S Stach, S N Ramadas, S Dixon, Centre for Industrial Ultrasonics, Department of Physics, University of Warwick, United Kingdom,

E-mail: s.stach@warwick.ac.uk

Square Flexural Transducer Design for Air-Coupled Ultrasonic Application

IntroductionFlexural mode piezoelectric transducers were first conceived of in the 1930s and interest in them remains high due to their low mechanical impedance and large radiation surface [1]. They are more easily acoustically matched to gases and liquids than other transducer types which make them widely used in gas and liquid coupled applications such as gas flow measurements and Non Destructive Testing (NDT) [2]. Flexural plate transducers exploit the piezoelectric behaviour of piezoceramics to flex a bonded metal plate to create ultrasonic waves. Flexural transducers can be split into two main types based on the shape of the flexural plate; circular or rectangular. Square plate flexural transducers and their comparisons with circular plates were investigated.

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Figure 2. Example of a resonance peaks as a function of a changing variable. From the fits of the peaks quantitative rules for tuning the resonance frequencies by manipulating the cap

size could be found.

Figure 1 The model of the square cap transducer rendered by

PZFlex.

Manufacturing and Assembly of Transducer

The aluminium square caps with dimensions given in Table 1 were created using Computer Numerical Control (CNC) machining. CNC milling was chosen because it is capable of creating complicated designs that are not practical on a traditional lathe and also create very accurate caps with dimensions in agreement with the CAD design to within ±0.01mm. The caps had a 0.1mm thick and 6.5mm diameter circular recess into the front plate on the back to act as a guide for placement of the piezoceramic.PZT5a discs were attached to the caps by applying a thin film of silver backed epoxy onto one side of the ceramic (Figure 3).The wire was bonded to the ceramic using silver back epoxy at the tip of the wire to provide an electrical connection and a regular permabond epoxy on the rest of the wire in contact with the ceramic to provide support.

Finite Element ModellingFinite element modelling with PZFlex software was used to gain an understanding of the performance of a square flexural cap and how changes in the dimension of the metal cap would effect this performance.

The cap material was set as aluminium because of its ease to manufacture into the cap shape we wanted.

Default cap dimensions (Table 1) were set to create a square cap with similar dimensions and the same front surface area as a previously characterised cylindrical cap. The piezoceramic used was set as a 6.5mm diameter and 0.5mm thick PZT5a ceramic to emulate ceramics available. Each dimension of the cap defined in table 1 was varied individually whilst keeping the rest constant and PZFlex output the front face displacement of the transducer and impedance curves.Maximum amplitudes of displacement and resonance frequencies (obtained from the Fourier transform) of the centre point of the front face were plotted as a function of each variable for both square and circular cap models.

From the simulations it was found that the front plate thickness and side length impacted the caps resonance frequencies most. An increasing side length reduced the resonance frequencies (Figure 2) and increasing the front plate thickness increased the resonance frequencies.

Variable Default Value (mm)

Front Plate Thickness

0.50

Side Length 10.0

Cap Side Wall Thickness

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Cap Depth 4.80

PZT5a Radius 3.25

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Table 1. Default dimensions used for Square cap

modelling

Figure 3. The two square caps with the recess and the ceramics already glued in with silver backed epoxy. Once the

epoxy set, a wire was glued to ceramic with an epoxy adhesive then electrical contact with the ceramic was made

using silver backed epoxy.

Experimental ResultsThe resonance frequencies of just the caps without the PZT5a discs attached was found from firing am Nd:YAG (neodymium-doped yttrium aluminium garnet) laser at the back of the cap and using an IOS AIR-1550-TWM laser ultrasonic receiver pointed at the centre of the front plate to measure the displacements. Fourier transforms of the displacement showed a dominant peak in excellent agreement with the PZFlex modelling at 56200±700Hz.

Figure 5. Impedance phase and amplitude for the two transducers produced and an equivalent PZFlex model.

The differences in the two transducers curves comes from the assembly process

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Impedance amplitude and phase curves were recorded for both prototypes using an Agilent 4294A Impedance Analyzer, the prototype impedance curves are plotted against PZFlex simulations in Figure 5.The two lowest frequency peaks seen in the PZFlex model can’t be seen on the normalized impedance curves of the prototypes however when using the laser vibrometer there were resonance frequencies found in the 40-100 kHz range. The lowest frequency peak seen in the simulation and on prototype 2 match up with the frequency of the dominant peak of the Nd:YAG experiment.The displacements of the front plates whilst the ceramic was driven by a 5V continuous sine wave of varying frequency were measured using laser interferometry. Figure 6. Area scan of the front face displacement of prototype 1

driven at 42.8kHz. Prototype 2 at 47.1kHz showed the same shape.Displacement readings were taken across the length of the cap along both axis of symmetry at resonance frequencies of the centre point of the front plate. Area scans were taken at the lowest resonance frequencies, (Figure 6.) and at 220.7 kHz, which gave symmetrical diameter scans.

The higher frequency modes, whilst showing symmetrical diameter scans had asymmetric area scans and thus gave irregular pressure scans when using the microphone to scan the far field pressure distribution. This suggests that the square cap may not be suitable for high frequency (>200 kHz) applications without scaling the length down to micro-machining levels. There was also significant differences in peak frequencies between the two as seen in Figure 5 most likely caused by the differing quality of assembly.

Conclusions and Further WorkThe two square cap flexural transducers were successful in effectively propagating ultrasonic waves into air without the use of a matching layer. The performance of the caps produced was in good qualitative agreement with the PZFlex simulations giving validation to the results of the resonance frequencies peaks fits. The trends seen in the simulation are very similar to the results seen for the cylindrical caps, with an increasing resonance frequency roughly proportional to the thickness of the front plate thickness and decreasing frequency with increased length/diameter.The next stage would be to scale these single caps into a 1D or 2D array or to experiment with piezoelectric composites.

References:[1] C. B. Sawyer, “The use of Rochelle salt crystals for electrical reproducers and microphones,” Proc. IRE, vol. 19, Nov. 1931, pp. 2020-2029.[2] Grandia WA, Fonunko CM. "NDE applications of air-couplcd ultrasonic transduccrs", Pmc IEEE Ultrasan Symp 1995: pp. 697-710.

Acknowledgements:Mike Laws, Tobias Eriksson (Researchers at CIU)Charles Joyce, Robert Edwards (School of Engineering)