceler-ation due to gravity and so on.When the term grms is encoun-tered, it is used to specify the rms(root mean square) g level of arandom acceleration profile. Sineand shock acceleration levels are

expressed in terms of g pk, wherepk stands for peak. The accelera-tion component of a vibration testis typically prescribed by the testspecification.

Frequency RangeElectrodynamic shakers operatethrough a wide frequency rangethat is typically from 5 Hz to 3,000Hz. Most test specifications in theautomotive and transportationindustry emphasize low frequen-cies (ie: below 1,000 Hz) whilemilitary vibration specificationsnormally call for testing out to2,000Hz and electronics industryspecs can go as high as 3,000 Hz.

Armatures

Among the general rules of thumbfor armature design and construc-tion are:


above: A 16” armature


• A lightweight armature is favor-able and will permit testing at higher g levels.

• The armature structure should provide a significant amount of stiffness.

• Material of construction is oftenmagnesium or aluminum.

• Magnesium has a very high strength-to-weight ratio and provides superior damping, making it a favored material.

• Smaller lighter armatures may be appropriate for testing small-er products, while larger arma-tures can eliminate the need to use a head expander, reducing system mass and improving transmissibility.

Centering & SupportThe armature needs to remain cen-tered in its travel. Using an opti-cal sensor to locate the armatureand an automated pneumatic fill &drain system, the armature, baretable or loaded, will stay true to itscourse. Merely centering thearmature at the beginning of a testis neither adequate nor safe.Advanced systems possess theability to continuously center thearmature while a test is inprogress. Another feature of mostshakers is a centerpole and bearingshaft that helps to keep the arma-

ture properly aligned during oper-ation. It is good practice to loadfixture and product weight overthe center of the armature to avoidoverturning moments. In theevent the payload center of gravitycannot be located over the centerof the armature, additional guid-ance may need to be added to thesystem to prevent shaker damage.

Head Expanders & Plates

If large or multiple productsextend too far beyond the edge ofthe armature, the product could bedamaged or overtested. Using ahead expander or head plate toincrease the armature mountingarea and properly tie the fixturingand products should alleviate thispotential problem.

Head expanders and plates shouldbe designed for proper stiffness(ie: gusseted and welded) and


above: Head expanders are used forlarge or multiple products


should not be bolt-together struc-tures since bolted joints reduceenergy transmission. Favoredmaterials of construction are mag-nesium or aluminum.

FixturingIn addition to acting as a mountinginterface between the shaker andthe product to be tested, a vibra-tion fixture needs to be rigid andlightweight. The vibration fixtureshould also transmit a uniform dis-tribution of energy from the arma-ture to the test item. In manycases, vibration is applied in threeorthogonal axes. Specializedvibration fixture designs permit thefixture to be rotated for testing inthe X, Y, and Z axis. It is commonto find the weight of a fixture to betwo to three times heavier than theproducts to be tested. Fixturesshould mount easily to the arma-ture and products should mounteasily to the fixture. Quickchanges from product to productand axis to axis help to maximizeequipment utilization and improvelab productivity.

SliptablesA sliptable assembly is used whenvibration is required in the hori-zontal axis. For this purpose, theshaker is mounted in a trunnion

which allows the shaker to berotated 90°. A single piece tableconstruction with a solid trunnion limits the relative bodymotion of the shaker and improveslow frequency/high displacementperformance of the overall systemby solidly linking all of the reac-tion mass of the shaker to the slipt-able base. The solid trunnion andbase configuration also limits thepotential problems associated with


above: Sliptable assembly.

above: A Thermotron horizontal sliptableavailable in various sizes.


misalignment which can plague atwo piece system. Beyond the standard oil film systems, sev-eral options such as guidelinetracking and hydrostatic bearings,are available to further control trueand consistent horizontal vibrationperformance.

