Harris'''' Shock and Vibration Handbook Part 8 pdf

in order to reduce the effect of measurement noise, curve fitting may be used to esti- mate the step value. Equation (18.7) shows how the sensitivity of the reference force transducer is related to the other parameters of the system. S r ϭ S rf M ϭ M ϭ (18.7) where S r = acceleration sensitivity of the reference force transducer, in mV/ms Ϫ2 S rf = force sensitivity of the reference force transducer, in mV/N M = total mass on the force transducer, in kg e g = output of the force transducer, in mV g = acceleration of free fall due to gravity, in ms Ϫ2 Note that e g is numerically equal to S r expressed in mV/g. Step 2. Measure the voltage ratio e t /e r . Remove the reference force transducer, reference mass, and the pickup being calibrated from the drop-test fixture; then mount them on the vibration exciter, as shown in Fig. 18.6. By measuring the trans- fer function e t /e r (i.e., the ratio of the voltage output of the signal conditioner from the test pickup to the voltage output of the signal conditioner from the reference force transducer, shown in Fig. 18.6) the frequency response of the test pickup can be e g ᎏ g e g ᎏ gM CALIBRATION OF PICKUPS 18.9 FIGURE 18.6 System configuration for frequency response calibration by measuring acceleration- to-force ratio. measured over 0.1 to 100,000 Hz, depending upon frequency range of the vibration exciter and signal-to-noise ratio of the system. For use at low frequencies, the dis- charge time constant of the reference force transducer should be ten times greater than that of the test pickup. Step 3. Calculate the sensitivity S t of the test pickup. If the reference force trans- ducer and the test pickup are linear, the acceleration sensitivity of the test pickup S t , expressed in the same units as S r , can be calculated from Eq. 18.1. If either velocity or displacement sensitivity of the test pickup is required, it can be obtained by divid- ing the acceleration sensitivity by 2␲f or (2␲f ) 2 , respectively. CENTRIFUGE CALIBRATOR A centrifuge provides a convenient means of applying constant acceleration to a pickup. Simple centrifuges can be obtained readily for acceleration levels up to 100g 8434_Harris_18_b.qxd 09/20/2001 12:13 PM Page 18.9 and can be custom-made for use at much higher values because of the light load requirement by this application. They are particularly useful in calibrating rectilinear accelerometers whose frequency range extends down to 0 Hz and whose sensitivity to rotation is negligible. Centrifuges are mounted so as to rotate about a vertical axis. Cable leads from the pickup, as well as power leads, usually are brought to the table of the centrifuge through specially selected low-noise slip rings and brushes. To perform a calibration, the accelerometer is mounted on the centrifuge with its axis of sensitivity carefully aligned along a radius of the circle of rotation. If the cen- trifuge rotates with an angular velocity of ω rad/sec, the acceleration a acting on the pickup is a =ω 2 r (18.8) where r is the distance from the center-of-gravity of the mass element of the pickup to the axis of rotation. If the exact location of the center-of-gravity of the mass in the pickup is not known, the pickup is mounted with its positive sensing axis first out- ward and then inward; then the average response is compared with the average acceleration acting on the pickup as computed from Eq. (18.8) where r is taken as the mean of the radii to a given point on the pickup case. The calibration factor is determined by plotting the output e of the pickup as a function of the acceleration a given by Eq. (18.8) for successive values of ω and then determining the slope of the straight line fitted through the data. INTERFEROMETER CALIBRATORS A primary (absolute) method of calibrating an accelerometer using standard laser interferometry is shown in Fig. 18.2.All systems in the following category of calibra- tors consist of three stages: modulation, interference, and demodulation. The differ- ences are in the specific type of interferometer that is used (for example, a Michelson or Mach-Zehnder) and in the type of signal processing, which is usually dictated by the nature of the vibration. The vibratory displacement to be measured modulates one of the beams of the interferometer and is consequently encoded in the output signal of the photodetector in both magnitude and phase. Figure 18.7 shows the principle of operation of the Michelson interferometer. One of the mirrors, D in Fig. 18.7A, is attached to the plate on which the device to be calibrated is mounted. Before exciting vibrations, it is necessary to obtain an inter- ference pattern similar to that shown in Fig. 18.7B. The relationship underlying the illustrations to be presented is the classical interference formula for the time aver- age intensity I of the light impinging on the photodetector surface. 