Parametrically excited MEMS vibration energy harvesters with design approaches to overcome the initiation threshold amplitude

Resonant-based vibration harvesters have conventionally relied upon accessing the fundamental mode of directly excited resonance to maximize the conversion efficiency of mechanical-to-electrical power transduction. This paper explores the use of parametric resonance, which unlike the former, the resonant-induced amplitude growth, is not limited by linear damping and wherein can potentially offer higher and broader nonlinear peaks. A numerical model has been constructed to demonstrate the potential improvements over the convention. Despite the promising potential, a damping-dependent initiation threshold amplitude has to be attained prior to accessing this alternative resonant phenomenon. Design approaches have been explored to passively reduce this initiation threshold. Furthermore, three representative MEMS designs were fabricated with both 25 and 10 μm thick device silicon. The devices include electrostatic cantilever-based harvesters, with and without the additional design modification to overcome initiation threshold amplitude. The optimum performance was recorded for the 25 μm thick threshold-aided MEMS prototype with device volume ~0.147 mm3. When driven at 4.2 ms−2, this prototype demonstrated a peak power output of 10.7 nW at the fundamental mode of resonance and 156 nW at the principal parametric resonance, as well as a 23-fold decrease in initiation threshold over the purely parametric prototype. An approximate doubling of the half-power bandwidth was also observed for the parametrically excited scenario

Exploiting the Principal Parametric Resonance of an RLC Circuit for Vibratory Energy Harvesting

The use of ambient energy sources to independently power small electronic devices, a process commonly known as energy harvesting, has recently become a focus of research due to advances in low-power electronic applications. A particular class of energy harvesting devices, known as vibratory energy harvesters (VEHs), utilizes low-level vibrations present in numerous natural and man-made environments to generate electrical energy for electronic devices. This work investigates the use of a new technique to harvest energy from ambient vibrations by parametrically exciting a resonance condition of the electric current in a nonlinear oscillating circuit. To accomplish this parametric resonance phenomenon, we consider an electromechanical coupling device, an oscillating cantilever beam with a ferromagnetic tip mass, which changes the permeability of an iron-alloy cored inductor coil to produce a harmonically-varying modulation of the inductance. Such a type of harvester possesses the potential to generate large amplitude System response that is not limited by the linear damping of the system, as is the case with directly-excited systems, but rather whose behavior is governed by the nonlinearity of the system. In order to study the ability of such an energy harvesting system to generate electricity when subject to external vibrations, we develop a second-order differential equation to model the theoretical dynamic behavior of a parametrically-driven nonlinear circuit. Due to the complexity of the nonlinear and harmonically-varying components of the governing equation, we use the Method of Multiple Scales to derive an approximate analytical solution for the steady-state current response and output power of the circuit near the principal parametric resonant frequency. We show that the relationship of parameter modulation depth and load resistance characterize the bandwidth of the response and define a critical forcing threshold, below which no energy is harvested. The harvested power is maximized when the load resistance is half of the maximum load resistance at which the critical threshold is still achieved for a given forcing level. We also demonstrate the need for nonlinear damping in the system to attenuate the growth of the response to a physically attainable level. We show the dependence of the natural frequency of the circuit on the parametric forcing parameter, which can lead detuning of the system at different forcing levels. An experimental set up is developed to test the assertions presented by the analytical model. Numerous parameter constraints are balanced in the experimental design in order to be able to achieve the critical forcing threshold necessary for exciting the parametric resonance condition. The frequency response behavior of the electrical current and load power in the circuit is observed by varying the natural frequency of the system, which is compared against the variation of forcing frequency presented in the theoretical section. The beam is excited at its natural frequency of 85.8 Hz across input accelerations ranging from 1:1g – 1:5g. A maximum output power of 28.67 mW across an 8 Ω resistance is achieved at an input acceleration of 1:5g. The behavior of the experimental data is in good agreement with the findings of the theoretical model with respect to the bandwidth, nonlinear behavior, and sensitivity to forcing and damping parameters. The analytical model under predicts the peak power measured experimentally, but the general trend is well modeled. Furthermore, several key observations are noted during the experimental procedures, notably the effects of eddy current damping on the behavior of the response and the development of quasiperiodic solutions near the saddle node bifurcation point

