Kookjin Kang

Optimization of structural variables of a flextensional transducer by the statistical multiple regression analysis method.

The performance of an acoustic transducer is determined by the effects of many structural variables, and in most cases the influences of these variables are not linearly independent of each other. To achieve optimal performance of an acoustic transducer, we must consider the cross-coupled effects of its structural variables. In this study, with the finite-element method, the variation of the operation frequency and sound pressure of a flextensional transducer in relation to its structural variables is analyzed. Through statistical multiple regression analysis of the results, functional forms of the operation frequency and sound pressure of the transducer in terms of the structural variables were derived, with which the optimal structure of the transducer was determined by means of a constrained optimization technique, the sequential quadratic programming method of Phenichny and Danilin. The proposed method can reflect all the cross-coupled effects of multiple structural variables, and can be extended to the design of general acoustic transducers.

Analysis and Design of a Flextensional Transducer by Means of the Finite Element Method

A class IV flextensional transducer is a typical underwater acoustic transducer capable of generating high power sound waves. The small extensional displacement of a piezoceramic stack in the major axis of the transducer causes a large displacement along the minor axis by the leverage effect of a compliant shell, and this provides the large volume displacement for high power acoustic waves. High power and long term usage of the transducer causes accumulation of a lot of heat inside the structure, which results in the transducer performance to deteriorate. In this study, the effects of the structural variables of the transducer were investigated using the finite element method, and their influences were prioritized to design a transducer to have the highest sound pressure with the lowest heat generation at a desired operation frequency. The transducer designed showed an 11.2% increase in its sound pressure and a 16.5% decrease in its heat generation in comparison with a basic model of a conventional structure.

P2O-7 Design and Construction of an Acoustic Horn for High Power Ultrasonic Transducers

Typical high power transducers consist of a piezoelectric or magnetostrictive element of transduction and a solid acoustic horn that acts as a vibration amplifier. In order to obtain high power capacity, the acoustic horn needs to be optimized to match the active element. In this study, we did optimal design of an acoustic horn for a high power magnetostrictive transducer and constructed a sample prototype of the horn to verify the validity of the design. For the design, we derived the theoretical output power of a horn as a function of its dimensions, and determined the optimal dimensions to achieve the maximum power through finite element analyses with ANSYSreg. The analytical method could quite quickly determine the horn length while the finite element method could refine the planar dimensions of the structure. The transducer had the resonant frequency of 19.3 kHz and had the maximum sound pressure level of 199 dB with an omni-directional radiation pattern in water. The analysis method developed in this study is so general that it can be applied to the design of acoustic horns for high power transducers of various operating frequencies and transduction materials

Finite element analysis on reduction of the cross talk in ultrasonic transducers

In an ultrasonic transducer, the cross talk between array elements is an important performance degrading factor, and there is strong need to identify the sources of the problem and to find the means to reduce its level. This paper considers two most representative ultrasonic transducers, capacitive micromachined ultrasonic transducer (cMUT) and piezoelectric transducer. Both are linear array immersion transducers. Two-dimensional finite element models of the transducers are constructed using the commercial code ANSYS. We analyze the origin and level of the cross talk between array elements, with evidence of coupling through certain waves such as the Stoneley wave propagating at the transducer-water interface and the Lamb wave propagating in the substrate or the impedance matching layer. For reduction of the cross talk level, the effects of various structural schemes are investigated. They are the change of wafer thickness, the installation of etched trenches of various dimension and sound absorbing materials inside, and installation of polymer walls between array elements for a cMUT as well as the change of the dimension and material of kerfs for a piezoelectric transducer. Results for the two transducers are discussed to describe the general method to reduce the cross talk level in ultrasonic transducers.

Optimal Structural Design of a Flextensional Transducer Considering the Working Environment

The performance of an acoustic transducer is determined by the effects of many design variables, and mostly the influences of these design variables are not linearly independent of each other. To achieve the optimal performance of an acoustic transducer, we must consider the cross-coupled effects of the design variables. In this study, the variation of the performances of underwater acoustic transducer in relation to its structural variables was analyzed. In addition, the new optimal design scheme of an acoustic transducer that could reflect not only individual but also all the cross-coupled effects of multiple structural variables, and could determine the detailed geometry of the transducer with great efficiency and rapidity was developed. The validation of the new optimal design scheme was verified by applying the optimal structure design of a flextensional transducer which are the most common use for high power underwater acoustic transducer. With the finite element analysis(FEA), we analyzed the variation of the resonance frequency, sound pressure, and working depth of a flextensional transducer in relation to its design variables. Through statistical multiple regression analysis of the results, we derived functional forms of the resonance frequency, sound pressure, and working depth in terms of the design variables. By applying the constrained optimization technique, Sequential Quadratic Programming Method of Phenichny and Danilin(SQP-PD), to the derived function, we designed and verified the optimal structure of the Class IV flextensional transducer that could provide the highest sound pressure level and highest working depth at a given operation frequency of 1 kHz.

