Comparative Analysis of Triaxial Shock Accelerometer Output

Transcription

1 Comparative Analysis of Triaxial Shock Accelerometer Output Jacob C. Dodson, Lt. Lashaun Watkins, Dr. Jason R. Foley* Air Force Research Laboratory * AFRL/RWMF; 306 W. Eglin Blvd., Bldg. 432; Eglin AFB, FL , jason.foley@eglin.af.mil Dr. Alain Beliveau Applied Research Associates, Valparasio, FL Proceedings of the IMAC-XXVIII February 1 4, 2010, Jacksonville, Florida USA 2010 Society for Experimental Mechanics Inc. NOMENCLATURE Number of data points Sampling frequency measurement in the ensemble Fourier transform of Energy spectral density of Averaged energy spectral density Spectral Energy Ratio of Spectral Energy ABSTRACT Shock accelerometer internal and mounting dynamics are analyized and the contribution to the sensor output is evaluated. This includes an analysis of uniaxial and triaxial accelerometer cross-talk (cross axis sensitivity effects), the filtering characteristics of polysulfide films, and the influence of triaxial block transient dynamic response on the shock accelerometer output. It is shown that the polysulfide acts as a lowpass filter and dissipates energy in the frequency range of sensor resonance. Features in the data, such as energy spectral density, cross axis sensitivity, and mode shapes of the triaxial block are highlighted. INTRODUCTION Shock accelerometers are essential for measuring the response of systems that undergo large mechanical shock, i.e., high amplitude impulsive loadings with short recovery time. These accelerometers are used to capture the dynamics of the objects under test however, both uniaxial and triaxial accelerometer outputs contain other dynamics as well. A typical triaxial accelerometer array is made up of three uniaxial accelerometers orthogonally mounted on a substructure such as a block. The output of such shock accelerometers consists of contributions from off-axis dynamic response, sensor resonance, mounting block dynamics, shock filtering materials, and environmental noise. Understanding sensor and mounting dynamics is vital to interpreting the recorded data of inertial sensors. When using shock accelerometers in applications where large amplitudes and broadband excitation is common [1] the accelerometer and mounting dynamics influence and can dominate the measurement of the dynamic structure. This paper focuses on the mounting and sensor dynamics that may affect the output of shock accelerometers in harsh broadband excitation environments. The three specific areas examined are the mitigating properties of polysulfide layers, the dynamics of triaxial blocks, and cross-axis sensitivity of the shock accelerometers. POLYSULFIDE FILTERING The dynamics of several mechanical isolators that contain polysulfide have been examined by Bateman, Brown and Nusser, however, the effect of just the polysulfide layers has not been analyzed in much detail [2, 3]. Winfree and Kang have examined shock mitigation through multiple different metallic layers and have also experimentally shown that the elastomer polysulfide reduces the spectral energy ratio in the frequency range of sensor resonance using a pendulum impact test [4]. In the method presented polysulfide mechanical filtering effects were evaluated through a test series using a direct impact Hopkinson bar, several different flyaways, and multiple layers of polysulfide. The polysulfide layers are evaluated to see how well they act as a high frequency filter, one that does not affect the low frequencies (below 100kHz), but filters the energy in the region of sensor resonance ( khz).

2 Experiment The Hopkinson pressure bar is an experimental apparatus used to input reproducible controlled pressure waves, or elastic stress waves into a specimen located at the end of the bar. The direct-impact Hopkinson bar used in this study is located at the Shock Dynamics Laboratory of the Air Force Research Laboratory Munitions Directorate at Eglin AFB, FL. The bar used in the setup, shown in Figure 1 below, is 2 m long and 3.81 cm in diameter and is ASTM Grade 5 (6% Al, 4%V) Ti alloy (ρ = 4.43 g/cm 3,E = 114 GPa, ν = 0.33). Figure 1: AFRL Hopkinson Pressure Bar setup The bar is used to transmit the pressure wave to the f l ya w a y which is a 1.12 cm thick cylindrical disk of the same material and diameter of the bar. Accelerometers are mounted on the flyaway which is held in place by a vacuum chuck. The flyaway is released from the end of the bar upon the arrival of the first longitudinal stress wave which creates a single impulse on the flyaway and attached sensors. Three different flyaways were used: one that is flat with no pocket, the second with a pocket where the accelerometer under test was mounted and no polysulfide layers were used, and the third has a pocket such that a shock accelerometer was compressed between layers of polysulfide on either side of the sensor, all flyaways are shown in figure 2. Two piezoresistive Endevco model 7270A-60k shock accelerometers (60 kg n full scale, 700 khz bandwidth) are mounted on each flyaway [5]. Data from both accelerometers is recorded on a Gagescope PC card at 125 MSa/sec. The output from the accelerometers are preamplified and conditioned by ADA-400A differential pre-amplifiers at full bandwidth (1Mhz). A set of four tests was completed, and for each test an ensemble of five measurements were recorded. The first three tests each used a different flyaway mounting for the accelerometers. The third test which used the flyaway with the compression mount for the accelerometer under test has one layer of polysulfide on both the top and bottom of the sensor, illustrated in Figure 2 (c), and the fourth test uses the same flyaway, but has 2 layers of polysulfide on both top and bottom of the sensor, which is illustrated in Figure 2 (d). Analysis The periodogram, also known as the power spectral density or the energy spectral density, is the spectral energy density of the measurement of a signal and is calculated by where is the Fourier transform of, is the sampling frequency, and is the number of samples in the recorded signal [6]. The averaged energy spectral density is defined as (1) (2) where M is the size of the ensemble for each test. The signal energy as over a certain frequency range is defined