CoolingShakers consume significant elec-trical power which is converted toheat. Cooling of field coils andarmature coils is mandatory in anelectrodynamic vibration system.Shakers up to 15,000 lbf are typi-cally air-cooled,while high forceshakers (20,000 lbfand above) are liq-uid-cooled. Air-cooled shakers canbe set up to exhaustwarm air outsidethe facility duringwarm months.Provisions can bemade to damper thewarm air back intothe facility duringcolder months.The blower for anair-cooled shakercan be mountedoutdoors or it can beplaced in a sound deadening pack-

age and remain indoors.

Chamber InterfaceWhen integrated with a chamberto perform combined environmenttests, the shaker needs to beequipped with certain items. Athermal barrier, using sheets ofG10 material and/or flexible sili-con rubber will protect the shakerfrom being exposed to the temper-ature extremes of the test chamber.Properly designed, this flexibleseal will also provide a protectivebarrier against moisture. Castersand track are one way to roll the


above: Thermotron combined AGREE system.This system allows for electrodynamic andrepetitive shock shakers.


shaker under a chamber. Anotheroption is to utilize an air-glide sys-tem that floats the shaker on a cushion of compressed air.

Applications where the shakerremains fixed in its position andthe chamber rolls back and forthpresent another viable option.

The ability to generate and runsophisticated combined environ-ment tests from a single user inter-face can be a huge advantage.This simplifies data entry and syn-chronizes the individual pieces ofequipment so they work in concertto carry out a fully integrated test.

Vibration IsolationElectrodynamic shakers are capa-ble of generating high forces overa wide range of frequencies. Tolimit the amount of unwantedvibration energy from being trans-mitted into the floor and through-out the facility, pneumatic mountsbetween the shaker and the floorare filled with compressed air toisolate the transmission of thisenergy. Shakers are relativelyheavy pieces of equipment and, assuch, are typically mounted on theground floor of the facility.

Noise LevelsAn electrodynamic shaker runninga full force random profile can beas loud as a jet engine. While per-forming a sine sweep to find a res-onance point, the shaker can startout as a low-pitched hum and riseto an ear piercing scream. It is forthese reasons that a sound enclo-sure should house the shaker sys-tem. It is a wise idea to place thecontrol and amplifier console out-side of the room for purposes of safety and comfort. A multi-panewindow providing a view from the control room into the shaker roomis advised for those situationswhere visual access to the productunder test is critical.



Random

Random vibration is used to close-ly approximate real world applica-tion environments. A wide rangeof frequencies are excited simulta-neously at closely controlled ener-gy levels. There are many exam-ples of random vibration profileswhich plot power spectral density(in units of g2/Hz) vs. frequency.

Test specifications with frequen-cies up to and greater than 2,000Hz are considered broad band.Random vibration test specifica-tions with upper frequencies lessthan 500 Hz are referred to as nar-row band. Full system force is notachievable for narrow band, andthe performance must be deratedto protect the equipment.

One very popular random vibra-

tion test specification is NAVMATP9492 called out in the NavyManufacturing ScreeningProgram. This spectrum slopes upfrom 20 to 80 Hz at +3dB/octaveto 0.04 g2/Hz, remains flat at 0.04g2/Hz from 80 to 350 Hz, androlls off at -3dB/octave from 350to 2000 Hz. The overall grmsvalue for this profile is 6.0 grms.

Real Data Acquisition &Playback (RDAP)

RDAP is a more recent develop-ment which allows actual vibra-tion data to be recorded in thefield and replicated on the shakerin the lab. This method of testingprovides very accurate feedbackregarding how a product will per-


B. Vibration Test Types

above: A typical NAVMAT profile.

above: Thermotron’s Real DataAcquisition and Playback allows actualtest data to be recorded in the field andreplicated on the shaker, as in the case ofrecording engine vibrations in a car.


form under normal operating con-ditions. Recorded vibration levelscan be stepped-up to higher levelsto accelerate the stress testingprocess if so desired.

Sine with Resonant Search &Dwell

During sine testing, energy is out-put at a single frequency. A sinesweep test is a useful engineeringdevelopment technique which isperformed as a means to locate theresonance of a product. The reso-nance, or natural frequency, is thepoint where small vibration levelscause the system to exhibit highamplitude levels. Dwelling at theresonance point is a common prac-tice to determine if a product canwithstand a higher level of stress.

