# Transducer degradation and high amplitude behavior of broadband piezoelectric stack transducer for vibrothermography

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6 Output frequency(hz) Spectogram of transducer velocity Force(N) Net force on piezoelectric stack excitation frequency (Hz) FIGURE 2. Spectogram of transducer open circuit velocity and the net force on transducer stack. The top plot shows the output freuqency content for a frequency sweep excitation. The bottom plot shows the net force on the stack for the same frequency sweep excitation. The net force is compressive and the spectrum has harmonics which come from inherent nonlinearity of the transducer. When this happens, the stack undergoes tension and the tip can break free and collide with stack causing damage to the transducer. To understand the effect of preload on the transducer, we plotted the spectogram of the open circuit velocity. A Spectogram is a time-frequency representation of a signal[3]. We represent the input frequency instead of time, since, for a frequency sweep excitation, the input frequency is a known linear function of time. The top plot of fig. 2 shows the spectogram of the transducer open circuit velocity. In the spectogram, the horizontal axis is the input excitation frequency (for a frequency sweep excitation) and the vertical axis is the frequency in the output velocity spectrum. The colorbar (intensity) represents the spectral density. The bottom plot of fig. 2 shows the force on the stack versus the input excitation frequency. In this plot, the net force is compressive (less than zero) at all excited frequencies and the spectogram intensity has peaks only at higher order harmonics apart from the fundamental component. The harmonics are primarily the manifestation of the inherent material nonlinearity as seen in Fig 1. However, this is not the case when the net force becomes tensile (greater than zero). Fig 3 shows the velocity spectogram and net force at a higher excitation amplitude. The net force on the stack becomes positive at 17 khz. At this frequency, the spectogram intensity has peaks not only at the fundamental (17kHz) and harmonics (multiples of 17kHz), but also at the sub-harmonic frequencies and the harmonics of sub-harmonics (8.5kHz, 25.5kHz etc). It means that when the piezoelectric stack of the transducer undergoes dynamic tensile forces, sub-harmonics as well as harmonics appear in the open circuit velocity. The appearance of sub-harmonics in the spectrum indicate that the preload force is not sufficient to keep the stack under compression. If the transducer is used for longer periods under this condition, the risk of damage to the stack increases. 554

7 Output frequency(hz) Spectogram of transducer velocity Force(N) Net force on piezoelectric stack excitation frequency (Hz) FIGURE 3. Spectogram of transducer open circuit velocity and the net force on transducer stack. The top plot shows the output freuqency content for a frequency sweep excitation. The bottom plot shows the net force on the stack for the same frequency sweep excitation. When the net force on the stack becomes tensile, sub harmonics start to appear in the spectrum as well apart from the harmonics. DEGRADATION OF TRANSDUCER VELOCITY SPECTRUM The stress levels achieved in Vibrothermography using a broadband transducer degrade over time and usage. we used a PI2533 (manufacturer: Physik Instrumente Inc, Stack length: 33mm, Stack diameter: 25mm) transducer to investigate its long term reliability. We triggered the transducer periodically without attaching a specimen to its tip and monitored the open circuit velocity(v oc ) after each trigger. The transducer was allowed to cool between successive triggers so that the effect of the piezo stack heating up (due to prolonged high amplitude excitations) on the test is minimized. To keep track of how the overall spectrum of transducer changes as it degrades, we excited the transducer with a low amplitude frequency sweep (from 100 Hz to 20 Khz at 17V peak to peak voltage) periodically after every 10 bursts and a high amplitude frequency sweep (from 100 Hz to 20 Khz at 175V peak to peak voltage) after every 100 low amplitude sweeps and saved the velocity waveforms after each trigger. The test was stopped after a total of 6397 triggers (5800 tone bursts, 585 low amplitude sweeps and 12 high amplitude sweeps). The data sets for burst excitation, low amplitude sweep and high amplitude sweep were analyzed separately. The velocity spectrum for all the sweep tests has been calculated from the data. Fig. 4 shows the magnitude of small signal spectrum of the transducer at various stages of testing. The spectrum of the tranducer remained almost unchanged upto a frequency of about 8 Khz. At frequencies above 8 Khz, even though the magnitude of the spectrum did not follow a clear trend, the resonance frequencies have shifted across all the 6400 triggers. Fig. 5(a) shows the plots of the transducer high amplitude spectrum as the test progressed. We could not observe any obvious trends in the original spectrum because of the interference between fundamental and harmonic components as seen in fig. 5(a). So, we separated the harmonics and the fundamental component from the original spectrum and plotted 555

