Parameter identification of piezoelectric bimorphs for dynamic applications considering strain and velocity dependent effects

Abstract

Piezoelectric bimorph elements are commonly used in a wide area of applications, among them various actuator applications in textile machines, applications in sensing like medical tissue identification, or the use in energy harvesting systems. Especially the last field may create a mass market for piezoelectric elements. Due to their easy use and low resonance frequency, bimorphs seem to fit energy harvesting demands quite well. To get the best possible power output, the element has to be designed as good as possible to fit the environmental excitation characteristics as excitation frequency and amplitude. Due to the need of a good understanding of the resulting system, a model based approach is desirable for the design of the used bimorphs. This is the case not only in Energy Harvesting systems but in most of the mentioned applications. A typical modeling technique is the utilization of modal models using electro-mechanical analogies. The needed parameters can either be identified by measurements of the piezoelectric system or they can be calculated using a dynamic mechanical model. This kind of modeling is well known for a good approximation of the behavior of piezoelectric transducers -as long as they are driven in the linear range. Unlike most Langevin transducers, piezoelectric bimorph elements show a smaller range of linearity in experimental investigations. Obviously, the bimorph elements have a big shift of resonance frequency and a considerable increase of damping with increasing excitation. The change in frequency and damping leads to complications in system design. It is hypothesized that the nonlinear behavior mainly depends on the strain level of the bending element. Considering that strain is proportional to the velocity amplitude of the free end of the bimorph around the first mode, measurements with constant strain levels are performed. Experiments verify the relationship between the appearing nonlinearities and strain as well as velocity of the bending element. Furthermore, measurement results of electrical excited bimorphs with different constant strain levels are used to identify parameter sets. Gained data allows the phenomenological definition of the behavior of the modal model parameters according to excitation levels. This enables the derivation of strain dependent parameter sets for specific materials. The measurement data is also used to enhance the well known lumped parameter model for piezoelectric systems to handle the nonlinear behavior using the strain dependent parameter sets. The enhancement of the model allows the correct description and simulation of piezoelectric bending elements like bimorphs for different mechanic as well as electric excitation levels. This leads to a suitable design procedure to reduce development efforts.