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Design and evaluation of adopized piezoelectric transducers
Ultrasonics International 87 abstracts Depth measurement for corner cracks using rayleigh wave spectrum modulation
P.A. Doyle and C.M. Scala, Aeronautical Research Laboratories, Melbourne, Australia The measurement of the depth of surface breaking cracks in specimens of arbitrary geometry is an important requirement for non-destructive evaluation. For the case of vertical surface cracks in a half-space, Achenbach et aL 1 proposed a simple technique, which uses normally incident Rayleigh (R) waves in essentially a two-dimensional configuration. This technique relates crack depth to the spacing A£~ between successive interference fringes in the spectrum of back or forward-scattered R-waves by the simple equation d = CR/2A• where CR is the R-wave speed. The fringes result from interference between R-wave reflection from the mouth and from the tip of the crack. This paper uses elastodynamic ray theory to show that the technique is also applicable to depth measurement for cracks in corners. The method is independent of the angle of the crack and the angle of the corner. Interference fringes in the back-scattered spectrum are shown theoretically to exhibit stronger modulation than those in the forward scattered spectrum. A surprising prediction is that within the high frequency approximation used, the R-wave transmitted around a check of any angle in a corner of any angle is independent of which specimen face is chosen for the incident wave. An experimental test of the method will be reported, first simulating cracks by artificial slots machined at various angles in corners of various angles. These initial measurements use a strong, broadband R-wave pulse generated by several methods including the fracture of a pencil lead on the specimen surface, a technique well known in acoustic emission calibration work to give surprisingly reproducible waveforms, with substantial content in the MHz range. Further tests will be discussed which evaluate the technique for real cracks in corners, rather than artificial slots.
new adapative and" myopic' deconvolution procedure which can be summarized as follows: •
The sampled reflected signal is considered as the discrete convolution of an unknown time-varying wavelet and a white (uncorrelated) reflectivity. • The observed signal is assumed locally stationary, i.e. with slow statistical variations if compared to the signal amplitude fluctuations. • An adaptive spectrum estimation 3 is done first to get a time-frequency representation and to organize the sampled data into adjacent blocks of various length wherein a local stationarity assumption may be inferred. • Within each data block, a myopic deconvolution is done that sequentially combines (i) an input (or reflectivity) estimation step 2 and (ii) an identification (wavelet and Signal-to-Noise Ratio estimation) step4; and sequentially maximizes a generalized likelihood criterion. • The estimated wavelet and SNR of a given data block are taken as initial values for the following block to be processed. The initial wavelet and SNR for the first block are experimentally determined. Convergence conditions of such an iterative technique are given. The numerical complexity of the above method is significantly reduced by the systematic use of state-space representations of the observed signal which allows one to perform the estimation recursively, with fast Kalman filters of the Chandrasekhar-type, during the three steps of spectrum estimation, input estimation, and identification. The interest of the method is illustrated with experimental results obtained on actual weld defects. References
1. Achenbach, J.D., Gautesen, A.K. and Mendelsohn, D.A. IEEE Trans Sonics Ultrasonics (1980) SU-27 124 129
1. Mendel, J.M. Optimal Seismic Deconvolution Academic Press (1983) 2. Demoment, G., Reynaud, R. and Herment, A. Range resolution improvement by a fast deconvolution method Ultrasonic Imaging (1984) 6 435-451 3. Houacine, A. and Demoment, G. Fast adaptive spectrum estimation: Bayesian approach and long AR models Proc IEEE ICASSP 87 Dallas (1987) 4. Houacine, A. and Demoment, G. Chandrasekhar adaptive regularizer for adaptive filtering Proc IEEE ICASSP 86 Tokyo (1986) 2967-2970
Resolution improvement in ultrasonic nondestructive
Transducer considerations for point-source/point-receiver
testing with fast adaptive myopic deconvolution
materials measurements
Reference
Tr ansducer s
L. Vivet, B. Comu and G. Demoment, C.E.N. Cadarache, Saint Paul-lez-Durance, France The resolution achieved by ultrasonic inspection in austenitic welds is severely limited by the considerable scattering and attenuation in the medium investigated. This attenuation being highly frequency-dependent, the maximum oscillatory frequency commonly used to investigate a ten millimeter length is about only a few MHz, which gives a maximum resolution of about one millimeter with current detection techniques. At the acoustic intensities used, the implied phenomena may be considered linear. The received signal can therefore be modelled as the convolution of an ideal unknown signal (or reflectivity of the medium) and an acoustic wavelet which describes the resolution limitation. A technique often used in the seismic I and biomedical 2 fields is then to perform a deconvolution of the received signal to improve resolution. But the main difficulty in applying these techniques to Non Destructive Testing imaging lies in the important absorption which makes the wavelet and the observed signal highly nonstationary. To remedy this drawback, we developed a