24,25 I = A + B cos 4πδ/λ (18.9) where A and B are system constants depending on the transfer function of the detec- tor, the intensities of the interfering beams, and alignment of the interferometer.The vibration information is contained in the quantity δ,2δ being the optical-path differ- ence of the interfering beams. The absoluteness of the measurement comes from λ, the wavelength of the illumination, in terms of which the magnitude of vibratory dis- placement is expressed. Velocity and acceleration values are obtained from dis- placement measurements by differentiation with respect to time. Fringe-Counting Interferometer. An optical interferometer is a natural instru- ment for measuring vibration displacement.The Michelson and Fizeau interferome- 18.10 CHAPTER EIGHTEEN 8434_Harris_18_b.qxd 09/20/2001 12:13 PM Page 18.10 ters are the most popular configurations. A modified Michelson interferometer is shown in Fig. 18.8. 26 A corner cube reflector is mounted on the vibration-exciter table. A helium-neon laser is used as a source of illumination. The photodiode and its amplifier must have sufficient bandwidth (as high as 10 MHz) to accommodate the Doppler frequency shift associated with high velocities. An electrical pulse is generated by the photodiode for each optical fringe passing it. The vibratory dis- placement amplitude is directly proportional to the number of fringes per vibration cycle.The peak acceleration can be calculated from a = (18.10) where λ=wavelength of light ν=number of fringes per vibration cycle f = vibration frequency Interferometric fringe counting is useful for vibration-displacement measurement in the lower frequency ranges, perhaps to several hundred hertz depending on the characteristics of the vibration exciter. 27,28 At the low end of the frequency spectrum, conventional procedures and commercially available equipment are not able to meet all the present requirements. Low signal-to-noise ratios, cross-axis components of motion, and zero-drifts are some of the problems usually encountered. In re- sponse to those restrictions an electrodynamic exciter for the frequency range 0.01 to 20 Hz has been developed. 29 It features a maximum displacement amplitude of 0.5 meter, a transverse sensitivity less than 0.01 percent, and a maximum uncorrected distortion of 2 percent. These characteristics have been achieved by means of a spe- cially designed air bearing, an electro-optic control, and a suitable foundation. Figure 18.9 shows the main components of a computer-controlled low-frequency calibration system which employs this exciter. Its functions are (1) generation of sinu- soidal vibrations, (2) measurement of rms and peak values of voltage and charge, (3) measurement of displacement magnitude and phase response, and (4) control of non- linear distortion and zero correction for the moving element inside a tubelike mag- net. Position of the moving element is measured by a fringe-counting interferometer. Uncertainties in accelerometer calibrations using this system have been reduced to about 0.25 to 0.5 percent, depending on frequency and vibration amplitude. λνπ 2 f 2 ᎏ 2 CALIBRATION OF PICKUPS 18.11 FIGURE 18.7 The principle of operation of a Michelson interferometer: (A) Optical system. (B) Observed interference pattern. (C) Variation of the light intensity along the X axis. (A) (C) (B) 8434_Harris_18_b.qxd 09/20/2001 12:13 PM Page 18.11 Fringe-Disappearance Interferometer. The phenomenon of the interference band disappearance in an optical interferometer can be used to establish a precisely known amplitude of motion. Figure 18.7 shows the principle of operation of the Michelson interferometer employed in this technique. One of the mirrors D, in Fig. 