Finite element modeling and characterization of a magnetoelastic broadband energy harvester
Graphical abstract
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)
- et al.
A study of low level vibrations as a power source for wireless sensor nodes
Comput. Commun.
(2003) - et al.
Design and fabrication of a new vibration-based electromechanical power generator
Sens. Actuators A: Phys.
(2001) - et al.
Piezoelectric properties and residual stress of sputtered AlN thin films for MEMS applications
Sens. Actuators A: Phys.
(2004) - et al.
Deposition, characterization and optimization of zinc oxide thin film for piezoelectric cantilevers
Appl. Surf. Sci.
(2012) - et al.
A single-magnet nonlinear piezoelectric converter for enhanced energy harvesting from random vibrations
Sens. Actuators A: Phys.
(2011) - et al.
Improved energy harvesting from wideband vibrations by nonlinear piezoelectric converters
Sens. Actuators A: Phys.
(2010) - et al.
Revisiting a magneto-elastic strange attractor
J. Sound Vib.
(2014) - et al.
Broadband piezoelectric power generation on high-energy orbits of the bistable Duffing oscillator with electromechanical coupling
J. Sound Vib.
(2011) Experimental characteristics of electret generator, using polymer film electrets
Jpn. J. Appl. Phys.
(1992)- et al.
Cantilever-based electret energy harvesters
Smart Mater. Struct.
(2011)