356
Ultrasonics 1987 Vol 25 November
W. Sachse, Theoretical and Applied Mechanics, Cornel/ University, Ithaca, NY 14853 USA This paper reviews the requirements and operational characteristics of several sources and receivers which can be used as the basis of a point-source/point-receiver (PS/PR) materials testing system. Considered are sources and receivers whose temporal and spatial characteristics most nearly approximate those needed for making PS/PR measurements directly. Consideration is also given to means for utilizing non-ideal transducers, that is, those whose temporal response is bandlimited or which are not operating as a force source, or as a velocity or displacement receiver and those whose aperture is finite. Design and evaluation of adopized piezoelectric transducers
D.J. Mehrl, H.H. Lin, A. Korpel and R.F. Vogel, The University of Iowa, USA It is often desirable to apodize the acoustic near field
Ultrasonics International 87 abstracts emanated by a piezo-electric transducer so as to get rid of the side lobes in the far field acoustic radiation pattern. Transducers so apodized are, for instance, very useful in acoustic pulse echo imaging where side lobes are likely to cause spurious echoes, and in acousto-optic signal processing where side lobe scattering gives rise to noise and distortion in the frequency plane. Previously developed methods of apodization use the fringing field of a single narrow transducer, tailor the electronic excitation profile, or use specially shaped electrodes. All of these methods have serious disadvantages: the narrow transducer is power limited; the electronic excitation profile is hard to implement, and may cause unacceptable dissipation; the specially shaped electrodes interfere with the basic acousto-optic scattering mechanism. In our method we avoid these drawbacks by using multiple, similarly shaped transducer segments activated by a common voltage. Effective apodization of the acoustic near field is achieved by width- or density modulation of the array of transducer segments. In this way and desired apodization profile can be achieved, limited only by geometrical accuracy. In the paper we will first outline the design procedure and implementation. Next we will compare the results of acousto-optics measurements on the acoustic radiation pattern with simulation by coherent optics and simulation by computer. Finally, we will discuss spurious wide angle side lobe generation, and its suppression by position randomization, controlled fringing or controlled radiation cut-off.
Improvements in the lateral resolution of electrostatic
Design of the front electrode Besides condition (2), the metallized parts of the front electrode must be electrically connected. We thus chose •crown" and' star' geometries. Para meters defi n i ng metallization (number of crowns or branches, Ro) were obtained by numerical resolution of the Rayleigh-Sommerfeld equation.
Experimental results Various back electrode structures were tested: smooth, electro-eroded, groved. Some incompatibilities with front electrodes affected the improvements of the directivity. Good agreement with the theory were obtained with a smooth back electrode: the first side lobe level was attenuated by 10 dB, using the star electrode and by 15 dB with the crown electrode.
Conclusion We have achieved an EUT, functioning in air, characterized by very low side lobe levels, which is useful in many applications. Time was gained by numerical simulation. From good agreement with experimental results, we can conclude that the hypotheses used were correct. References 1. Kiichiro Matsuzawa Condenser microphones with plastic diaphragms for airborne ultrasonics Physical Soc Japan (1958) 13 1533-1543 2. Filipczynski, L. and Etienne, J. Theoretical study and experiments on spherical focusing transducers with Gaussian surface velocity distribution Acustica (1973) 28 121-128
ultrasonic transducers (EUT)
R. Kalberer and J.J. Meister, Swiss Federal Institute of Technology, Lausanne, Switzerland
A 3D finite element-plane wave decomposition coupling
Introduction
method to calculate mutual radiation impedances in
The realization of ultrasonic transducers functioning in air is delicate due to the very low acoustical impedance of this medium. The EUT, made of a dielectric sheet which is metallized on the front side and fixed on a rigid back electrode, has, in the optimum case, a high efficiency and large bandwidth. The resonant frequency of the EUT is related to the structure of the back electrode 1. The phenomenon of side lobes in the radiation diagram of a plane transducer, working in the piston mode, is well known. Dynamics used can cause a reduction in the directivity of the system.