18.7A, is attached to the mounting plate of the calibrator. Before exciting vibrations it is necessary to obtain an interference pattern similar to that shown in Fig. 18.7B. When the mirror D vibrates sinusoidally 30 with a frequency f and a peak dis- placement amplitude d, the time average of the light intensity I at position x, meas- ured from a point midway between two dark bands, is given by I = A + BJ 0 ΂΃ cos ΂΃ (18.11) where J 0 = zero-order Bessel function of the first kind A and B = constants of measuring system h = distance between fringes, as shown in Fig. 18.11B and C For certain values of the argument, the Bessel function of zero order is zero;then the fringe pattern disappears and a constant illumination intensity A is present. Elec- tronic methods for more precisely establishing the fringe disappearance value of the vibratory displacement have been successfully used at the National Institute of Stan- dards and Technology 17,31 and elsewhere. The latter method has been fully auto- mated using a desktop computer. The use of piezoelectric exciters is common for high-frequency calibration of accelerometers. 32 They provide pistonlike motion of relatively high amplitude and 2πx ᎏ h 4πd ᎏ λ 18.12 CHAPTER EIGHTEEN FIGURE 18.8 Typical laboratory setup for interferometric measurement of vibratory displacement by fringe counting. (After R. S. Koyanagi. 26 ) 8434_Harris_18_b.qxd 09/20/2001 12:13 PM Page 18.12 FIGURE 18.9 Simplified block diagram of a low-frequency vibration standard. (After H. J. von Martens. 29 ) 18.13 8434_Harris_18_b.qxd 09/20/2001 12:13 PM Page 18.13 18.14 CHAPTER EIGHTEEN are structurally stiff at the lower frequencies where displacement noise is bother- some. When electrodynamic exciters are used with fringe disappearance methods, it is generally necessary to stiffen the armature suspensions to reduce the background displacement noise. Signal-Nulling Interferometer. This method, although mathematically similar to fringe disappearance, relies on finding the nulls in the fundamental frequency compo- nent of the signal from a photodetector. 17,25,33 The instrumentation is, therefore, quite different, except for the interferometer. One successful arrangement is shown in Fig. 18.10. Laboratory environmental restrictions are much more severe for this method. FIGURE 18.10 Interferometric measurement of displacement d as given by J 1 (4πd/λ) = 0. The interferometer apparatus should be well-isolated to ensure stability of the pho- todetector signals.Air currents in the room may contribute to noise problems by phys- ically moving the interferometer components and by changing the refractive index of the air.An active method of stabilization has also been successfully employed. 34 To make displacement amplitude measurements, a wave analyzer tuned to the frequency of vibration can be used to filter the photodetector signal.The filtered sig- nal amplitude will pass through nulls as the vibration amplitude is increased, accord- ing to the following relationship: I = 2BJ 1 ΂΃ (18.12) where J 1 is the first-order Bessel function of the first kind, and the other terms are as previously defined. The signal nulls may be established using a wave analyzer. The null amplitude will generally be 60 dB below the maximum signal level of the pho- todetector output. The accelerometer output may be measured by an accurate voltmeter at the same time that the nulls are obtained. The sensitivity is then calculated by dividing the output voltage by the displacement. Because the filtered output of the photode- tector is a replica of the vibrational displacement, a phase calibration of the pickup can also be obtained with this arrangement. 