NDT.net • June 2006 • Vol. 11 No.6 
Nondestructive Methods for the Fast Determination of The Acoustic Parameters and Their ApplicationsPetre Petculescu, Gabriel ProdanOvidius University of Constanta, Mamaia Ave. 124, Constanta, 900527, Romania, email: petculescu@univovidius.ro AbstractIn this paper we describe two fast NDT methods to determine the acoustic parameters. Both methods apply the echo technique in immersion. The first method refers to the determination of the propagation times between the transducer, sample and reflector and calculates the sample velocity and thickness. Gate sizes for an optimum arrangement of the transducersample, samplereflector or transducerreflector distances are given. The second method consists of a program with certain input data that leads to obtaining the acoustic and spectral parameters in real time. The methods are applied (i) in the time domain by determining the longitudinal ultrasonic velocity, the reflection coefficient, the density of the material, and the time of flight (TOF), and (ii) in the frequency domain by determining the frequency dependence of the attenuation and the attenuation peak. For each measured point, the saved information consists of the amplitude and TOF determined from the reflected RF signal. The ultrasonic equipment used in this work consisted of pulserreceiver card (NDT Automation IPR 100), an analogtodigital converter (A/D 90), a stepper motor controller SMC4 from Physical Acoustics Corporation. We have used the point focused (H10MP15) transducer produced Krautkramer for the aluminum sample.INTRODUCTIONModern new structures have been developed to satisfy the requirements brought about by technological advances. The method with focused transducers [1,2] is an important instrument for the nondestructive examination of these structures, since it allows high resolution imaging of the areas located right below the surface, which are practically impossible to probe by conventional examination techniques. Recent advances in hardware and software have generated a remarkable enhancement in the image quality and have broadened the obtainable information spectrum.In the domain of ultrasonic material characterization, the longitudinal ultrasonic velocity, time of flight and the attenuation are the most widely used acoustic parameters. Ultrasonic velocity is also indicative of the mechanical behavior of the material via relationships involving the latter's elastic properties and their offshoots such as fracture toughness, thermal coefficient of expansion etc. Elastic properties can be calculated from the measured ultrasonic velocity data and references to the use of these properties in nondestructive evaluation (NDE) and materials evaluation are provided in the literature. The monitored echoes can be from the front and back surfaces of the component or from intermediate layers within the sample. Essentially, the timeofflight between echo peaks within selected gates (time windows) is measured. In the simplest form of the measurement, the ability to precisely locate the peaks depends on the sampling interval of the digitizer, which is the reciprocal of the sampling frequency. Such a method serves first of all to increase the speed of data interpretation. By progressively sweeping the frequency of the driving transducer over an appropriate range and recording the amplitude and TOF of the receiving transducer, one can acquire the ultrasonic spectrum characteristic of the sample. APPARATUSThe experimental setup has two parts: an automated mechanical system for the immersion measurements and data analysis software for the determination of the longitudinal ultrasonic velocity and the attenuation (acoustic parameters). The mechanical system allows threeaxis scanning with a maximum displacement of 100mm in each direction. The transducer displacement is achieved using stepper motors (1.8 deg/step) while the automated position is accomplished through the acquisition software USCAN 95 [3]. For each measurement point, the acquired data is transmitted through the serial interface to the personal computer and then is saved as data files. For each measurement point the following information is recorded: the radiofrequency (RF) signal, the amplitude, and the time of flight (TOF). The experimental system, shown in Figure 1, consists of the following: a pulserreceiver card (NDT Automation IPR 100), an analogtodigital converter (A/D 90), a stepper motor controller SMC4 (Physical Acoustics Corporation), and (H10MP15) a pointfocused transducer (Krautkramer).The first method. The experimental technique requires a single ER transducer in immersion and the scanning is performed on one side of the sample. Two plastic holders situated between the sample and the reflector ensure the distance d2 between the sample and the reflector. We took into consideration the echoes obtained from the frontal surface, the bottom surface, and from the reflector with or without the sample. With the transducer located on the top of the sample the obtained multiple echoes correspond to the pulses reflected within the sample and those reflected from the reflector. The sample is aluminum of 12.4 mm thickness and we have used the H10MP15 pointfocus transducer. The measured distances between the transducer and the frontal (d_{1}) and bottom (d_{2}) surfaces give the outline of the same surface, where d0 is constant, being the distance between the transducer and the reflector (Figure 2). The software calculates automatically the TOF corresponding to the propagation distances d_{0}, d_{1}, and d_{2}, called t_{w}, t_{1},t_{2}, and t_{3} respectively. One can determine the ultrasonic velocity v_{s} and the thickness ds in the sample knowing these propagation