Sine vibration performance forelectrodynamic shakers is dictatedby a curve which is limited by

maximum displacement (typically2” [50 mm] peak-to-peak at lowfrequency, maximum velocity upto 100 inches/sec [2.5 m/sec])through mid-range frequencies,and maximum acceleration (afunction of shaker capacity andmoving mass) at the higher fre-quencies.

Classical Shock

Shock conditions, such as suddenand severe impacts, are encoun-tered by a variety of products as aresult of transportation, mishan-dling, and actual use environ-ments: dropped cell phones, auto-mobile collisions, aircraft landingsand missile launches are all exam-ples. Most electrodynamic vibra-tion systems have the capability ofperforming shock. The armature isgiven an initial displacement (pre-loaded) and a pulse of energy is



delivered by the amplifier whichtranslates into a particular wave-form. Classical shock pulses aredetermined by shape, amplitudeand duration. The most commonare half sine, sawtooth, triangular,and trapezoidal.

Shock Response Spectrum(SRS) SRS Testing is a way to synthesizea complex waveform that can beused on an electrodynamic shakerin a controlled manner withrepeatability. This avoids theinconsistencies of shock testmachines that limit the shape ofthe excitation pulse. SRS is a use-ful tool for estimating the potentialdamage of a shock pulse. SRStests are used to qualify equipmentinstalled in nuclear power plantsas well as to simulate seismic,pyrotechnic, gun fire and aircrafttake-off and landing vibrations.

Sine-on-RandomCertain applications involvingrotating equipment in movingvehicles require a vibration profilethat combines fixed or swept sineand random vibration. Sine-on-Random software simulates thevibration environment experiencedby helicopters, automobiles, andtrains where the sine component

of a rotor or a reciprocating pistonengine is placed on top of a broad-band random vibration profileindicative of the moving vehicle.

Random-on-Random

Random-on-Random profilescombine fixed or sweeping narrowbands of random superimposed ona background broadband randomspectrum. This vibration signatureis typical of tracked vehicles, pro-peller aircraft and turbine engines.



The electronics for an electrody-namic shaker have become socompact that the inverters, magnet-ic field power supply, vibrationcontroller, electrical interconnects,and any optional instrumentationcan fit into one console commonlyand collectively referred to as theamplifier.

InvertersInverters supply the armature drivecurrent. Due to their exceptionalefficiency, class D solid stateswitching inverters have becomethe industry standard for electrody-namic shakers. These inverters areof modulardesign andamplifiersare config-ured withone or moremodules.

Currentlytwo types ofpowerdevices areused for shaker inverters: theIGBT (Insulated Gate BipolarTransistor) and the MOSFET(Metal Oxide Semiconductor FieldEffect Transistor). The targetapplication for these devices is notshaker inverters and no significant

advantage exists for one deviceover the other. Rather, advancedshaker inverters have the ability tocommunicate with the vibrationcontroller which in turn is able totune inverter parameters providingoptimum system dynamic range,power consumption, etc.

Magnetic Field Power SupplyCommonly referred to as the fieldsupply, this benign componentsupplies the current to energize thefield coils located in the shakerbody. High performance field sup-plies also possess the ability tocommunicate with and be tuned bythe vibration controller.

Console DesignA manufacturer should possess theability to supply a power panelthat complies with appropriate UL,CE, or CSA standards, includinginterlocked access doors. Theseinterlocks will prevent accidentalpersonnel exposure to high volt-ages. It is also expected that theamplifier be protected from overtemperature and over current con-ditions. Finally, appropriate cabi-net design and circuitry includesRFI/EMI suppression to minimizeinterference from the vibrationsystem’s amplifier.


