Pierre G

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Developments in Acoustic Emission at the UKs
National Physical Laboratory
Pierre Gélat National Physical Laboratory 3
April 2003
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The Finite Element Method

• The FE method is a numerical method to solve
  arbitrary PDEs
• The method consists of approximating the
  structure in small domain portions called finite
  elements
• Each element has a set of material properties
  associated with it (Youngs modulus, material
  density, Poissons ratio, etc.)
• A set of output quantities (e.g. displacement)
  can be obtained for given forcing/boundary
  conditions

http//www.npl.co.uk/npl/acoustics
3
Axisymetric and Three Dimensional Transducer
Modelling

• Use of PAFEC 8.6 Vibroacoustics software (soon to
  be upgraded to 8.8) used for modelling the
  behaviour of ultrasonic and audio-range
  transducer, with fluid loading or in vacuum, for
  both continuous and transient excitation
• Allows the coupling of vibrating structures to
  the modelling of finite and infinite regions of
  fluid (boundary elements, wave envelope elements)
• Piezoelectric elements can be defined
• PAFECs mathematicians are working with NPL both
  to extend the functionality of the software and
  to provide NPL with bespoke software to tackle
  specific modelling problems
• Quantities routinely obtained from PAFEC include
  acoustic pressure, structural displacement and
  electrical impedance
• Sensitivity analysis and optimisation
  capabilities

http//www.npl.co.uk/npl/acoustics
4
Sensor Modelling Using the Finite Element Method

• Understanding the dynamics of piezoelectric
  sensor
• Investigating the effect of variations in design
  on overall sensitivity
• Designing novel sensor configurations
• Sensitivity analysis and optimisation
  (sensitivity vs. bandwidth)

http//www.npl.co.uk/npl/acoustics
5
AE sensor modelling

• Sensor is assumed to be axisymmetric
• Piezoelectric material is PZT5-A
• Apply unit voltage across PZT5-A between 0.1 MHz
  and 1MHz
• Obtain electrical impedance

http//www.npl.co.uk/npl/acoustics
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Electrical Impedance of AE sensor
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Modelling of AE reference facility

• Aim is to develop a methodology to model a simple
  AE system from the electrical excitation of the
  reference transducer to the electrical output of
  the sensor
• Requires the combination of more than one
  technique
• one to model the transducer and sensor
• the other to model the stress wave propagation in
  the medium
• NPLs Finite Element (FE) method used to
• predict displacement output of transducer for a
  given electrical input
• predict electrical response of sensor for a given
  displacement at its face
• Fraunhofers Finite Difference/Integral (EFIT)
  method used to
• predict displacement as a function of time at a
  given point in an elastic medium

http//www.npl.co.uk/npl/acoustics
8
Experimental arrangement

• The reflective coating is Aluminium or Chromium
• The displacement equivalent noise floor of the
  interferometer is around 3.5 pmRMS

1. Out-of-plane displacement history of surface
   measured using interferometer
2. Repeated with sensor coupled in place of
   interferometer

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Modelling of AE reference facilityComparison of
NPLs FE and Fraunhofers EFIT method
Peter D. Theobald

• Comparison performed using a simple problem for
  validation
• point displacement excitation
• small cylindrical glass block allows treatment as
  an axisymmetric problem
• displacements compared at chosen points

.
.
Force f A sin (2pft) . B sin (pft) excited at r
0, z 0
http//www.npl.co.uk/npl/acoustics
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Reference source - Finite Element modelling of
conical transducer
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Reference source - Finite Element modelling of
conical transducer
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Modelling of AE reference facilityComparison
results at 200 kHz
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Modelling of AE reference facilityComparison
results at 200 kHz
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Modelling of AE reference facilityComparison
results at 200 kHz
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Modelling of AE reference facility - Conclusions

• Validation is complete and shows good comparison
  between techniques
• Work is now progressing on the modelling of a
  complete system comprising of source transducer,
  glass cylinder and sensor
• If successful this should produce a complete
  transfer function for the AE system for each wave
  mode received at the sensor
• Next stage of work is to model the NPL test
  facility
• would provide more information for the
  calibration of sensors
• could be combined with a calibrated reference
  source to provide system calibration