4πd ᎏ λ 8434_Harris_18_b.qxd 09/20/2001 12:13 PM Page 18.14 CALIBRATION OF PICKUPS 18.15 Heterodyne Interferometer. A homodyne interferometer is an interferometer in which interfering light beams are created from the same beam by a process of beam splitting. All illumination is at the same optical frequency. In contrast, in the hetero- dyne interferometer, 35 light from a laser-beam source containing two components, each with a unique polarization, is separated into (1) a measurement beam and (2) a reference beam by a polarized beam splitter. When the mounting surface of the device under test is stationary, the interference pattern impinging on the photode- tector produces a signal of varying intensity at the beat frequency of the two beams. When surface moves, the frequency of the measurement beam is shifted because of the Doppler effect, but that of the reference beam remains undisturbed. Thus, the photodetector output can be regarded as a carrier that is frequency modulated by the velocity waveform of the motion. The main advantages of the heterodyne interferometer are greater measurement stability and lower noise susceptibility. Both advantages occur because displacement information is carried on ac waveforms; hence, a change in the average value of beam intensity cannot be interpreted as motion. Digitization and subsequent phase demodulation of the interferometer output reduce measurement uncertainties. 36 This can yield significant improvements in calibration results at high frequencies, where the magnitude of displacement typically is only a few nanometers. As in the case of homodyning, variations of the heterodyning technique have been developed to meet specific needs of calibration laboratories. Reference 37 describes an accelerometer calibration system, applicable in the frequency range from 1 mHz to 25 kHz and at vibration amplitudes from 1 nanometer to 10 meters. The method requires the acquisition of instantaneous position data as a function of the phase angle of the vibration signal and the use of Fourier analysis. HIGH-ACCELERATION METHODS OF CALIBRATION Some applications in shock or vibration measurement require that high amplitudes be determined accurately. To ensure that the pickups used in such applications meet certain performance criteria, calibrations must be made at these high amplitudes. The following methods are available for calibrating pickups subject to accelerations in excess of several hundred g. SINUSOIDAL-EXCITATION METHODS The use of a metal bar, excited at its fundamental resonance frequency, to apply sinusoidal accelerations for calibration purposes has several advantages: (1) an inherently constant frequency, (2) very large amplitudes of acceleration (as much as 4000g, and (3) low waveform distortion. A disadvantage of this type of calibrator is that calibration is limited to the resonance frequencies of the metal bar. The bar can be supported at its nodal points, and the pickup to be calibrated can be mounted at its mid-length location. The bar can be energized by a small electro- magnet or can be self-excited. Acceleration amplitudes of several thousand g can thus be obtained at frequencies ranging from several hundred to several thousand hertz.The bar also may be calibrated by clamping it at its midpoint and mounting the pickup at one end. 38 The displacement at the point of attachment of the pickup can be measured optically since displacements encountered are adequately large. 8434_Harris_18_b.qxd 09/20/2001 12:13 PM Page 18.15 18.16 CHAPTER EIGHTEEN The resonant-bar calibrator shown in Fig. 18.11 is limited in amplitude primarily by the fatigue resistance of the bar. 38 Accelerations as much as 500g have been attained using alu- minum bars without special designs. Peak accelerations as large as 4000g have been attained using tempered vanadium steel bar.The bar is mounted at its mid-length on a conventional electrodynamic exciter. The acceler- ometer being calibrated is mounted at one end of the bar, and an equivalent balance weight is mounted at the oppo- site end in the same relative position. Axial resonances of long rods have been used to generate motion for accu- rate calibration of vibration pickups over a frequency range from about 1 to 20 kHz and at accelerations up to 12,000g. 39,40 The use of axially driven rods has an advantage over the beams discussed above in that no bending or lateral motion is present. This minimizes errors from the pickup response to such unwanted modes and also from the direct measurement of the displacement having nonrec- tilinear motion. SHOCK-EXCITATION METHODS There are several methods by which a sudden velocity change may be applied to pickups designed for high-frequency acceleration measurement, for example, the ballistic pendulum, drop-test, and drop-ball calibrators, described below. Any method which generates a reproducible velocity change as function of time can be used to obtain the calibration factor. 