C. Amplifier Console


Vibration controllers have come toadopt the power and speed afford-ed by today’s personal computers.It is important that the operatingsystems and interface be robustand familiar to the user. USB andEthernet connections providequick and easy access to data andperipherals that make the tasks ofdata mining and manipulationquick and effective. Vibrationcontrollers will be capable ofreproducing the various vibrationtest types listed previously (ran-dom, sine, shock, etc.) as long asthey are loaded with the appropri-ate software.

SoftwareOutfitting a control system withthe software to provide a compre-hensive suite of vibration tests isnormally an ala carte affair.

Digital vibration controllers can beconfigured with software to meetsine, random, shock (half sine,sawtooth, triangular and squarewave), shock response spectrum(SRS), sine-on-random, random-on-random, and real data acquisi-tion and playback as the applica-tion dictates.

It is vital to the safe performanceof the vibration system and protec-tion of the product under test thatcertain safety measures be inplace. The control softwareshould be capable of performing aloop check at the beginning ofeach test to insure that all systemsare in operating order. High andlow tolerance and abort limitsshould be set at prescribed levelsthat will provide warning andautomatic shutdown when these


D. Vibration Controllers & Instrumentation

above: Thermotron’s VIO module box,part of the vibration control system.

above: Thermotron’s vibration controllerallows the user to set control limits forthe safety of the equipment.


out-of-range limits are exceeded.

Dynamic RangeThe dynamic range of a system isthe largest signal amplitude thatthe entire system can processdivided by the inherent noise ofthe system. It is also used to indi-cate the number of bits (resolution)of the data converters used in avibration controller. There areroughly 6 decibels (dB) of dynam-ic range per bit.

Inexpensive professional audiograde 24 bit data converters aremaking their way into vibrationcontrollers. The target market forthese converters are not vibrationcontrollers, and they do not pro-vide the best solution for the appli-cation. It is important to remem-ber the vibration controller is partof a control system consisting ofitself, an amplifier, and a shaker.Therefore, the dynamic range ofthe system is subject to the “chainis only as strong as its weakestlink” principle - meaning thedynamic range of the system can-not be better than the dynamicrange of any single component ofthe system.

Since state of the art inverters andshakers are hard pressed to provide

60 dB of dynamic range, a vibra-tion controller with 10 to 12 bitdata converters used in conjunc-tion with a properly designed pro-grammable input amplifier canoutperform a vibration controllerwith 24 bit converters. The highresolution data converters areessentially using their “extra” bitsas a limited programmable inputamplifier when used in vibrationcontroller applications.

High performance vibration con-trollers also possess the ability tocommunicate with the amplifier’sinverters and field supply to maxi-mize system dynamic range.

Spectral ResolutionSpectral resolution, commonlyreferred to as lines, or bins, is thenumber of frequency segments thata random vibration profile is divid-ed into. The higher the spectralresolution, the greater the numberof points used to calculate andcontrol the test frequency spec-trum.

Current hardware and softwarealgorithms make it a simple matterfor a controller manufacturer toadd absurd amounts of lines. Forany random vibration profile, thetime it takes to acquire the data is



directly proportional to the num-ber of lines. There is no knownway to sidestep this physical con-straint. This added acquisitiontime adversely effects the time ittakes the controller to correct anyerrors in the random vibration pro-file. Experts in the field rarely usemore than 800 lines. For example,a controller will take 20 timeslonger to correct a 16,000 line testthan it would for an 800 line test.The number of lines are userselectable. In the hands of anovice user, this “feature” of manylines could actually be detrimen-tal.

Data Acquisition

Most controllers are capable ofaccommodating multipleaccelerometer inputs. These

accelerometers can be used tomonitor or control the vibrationresponse characteristics at variouslocations on the product undertest, the fixture, or the armature.The results of data acquired duringvibration testing can be used toprove the vibration test was com-pleted successfully. Data acquiredin this manner can also be used todetermine how and why a productmay have failed.

In addition to monitoring, it is alsobeneficial in certain circumstancesto control the vibration spectrumbased on more than one inputaccelerometer signal. The vibra-tion controller should have thecapability of supporting variouscontrol strategies such as multi-point averaging, maximum orminimum, etc.


above: Thermotron’s vibration controlsoftware allows up to eight channels ofinput.

above: Close-up of Thermotron’s vibra-tion controller located in the console.