8 FIGURE 4. Small signal spectrum of the transducer PI2533 after 2, 1532, 3279, 5466 and 6391 triggers in increasing order of grayscale. The higher resonance frequencies are shifted across the triggers, but the magnitude of the spectrum did not change significantly. (a) raw spectrum (b) fundamental component (c) second harmonic (d) residuals FIGURE 5. High amplitude spectrum of the transducer PI2533 calculated after 3, 915, 2265, 3878 and 5709 triggers with decreasing gray scale levels. The plot on the top left shows the complete raw spectrum without any filtering. The plot on top right shows the fundamental component of the spectrum and the plot on bottom left shows the 2nd harmonic. The plot on bottom right shows the residuals after subtracting the fundamental and second harmonic from the raw spectrum. Legend shows the trigger number of the corresponding test. 556

9 FIGURE 6. rms value of velocity of all the tone burst excitations of the tranducer PI2533. them separately as shown in fig. 5(b)-5(d). The fundamental component of the spectrum again remained almost unchanged upto about 8 Khz. At higher frequencies, however, the spectrum magnitude has reduced siginificantly across all the 6400 triggers. Even the resonance frequencies have shifted considerably as seen in fig. 5(b). For instance, the resonance frequency at 18kHz at trigger no. 3 moved to 14kHz at trigger no Also, the originally wider high frequency resonance peaks started to shrink in width. We hypothesize that this might be an indication of the piezo stack degrading, because when the stack degrades or cracks, its stiffness changes and therefore the resonances change too. Finally, the root mean square (RMS) value of the velocity waveforms for burst excitation was calculated as a measure of the velocity amplitude. This value is plotted with the trigger ID as shown in fig. 6. The overall RMS value of the velocity decreased by about 20% over the 6400 triggers. The fact that the resonance frequencies shifted around as the test progressed (as seen in fig. 5(a)) might be an explanation for the local variations in the velocity. But clearly, there is a decrease in excitation effectiveness as the transducer degrades. CONCLUSION Transducer plays a critical role for defect detection in Vibrothermography. PZT is inherently nonlinear and the nonlinear behavior becomes pronounced at high amplitudes. The transducer resonance frequencies become lower as the excitation amplitude increases. Also, the magnitude of higher order harmonics becomes significant compared to the fundamental. When the preload force is not adequate to keep the stack under compression, the transducer tip breaks contact and collides with the stack. This leads to sub-harmonic generation in the velocity spectrum. The transducer spectrum changes significantly with time and usage of the transducer. The magnitude and resonances of low amplitude spectrum do not change significantly but the magnitude of high amplitude spectrum deteriorates and resonance frequencies decrease as the transducer ages. ACKNOWLEDGEMENTS This material is based upon work supported by Thermal Wave Imaging, Inc. under an STTR contract by the US Navy (Federal Agency) and performed at the Center for Nonde- 557

10 structive Evaluation at Iowa State University. REFERENCES 1. S.D. Holland, First measurements from a new broadband vibrothermography measurement system, Review of Progress in Quantitative Nondestructive Evaluation, D.O. Thompson and D.E. Chimenti, Eds., Vol 26A, pp , J. Vaddi, R. Reusser, and S.D. Holland, characterization of piezoelectric stack actuators for Vibrothermography Review of Progress in Quantitative Nondestructive Evaluation, D.O. Thompson and D.E. Chimenti, Eds., Vol 30A, pp , A.V. Oppenheim and R.W. Schafer, Discrete-Time Signal Processing, (Prentice-Hall Inc., Upper Saddle River, NJ, 2010), pp D. Zhou, M. Kamlah, and D. Munz, Rate dependence of soft PZT ceramics under electric field loading, Proc. SPIE 4333, 64 (2001); doi: /

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