Abstract
A simple theoretical model which captures the statistical nature of an acoustic emission (AE) signal generated by a stream of solid particles impinging on a flat solid surface is presented. It rests on well-known results dating back to the fundamental work by Hertz, which assumes the impact to be elastic, the particle to be spherical, and the surface on which the particle bounces perfectly flat. The average power of the signal is evaluated in two limits. In the first one, the frequency content of the signal is identical to that of the forces developed during impact. In the second limit, only the low frequency part of the source function contributes to the spectrum of the recorded signal, the transfer function of the measuring system acting as a low-pass filter. In this case, it is shown that the result has an immediate physical interpretation, although its practical relevance is still limited. Additional progress is accomplished by experimentally proving that the statistical average of the particles’ momentum may be replaced with the average flow velocity, a quantity that may be directly measured in real life situations. It is suggested that this simplified version of the theoretical result may provide a useful tool to characterize particle flow in systems of industrial interest.
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Notes
The reader, who may be interested in forming a broader view of the literature on this subject, may find numerous citations in the references reported here.
References
Boschetto, A., Quadrini, F.: Powder size measurement by acoustic emission. Measurement 44, 290–297 (2011)
Buttle, D.J., Martin, S.R., Scruby, C.B.: Particle sizing by quantitative acoustic emission. Res. Nondestruct. Eval. 3, 1–26 (1991)
Droubi, M.G., Reuben, R.L., White, G.: Statistical distribution models for monitoring acoustic emission (AE) energy of abrasive particle impacts on carbon steel. Mech. Syst. Signal Process. 30, 356–372 (2012)
Ivantsiv, V., Spelt, J.K., Papini, M.: Mass flow rate measurement in abrasive jets using acoustic emission. Meas. Sci. Technol. 20, 095402 (2009)
Carson, G., Mulholland, A.J., Nordon, A., Tramontana, M., Gachagan, A., Hayward, G.: Particle sizing using passive ultrasonic measurement of vessel wall vibrations. J. Sound Vib. 317, 142–157 (2008)
Carson, G., Mulholland, A.J., Nordon, A., Tramontana, M., Gachagan, A., Hayward, G.: Estimating particle concentration using passive ultrasonic measurement of impact vibrations. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56, 345–352 (2009)
Carson, G., Mulholland, A.J., Nordon, A., Gachagan, A., Hayward, G.: Theoretical analysis of ultrasonic vibration spectra from multiple particle-plate impacts. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56, 1034–1041 (2009)
Uher, M., Beneš, P.: Measurement of particle size distribution by the use of acoustic emission method. In: IEEE International Instrumentation and Measurement Technology Conference (I2MTC), pp. 1194–1198 (2012)
McLaskey, G.C., Glaser, S.D.: Hertzian impact: experimental study of the force pulse and resulting stress waves. J. Acoust. Soc. Am. 128, 1087–1096 (2010)
Hutchings, I.M.: Strain rate effects in microparticle impact. J. Phys. D, Appl. Phys. 10, L179–L184 (1977)
Buttle, D.J., Scruby, C.B.: Characterization of particle impact by quantitative acoustic. Wear 137, 60–90 (1990)
Acknowledgements
The author would like to thanks Prof. P.B. Nagy for suggesting the analysis of the signals in the low-frequency limit and for systems with infinite wide-band, and for pointing out their main steps.
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Pecorari, C. Characterizing Particle Flow by Acoustic Emission. J Nondestruct Eval 32, 104–111 (2013). https://doi.org/10.1007/s10921-012-0163-7
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DOI: https://doi.org/10.1007/s10921-012-0163-7