Advantages & Size

An accelerometer is a device thatsenses the motion of the surface towhich it is attached, providing anelectrical output signal.Piezoelectric materials are used inaccelerometers that produce a“charge” proportional to themotion. Years ago larger velocitytype pickups were used to measurevibration. These were bulky andhad a limited frequency range.Accelerometers are now mademechanically smaller and have awide frequency range (2-10,000Hz). Typical weights ofaccelerometers used on shakersrange from a few grams (miniatureaccelerometers) to 10 or 20 grams(general purpose accelerometers).

MountingFor accurate measurements, it is

important that accelerometers bemounted correctly on shaker sys-tems. The mounting surfacesbetween the accelerometer andsurface should be smooth andclean. The two most commonmethods of mounting accelerome-ters are threaded stud mountingand adhesive mounting.Sometimes a non-conductive spac-er is required to prevent unwantedground-loop interference.

Stud mounting is the preferredmethod because the accelerometeris tightly coupled to the surfacebeing measured, assuring excellenttransmissibility, especially at highfrequencies. A torque wrench setto the manufacturer’s specificationis used to ensure repeatability andprevent thread damage. A thinlayer of grease can be used to fillany voids resulting in a joint with


above: Accelerometer mounted to a fix-ture on a shaker.

E. Accelerometers

above: Typical accelerometers in varioussizes.


improved stiffness. This type ofmounting is typically used on con-trol accelerometers mounted onfixtures.

Adhesive mounting is used whenit is impractical or impossible touse the stud mounting method.This technique is frequently usedwhen measuring the vibrationresponse from a product undertest. For this type of measurementminiature accelerometers withsmooth, flat surfaces are well suit-ed. A common and reliable adhe-sive used is cyanoacrylate alsoknown as “Crazy Glue” or“Instant Bond.” Removing theadhesive mounted accelerometerrequires great care. Solventsshould be used to soften the bond,supplemented by a light shearingtorque.

Types & ConditioningThroughout the years twoaccelerometer types have beenused:1) Charge Mode 2) Voltage ModeCharge mode accelerometers pro-duce a high impedance chargefrom internal crystals. Eachaccelerometer has its own sensitiv-ity in pC/g (pico coulomb per g).This charge must be converted to

a voltage for vibration measure-ment readout and analysis. Speciallow noise cables are used forcharge mode accelerometers toeliminate the adverse effects ofelectrical noise and cable move-ment. Devices called chargeamplifiers are connected to theseaccelerometers to convert thecharge signal to a low impedancevoltage signal. Charge amplifierscan be simple in-line devices orcomplex instruments with sensi-tivity dials and various outputs formonitoring and analysis.

The most popular accelerometersused today are the voltage modeaccelerometers. Voltage modeaccelerometers have an internalamplifier that converts the highimpedance charge signal to a lowimpedance output voltage signal.A voltage mode accelerometer hasits sensitivity expressed in mV/g(millivolts per g). The chargeamplifier is replaced by a currentsource, typically 4 mA, that pow-ers the internal amplifier. Theinternal amplifier allows theaccelerometer to be convenientlycoupled to read-out instruments(scopes, analyzers, meters, etc).The low output impedance elimi-nates the need for expensive lownoise cable.



Sensitivity & EnvironmentsAs mentioned earlier, eachaccelerometer has its own outputsensitivity, either in pC/g or mV/g.The sensitivity depends on thepiezo-electric properties of thecrystal used. Typically smalleraccelerometers have low sensitivi-ties (0.5 pC/g, 1 mV/g, etc.) and awider frequency response. Largeraccelerometers have higher sensi-tivities (10 pC/g, 100 mV/g, etc.)but a lower frequency range.Sensitivity and frequency responseare two important properties toconsider when selectingaccelerometers.