1 Impact techniques can be employed to obtain calibrations over an amplitude range from a few g to over 100,000g.An example of the latter is the Hopkinson bar, in which the test pickup is mounted at one end and stress pulses are generated by an air gun firing projectiles impacting at the other end, described below. An accurate determination of shock performance of an accelerometer depends not only upon the mechanical and electrical characteristics of the test pickup but also upon the characteristics of the instrumentation and recording equipment. It is often best to perform system calibrations to determine the linearity of the test pickup as well as the linearity of the recording instrumentation in the range of intended use. Several of the following methods make use of the fact that the veloc- ity change during a transient pulse is equal to the time integral of acceleration: v = ͵ t 2 t 1 a dt (18.13) where the initial or final velocity is taken as reference zero, and the integration is performed to or from the time at which the velocity is constant. If the output closely resembles a half-sine pulse, the area is equal to approximately 2h(t 2 − t 1 )/π, where h is the height of the pulse, and (t 2 − t 1 ) is its width. FIGURE 18.11 Resonant-bar calibrator with the pickup mounted at end and a counterbalanc- ing weight at the other. (After E. I. Feder and A. M. Gillen. 38 ) 8434_Harris_18_b.qxd 09/20/2001 12:13 PM Page 18.16 CALIBRATION OF PICKUPS 18.17 In this section, several methods for applying known velocity changes v to a pickup are presented. The voltage output e and the acceleration a of the test pickup are related by the following linear relationship: S = (18.14) where S is the pickup calibration factor. After Eq. (18.14) is substituted into Eq. (18.13), the calibration factor for the test pickup can be expressed as S = (18.15) where A = ͵ t 2 t 1 e dt (18.16) the area under the acceleration-versus-time curve. The calibration factor assumes that no significant spectral energy exists beyond the frequency region in which the test pickup has nominally constant complex sensi- tivity (uniform magnitude and phase response as functions of frequency). In general, this assumption becomes less valid with decreasing pulse duration resulting in increasing bandwidth in the excitation signal. Sometimes it is convenient to express acceleration as a multiple of g. The corre- sponding calibration factor S 1 is in volts per g: S 1 == (18.17) In either case, the integrals representing A and v must first be evaluated.The lin- ear range of a pickup is determined by noting the magnitude of the velocity change v at which the calibration factor S or S 1 begins to deviate from a constant value. The minimum pulse duration is similarly found by shortening the pulse duration and not- ing when S changes appreciably from previous values. Hopkinson Bar Calibrator. An apparatus called a Hopkinson bar 41–43 provides very high levels of acceleration for use in the calibration and acceptance testing of shock accelerometers.As shown in Fig. 18.12, a controlled-velocity projectile strikes one end of the bar, at x = 0; a strain gage is placed at the middle of the bar, at x = L/2; and the accelerometer under test is mounted at the other end of the bar, at x = L. When the projectile strikes the bar, a strain wave is initiated at x = 0.This wave trav- els along the bar, producing a large acceleration at the accelerometer. The duration and shape of the strain wave can be controlled by varying the geometry and mate- Ag ᎏ v e ᎏ (a/g) A ᎏ v e ᎏ a FIGURE 18.12 A Hopkinson bar, showing a projectile striking the bar at x = 0; a strain gage mounted on the bar at x = L/2; and the accelerometer under test is attached to the bar at x = L. Impact of the projectile on the bar generates a strain wave which travels down the bar. 8434_Harris_18_b.qxd 09/20/2001 12:13 PM Page 18.17 [...]... 7626 TC 1 08 ANSI S2.31–34 Isolators ISO 2017 TC 1 08 ANSI S2 .8 Balancing ISO 1940 TC 1 08/ SC 1 ANSI S2.19, S2.42, and S2.43 Balancing machines ISO 2953 TC 1 08/ SC 1 ANSI S2. 38 Machines/machinery ISO 7919 and 1 081 6 TC 1 08/ SC 2 ANSI S2.13, S2.40, and S2.41 Vehicles ISO 80 02 TC 1 08/ SC 2 Ships ISO 486 7, 486 8, 6954, and 10055 TC 1 08/ SC 2 ANSI S2.16 and S2.25; MIL-STD-167 Buildings ISO 486 6 and 85 69 TC 1 08/ SC 2... S2.47 Calibration ISO 5347 and 16063 TC 1 08/ SC 3 ANSI S2.2 Human response ISO 80 41 TC 1 08/ SC 3 Human exposure ISO 2631, 5349, 689 7, 87 27, and 13090 TC 1 08/ SC 4 ANSI S3. 