資源目錄里展示的全都有，所見即所得。下載后全都有,請放心下載。原稿可自行編輯修改=【QQ：401339828 或11970985 有疑問可加】 A A A A PracticalPracticalPracticalPractical ApproachApproachApproachApproach totototo VibrationVibrationVibrationVibration DetectionDetectionDetectionDetection andandandand MeasurementMeasurementMeasurementMeasurementPhysicalPhysicalPhysicalPhysical PrinciplesPrinciplesPrinciplesPrinciples andandandandDetectionDetectionDetectionDetection TechniquesTechniquesTechniquesTechniquesBy: John Wilson, the Dynamic Consultant, LLCThis tutorial addresses the physics ofvibration; dynamics of a spring masssystem; damping; displacement, velocity,and acceleration; and the operatingprinciples of the sensors that detect andmeasure these properties.Vibration is oscillatory motion resultingfrom the application of oscillatory orvarying forces to a structure. Oscillatorymotion reverses direction. As we shall see,the oscillation may be continuous duringsome time period of interest or it may beintermittent. It may be periodic ornonperiodic, i.e., it may or may not exhibita regular period of repetition. The nature ofthe oscillation depends on the nature of theforce driving it and on the structure beingdriven.Motion is a vector quantity, exhibitinga direction as well as a magnitude. Thedirection of vibration is usually describedin terms of some arbitrary coordinatesystem (typically Cartesian or orthogonal)whose directions are called axes. Theorigin for the orthogonal coordinate systemof axes is arbitrarily defined at someconvenient location.Most vibratory responses of structurescan be modeled assingle-degree-of-freedom spring masssystems, and many vibration sensors use aspring mass system as the mechanical partof their transduction mechanism. Inaddition to physical dimensions, a springmass system can be characterized by thestiffness of the spring, K, and the mass, M,or weight, W, of the mass. Thesecharacteristics determine not only the staticbehavior (static deflection, d) of thestructure, but also its dynamiccharacteristics. If g is the acceleration ofgravity:F = MAW = MgK = F/d = W/dd = F/K = W/K = Mg/KDynamicsDynamicsDynamicsDynamics ofofofof a a a a SpringSpringSpringSpring MassMassMassMass SystemSystemSystemSystemThe dynamics of a spring mass system canbe expressed by the systems behavior infree vibration and/or in forced vibration.FreeFreeFreeFree VibrationVibrationVibrationVibration. Free vibration is the casewhere the spring is deflected and thenreleased and allowed to vibrate freely.Examples include a diving board, a bungeejumper, and a pendulum or swing deflectedand left to freely oscillate.Two characteristic behaviors shouldbe noted. First, damping in the systemcauses the amplitude of the oscillations todecrease over time. The greater thedamping, the faster the amplitudedecreases. Second, the frequency or periodof the oscillation is independent of themagnitude of the original deflection (aslong as elastic limits are not exceeded).The naturally occurring frequency of thefree oscillations is called the naturalfrequency, fn:ForcedForcedForcedForced VibrationVibrationVibrationVibration. Forced vibration isthe case when energy is continuouslyadded to the spring mass system byapplying oscillatory force at some forcingfrequency, ff. Two examples arecontinuously pushing a child on a swingand an unbalanced rotating machineelement. If enough energy to overcome thedamping is applid, the motion willcontinue as long as the excitation continues.Forced vibration may take the form ofself-excited or externally excited vibration.Self-excited vibration occurs when theexcitation force is generated in or on thesuspended mass; externally excitedvibration occurs when the excitation forceis applied to the spring. This is the case, forexample, when the foundation to which thespring is attached is moving.TransmissibilityTransmissibilityTransmissibilityTransmissibility. When the foundationis oscillating, and force is transmittedthrough the spring to the suspended mass,the motion of the mass will be differentfrom the motion of the foundation. We willcall the motion of the foundation the input,I, and the motion of the mass the response,R. The ratio R/I is defined as thetransmissibility, Tr:Tr = R/IResonanceResonanceResonanceResonance. At forcing frequencieswell below the systems natural frequency,R I, and Tr 1. As the forcing frequencyapproaches the natural frequency,transmissibility increases due to resonance.Resonance is the storage of energy in themechanical system. At forcing frequenciesnear the natural frequency, energy is storedand builds up, resulting in increasingresponse amplitude. Damping alsoincreases with increasing responseamplitude, however, and eventually theenergy absorbed by damping, per cycle,equals the energy added by the excitingforce, and equilibrium is reached. We findthe peak transmissibility occurring whenfffn. This condition is called resonance.IsolationIsolationIsolationIsolation. If the forcing frequency isincreased above fn, R decreases. Whenff=1.414 fn, R = I and Tr = 1; at higherfrequencies R I and Tr 1. At frequencieswhen R 0.1 in., to make them practical.The change in intensity or angle of alight beam directed onto a reflectivesurface can be used as an indication of itsdistance from the source. If the detectionapparatus is fast enough, changes ofdistance can be detected as well.The most sensitive, accurate, andprecise optical device for measuringdistance or displacement is the laserinterferometer. With this apparatus, areflected laser beam is mixed with theoriginal incident beam. The interferencepatterns formed by the phase differencescan measure displacement down to 1 MHz insome PR