The Convergence of Parametric Resonance and Vibration Energy Harvesting

Energy harvesting is an emerging technology that derives electricity from the ambient environment in a decentralised and self-contained fashion. Applications include self-powered medical implants, wearable electronics and wireless sensors for structural health monitoring. Amongst the vast options of ambient sources, vibration energy harvesting (VEH) has attracted by far the most research attention. Two of the key persisting issues of VEH are the limited power density compared to conventional power supplies and confined operational frequency bandwidth in light of the random, broadband and fast-varying nature of real vibration. The convention has relied on directly excited resonance to maximise the mechanical-to-electrical energy conversion efficiency. This thesis takes a fundamentally different approach by employing parametric resonance, which, unlike the former, its resonant amplitude growth does not saturate due to linear damping. Therefore, parametric resonance, when activated, has the potential to accumulate much more energy than direct resonance. The vibrational nonlinearities that are almost always associated with parametric resonance can offer a modest frequency widening. Despite its promising theoretical potentials, there is an intrinsic damping dependent initiation threshold amplitude, which must be attained prior to its onset. The relatively low amplitude of real vibration and the unavoidable presence of electrical damping to extract the energy render the onset of parametric resonance practically elusive. Design approaches have been devised to passively minimise this initiation threshold. Simulation and experimental results of various design iterations have demonstrated favourable results for parametric resonance as well as the various threshold-reduction mechanisms. For instance, one of the macro-scale electromagnetic prototypes (∼1800 cm3) when parametrically driven, has demonstrated around 50% increase in half power band and an order of magnitude higher peak power (171.5 mW at 0.57 ms−2) in contrast to the same prototype directly driven at fundamental resonance (27.75 mW at 0.65 ms−2). A MEMS (micro-electromechanical system) prototype with the additional threshold-reduction design needed 1 ms−2 excitation to activate parametric resonance while a comparable device without the threshold-reduction mechanism required in excess of 30 ms−2. One of the macro-scale piezoelectric prototypes operated into auto-parametric resonance has demon-strated notable further reduction to the initiation threshold. A vacuum packaged MEMS prototype demonstrated broadening of the frequency bandwidth along with higher power peak (324 nW and 160 Hz) for the parametric regime compared to when operated in room pressure (166 nW and 80 Hz), unlike the higher but narrower direct resonant peak (60.9 nW and 11 Hz in vacuum and 20.8 nW and 40 Hz in room pressure). The simultaneous incorporation of direct resonance and bi-stability have been investigated to realise multi-regime VEH. The potential to integrate parametric resonance in the electrical domains have also been numerically explored. The ultimate aim is not to replace direct resonance but rather for the various resonant phenomena to complement each other and together harness a larger region of the available power spectrum

Parametrically excited mems vibration energy harvesters

Resonant-based vibration harvesters have conventionally relied upon accessing the fundamental mode of resonance to maximise the conversion efficiency of mechanical-to-electrical power transduction. This paper explores the use of parametric resonance, which is not limited by linear damping and can potentially offer higher and broader nonlinear peaks. Despite the promising potential, a damping-dependent initiation threshold amplitude has to be overcome first. Design approaches have been explored to resolve this limitation. A numerical model has been constructed to analysis the improvements over the convention. An out-of-plane (to accommodate large displacements) electrostatic MEMS prototype (~ 0.147 mm3), driven at 4.2 ms-2, has demonstrated a peak power of 0.011 ?W at the fundamental mode of resonance and 0.16 ?W at the principal parametric resonance. A two fold increase in frequency bandwidth was also observed for the parametrically excited device

ELECTROMECHANICAL MODELING OF A HONEYCOMB CORE INTEGRATED VIBRATION ENERGY CONVERTER WITH INCREASED SPECIFIC POWER FOR ENERGY HARVESTING APPLICATIONS

Innovation in integrated circuit technology along with improved manufacturing processes has resulted in considerable reduction in power consumption of electromechanical devices. Majority of these devices are currently powered by batteries. However, the issues posed by batteries, including the need for frequent battery recharge/replacement has resulted in a compelling need for alternate energy to achieve self-sufficient device operation or to supplement battery power. Vibration based energy harvesting methods through piezoelectric transduction provides with a promising potential towards replacing or supplementing battery power source. However, current piezoelectric energy harvesters generate low specific power (power-to-weight ratio) when compared to batteries that the harvesters seek to replace or supplement. In this study, the potential of integrating lightweight cellular honeycomb structures with existing piezoelectric device configurations (bimorph) to achieve higher specific power is investigated. It is shown in this study that at low excitation frequency ranges, replacing the solid continuous substrate of a conventional piezoelectric bimorph with honeycomb structures of the same material results in a significant increase in power-to-weight ratio of the piezoelectric harvester. In order to maximize the electrical response of vibration based power harvesters, the natural frequency of these harvesters is designed to match the input driving frequency. The commonly used technique of adding a tip mass is employed to lower the natural frequency (to match driving frequency) of both, solid and honeycomb substrate bimorphs. At higher excitation frequency, the natural frequency of the traditional solid substrate bimorph can only be altered (to match driving frequency) through a change in global geometric design parameters, typically achieved by increasing the thickness of the harvester. As a result, the size of the harvester is increased and can be disadvantageous especially if the application imposes a space/size constraint. Moreover, the bimorph with increased thickness will now require a larger mechanical force to deform the structure which can fall outside the input ambient excitation amplitude range. In contrast, the honeycomb core bimorph offers an advantage in terms of preserving the global geometric dimensions. The natural frequency of the honeycomb core bimorph can be altered by manipulating honeycomb cell design parameters, such as cell angle, cell wall thickness, vertical cell height and inclined cell length. This results in a change in the mass and stiffness properties of the substrate and hence the bimorph, thereby altering the natural frequency of the harvester. Design flexibility of honeycomb core bimorphs is demonstrated by varying honeycomb cell parameters to alter mass and stiffness properties for power harvesting. The influence of honeycomb cell parameters on power generation is examined to evaluate optimum design to attain highest specific power. In addition, the more compliant nature of a honeycomb core bimorph decreases susceptibility towards fatigue and can increase the operating lifetime of the harvester. The second component of this dissertation analyses an uncoupled equivalent circuit model for piezoelectric energy harvesting. Open circuit voltage developed on the piezoelectric materials can be easily computed either through analytical or finite element models. The efficacy of a method to determine power developed across a resistive load, by representing the coupled piezoelectric electromechanical problem with an external load as an open circuit voltage driven equivalent circuit, is evaluated. The lack of backward feedback at finite resistive loads resulting from such an equivalent representation is examined by comparing the equivalent circuit model to the governing equations of a fully coupled circuit model for the electromechanical problem. It is found that the backward feedback is insignificant for weakly coupled systems typically seen in micro electromechanical systems and other energy harvesting device configurations with low coupling. For moderate to high coupling systems, a correction factor based on a calibrated resistance is presented which can be used to evaluate power generation at a specific resistive load