3 Figure 2: The three flyaways and four setups used in testing. (a) is the flyaway with no pocket or polysulfide, (b) is the flyaway with an accelerometer mounted in a pocket, but no polysulfide, (c) is the flyaway with the compression mount with one layer of polysulfide on either side of the pocketed accelerometer, and (d) is the same flyaway as (c) but with two layers of polysulfide on either side of the accelerometer. and for the discrete signals equation (3) can be written as (3). (4) The spectral energy of both accelerometers over the range of the resonance frequencies on each flyaway was calculated for a series of 5 measurements. According to the datasheet the shock accelerometers are linear up to 100kHz [5], after which the sensor dynamics exhibit non-linear resonance. The averaged energy spectral density for each test is shown in Figure 3. Each sensor has two natural frequencies between 700kHz and 900kHz and can be seen in Figure 4. The resonance frequencies shift a small amount with the mounting on the different flyaways. The resonant frequencies can be seen in the averaged energy spectral densities for the frequency range of kHz in Figure 4. The spectral energy ratio is given by where is the spectral energy of the accelerometer under test, in the pocket or sandwiched between polysulfide layers, and is the spectral energy of the reference accelerometer [4]. To compare the filtering effect of the polysulfide layers the ratios of both the linear region (0-100kHz) and the frequency range where sensor resonance occurs ( khz) were calculated and are given in Table 1. (5)

4 Figure 3: Averaged Energy Spectral Densities Figure 4: Averaged Energy Spectral densities in the frequency range of accelerometer resonance.

5 Table 1: Spectral Energy ratios for the different flyaway setups Spectral Energy Ratio ( ) Flyaway Setup 0-100khz kHz Side-by-Side Pocket Polysulfide layer Polysulfide layers An increase in the spectral energy ratio means that there is an increase in relative energy in the frequency range of the accelerometer under test. A decrease in the spectral energy ratio indicates a decrease in energy in the frequency bin of the accelerometer under test, or a filtering of the energy in that frequency range. The spectral energy ratios in the linear range of the accelerometers are all around 1, so the same amount of energy propagates to both accelerometers in all setups for the frequency range of 0 100kHz. It can also be seen that in the range of sensor resonance the pocketed flyaway increases the energy received by the accelerometer under test, while the polysulfide layers do attenuate the energy received by the filtered sensor. The two layers of polysulfide do increase attenuation, but only by an additional 5%. The polysulfide acts as a low-pass filter; while the cut-off frequency is unknown it is shown that the frequency range of resonance is filtered. TRIAXIAL MOUNTING BLOCKS The Munitions Directorate Shock Dynamics Laboratory uses titanium triaxial mounting blocks in measuring harsh multi-axial environments. The mounting blocks allow three uniaxial shock accelerometers to act as a triaxial sensor. Two types of triaxial mounting blocks are examined. The first is built for undamped shock accelerometers and includes the pockets for compression mounting with polysulfide layers, shown in Figure 5 (a). The second is intended to mount damped shock accelerometers can be seen in Figure 5 (b). Using a solid modeling program Solidworks COSMOS the natural frequencies and corresponding mode shapes of the solid models of the two triaxial blocks were computed. It was assumed that there is no relative motion between the bottom of the block and the mounting surface so in the simulation the bottom elements were fixed. Figure 5: Titanium triaxial mounting blocks for (a) undamped shock accelerometers and (b) for damped accelerometers. The mode shapes for the first mounting block can be found in Figure 6 and the natural frequencies range from 45 khz to 62.8 khz, while the mode shapes for the second mounting block can be found in Figure 7 and the natural frequencies range from 115 khz to 144kHz. It can be seen from the geometry of the blocks that the 2 nd triaxial

6 Figure 6: Mode Shapes at the first five natural frequencies of the mounting block for undamped shock accelerometers. The mode shapes are for the corresponding natural frequencies (a) 45 khz, (b) 50 khz, (c) 52.8 khz, (d) 61.3 khz, and (e) 62.8 khz. Figure 7: Mode Shapes at the first five natural frequencies of the mounting block for damped shock accelerometers. The mode shapes are for the corresponding natural frequencies (a) 115 khz, (b) 118 khz, (c) 119 khz, (d) 140 khz, and (e) 144 khz.