shock accelerometers.Most contemporary PR sensors aremanufactured from a single piece of silicon.In general, the advantages of sculpting thewhole sensor from one homogeneous blockof material are better stability, less thermalmismatch between parts, and higherreliability. Underdamped PRaccelerometers tend to be less rugged thanPE devices. Single-crystal silicon can haveextraordinary yield strength, particularlywith high strain rates, but it is a brittlematerial nonetheless. Internal friction insilicon is very low, so resonanceamplification can be higher than for PEtransducers. Both these features contributeto its comparative fragility, although ifproperly designed and installed they areused with regularity to measure shockswell above 100,000 g. They generally havewider bandwidths than PE transducers(comparing models of similar full-scalerange), as well as smaller nonlinearities,zero shifting, and hysteresis characteristics.Because they have DC response, they areused when long-duration measurements areto be made.In a typical monolithic silicon sensingelement of a PR accelerometer, the 1 mmsquare silicon chip incorporates the entirespring, mass, and four-arm PR strain gaugebridge assembly. The sensor is made froma single-crystal silicon by means ofanisotropic etching and micromachiningtechniques. Strain gauges are formed by apattern of dopant in the originally flatsilicon. Subsequent etching of channelsfrees the gauges and simultaneouslydefines the masses as simply regions ofsilicon of original thickness.The bridge circuit can be balanced byplacing compensation resistor(s) in parallelor series with any of the legs, correctingfor the matching of either the resistancevalues and/or the change of the values withtemperature. Compensation is an art;because the PR transducer can havenonlinear characteristics, it is inadvisableto operate it with excitation different fromthe conditions under which it wasmanufactured or calibrated. For example,PR sensitivity is only approximatelyproportional to excitation, which is usuallya constant voltage or, in some cases,constant current, which has someperformance advantages. Because thermalperformance will in general change withexcitation voltage, there is not a preciseproportionality between sensitivity andexcitation. Another precaution in dealingwith voltage-driven bridges, particularlythose with low resistance, is to verify thatthe bridge gets the proper excitation. Theseries resistance of the input lead wiresacts as a voltage divider. Take care that theinput lead wires have low resistance, orthat a six-wire measurement be made (withsense lines at the bridge to allow theexcitation to be adjusted) so the bridge getsthe proper excitation.Constant current excitation does nothave this problem with series resistance.However, PR transducers are generallycompensated assuming constant voltageexcitation and might not give the desiredperformance with constant current. Thebalance of the PR bridge is its mostsensitive measure of health, and is usuallythe dominant feature in the totaluncertainty of the transducer. The balance,sometimes called bias, zero offset, or ZMO(zero measurand output, the output with 0g), can be changed by several effects thatare usually thermal characteristics orinternally or externally induced shifts instrains in the sensors. Transducer casedesigns attempt to isolate the sensors fromexternal strains such as thermal transients,base strain, or mounting torque. Internalstrain changes, e.g., epoxy creep, tend tocontribute to long-term instabilities. Allthese generally low-frequency effects aremore important for DC transducers thanfor AC-coupled devices because they occurmore often in the wider frequency band ofthe DC-coupled transducer.Some PR designs, particularlyhigh-sensitivity transducers, are designedwith damping to extend frequency rangeand overrange capability. Dampingcoefficients of 0.7 are considered ideal.Such designs often use oil or some otherviscous fluid. Two characteristics dictatethat the technique is useful only atrelatively low frequencies: damping forcesare proportional to flow velocity, andadequate flow velocity is attained bypumping the fluid with large displacements.This is a happy coincidence for sensitivetransducers in that they operate at the lowacceleration frequencies wheredisplacements are adequately large.Viscous damping can effectively eliminateresonance amplification, extend theoverrange capability, and more than doublethe useful bandwidth. However, becausethe viscosity of the damping fluid is astrong function of temperature, the usefultemperature range of the transducer issubstantially limited.VariableVariableVariableVariable CapacitanceCapacitanceCapacitanceCapacitance. VCtransducers are usually designed asparallel-plate air gap capacitors in whichmotion is perpendicular to the plates. Insome designs the plate is cantilevered fromone edge, so motion is actually rotation;other plates are supported around theperiphery, as in a trampoline. Changes incapacitance of the VC elements due toacceleration are sensed by a pair of currentdetectors that convert the changes intovoltage output. Many VC sensors aremicromachined as a sandwich ofanisotropically etched silicon wafers with agap only a few microns thick to allow airdamping. The fact that air viscositychanges by just a few percent over a wideoperating temperature range provides afrequency response more stable than isachievable with oil-damped PR designs.In a VC accelerometer, ahigh-frequency oscillator provides thenecessary excitation for the VC elements.Changes in capacitance are sensed by thecurrent detector. Output voltage isproportional