Finite element modeling and characterization of a magnetoelastic broadband energy harvester

https://doi.org/10.1016/j.sna.2020.112104Get rights and content

Highlights

  • A small scale silicon-based cantilever is fabricated and implemented into a system that includes a pair of external magnets.

  • The two possible different magnets configurations (NN and NS) are studied by FEM simulations and experimentally.

  • Realistic values of distances between the magnets and cantilever and between the cantilevers themselves allow for a spring softening effect, i.e. a broadband energy harvester.

  • Experimentally, a decrease of 49.

Abstract

Piezoelectric-based vibration energy harvesters have been extensively developed to the end of replacing low-power batteries. However, matching the frequency of the ambient vibration is not always possible and to broaden the frequency response of the harvesters, different proof-of-concept devices have been developed. This work presents a miniaturized device intended for magnetoelastic broadband vibration energy harvesting. The device consists of a silicon beam where ferromagnetic foils act as proof mass and interacts with an external pair of permanent magnets. The interaction is first simulated using a Finite Element Method (FEM) model for different distances between the magnets and beam (a) and between the magnets (b). This is done for both an attractive and a repulsive magnet configuration and the calculation is performed for a set of a and b values. Both spring softening and hardening effects are observed for the two magnet configurations. The attractive configuration has a monostable potential energy landscape with an associated spring softening for a large range of a and b values which makes this configuration very useful for energy harvesting applications. The attractive configuration is experimentally investigated by impedance measurements. These measurements are performed for a ∈ [400 μm, 2500 μm] and b ∈ [320 μm, 3140 μm] and a region that allows for broadband harvesting is found experimentally. Compared to the linear case the largest spring softening effect yielded a decrease in the effective spring constant of 74%, a decrease in the resonant frequency of 49%, and the coupling coefficient was increased with a factor of 2.6.

Introduction

The demands on power sources limit the applicability of wireless miniature sensor systems for use in off-the-grid applications where it is difficult or impossible to change batteries. Two of the main requirements for miniaturized systems used as power sources are physical dimensions in the millimeter-scale range and long lifetime. Conventional batteries imply continuous and sometimes expensive replacement cost. Furthermore, they impose a limit on system miniaturization. This means that for some applications a replacement for conventional batteries must be found. Vibration energy harvesters (VEHs), which can harvest energy from ambient vibrations and convert it into electrical energy automatically, have become a promising alternative for a range of applications. There are three main approaches to harvesting energy from vibrations, which involve the use of either electrostatic [1], [2], [3], [4], [5], [6], electromagnetic [7], [8] or piezoelectric [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19] principles. As a general rule, the main challenge in vibrational energy harvesting is that the maximum system performance is achieved when the resonant frequency of the VEH matches the external vibration source. The key parameters for VEHs are the output power and the frequency bandwidth. The output power can be increased by optimizing the coupling factor, the design or the energy conversion scheme. Most of the available published material presents studies of systems under resonant excitation. However, most ambient vibration sources have a frequency shift over time [20]. For that reason, either continuously tuning the resonant frequency using for example passive or active methods [21], [15] or widening the frequency bandwidth of the VEHs has become of utmost importance before their practical implementation.

The frequency bandwidth of the VEH can be increased using non-linear effects [22], [23], [24], [25], [26]. These non-linear effects can be introduced by using permanent magnets and ferro electric materials [22], [23], [24], for example by having a ferromagnetic cantilever and one or more permanent magnets located close to the cantilever [22], [23], [27]. This will effectively change the potential energy landscape. Due to dimensional constraints, the magnetoelastic method is more suitable for small systems than the approach where several harvesters operate in parallel [28].

Piezoelectric-based VEHs have attracted much attention because it is feasible to produce them in millimeter-scale whilst having large power densities [29], [30]. They typically consist of a cantilever structure with piezoelectric layers on top. For such a device, the non-linear effect can be accomplished by externally implementing a magnetic set-up and adding ferromagnetic material to the tip of the cantilever, as illustrated in Fig. 1. Commonly, the external magnetic set-up consists of either one or a pair of magnets. It has previously been demonstrated that the latter one leads to increased generated power when compared to the former set-up [31]. Therefore, the two-magnet configuration shown in Fig. 1 will be studied in this work. A similar, however much larger system, has been previously studied [32]. It consisted of a beam with a length of about 11 cm placed vertically and two cylindrical magnets. In that work, an analytical model was developed. There, the force acting on the cantilever beam was directly calculated from an expression of the magnetic field. However, the method presented in that study does not directly apply to smaller system dimensions where tiny square magnets are used.

A numerical study of a non-linear oscillator for broadband energy harvesting was presented by [33]. Nonetheless, the study did not consider any external magnetic setup, therefore lacking any dimensional analysis. On the other hand, it has been found that for a given set-up, like the one under study in this work, the parameters that determine whether the cantilever presents a softening effect or a bi-stable behavior are the distance between the magnets and the tip of the cantilever, a, and the distance between the magnets, b [34], [15], [16]. The position of the magnets with respect to the cantilever beam is illustrated in Fig. 1. When a pair of magnets is used they can be positioned in either an attractive magnetic configuration, Fig. 1a, or a repulsive magnetic configuration, Fig. 1b. As a consequence, it becomes of utmost importance to find the dimensional parameters, a and b, that allows for a VEH that presents a softening effect.