7 block is more rigid and the natural frequencies are expected to be higher. The mode shapes of the first triaxial block fall within the linear frequency range of the undamped shock accelerometer. It should be noted that the stiffness of the blocks will increase when accelerometers are mounted on the blocks, and when the covers to the pocketed block are put on. The increase in stiffness will increase the natural frequencies. Also the mode shapes shown of the second triaxial block may contribute to sensor case bending which will affect the measurement. While no definite conclusions may be drawn from this analysis, the natural frequencies and mode shapes provide frequency ranges to monitor when using the triaxial blocks for measurement. Future work will evaluate how much these modes affect the accelerometer measurement. While some of these modes are in the sensor s linear frequency range, accurate measurements at that high of frequency range are difficult to measure accurately and the contribution may be difficult to see. FUTURE WORK: CROSS-AXIS SENSITIVITY To further characterize the dynamics of shock accelerometers, the cross axis sensitivity will be examined. There are a few existing measurement techniques of cross axis sensitivity in shock accelerometers. Bateman and Brown examined the cross-axis sensitivity of shock accelerometers using a beryllium Hopkinson bar technique [7, 8]. Sill and Seller more recently developed a transverse sensitivity measurement technique for accelerometers using planar orbital motion [9]. The method proposed expands the capability of the titanium Hopkinson bar located at the Shock Dynamics Laboratory. Two new flyaways have been designed that will allow the measurement of cross axis acceleration with one accelerometer and the in axis acceleration with a reference accelerometer. The two cross axis flyaways can be seen in Figure 8. The calculations of the cross axis sensitivity take into account the transverse motion of the flyaway as well as the radial acceleration due to Possion s ratio of titanium. The cross axis sensitivity of damped and undamped shock accelerometers will be analyzed and compared. These experiments are planned and will be completed shortly. Figure 8: Two cross axis flyaway designs (a) has only one cross axis accelerometer and (b) has two accelerometers to be mounted transverse to the acceleration. SUMMARY The results from a test series examining mounting and filter dynamics of shock accelerometers are presented. Polysulfide layers measurably attenuate the energy received by the filtered sensor, but the additional layers of polysulfide do not increase the attenuation linearly. The resonant frequencies of the mounting blocks may affect the accelerometers output, but the frequencies where the resonance occurs are above the easily measurable frequency range of the sensors. The sensor and mounting dynamics can greatly affect the sensor output and must be acknowledged and taken into consideration when analyzing shock accelerometer data.

8 AKNOWLEDGEMENTS J. D. would like to acknowledge support from the Department of Defense SMART (Science, Mathematics, And Research Transformation) scholarship program. The authors also wish to thank the Air Force Office of Scientific Research (PM: Dr. David Stargel) for supporting this project. Opinions, interpretations, conclusions and recommendations are those of the authors and are not necessarily endorsed by the United States Air Force. REFERENCES [1] Foley, J. R., Dodson, J. C., Schmidt, M., Gillespie, P., Dick, A., Idesman, A. and Inman, D. J., "Wideband Characterization of the Shock and Vibration Response of Impact Loaded Structures," in SEM IMAC XXVII, Orlando, FL, 2009 [2] Bateman, V. I., Brown, F. A. and Nusser, M. A.,"High Shock, High Frequency Characteristics of a Mechanical Isolator for a Piezoresistive Accelerometer, the ENDEVCO 7270AM6", Sandia National Laboratory Report SAND , 2000 [3] Bateman, V. I., R.G., B., Brown, F. A. and Davie, N. T., "Evaluation of Uniaxial and Triaxial Shock Isolation Techniques for a Piezoresistive Accelerometer," in 61st Shock and Vibration Symposium, 1990 [4] Winfree, N. A. and Kang, J. H., "Resonance Prevention of Accelerometers Using Multiple-Layer Rigid Filters," in 79th Shock and Vibration Symposium, Orlando, FL, 2008 [5] "Model 7270A Accelerometer Data Sheet", Endevco Corporation, 2005 [6] Hegge, B. J. and Masselink, G., "Spectral Analysis of Geomorphic Time Series: Auto-Spectrum", Earth Surface Processes and Landforms, Vol 21 No 11, pp , 1996 [7] Bateman, V. I. and Brown, F. A.,"The Use of a Beryllium Hopkinson Bar to Characterize In-Axis and Cross- Axis Accelerometer Response in Shock Environments", Sandia National Laboratory Report SAND , 1999 [8] Bateman, V. I., Brown, F. A. and Davie, N. T., "Use of a Beryllium Hopkinson Bar to Characterize a Piezoresistive Accelerometer in Shock Enviroments", Journal of the Institute of Environmental Sciences, Vol 39 No 6 Nov/Dec, pp 33-39, 1996 [9] Sill, R. D. and Seller, E. J., "Accelerometer Transverse Sensitivity Measurement Using Planar Orbital Motion," in 77th Shock and Vibration Symposium, Monterey, CA, 2006