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Numerical modeling of piezoelectric transducers using physical parameters

机译：使用物理参数对压电换能器进行数值建模

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摘要

Design of ultrasonic equipment is frequently facilitated with numerical models. These numerical models, however, need a calibration step, because usually not all characteristics of the materials used are known. Characterization of material properties combined with numerical simulations and experimental data can be used to acquire valid estimates of the material parameters. In our design application, a finite element (FE) model of an ultrasonic particle separator, driven by an ultrasonic transducer in thickness mode, is required. A limited set of material parameters for the piezoelectric transducer were obtained from the manufacturer, thus preserving prior physical knowledge to a large extent. The remaining unknown parameters were estimated from impedance analysis with a simple experimental setup combined with a numerical optimization routine using 2-D and 3-D FE models. Thus, a full set of physically interpretable material parameters was obtained for our specific purpose. The approach provides adequate accuracy of the estimates of the material parameters, near 1%. These parameter estimates will subsequently be applied in future design simulations, without the need to go through an entire series of characterization experiments. Finally, a sensitivity study showed that small variations of 1% in the main parameters caused changes near 1% in the eigenfrequency, but changes up to 7% in the admittance peak, thus influencing the efficiency of the system. Temperature will already cause these small variations in response; thus, a frequency control unit is required when actually manufacturing an efficient ultrasonic separation system.
机译：数值模型经常促进超声设备的设计。然而，这些数值模型需要校准步骤，因为通常并不是所用材料的所有特性都是已知的。材料特性的表征与数值模拟和实验数据相结合可用于获取材料参数的有效估计值。在我们的设计应用中，需要由超声换能器以厚度模式驱动的超声颗粒分离器的有限元（FE）模型。从制造商那里获得了压电换能器的有限材料参数集，因此在很大程度上保留了现有的物理知识。剩余的未知参数是通过简单的实验设置通过阻抗分析估算的，并结合使用2-D和3-D FE模型的数值优化例程。因此，针对我们的特定目的，获得了完整的可物理解释的材料参数集。该方法提供了足够的材料参数估计精度，接近1％。这些参数估计值随后将用于未来的设计仿真中，而无需经历整个系列的表征实验。最后，敏感性研究表明，主要参数的1％的微小变化会导致本征频率的变化接近1％，但导纳峰的变化高达7％，从而影响系统的效率。温度将已经引起这些微小的响应变化。因此，在实际制造高效的超声分离系统时，需要一个频率控制单元。

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