to capacitance changes, and,therefore, to acceleration. Theincorporation of overtravel stops in the gapcan enhance ruggedness in the sensitivedirection, although resistance to overrangein transverse directions must rely solely onthe strength of the suspension, as is true ofall other transducer designs withoutovertravel stops. Some designs can surviveextremely high acceleration overrangeconditions-as much as 1000 full-scalerange .The sensor of a typicalmicromachined VC accelerometer isconstructed of three silicon elementsbonded together to form a hermeticallysealed assembly. Two of the elements arethe electrodes of an air dielectric,parallel-plate capacitor. The middleelement is chemically etched to form arigid central mass suspended by thin,flexible fingers. Damping characteristicsare controlled by gas flow in the orificeslocated on the mass.VC sensors can provide many of thebest features of the transducer typesdiscussed earlier: large overrange, DCresponse, low-impedance output, andsimple external signal conditioning.Disadvantages are the cost and sizeassociated with the increased complexityof the onboard conditioning. Also,high-frequency capacitance detectioncircuits are used, and some of thehigh-frequency carrier usually appears onthe output signal. It is generally not evennoticed, being up to three orders ofmagnitude (i.e., 1000 ) higher infrequency than the output signals.ServoServoServoServo (Force(Force(Force(Force Balance)Balance)Balance)Balance). Althoughservo accelerometers are usedpredominantly in inertial guidance systems,some of their performance characteristicsmake them desirable in certain vibrationapplications. All the accelerometer typesdescribed previously are open-loop devicesin which the output due to deflection of thesensing element is read directly. Inservo-controlled, or closed-loop,accelerometers, the deflection signal isused as feedback in a circuit that physicallydrives or rebalances the mass back to theequilibrium position. Servo accelerometermanufacturers suggest that open-loopinstruments that rely on displacement (i.e.,straining of crystals and piezoresistiveelements) to produce an output signal oftencause nonlinearity errors. In closed-loopdesigns, internal displacements are keptextremely small by electrical rebalancingof the proof mass, minimizing nonlinearity.In addition, closed-loop designs are said tohave higher accuracy than open-loop types.However, definition of the termaccuracyvaries. Check with the sensormanufacturer.Servo accelerometers can take eitherof two basic geometries: linear (e.g.,loudspeaker) and pendulous (metermovement).Pendulous geometry is most widelyused in commercial designs. Until recently,the servo mechanism was primarily basedon electromagnetic principles. Force isusually provided by driving currentthrough coils on the mass in the presenceof a magnetic field. In the pendulous servoaccelerometer with an electromagneticrebalancing mechanism, the pendulousmass develops a torque proportional to theproduct of the proof mass and the appliedacceleration. Motion of the mass isdetected by the position sensors (typicallycapacitive sensors), which send an errorsignal to the servo system. The error signaltriggers the servo amplifier to output afeedback current to the torque motor,which develops an opposing torque equalin magnitude to the acceleration-generatedtorque from the pendulous mass. Output isthe applied drive current itself (or across anoutput resistor), which, analogous to thedeflection in the open-loop transducers, isproportional to the applied force andtherefore to the acceleration.In contrast to the rugged springelements of the open-loop transducers, therebalancing force in the case of theclosed-loop accelerometer is primarilyelectrical and exists only when power isprovided. The springs are as flimsy in thesensitive direction as feasible and mostdamping is provided through theelectronics. Unlike other DC-responseaccelerometers whose bias stabilitydepends solely on the characteristics of thesensing element(s), it is the feedbackelectronics in the closed-loop design thatcontrols bias stability. Servoaccelerometers therefore tend to offer lesszero drifting, which is the major reason fortheir uses in vibration measurements. Ingeneral, they have a useful bandwidth of1000 Hz and are designed for use inapplications with comparatively lowacceleration levels and extremely lowfrequency components.ReferencesReferencesReferencesReferences1.A. Chu.Zero Shift of PiezoelectricAccelerometers in PyroshockMeasurements, Endevco TP No. 293.2. Shock & Vibration MeasurementTechnology. 1987. Endevco.3. Measuring Vibration. 1982. Bruel &Kjaer.4. C. Harris. 1995. Shock and VibrationHandbook, 4th Ed., McGraw Hill.5. General Guide to ICP Instrumentation.March 1973. PCB Piezotronics, #G-0001.6. Introduction to Piezoelectric Sensors.March 1985. PCB Piezotronics, #018.7. Application of Integrated-CircuitElectronics to Piezoelectric Transducers.March 1967. PCB Piezotronics, #G-01.8. Isotron Instruction Manual. 1995.Endevco, IM 31704.9. Instruction Manual for EndevcoPiezoresistive Accelerometers. 1978.Endevco, #121.10. Entran Accelerometer Instruction andSelection Manual. 1987. Entran Devices.11. R. Sill. Testing Techniques Involvedwith the Development of High ShockAcceleration Sensors. Endevco, TP 284.12. R. Sill. Minimizing MeasurementUncertainty in Calibration and Use ofAccelerometers. Endevco, TP 299.13. P.K. Stein. The Constant CurrentConcept for Dynamic StrainMeasurement. Stein Engineering Services,Inc., Lf/MSE Publication 46.14. B. Link. Shock and VibrationMeasurement Using VariableCapacitance. Endevco, TP 296.