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.
The increased demand for mobile systems using low-power electronics leads to a need for new power sources.
Using batteries as power source may be inapplicable in distributed systems like wireless sensor networks because
the batteries have to be exchanged frequently. Energy Harvesting systems are one possible energy source for
such systems exploiting environmental energy like mechanical vibrations. One good solution to convert vibration
energy is the use of piezoelectric generators usually realised as piezoelectric bending beams.
The generators convert mechanical energy to electrical energy due to resulting strain of the element. However,
the power output of piezoelectric generators is a challenging task even if low-power applications have to be driven.
Due to the low electric power output of piezoelectric generators, it is an important task to obtain a suitable
geometric design of the transducer element. Beside the element dimensions the electric power output depends
on the input excitation as well as on the electric load to be powered.
To analyse the system behaviour, input variables and the generator itself have to be described in a mathematical
model. This enables the calculation of optimal elements in principle. A modal electro-mechanical model
of the piezoelectric element assuming to be base-excited is used in this paper. Although the modal model is very
helpful to analyse the system, it cannot be easy used to determine a proper design of the piezoelectric elements.
The problem is that the parameters of the model do not show any apparent relations to geometric dimensions
or material data. Therefore, a mathematical method to obtain the parameters from the physical properties of
a piezoelectric bending element is briefly described. The knowledge of the link between physical and modal
parameters allows the usage of the mathematical model as a qualified design method. The input parameters of
the linked model are the material data which can be found on data sheets. Additionally, boundary conditions
of the environment like the impedance of the driven load and the vibration excitation has to be specified. The
linked model shows the influences on power output to connected electric loads. The given power demands of
applications which have to be satisfied yields in a design space of suitable elements. The design method enables
the development engineer to select piezoelectric generator elements.
In the design process of energy harvesting systems based on piezoelectric elements, achievable energy output is the most interesting factor. To estimate this amount a priori manufacturing of prototypes a mathematical model is very helpful. Within this contribution we will introduce a model based on electro-mechanical circuit theory. Its parameters are identified by measurements and the model is validated by comparison to experimental results.
The model is designed to support the development-engineer in the dimensioning of energy harvesting units to specific application demands. Two main challenges in device design are investigated with the mathematical
model: influence of the ambient excitation frequency, and influence of the load impedance.
Typically, the equivalent model approach delivers models for piezoelectric elements that are driven in resonance by electrical excitation. In the case of energy harvesting the piezoelectric elements are excited mechanically and most often non-resonant. Thus, we first set up a mechanical equivalent model for base excited systems. In first approximation it represents an energy harvesting unit around one resonance frequency. The model is expandable for a wider frequency range using the superpositioning of multiple circuits.
From the viewpoint of optimum energy transformation between mechanical and electrical energy it is favorable to drive piezoelectric elements at resonance or anti-resonance. Thus, an energy harvesting system should be tuned to the excitation frequency.