plane arrays (1)
Suppression of side lobes Side lobes are suppressed by imposing a gaussian variation of the vibration amplitude of the front face 2. For a circular transducer, the amplitude is given by:
A (r) = Ao exp ( - r2/Ro 2)
(1
with A(r) = amplitude as a function of the radius r Ao = amplitude at the center for the transducer Ro = radius for which the amplitude equal 1/e Ao Contrarily to piezoelectric transducers, this condition ~s difficult to realize practically with the EUT. We therefore chose a gaussian repartition for the emitting surface proportion, which, when the bidimensional sampling theorem is respected, is equivalent. This proportion is given by:
M(S)/S = exp ( - r2/Ro 2) withM(S)=ffm(x,y)dxdy S
m(x, y) = 1 if the surface is metallized, 0 otherwise S = integration surface r = centre of S
(2)
D. Lahalle, W. Steichen, G. Vanderborck, Thomson-Sintra ASM, Cagnes Sur Met Cedex, France Individual transducers behaviour can be precisely analysed by experimental as well as numerical methods, one of the most powerful being the Finite Element Method 1. On the other hand, the mutual transducer interaction case, when encountered in literature, only concerns rigid piston behaviour 2. In this paper, interactions between transducers setted into a plane array with elastic deformations are studied. The superficial rubber skin is discretized into finite elements in a thin layer in contact with the transducers, while a plane wave decomposition of the displacement potential is performed in the upper part of the skin as well as in the fluid. Exact boundary conditions are taken into account and lead to an integral representation which is embedded in the finite element formulation. A former paper 3 dealt with 2D formulation, this one concerns 3D cases. Theoretical results are presented, showing the connection of this technique with the classical Green formulation. The main interest of this method lies in the reduction of the mesh size, as only a part of the rubber skin is discretized into finite elements. Numerical results of mutual radiation impedances are presented for a set of polygonal speaking areas as well as a HF stub, compared with experiments or literature when available. Various parameters have been analysed, such as speaking areas geometry, width of clearance between them, rubber skin acoustical properties including losses, rubber skin thickness, and lateral baffle conditions. As a post-processing, the three-dimensional directivity diagram for the hole array can be easily obtained through the plane wave decomposition in the fluid.
Ultrasonics 1987 Vol 25 November
357
P.A. Doyle and C.M. Scala, Aeronautical Research Laboratories, Melbourne, Australia The measurement of the depth of surface breaking cracks in specimens of arbitrary geometry is an important requirement for non-destructive evaluation. For the case of vertical surface cracks in a half-space, Achenbach et aL 1 proposed a simple technique, which uses normally incident Rayleigh (R) waves in essentially a two-dimensional configuration. This technique relates crack depth to the spacing A£~ between successive interference fringes in the spectrum of back or forward-scattered R-waves by the simple equation d = CR/2A• where CR is the R-wave speed. The fringes result from interference between R-wave reflection from the mouth and from the tip of the crack. This paper uses elastodynamic ray theory to show that the technique is also applicable to depth measurement for cracks in corners. The method is independent of the angle of the crack and the angle of the corner. Interference fringes in the back-scattered spectrum are shown theoretically to exhibit stronger modulation than those in the forward scattered spectrum. A surprising prediction is that within the high frequency approximation used, the R-wave transmitted around a check of any angle in a corner of any angle is independent of which specimen face is chosen for the incident wave. An experimental test of the method will be reported, first simulating cracks by artificial slots machined at various angles in corners of various angles. These initial measurements use a strong, broadband R-wave pulse generated by several methods including the fracture of a pencil lead on the specimen surface, a technique well known in acoustic emission calibration work to give surprisingly reproducible waveforms, with substantial content in the MHz range. Further tests will be discussed which evaluate the technique for real cracks in corners, rather than artificial slots.