times and the ultrasonic velocity in water [4]: Gate level determination. The rigorous impulse selection and the recording of the acoustic data (amplitude and TOF) can only be achieved by choosing the appropriate measurement gates. A gate must be long enough to cover all the possible TOF variations of the selected echo. However, this echo must not interfere with the neighboring gates. In order to obtain the necessary time difference, the echo superposition method is used. This method needs a considerable amount of data because the RF waveforms must be correlated for each scanning position. Accurate measurement of the location, amplitude, and polarity of each peak is needed in order to make certain that the TOF is recorded for the correct peak and subsequently used to compute the sample velocity and thickness. The gate width (expressed in microseconds) must cover all possible variations of the TOF for the echoes corresponding to the frontal and bottom surfaces, to the reflector and to the reflector without the sample (Figure 3). The second method. The second experimental method has been developed and tested for the ultrasonic investigation of material and structure characteristics (USIS program) [5]. An analysis of the frequency spectrum involves differentiation of two successive echoes E_{1} and E_{2} obtained from the time domain, being generated from the same emission impulse. Then, based on FFT, the power spectra of the echoes S_{1} and S_{2} are determined. The ratio of the two power spectra in the region of the peak allows the computing of the ultrasonic attenuation. In the frequency domain, the amplitude ratio for a series of frequency components forms the basis for the deduction of the functional relation between the attenuation and the frequency. After obtaining ranges S_{1} and S_{2} corresponding to the selected echoes, the results are graphically displayed indicating the peak frequency and the amplitude corresponding to the peak frequency. The method permits the selection of a frequency range in order to obtain the frequency dependence of the attenuation. Because the calculation includes the amplitude of two echoes, this method is susceptible to errors. Errors were also present in the measurements. A measurement is considered to be exact when the sample surface is plane and parallel with the transducer and with the reflector. These conditions must be insured during the measurements. Transducersample nonparallelism affects the transit times of the waves emitted from different parts of the transducer, which can in turn superimpose an interference pattern on the echo train. It was determined experimentally that a deviation of the perpendicularity of the sample from 0° to 0.5° (lefttoright) leads to a decrease in amplitude from 1 to 0.2. In the same time the deviation of 0.5° leads to a variation of 0.005 % in the time of flight, which doesn't affect the determinations [6]. At high frequencies, a focused transducer is less influenced by the angular deviation than is a normal, plane transducer. The reflector is also important because it has to be plane and must be fixed on two holders. Another error can be introduced by the coupling medium  water in this case  in which the ultrasonic propagation can be nonlinear and ultrasonic velocity varies with the water temperature [7]. The percent error in the pulseecho velocity v measurement was calculated from [8]: where x and Dx are the thickness and the error in thickness, respectively, and t and Dt are the time delay and the error in time delay, respectively. The error is also dependent on the error in frequency domain signal processing methods used in the calculation of acoustic parameters. The percent error in the reflection coefficient R measurement by pulseecho technique is calculated from: where SR = 250 is the signaltonoise ratio of the first frontsurface echo without of the sample. The percent error in the measurement of the sample thickness is calculated from: where d_{real} is the actual sample thickness and the d_{exp} is the sample thickness measured experimentally by the first method. The percent error in the measurement of velocity v inside the sample is calculated from where vusis is the velocity calculated from the USIS program by the second method and vexp is the velocity measured experimentally by the first method. Finally, the percent error in the reflection coefficient is calculated from: where R_{cal} is the reflection coefficient calculated from the acoustic impedances ( water and sample) and R_{exp} is the reflection coefficient experimentally measurement by the second method. RESULTS AND DISCUSSIONSThe first method. For the aluminum sample: d_{1} = 30mm, d_{2} = 16mm, d_{0} = 46 mm, we obtained the following values for the propagation time: t_{1} = 40.54 µs , t_{2} = 44.48 µs , t_{3} =66.10 µs, and for water, t_{w} = 78.5 µs. The sample velocity v and thickness d, calculated from Equations (1) and (2), respectively, are v = 6169 m/s and d = 12.15 mm.The second method. The input data of the application consists of: the sample thickness, the couplant acoustic impedance between the transducer and the sample, the sample rate, the gain, samples (points), the gate width and the frequency range. The method performs the following tasks: selects the first two echoes E_{1} and E_{2}, translates E_{2} for an overlap with E_{1}, performs the FFT of the E_{1} and E_{2} echoes, obtains S_{1} and S_{2} computes the spectrum amplitude ratios: B(f) =S_{1}/S_{2} over a specified frequency range, computes the diffraction correction [9,10] required by the chosen configuration , performs the curvefitting of the frequency dependence of the ultrasonic attenuation and computes the fitting coefficients.