18, S3.29, and S3.34 Generating systems ISO 5344, 6070, and 86 26 TC 1 08/ SC 6 ANSI S2.5, S2.45, S2. 48, and S2. 58 Shock machines ISO 85 68 TC 1 08 ANSI S2.3, S2.14, and S2.15 and transducers used in measurement and control SP37 has a number... Standard (NAIS) ANSI S2.1 Use and Calibration of Transducers and Instrumentation The use and calibration of shock and vibration transducers and instrumentation, including standardized calibration methods, measuring instrumentation for human response to vibration, and vibration condition monitoring transducers and instrumentation, is assigned to ISO TC 1 08/ SC 3 (Use and Calibration of Vibration and Shock. .. 19.1 CHAPTER 19 SHOCK AND VIBRATION STANDARDS David J Evans Henry C Pusey INTRODUCTION This chapter is concerned with shock and vibration standards covering (1) terminology; (2) use and calibration of transducers and instrumentation; (3) shock and vibration generators; (4) structures and structural systems; (5) vehicles including land-based, airborne, and ocean-going; (6) machines and machinery including... used in shock and vibration measurements, e.g., strain gages, accelerometers, servo-accelerometers, and force transducers SP37.20 is a separate subcommittee of SP37 devoted specifically to vibration transducers Shock and Vibration Generators ISO TC 1 08/ SC 6 (Vibration and Shock Generating Systems) has been assigned standards activities related to systems for the generation of shock and vibration and their... broadband random vibration, shock, drop and topple, free fall, and bump testing ASTM publishes standards that address using shock and vibration to test unpackaged manufactured products, packaging systems, shipping containers, and materials ISO 85 68 addresses shock testing machines ISO TC 1 08 has a work item on the analysis of the mechanical properties of visco-elastic materials using vibration, and there... covers the evaluation and reporting of hull and superstructure vibration in ships ISO TC 1 08/ SC 2 is also involved with vibration of land-based vehicles, and ISO 80 02, 86 08, and 10326 are specifically related to the evaluation and reporting of the vibration associated with either land-based vehicles or road surface profiles ISO TC 20 (Aircraft and Space Vehicles) is involved with standards related to... construction 84 34_Harris_19_b.qxd 09/20/2001 12:12 PM Page 19.5 SHOCK AND VIBRATION STANDARDS 19.5 Human Exposure to Shock and Vibration The program of work on human exposure to shock and vibration is assigned to ISO TC 1 08/ SC 4 (Human Exposure to Mechanical Vibration and Shock) ISO TC 1 08/ SC 4 maintains liaisons with about a dozen ISO technical committees and subcommittees including ISO TC 43 (Acoustics), as... U.S.Technical Advisory Group (TAG) for ISO TC 1 08 and all of its subcommittees except TC 1 08/ SC 4 on human exposure to shock and vibration The U.S counterpart to ISO TC 1 08/ SC 4 on human exposure to shock and vibration is ANSI-accredited standards committee S3 (Bioacoustics), which holds the U.S TAG for ISO TC 1 08/ SC 4 The ANSI-accredited standards committees S2 and S3 and their U.S TAGs are administered by... Organization (IMO), and the International Union of Railways (UIC) There are a number of ISO and ANSI standards on exposure to whole-body and hand-arm vibration including standards covering occupants of fixed-structures, single shocks, guidance on safety aspects of tests and experiments, transmissibility of gloves and resilient materials, and terminology (See Chap 42.) Testing Numerous standards and handbooks . Symposium, 1 984 . 12. Bouche, R. R. “Calibration of Shock and Vibration Measuring Transducers,” Shock and Vibration Monograph SVM-11,The Shock and Vibration Information Center,Washington, D.C., 1979. 13 Koyanagi. 26 ) 84 34_Harris_ 18_ b.qxd 09/20/2001 12:13 PM Page 18. 12 FIGURE 18. 9 Simplified block diagram of a low-frequency vibration standard. (After H. J. von Martens. 29 ) 18. 13 84 34_Harris_ 18_ b.qxd 09/20/2001. large- amplitude vibration at the free end of the beam, typically at a frequency between 300 and 80 0 Hz. A pair of vibration exciters, and associated electronic equipment, 84 34_Harris_ 18_ b.qxd 09/20/2001