Review of nonlinear vibration energy harvesting: Duffing, bistability, parametric, stochastic and others

Vibration energy harvesting typically involves a mechanical oscillatory mechanism to accumulate ambient kinetic energy, prior to the conversion to electrical energy through a transducer. The convention is to use a simple linear mass-spring-damper oscillator with its resonant frequency tuned towards that of the vibration source. In the past decade, there has been a rapid expansion in research of vibration energy harvesting into various nonlinear vibration principles such as Duffing nonlinearity, bistability, parametric oscillators, stochastic oscillators and other nonlinear mechanisms. The intended objectives for using nonlinearity include broadening of frequency bandwidth, enhancement of power amplitude and improvement in responsiveness to non-sinusoidal noisy excitations. However, nonlinear vibration energy harvesting also comes with its own challenges and some of the research pursuits have been less than fruitful. Previous reviews in the literature have either focussed on bandwidth enhancement strategies or converged on select few nonlinear mechanisms. This article reviews eight major types of nonlinear vibration energy harvesting reported over the past decade, covering underlying principles, advantages and disadvantages, and application-specific guidance for researchers and designers

Energy harvesting from the secondary resonances of a nonlinear piezoelectric beam under hard harmonic excitation

This paper investigates the dynamical response of a nonlinear piezoelectric energy harvester under a hard harmonic excitation and assesses its output power. The system is composed of a unimorph cantilever beam with a tip mass and exposed to an harmonic tip excitation with a hard forcing amplitude. First, the governing dimensionless nonlinear electromechanical ordinary differential equations (ODEs) are obtained. Next, the multiple scales method (MSM) is exploited to provide an approximate-analytical solution for the ODEs in hard and soft forcing scenarios. It is observed that, the hard force results in sub- and super-harmonic resonances. The MSM-based solutions are then validated by a numerical integration method and a good agreement is observed between the approximate-analytical and numerical results. Furthermore, utilizing the MSM-based solutions for the subharmonic, superharmonic, and soft primary resonances cases, the associated frequency and force response curves are constructed. It is revealed that the hard excitation leads to a remarkable voltage generation in the secondary resonances; this leads to a broadband energy harvesting. In addition, the time-domain electrical responses of the secondary resonances are also obtained and compared with each other. Finally, the three-dimensional graphs of the electrical power versus detuning parameter and time constant ratio in the cases of the secondary resonances are plotted. The results show that the optimum output power of the superharmonic resonance is considerably larger than the maximum power of the subharmonic resonance case

Parametric resonance for vibration energy harvesting with design techniques to passively reduce the initiation threshold amplitude

A vibration energy harvester designed to access parametric resonance can potentially outperform the conventional direct resonant approach in terms of power output achievable given the same drive acceleration. Although linear damping does not limit the resonant growth of parametric resonance, a damping dependent initiation threshold amplitude exists and limits its onset. Design approaches have been explored in this paper to passively overcome this limitation in order to practically realize and exploit the potential advantages. Two distinct design routes have been explored, namely an intrinsically lower threshold through a pendulum-lever configuration and amplification of base excitation fed into the parametric resonator through a cantilever-initial-spring configuration. Experimental results of the parametric resonant harvesters with these additional enabling designs demonstrated an initiation threshold up to an order of magnitude lower than otherwise, while attaining a much higher power peak than direct resonance