Research On Modeling, Simulation And Optimization Design Of Spherical Cymbal Transducer

Acoustic transducers are the most basic and the most important component of those underwater instruments for target-detecting, target-tracking, target-identifying, and target-locating. To improve the detection abilities of these transducers used in shallow water regions, we must reduce their resonance frequency, expand their bandwidth, increase their transmit power and receive sensitivity, and minish their volume and weight. Cymbal transducers, with their small size, light weight, simple design, low cost, and high sensitivity, have been widely used for underwater acoustic detection. This paper has presented a new structure of cymbal transducer, and has studied its key technologies such as theoretical model, simulation analysis, and optimization design etc.The research scope of this paper includes:(1) A new structure of piezoelectric composite transducer, called spherical cymbal transducer, was designed. Spherical cymbal transducer consists of a piezoelectric ceramic disk (poled in the thickness direction) sandwiched between two metal endcaps, each containing a shallow spherical inner cavity. The endcaps serve as mechanical transformers for converting and amplifying the small radial vibration displacement of the ceramic disk into a much larger axial vibration displacement normal to its surface, which can improve the transmit power of the transducer.(2) Some theoretical models of the spherical cymbal transducer were developed. 1) A displacement model of the spherical cymbal transducer's axial vibration was established based on statics theory of shallow shells, and a simplified displacement model was gained under the hypotheses that the endcaps and the piezoelectric ceramic stick together ideally, the endcaps only have simple geometric distortion, and there is no mechanical consumption during the deformation process. 2) The yield conditions of the endcaps were analyzed based on Tresca yield criterion. According to the plastic flow rules, the external power and the internal power of the endcaps were calculated. At last, a limit load model of the endcaps was established based on the kinematic method. 3) Under the basic hypothesis of elastic shell's vibration, the basic differential equations of shallow shell's vibration were used to solve the vibration of the transducer's endcaps, and then a resonance frequency model of the transducer's axisymmetric vibration was established.(3) An optimization design method, which is based on orthogonal experiment theory and combined with FEM (finite element method) virtual experiments, was developed. The method was used to optimize the design of the spherical cymbal transducer. Through the intuitionistic analysis of the experiment results, the effect of each design factor on the performances of the spherical cymbal transducer was found, and the optimal lever of each design factor was gained. The significant level of each design factor on the performances of the transducer was gained by the variance analysis of the experiment results. Finally, the comprehensive scoring method was used to analyze the experiment results of multi indexes, and the optimal combination level of design factors was gained.(4) To deploy random arrays in regular regions and irregular regions, two optimal deploy methods, which are based on Circle-Packing and Delaunay-Trianglulation respectively, were developed. MVDR beamforming was used to optimize the beams of the spherical cymbal transducer arrays, and the beam patterns were simulated using MATLAB. The results showed that the directivities of the random arrays are better than that of the uniform regular arrays configured in the same regions.(5) In order to manufacture the endcaps of the spherical cymbal transducer with higher quality and lower costs, free hydro-bulging technology was used to substitute the traditional punch technology, and the springback of the endcaps in free hydro-bulging was studied. ANSYS/LS-DYNA software was used to predict the springback of the endcaps, Mathematic models, which can discribe the process of the endcap's free hydro-bulging, were gained by nonlinear curve fitting. Flexible material, namely silicone rubber, was used as fundamental plate to support the spherical cymbal transducers in the fabrication process of the transducer arrays, which make it convenient to install the arrays onto the outside surface of the UUV or AUV.(6) FEM were used to calculate the vibration displacement, the resonance frequency, and the limit load of the spherical cymbal transducer, the results of FEM verified the correctness of the above mentioned theoretical models. The simulation results also indicated that compared to the traditional cymbal transducer with reference design parameters, the axial displacement of the spherical cymbal transducers improved 4.55% (in air) and 7.78% (in water), the resonance frequency decreased 4.41% (in air) and 7.86% (in water), and the limit load raised 9.42%. Elements of spherical cymbal transducer and a 10 elements equilateral triangular array were fabricated and their performances were tested. The results further showed that the above mentioned mathematic models are correct, test results simultaneously verified that the circle Packing method and the Delaunay triangulation method are effective for deploying random arrays in given regions.The above mentioned investigations have definite reference values and practical significances for enriching the products of cymbal transducers, broadening the application field and application scope, improving the design and fabrication technology, accelerating the application of cymbal transducer arrays.