The aim of this work is to find the positions of the magnets, a and b, that lead to a VEH having a softening effect. These positions are found by studying the potential energy of the system using finite element calculations. Experiments are performed to validate the proposed device. Since one of the requirements for powering wireless sensor systems, as described previously, is dimensions in the millimeter-scale range, the focus of this study is on small-size cantilevers with lateral dimensions no longer than 10 mm.

The article is organized as follows: First, the simulation methods used are explained. Secondly, the experimental methods are presented, together with a fabrication process description. Thirdly, the simulation results are presented followed by the experimental findings. Finally, the article ends with conclusions.

Section snippets

Simulation methods

The system studied in this work is depicted in Fig. 1 and relevant dimensions are given in Table 1. It consists of a silicon cantilever beam with a pair of iron foils attached on either side and two external neodymium magnets. The two magnets can be placed in either an attractive or a repulsive magnetic configuration as shown in Fig. 1a and b, respectively.

The materials used in the simulations are silicon for the cantilever structure, with a length of l = 6.5 mm, see Table 1; neodymium for the

Experimental methods

The piezo electric energy harvesters were fabricated by standard silicon micro- and nano fabrication methods using a (100) oriented n-type Si substrate with a resistivity of 0.0015 Ωcm. This very low resistivity allows the silicon substrate to be used as a bottom electrode for the piezoelectric material. The process proceeds as follows: First, a 3000 nm thick oxide layer was grown on both sides of the wafer. Holes were opened in the oxide using lithography and HF etching, and KOH etching was

Simulation results

The results obtained from the simulation study, explained in Section 2, are described in this section.

Fig. 3 shows the calculated potential energy landscapes for the linear configuration and three magnetoelastic cases (a = 1000 μm, a = 564 μm and, a = 200 μm, respectively) where the magnets are mounted in the attractive configuration, and extracted results are summarized in Table 2. In all cases, the distance between the magnets was b = 500 μm. The dashed curve in Fig. 3 corresponds to the

Experimental results

To experimentally investigate the potential energy landscape for the attractive configuration of the magnets, impedance measurements were performed for different positions of the magnets, i.e. for different a and b values, using the measurement set-up described in Section 3.

As an example of the results obtained the impedance spectra measured for b = 420 μm are presented in Fig. 8, Fig. 9, Fig. 10. A typical impedance measurement is shown in Fig. 8 where both the measured impedance magnitude and

Conclusion

A cantilever-based structure intended for broadband magnetoelastic vibrational energy harvesting was presented. The device was made using silicon micro fabrication techniques. Ferromagnetic foils were placed on either side of the beam and served both as proof mass and to provide interaction with an external pair of permanent magnets such that a magnetoelastic behavior is obtained. FEM simulations were performed for two different magnet configurations: repulsive and attractive, with sweeps over

Conflict of interests

There are no conflicts of interests between all the contributing authors of this paper.

Authors contribution statements

A. Lei developed the script used for the simulations in consultation with E.V. Thomsen, and L.R. Alcala carried out the simulations.

E.V. Thomsen improved the code for making the figures, code previously written by A. Lei.

L.R. Alcala manufactured the samples and characterized them fully. L.R. Alcala carried out the experiments and anlysed the data, E.V. Thomsen aided in interpreting the results.

L.R. Alcala drafted the article following E.V. Thomsen guidance. Then L.R. Alcala wrote the article

References (39)

  • A.H. Ramini et al.

    Theoretical and experimental investigation of the nonlinear behavior of an electrostatically actuated in-plane MEMS arch

    J. Microelectromech. Syst.

    (2016)
  • A.H. Ramini et al.

    Tunable resonators for nonlinear modal interactions

    Sci. Rep.

    (2016)
  • A. Ramini et al.

    Efficient primary and parametric resonance excitation of bistable resonators

    AIP Adv.

    (2016)
  • S.P. Beeby et al.

    A micro electromagnetic generator for vibration energy harvesting

    J. Micromech. Microeng.

    (2007)
  • R. Elfrink et al.

    Vibration energy harvesting with aluminum nitride-based piezoelectric devices

    Proceedings of the PowerMEMS Workshop, Sendai

    (2008)
  • A. Erturk et al.

    An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations

    Smart Mater. Struct.

    (2009)
  • S. Priya

    Advances in energy harvesting using low profile piezoelectric transducers

    J. Electroceram.

    (2007)
  • G. Shan et al.

    A spring-assisted adaptive bistable energy harvester for high output in low-excitation

    Microsyst. Technol.

    (2018)
  • T. Yildirim et al.

    A parametrically broadband nonlinear energy harvester

    J. Energy Resour. Technol.

    (2017)
  • Cited by (0)

    View full text