Optimal Structural Design of a Tonpilz Transducer Considering the Characteristic of the Impulsive Shock Pressure

The optimal structure of the Tonpilz transducer was designed. First, the FE model of the transducer was constructed, that included all the details of the transducer which used practical environment. The validity of the FE model was verified through the impedance analysis of the transducer. Second, the resonance frequency, the sound pressure, the bandwidth, and the impulsive shock pressure of the transducer in relation to its structural variables were analyzed. Third, the design method of experiments was employed to reduce the number of analysis cases, and through statistical multiple regression analysis of the results, the functional forms of the transducer performances that could consider the cross-coupled effects of the structural variables were derived. Based on the all results, the optimal geometry of the Tonpilz transducer that had the highest sound pressure level at the desired working environment was determined through the optimization with the SQP-PD method of a target function composed of the transducer performance. Furthermore, for the convenience of a user, the automatic process program making the optimal structure of the acoustic transducer automatically at a given target and a desired working environment was made. The developed method can reflect all the cross-coupled effects of multiple structural variables, and can be extended to the design of general acoustic transducers.

Analysis of elastic wave velocities in magnetostrictive materials

We developed nonlinear constitutive equations for magnetostrictive materials and thereby derived wave equations for the materials, the wave equations turned out to be too complicated to analyze. To facilitate the analysis, we defined a quasi-linear magnetostriction constant eijk and derived new wave equations with it. Velocities of the plane waves propagating inside magnetostrictive materials were determined with the quasi-linear wave equations and their numerical calculations were illustrated with a hexagonal symmetry material. Validities of the calculations were verified through comparison with experimental measurement results for the most representative magnetostrictive material, Terfenol-D.

Development of an algorithm for HIFU focus visualization

The ultrasound waves emitted from the HIFU transducer propagate through water and various tissue layers to a focus of the internal body. During propagation the multiple refractions and reflections occur due to in-homogeneity nature of the tissues. These cause the aberration of the focal location. Therefore, in the view of safety for the HIFU treatment it is important to know where the focus is exactly formed. In this study, the method of synchronization control between a HIFU and an imaging devices is proposed for the focus visualization. In order to get a clear focus image, the signal processing with the harmonics of the transmitted HIFU pulses is introduced. The convex imaging probe is installed at the center of the phased-array HIFU transducer. The time delays for the imaging probe as well as the HIFU array-elements are calculated along the HIFU focus location. The HIFU array elements send a short-pulse train of 1 MHz and the imaging probe starts receiving the echo-signal in sequence according to the delays. In this manner, the IQ data were collected using the ultrasound device, ECUBE 9 of ALPINION MEDICAL SYSTEMS. At this stage, the focus is not clear due to the random distribution of the scatters with non-uniform intensity. Through the FFT of the IQ data the spatial distribution of the amplitudes at the fundamental and the harmonic frequencies are extracted. The amplitudes at the harmonic frequencies are divided by the amplitude at the fundamental frequency. And then the results from the division are displayed on the B-mode ultrasound images. This algorithm was tested in ex-vivo and in-vivo. The algorithm was verified through the in-vivo and ex-vivo experiments. It is confirmed that the algorithm can provide the precise information of the focus location in a simple manner.

Coupled vibration analysis for a piezoelectric array element using superposition method

The coupled vibration was analyzed for a piezoelectric array element of two-dimensional structure whose vibration can be described by two coupled differential equations with coupled boundary conditions. The exact solutions satisfying both equations of motion and boundary conditions are not available. Therefore, the approximate solutions were obtained using the superposition method suggested for accurate vibration analysis of the elastic structures. To this end, the mechanical and electrical boundary conditions were satisfied approximately by summing the stress and the electric potential obtained from the displacements. The frequency spectrum and the electromechanical coupling factor of the element varying the width/thickness ratio were calculated and compared with the results of the finite element analysis and experiment. As the ratio of thickness to with increases, the fundamental frequency and the electromechanical coupling factor of the array element increase. The theoretically calculated results has shown good agreement with the results of the finite element analysis. The superposition method was verified to provide the accurate analysis for a piezoelectric array element.

Frequency Characteristics Variation of a Class I Flextensional Transducer

We constructed a Class I flextensional transducer, and analyzed the variation of the resonance frequency of the transducer in relation to its structural and material variables. We used the FEM for the analysis. Total length of the transducer, thickness and material properties of the shell have large effects on the resonance frequency. While outer radius of the ceramic stack and material properties of the ceramic stack have no effect on the resonance frequency. In addition, the validation of the FE model was verified by manufacturing and comparison of the impedance analysis. Results of the present work can be utilized to design a Class I flextensional transducers of various resonance frequency.