Characterization and modelling of 3D piezoelectric ceramic structures with ATILA software

Abstract

In this paper, the correspondence between ATILA-simulated and measured values of two piezoelectric ceramic structures, bulk and RAINBOW actuators, was determined. Modelling was started by creating a 2D wire model of the structures, after which a 3D model was created and simulation parameters were introduced (electric potentials, polarizations and boundary conditions). Harmonic type analysis was used in the simulations. The results obtained from the simulations contained information about displacements in the z-axis direction. Displacements of the measured structures behaved nonlinearly as a function of the electric field. Accordingly, effective piezoelectric coefficients (i.e. d 31, d 33) calculated from the electric field and the displacement also changed nonlinearly. However, the displacement results acquired from simulations are linear, since the ATILA program uses a linear approach for in the calculation. This causes the modelling results to differ from the measurement results, especially when large voltages are used. The problem was solved by modifying the constant parameters used in the simulations. In the study reported here, relative permittivity K 33, piezoelectric coefficient d 33 and approximated piezoelectric coefficient d 31 were used to obtain more accurate modelling results corresponding to the measurement results. The differences in the z-axis displacements between the modelling (using the original material parameters) and measurement results obtained with bulk and RAINBOW actuators were 6.5–17.7% and 6.0–27.9%, respectively. With modified material parameters, the differences were 1.1–1.6% and 3.1–8.5%, respectively.