Another factor that should be con-sidered is the environment inwhich the accelerometer will beoperated. Humidity and extremetemperatures can affect sensitivity.Rapid change in temperatures cancause thermal transients. For thisreason care should be taken whenselecting accelerometers to be usedunder extreme environmental con-ditions. Typical temperature limitsare -55°C to + 121°C for voltagemode devices. Since charge modeaccelerometers do not have inter-nal electronics, they can bedesigned for operation at substan-tially higher temperatures. Typicaltemperature ranges for charge

mode accelerometers are from -55°C to + 250°C.



A version of the calculator can bedownloaded from the Thermotronwebsite at: http://www.thermotron.com/resources/univconv.html This tool will allow you to quicklyand conveniently calculate impor-tant vibration parameters andmake common unit conversions.

G. References, Resources& WebsitesVibration Test Specificationsby IndustryAerospaceRTCAhttp://www.rtca.org

AutomotiveSAEhttp://www.sae.org

ElectronicsIPC / JEDEChttp://www.ipc.org

DefenseMIL-STDhttp://www.dscc.dca.mil

TelecommunicationsTelcordiahttp://telecom-info.telcordia.com

General Test SpecificationsJIShttp://www.jsa.or.jp

IEChttp://www.iec.ch

IHShttp://www.ihs.com

Trade PublicationsEvaluation Engineeringhttp://www.nelsonpub.com

IEST Journalhttp://www.iest.org

Sound & Vibrationhttp://www.SandV.com

Test & Measurement World http://www.tmworld.com

TEST Engineering & Management http://www.mattingley-publ.com


F. Universal Vibration Calculator

above: A nomograph.


Testing Technology Internationalhttp://www.ukintpress.com/test-ing2.html

Technical Organizations American National StandardsInstitute (ANSI) http://www.ansi.org

American Society for Quality(ASQ) http://www.asq.org

American Society for Testing andMaterials (ASTM) http://www.astm.org

Institute of EnvironmentalSciences and Technology (IEST) http://www.iest.org

International StandardsOrganization (ISO) http://www.iso.ch

Shock and Vibration InformationAnalysis Center (SAVIAC) http://saviac.bah.com

MIL-STD Searchhttp://astimage.daps.dla.mil/quick-search

Education and TrainingEquipment Reliability Institutewww.equipment-reliability.com

Q1. What provisions are includedfor lifting the shaker?A1. Heavy duty eye bolts or lift-ing ears are attached to the shakerbody. Straps or chains capable ofsupporting the weight of the shak-er are attached to the eye bolts orlifting ears. A forklift hoists theshaker up by the straps or chainsand gently moves and lowers theshaker into place.

Q2. How do we deal with thenoise issue?A2. Electrodynamic shakers areextremely loud. Under the rightconditions, the vibration systemcan sound like a jet engine readyfor take off. They should behoused in an enclosure that hasvery good absorbing qualities. Ifthe shaker is combined with achamber, the space below thechamber can be enclosed withsound absorbing panels. Baffledair inlet ducts must be incorporat-ed to supply the required flow ofcooling air.

Q3. Where should the controlconsole and amplifier be located?A3. The control and amplifiershould be located in a quiet area.Some installations have separate,dedicated control rooms for thisequipment, while others simplylocate the controls outside the


H. Move-in & Installation Questions & Considerations


deadened booth. In the case of acombined environment facility, theamplifier and control instrumenta-tion can be located next to thechamber if the area is largeenough.

Q4. What networking connec-tions need to be made?A4. Shaker controls have becomequite sophisticated. They can berun as stand-alone devices or beconnected to a local area networkvia Ethernet. They can also beremotely accessed via the internetif so desired. PCs used to drivethe control algorithms are avail-able with multiple USB connec-tions that will support peripheralappliances that will enhance datatransfer and storage as well asother test and measurement instru-ments.

Q5. Where should the coolingblower be located?A5. In a normal installation, theblower is mounted in a remoteoutdoor location, say on the roofof the building. The cooling air isdrawn through the shaker bodyand ducted out of the building.The warm air can be diverted backinto the building during coldmonths and used as a heat source.Some blowers are mounted insidethe building. In this case, a quiet

package or sound deadeningenclosure built around the enclo-sure should be considered.

