Maréchal Pierre, Levassort Franck, Tran-Huu-Hue Louis-Pascal, Lethiecq Marc
François-Rabelais University of Tours, LUSSI, ENIVL, BLOIS Cedex, France.
Ultrasonics. 2007 May;46(2):155-67. doi: 10.1016/j.ultras.2007.01.006. Epub 2007 Feb 8.
The goal of this work was to develop an extended ultrasound transducer model that would optimize the trade-off between accuracy of the calculation and computational time. The derivations are presented for a generalized transducer model, that is center frequency, pulse duration and physical dimensions are all normalized. The paper presents a computationally efficient model for lens-focused, circular (axisymmetric) single element piezoelectric ultrasound transducer. Specifically, the goal of the model is to determine the lens effect on the electro-acoustic response, both on focusing and on matching acoustic properties. The effective focal distance depends on the lens geometry and refraction index, but also on the near field limit, i.e. wavelength and source radius, and on the spectrum bandwidth of the ultrasound source. The broadband (80%) source generated by the transducer was therefore considered in this work. A new model based on a longitudinal-wave assumption is presented and the error introduced by this assumption is discussed in terms of its maximum value (16%) and mean value (5.9%). The simplified model was based on an extension of the classical KLM model for transducer structures and on the related assumptions. The validity of the implemented extended KLM model was evaluated by comparison with finite element modeling, itself previously validated analytically for the one-dimensional planar geometry considered. The pressure field was then propagated using the adequate formulation of the Rayleigh integral for both the extended KLM and finite element results. The simplified approach based on the KLM model delivered the focused response with good accuracy, and hundred-fold lower calculation time in comparison with a mode comprehensive FEM method. The trade-off between precision and time thus becomes compatible with an iterative procedure, used here for the optimization of the acoustic impedance of the lens for the chosen configuration. An experimental comparison was performed and found to be in good agreement with such an extension of the KLM model. The experiments confirm the accuracy of such a model in a validity domain up to -12 dB on the pulse-echo voltage within a relative error of 9% between experiment and modeling. This extended KLM model can advantageously be used for other transducer geometries satisfying the assumption of a predominantly longitudinal vibration or in an optimization procedure involving an adequate criteria for a particular application.
这项工作的目标是开发一个扩展的超声换能器模型，该模型将优化计算精度和计算时间之间的权衡。文中给出了一个广义换能器模型的推导过程，即中心频率、脉冲持续时间和物理尺寸均进行了归一化处理。本文提出了一种计算效率高的透镜聚焦圆形（轴对称）单元素压电超声换能器模型。具体而言，该模型的目标是确定透镜对电声响应的影响，包括聚焦和匹配声学特性方面。有效焦距不仅取决于透镜的几何形状和折射率，还取决于近场极限，即波长和源半径，以及超声源的频谱带宽。因此，本研究考虑了换能器产生的宽带（80%）源。提出了一种基于纵波假设的新模型，并从其最大值（16%）和平均值（5.9%）的角度讨论了该假设引入的误差。简化模型基于经典KLM换能器结构模型的扩展以及相关假设。通过与有限元建模进行比较，评估了所实现的扩展KLM模型的有效性，有限元建模本身之前已针对所考虑的一维平面几何结构进行了解析验证。然后，使用瑞利积分的适当公式对扩展KLM模型和有限元模型的结果传播压力场。基于KLM模型的简化方法能够以较高的精度给出聚焦响应，与模式全面的有限元方法相比，计算时间降低了百倍。因此，精度和时间之间的权衡变得与迭代过程兼容，这里使用该迭代过程来优化所选配置下透镜的声阻抗。进行了实验比较，发现与KLM模型的这种扩展结果吻合良好。实验证实了该模型在脉冲回波电压高达 -12 dB的有效域内的准确性，实验与建模之间的相对误差为9%。这种扩展的KLM模型可有利地用于满足主要为纵向振动假设的其他换能器几何结构，或用于涉及特定应用适当标准的优化过程。