new adapative and" myopic' deconvolution procedure which can be summarized as follows: •
The sampled reflected signal is considered as the discrete convolution of an unknown time-varying wavelet and a white (uncorrelated) reflectivity. • The observed signal is assumed locally stationary, i.e. with slow statistical variations if compared to the signal amplitude fluctuations. • An adaptive spectrum estimation 3 is done first to get a time-frequency representation and to organize the sampled data into adjacent blocks of various length wherein a local stationarity assumption may be inferred. • Within each data block, a myopic deconvolution is done that sequentially combines (i) an input (or reflectivity) estimation step 2 and (ii) an identification (wavelet and Signal-to-Noise Ratio estimation) step4; and sequentially maximizes a generalized likelihood criterion. • The estimated wavelet and SNR of a given data block are taken as initial values for the following block to be processed. The initial wavelet and SNR for the first block are experimentally determined. Convergence conditions of such an iterative technique are given. The numerical complexity of the above method is significantly reduced by the systematic use of state-space representations of the observed signal which allows one to perform the estimation recursively, with fast Kalman filters of the Chandrasekhar-type, during the three steps of spectrum estimation, input estimation, and identification. The interest of the method is illustrated with experimental results obtained on actual weld defects. References
1. Achenbach, J.D., Gautesen, A.K. and Mendelsohn, D.A. IEEE Trans Sonics Ultrasonics (1980) SU-27 124 129
1. Mendel, J.M. Optimal Seismic Deconvolution Academic Press (1983) 2. Demoment, G., Reynaud, R. and Herment, A. Range resolution improvement by a fast deconvolution method Ultrasonic Imaging (1984) 6 435-451 3. Houacine, A. and Demoment, G. Fast adaptive spectrum estimation: Bayesian approach and long AR models Proc IEEE ICASSP 87 Dallas (1987) 4. Houacine, A. and Demoment, G. Chandrasekhar adaptive regularizer for adaptive filtering Proc IEEE ICASSP 86 Tokyo (1986) 2967-2970
Resolution improvement in ultrasonic nondestructive
Transducer considerations for point-source/point-receiver
testing with fast adaptive myopic deconvolution
materials measurements
Reference
Tr ansducer s
L. Vivet, B. Comu and G. Demoment, C.E.N. Cadarache, Saint Paul-lez-Durance, France The resolution achieved by ultrasonic inspection in austenitic welds is severely limited by the considerable scattering and attenuation in the medium investigated. This attenuation being highly frequency-dependent, the maximum oscillatory frequency commonly used to investigate a ten millimeter length is about only a few MHz, which gives a maximum resolution of about one millimeter with current detection techniques. At the acoustic intensities used, the implied phenomena may be considered linear. The received signal can therefore be modelled as the convolution of an ideal unknown signal (or reflectivity of the medium) and an acoustic wavelet which describes the resolution limitation. A technique often used in the seismic I and biomedical 2 fields is then to perform a deconvolution of the received signal to improve resolution. But the main difficulty in applying these techniques to Non Destructive Testing imaging lies in the important absorption which makes the wavelet and the observed signal highly nonstationary. To remedy this drawback, we developed a
356
Ultrasonics 1987 Vol 25 November
W. Sachse, Theoretical and Applied Mechanics, Cornel/ University, Ithaca, NY 14853 USA This paper reviews the requirements and operational characteristics of several sources and receivers which can be used as the basis of a point-source/point-receiver (PS/PR) materials testing system. Considered are sources and receivers whose temporal and spatial characteristics most nearly approximate those needed for making PS/PR measurements directly. Consideration is also given to means for utilizing non-ideal transducers, that is, those whose temporal response is bandlimited or which are not operating as a force source, or as a velocity or displacement receiver and those whose aperture is finite. Design and evaluation of adopized piezoelectric transducers
D.J. Mehrl, H.H. Lin, A. Korpel and R.F. Vogel, The University of Iowa, USA It is often desirable to apodize the acoustic near field
Ultrasonics International 87 abstracts emanated by a piezo-electric transducer so as to get rid of the side lobes in the far field acoustic radiation pattern. Transducers so apodized are, for instance, very useful in acoustic pulse echo imaging where side lobes are likely to cause spurious echoes, and in acousto-optic signal processing where side lobe scattering gives rise to noise and distortion in the frequency plane. Previously developed methods of apodization use the fringing field of a single narrow transducer, tailor the electronic excitation profile, or use specially shaped electrodes. All of these methods have serious disadvantages: the narrow transducer is power limited; the electronic excitation profile is hard to implement, and may cause unacceptable dissipation; the specially shaped electrodes interfere with the basic acousto-optic scattering mechanism. In our method we avoid these drawbacks by using multiple, similarly shaped transducer segments activated by a common voltage. Effective apodization of the acoustic near field is achieved by width- or density modulation of the array of transducer segments. In this way and desired apodization profile can be achieved, limited only by geometrical accuracy. In the paper we will first outline the design procedure and implementation. Next we will compare the results of acousto-optics measurements on the acoustic radiation pattern with simulation by coherent optics and simulation by computer. Finally, we will discuss spurious wide angle side lobe generation, and its suppression by position randomization, controlled fringing or controlled radiation cut-off.