Q6. Do we need a special floorthat will support the weight of theshaker and eliminate vibrationtransmission?A6. Many low and medium forceshakers feature vibration isolationsystems that prevent energy frombeing transmitted directly into thefacility floor. It is not uncommonfor a shaker’s mass to exceed6,000 lbm (2,700 kg). A mass of10,000 lbm (4,500 kg) or morecan be expected if a concrete filledgranite topped sliptable is includ-ed.

Q7. Should the shaker roll or bestationary?A7. If the shaker is used strictlyfor vibration testing at ambientconditions, it should be left in astationary configuration. Whencombined with a chamber, consid-eration has to be given to whetherto move the shaker or the chamberfor product loading. The installa-tion can be configured either way,but it is more common to movethe shaker. If the chamber ismoved, provisions may need to bemade for flexible refrigerationlines, and in extreme cases, raisingand lowering the chamber.



Chambers can also be designed withseveral different door configurations.When equipped with vertical lift doorsor horizontal sliding doors, moving thechamber becomes much more chal-lenging.

Q8. What is the best way to move ashaker around?A8. Some shakers have v-groove cast-ers and mating sections of reinforcedsteel track that allow them to bemoved back and forth (usually intoand out from under a test chamber).An automated power tow can greatlyease the rolling around of shakers.Shakers are also available with an air-glide transport system that permits theequipment to be easily maneuvered ona cushion of compressed air.



Shaker ForceThe shaker force required is inde-pendent of frequency and is calcu-lated by the following force equa-tion using weight in place of massand acceleration in normalizedunits of standard g’s.

Shaker Force = (Payload mass +Fixture mass + shaker Armaturemass) X Acceleration (g’s)

Units: Sine: pounds force peak = (pounds+ pounds + pounds) X g’s peakRandom: pounds force rms =(pounds + pounds + pounds) X g’srms

Shaker Displacement &VelocityThe required shaker displacementis a strong function of low fre-quencies. The table below ofsinusoidal motion equations canbe used to calculate the requireddisplacements and velocities forsinusoidal vibration. Random dis-placements and velocities must becalculated from acceleration spec-tral density information.

The universal vibration calculatorshould be used to calculate dis-placements and velocities require-ments for random vibration test-ing.


I. Handy Equations & Engineering Reference

Sinusoidal Equations of MotionAcceleration, velocity, displacement and frequency are related by twoindependent equations, therefore specifying any two fully defines themotion.

Known Values

g & f v & f D & f D & g v & g D & v

g (g’s)peak acceleration

f v/61.45 f2D/19.56 v2/193.0D

v (inch/sec.)peak velocity

61.45 g/f πfD 13.89 (gD)1/2

D (inch)pk-pk displacement

19.56 g/f2 v/πf v2/193.0 g

f (Hz)frequency 4.423 (g/D)1/2 61.45 g/v v/ πD



J. Handy Conversion Factors & Material Properties

ConvertingFrom

ConvertingTo

Multiply By

Forcelbf N 4.448

Ton Force kN 8.896

Densitylb/in3 kg/m3 27,680

lb/ft3 kg/m3 16.018

Pressure lbf/in2 kPa 6.895

Volume

ft3 m3 0.02832

in3 cm3 16.39

ft3 in3 1,728

Velocity in/Sec m/Sec 0.0254

Power Hp Watt 746

Volume Flow ft3/Min m3/Sec 0.0004719

Acceleration g m/Sec2 9.807

Item DensityMetric

Density

Magnesium 0.065 lb/in3 1,799.2 kg/m3

Aluminum 0.098 lb/in3 2,712.6 kg/m3

Stainless Steel (304) 0.286 lb/in3 7,916.5 kg/m3

G-10 PCB Material 0.065 lb/in3 1,799.2 kg/m3


fundamentals of electrodynamic vibration testing...

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