A model-based measurement procedure for the characterization of frequency-dependent material properties of piezoceramics using a singleton specimen

越来越多的基于仿真的超声波换能器设计过程要求尽可能地描述所使用的材料以获得真实的结果。压电陶瓷材料可以使用至少10个参数进行建模。这些参数的确定是根据目前的标准使用不同试样几何形状的共振频率的评估完成的。然而，由于这些不同的试样总是受到不同的工艺和极化条件，当单个材料参数组合在一起时，可能会导致不合理或不一致的参数集。在单个样品上对压电陶瓷进行表征是困难的，因为通常没有足够高的所有相关参数的灵敏度。在之前的项目中，通过优化压电陶瓷盘上的电极拓扑结构，实现了灵敏度的提高，从而确定了完整的材料参数集。由于更复杂的电极结构不能再用解析近似来表示，因此材料参数由逆方法确定。在此过程中，以有限元方法模型的形式创建数字孪生，该模型包含材料参数作为输入变量。然后，可以使用问题适应优化算法来影响模型的材料参数，从而尽可能地反映真实系统的行为。然而，目前需要在压电陶瓷盘上进行几种阻抗测量。电极拓扑的一个更动态的数学优化应该减少到一个单一的测量。此外，要找到一个因果阻尼模型，它可以更好地映射物理材料的行为，从而产生更真实的模拟。同样，反问题的可靠解必须由足够大的灵敏度来保证。

The increasingly simulation-based design processes of ultrasonic transducers require the best possible descriptions of the used materials for realistic results.Piezoceramic materials can be modeled using at least 10 parameters.The determination of these parameters is done according to current standards using the evaluation of resonance frequencies of different specimen geometries.However, since these different specimens are always subject to different process and polarization conditions, implausible or inconsistent parameter sets can result when the individual material parameters are combined.The characterisation of a piezoceramic on a single specimen is difficult, since there are usually no sufficiently high sensitivities for all relevant parameters.An increase of the sensitivities and thus a determination of a complete material parameter set was realised with an optimised electrode topology on piezoceramic disks in the previous project.Since the more complex electrode structure can no longer be represented by analytical approximations, the material parameters are determined by an inverse method.In the process, a digital twin is created in the form of a finite element method model, which contains the material parameters as input variables.Problem-adapted optimisation algorithms can then be used to influence the material parameters of the model in such a way that the behaviour of the real system is mirrored as well as possible.However, several impedance measurements on a piezoceramic disc are currently necessary for this.A more dynamic mathematical optimisation of the electrode topology should reduce this to a single measurement.In addition, a causal damping model is to be found which better maps the physical material behaviour and thus results in a more realistic simulation.Again, a reliable solution to the inverse problem must be ensured by sufficiently large sensitivities.