Absolute Measurement of Elastic Waves Excited by Hertzian Contacts in Boundary Restricted Systems
Tribol Lett
Absolute Measurement of Elastic Waves Excited by Hertzian Contacts in Boundary Restricted Systems
S. Schnabel 0 1 2
S. Golling 0 1 2
P. Marklund 0 1 2
R. Larsson 0 1 2
0 Division of solid mechanics, Lulea ̊ University of Technology , 97187 Lulea ̊ , Sweden
1 Division of machine elements, SKF-University technology center, Lulea ̊ University of Technology , 97187 Lulea ̊ , Sweden
2 Division of machine elements, Lulea ̊ University of Technology , 97187 Lulea ̊ , Sweden
In most applied monitoring investigations using acoustic emission, measurements are carried out relatively, even though that limits the use of the extracted information. The authors believe acoustic emission monitoring can be improved by instead using absolute measurements. However, knowledge about absolute measurement in boundary restricted systems is limited. This article evaluates a method for absolute calibration of acoustic emission transducers and evaluates its performance in a boundary restricted system. Absolute measured signals of Hertzian contact excited elastic waves in boundary restricted systems were studied with respect to contact time and excitation energy. Good agreement is shown between measured and calculated signals. For contact times short enough to avoid interaction between elastic waves and initiating forces, the signals contain both resonances and zero frequencies, whereas for longer contact times the signals exclusively contained resonances. For both cases, a Green's function model and measured signals showed good agreement.
Hertz contact; Elastic waves; Acoustic emission; Green's function; Boundary restricted system; Condition monitoring
1 Introduction
Acoustic emissions (AE), or as well called high frequency
elastic wave emissions, have over the past decade become
increasingly popular in the application of nondestructive
testing and condition monitoring. This technique has been
proven in the separation of failure modes [2], the
monitoring of wear [4, 21], the specification of contaminated
systems [16, 20] and to differentiate lubricants [17] and
lubrication regimes [7]. However, most of the
investigations use simple signal processing methods such as root
mean square (RMS) [7, 20] and activation counts (AC)
[2, 16, 17, 21]. All these investigations use relative
measurement methods, and signals are acquired using
piezoelectric transducers, which limits investigations without
further calibration to measure relatively. This use of
relative measurement methods also limits the extraction of
information of the acoustic wave.
The authors hypothesize that condition monitoring
techniques could be improved by improving processing of
the signal. A fuller understanding of the relation between
the source of the wave and the actual measured signal
would improve the processing of the signal. Being able to
calculate the force function of the initial source based on
sensor signals would increase the possibility to distinguish
between different failure types and failure sizes. However,
absolute measurement would therefore be required so that
the relation between the signal and the wave source could
be ascertained. Both McLaskey and Glaser [15] and Jacobs
and Woolsey [10] have presented methods for absolute
calibration of piezoelectric transducers. However, there are
no evaluations of the validity of the methods which are
independent of the system. McLaskey’s and Glaser’s
method for absolute calibration of piezoelectric transducers
is used. The method is evaluated for boundary restricted
systems using a Laser–Doppler vibrometer (LDV) and
Green’s function based on an FEM simulation as a
comparison. The term ‘‘boundary restricted systems’’ is used
for systems where reflections of all dimensions are taken
into account (in this investigation disc samples), whereas
systems which are boundary free in one or two dimension
are not included in this definition (calibration
plate—reflection is only considered in one dimension).
An absolute measurement is required to improve
condition monitoring capability of high frequency emissions.
However, a better understanding of the relation between
source and signal is as well an essential knowledge for
improving condition monitoring by acoustic emission.
Several researchers have successfully connected source and
signal for high frequency emissions. McLaskey and Glaser
[14] have, for example, related a signal of a piezoelectric
transducer to the actual force function by using a Green’s
function approach. Kundu et al. [12] have presented a
mathematical method to locate Hertzian impacts by
minimizing error functions. The impact of cracks on wave
propagation in plates was studied by Liu and Datta [13]
with FEM based on a Green’s function for transfer of the
initial source. Glaser et al. [5] were able to calculate the
wave propagation in an isotropic half space with a
viscoelastic propagator and compared it to actual
measurements. All these investigations either have used thin plates
in order t (...truncated)