Improvements in the lateral resolution of electrostatic
Design of the front electrode Besides condition (2), the metallized parts of the front electrode must be electrically connected. We thus chose •crown" and' star' geometries. Para meters defi n i ng metallization (number of crowns or branches, Ro) were obtained by numerical resolution of the Rayleigh-Sommerfeld equation.
Experimental results Various back electrode structures were tested: smooth, electro-eroded, groved. Some incompatibilities with front electrodes affected the improvements of the directivity. Good agreement with the theory were obtained with a smooth back electrode: the first side lobe level was attenuated by 10 dB, using the star electrode and by 15 dB with the crown electrode.
Conclusion We have achieved an EUT, functioning in air, characterized by very low side lobe levels, which is useful in many applications. Time was gained by numerical simulation. From good agreement with experimental results, we can conclude that the hypotheses used were correct. References 1. Kiichiro Matsuzawa Condenser microphones with plastic diaphragms for airborne ultrasonics Physical Soc Japan (1958) 13 1533-1543 2. Filipczynski, L. and Etienne, J. Theoretical study and experiments on spherical focusing transducers with Gaussian surface velocity distribution Acustica (1973) 28 121-128
ultrasonic transducers (EUT)
R. Kalberer and J.J. Meister, Swiss Federal Institute of Technology, Lausanne, Switzerland
A 3D finite element-plane wave decomposition coupling
Introduction
method to calculate mutual radiation impedances in
The realization of ultrasonic transducers functioning in air is delicate due to the very low acoustical impedance of this medium. The EUT, made of a dielectric sheet which is metallized on the front side and fixed on a rigid back electrode, has, in the optimum case, a high efficiency and large bandwidth. The resonant frequency of the EUT is related to the structure of the back electrode 1. The phenomenon of side lobes in the radiation diagram of a plane transducer, working in the piston mode, is well known. Dynamics used can cause a reduction in the directivity of the system.
plane arrays (1)
Suppression of side lobes Side lobes are suppressed by imposing a gaussian variation of the vibration amplitude of the front face 2. For a circular transducer, the amplitude is given by:
A (r) = Ao exp ( - r2/Ro 2)
(1
with A(r) = amplitude as a function of the radius r Ao = amplitude at the center for the transducer Ro = radius for which the amplitude equal 1/e Ao Contrarily to piezoelectric transducers, this condition ~s difficult to realize practically with the EUT. We therefore chose a gaussian repartition for the emitting surface proportion, which, when the bidimensional sampling theorem is respected, is equivalent. This proportion is given by:
M(S)/S = exp ( - r2/Ro 2) withM(S)=ffm(x,y)dxdy S
m(x, y) = 1 if the surface is metallized, 0 otherwise S = integration surface r = centre of S
(2)
D. Lahalle, W. Steichen, G. Vanderborck, Thomson-Sintra ASM, Cagnes Sur Met Cedex, France Individual transducers behaviour can be precisely analysed by experimental as well as numerical methods, one of the most powerful being the Finite Element Method 1. On the other hand, the mutual transducer interaction case, when encountered in literature, only concerns rigid piston behaviour 2. In this paper, interactions between transducers setted into a plane array with elastic deformations are studied. The superficial rubber skin is discretized into finite elements in a thin layer in contact with the transducers, while a plane wave decomposition of the displacement potential is performed in the upper part of the skin as well as in the fluid. Exact boundary conditions are taken into account and lead to an integral representation which is embedded in the finite element formulation. A former paper 3 dealt with 2D formulation, this one concerns 3D cases. Theoretical results are presented, showing the connection of this technique with the classical Green formulation. The main interest of this method lies in the reduction of the mesh size, as only a part of the rubber skin is discretized into finite elements. Numerical results of mutual radiation impedances are presented for a set of polygonal speaking areas as well as a HF stub, compared with experiments or literature when available. Various parameters have been analysed, such as speaking areas geometry, width of clearance between them, rubber skin acoustical properties including losses, rubber skin thickness, and lateral baffle conditions. As a post-processing, the three-dimensional directivity diagram for the hole array can be easily obtained through the plane wave decomposition in the fluid.
Ultrasonics 1987 Vol 25 November
357