Non-linear losses study in strongly coupled piezoelectric device for broadband energy harvesting
Graphical abstract
Introduction
Vibration energy harvesting is recognized as a relevant solution to supply electrical power to wireless sensors nodes [1], [2], [3]. In order to reach sufficient power density, the use of electromechanical resonators have been shown required for inertial energy harvesting [4], [5]. However, the resulting narrow frequency bandwidth of vibration energy harvesters is still an important issue [6], [7]. A promising solution to address this problem is to use nonlinear electrical techniques [8], [9] and power management circuits [10], [11] able to tune the resonant frequency of piezoelectric harvesters. For example, this solution made it possible to expect a relative bandwidth of 43 % with a PZN-PT-based cantilever [9]. In order for this approach to be effective, it is necessary to employ piezoelectric harvesters with very strong global electromechanical coupling coefficients (). Proposals for the design of such harvesters have therefore recently been made in the literature [12], [13] and offer promising perspectives for broadband vibration energy harvesting. Nevertheless, the presence of nonlinear dielectric losses in the piezoelectric materials have been shown to considerably reduce the harvested power when strongly coupled materials are used [14]. Such dielectric losses must be taken into account in the models as neglecting them can lead to a significant error in the expected harvested power. Since a model to predict the behavior of the harvester taking into account non-linear dielectric losses is absent from the state of the art, this paper proposes a new nonlinear model corroborated by experimental results for strongly coupled energy harvester.
The linear losses of piezoelectric materials have already been studied in the prior art for various piezoelectric devices [15], [16]. As an example, Uchino et al. expressed the necessity to consider a piezoelectric loss tangent coefficient especially for actuator applications [17]. Recently, Wild et al. discussed the difficulty to distinguish dissipation origin (mechanical, dielectric and piezoelectric) depending on the piezoelectric constitutive equation form [18]. Concerning energy harvesting applications, dielectric and piezoelectric losses in piezoelectric materials are often neglected [19], [20] as they don’t have a significant influence for low and moderately coupled devices. The electric field experienced is indeed usually weak in the materials. Nevertheless, the consideration of a dielectric loss coefficient has been shown necessary for devices that include strongly coupled materials [14], [21]. While models to consider linear dielectric losses have been proposed in the literature [21], nonlinear dielectric losses can be experienced in the very strongly coupled devices. Indeed, Morel et al. demonstrated the increase of the equivalent dielectric loss tangent on a PZN-PT based cantilever under an increasing electric field [14]. They also observed such nonlinear dielectric losses with the increase of the vibration amplitude. They indeed showed an experimental decrease of 30% of the power due to the increasing electric field in the material. Therefore, considering nonlinear dielectric losses is necessary to model the behaviour of vibration energy harvesters in the case of prototypes involving strongly coupled materials.
In this paper, we introduce a model that takes material nonlinearities of strongly coupled piezoelectric harvesters into account. The model, based on the Rayleigh method, is introduced in Section 2. In order to validate this model, a strongly coupled prototype and the experiments conducted are then presented in Section 3. The Section 4 is dedicated to results presentation and discussion. In this last section, we discuss the importance of considering a dielectric nonlinear losses coefficient.
Section snippets
Discussion about dielectric loss coefficients
This section deals with the loss considerations made in the present work. Losses in piezoelectric materials have been discussed in various ways in the literature [17], [18]. It seems important to clearly state the intention of this paper and the definition of the loss coefficients used.
As mentioned by Wild et al. [18], the terms “dielectric loss”, “mechanical loss” and “piezoelectric loss” are intended to describe physical contributions that differ depending on the considered form of the
Device introduction
The experimental validation was carried out on the strongly coupled cantilever based on PMN-PT single crystals shown in Fig. 3. The PMN-PT material we used is the [0 0 1] poled PMN-0.29PT produced by TRS ceramics (TRS X2B). The PMN-PT patches have been cut to size by the manufacturer and glued in our laboratory on a steel beam with epoxy glue (Epotecny E505). The proof mass is made from two steel sheets bonded on the substrates with a 3M® epoxy glue. The geometrical parameters are given in Table 1
Discussion on model validation
It can be seen from Fig. 6 and Fig. 7 that the proposed model provides a good evaluation of the experimental behaviour of the cantilever-type generator. The presented model is therefore able to predict the nonlinear behaviour of strongly coupled harvesters subjected to various acceleration levels.
Furthermore, the linear parameter deduced from model fitting (Table 3) are close to the linear parameters deduced from the material parameters of the material supplier (Table 4), which means that the
Conclusions
This paper reports on the experimental validation of a new model that considers nonlinear material losses in piezoelectric harvesters. For this purpose, it takes into account a second order dielectric loss term in addition to a mechanical second order mechanical loss term. The presented model allows a better consideration of the harvested power under vibration than previous models and is proven to be necessary for accurately predicting the performance of strongly coupled harvesters. An
CRediT authorship contribution statement
David Gibus: Conceptualization, Methodology, Investigation, Writing - original draft, Writing - review & editing. Pierre Gasnier: Conceptualization, Methodology, Supervision, Writing - review & editing. Adrien Morel: Conceptualization, Investigation, Writing - review & editing. Nicolas Garraud: Conceptualization, Writing - review & editing. Adrien Badel: Conceptualization, Methodology, Supervision, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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