The three windows which constitute the application are shown in Figure 5 for the aluminum sample using the H10MP15 transducer and the USIS program. In the first window are visualized the echoes (four echoes) from the time domain (Fig. 5a) and also the input data, couplant acoustic impedance (water) Z_{c} (Kg/m^{2} s) = 1.48, sample thickness d = 12.4 mm, sample rate (MHz) = 256, gain (dB) = 54, delay (µs)= 8.00E6, number of samples(points)= 4096.00(in the left hand). In the second window (Figure 5b) is shown the superposition of the two echoes E_{1} and E_{2} along with the Fast Fourier Transform (FFT), the velocity value (experimentally determinate) 6.2538 mm/µs, and the work frequency (4.00E+6) for both echoes. The arrival time (TOF) of echo E_{1} (measured at the echo peak amplitude) is 8.80 µs while the arrival time (TOF) of echo E_{2} is 12.26 µs. The amplitude of echo E_{1} is 1.815E2 v and that of echo E_{2} is 1.540E2 v. Similarly, the amplitudes of echoes S_{1} and S_{2} are 23.95E3 and 1.750E3 respectively. The start and stop frequencies (for 6dB) are 3.56 MHz and 5.19 MHz respectively (Figure 5b). The last window (Fig. 5c) visualizes the attenuation dependence on frequency determined experimentally and theoretically from equations (811) In this window one obtains the reflection coefficient R = 0.84, the acoustic impedance of the material (aluminum) Z_{m} = 1.65 E+1 and the sample density d = 2.95E+0. Analyzing the curves obtained experimentally by equations 811 one can determine the proper coefficients. The method presents an option of the Equation (8), in the Rayleigh scattering case, where coefficient "b "is computed (b= 3.49E44) and the grain size is determined.
The calculated errors. The percent errors, calculated from Equations (3)  (7), are obtained as follows:
CONCLUSIONS.In this paper we present two methods to determine the acoustic and spectral parameters. The first method works in the time domain and is limited only to determine two acoustic parameters: the longitudinal velocity and the sample thickness knowing the time of flight (TOF). The experimental setup with the determined transducersamplereflector distances is shown. It was noticed experimentally that the optimum condition to obtain the results is d_{1}~ 2 d_{2}. The pulseecho technique in immersion was used here. The second method is based on the USIS program working both in the time and frequency domains. This is a complex method that determines the acoustic and spectral parameters in real time. From the calculated error it is noticed that the smallest errors are obtained using the equations (5,6,7) by applying the USIS program. The errors due to the analysis techniques used here to working in immersion, and to the nonparallelism between the transducer, sample, and reflector are explained. In the second method we determine the reflection coefficient, the acoustic impedance and the sample density and in the frequency domain we determine the peak attenuation, the attenuation vs. frequency and the grain size, both based on the same data set (RF signal). The ultrasonic equipment used in this work consisted of a pulserreceiver card IPR100, a converter A/D90 and stepper motors SMC4 from the Physical Acoustic Corporation. We have used the point focused transducer produced Krautkramer (H10MP15) for the aluminum sample.ACKNOWLEDGMENTWe gratefully acknowledge funding for this work form the Romanian Education Ministry, through grant RELANSIN no. 2075/01.10.2004.References

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