This paper explores using electrically induced damping (electrical damping) as a dual indicator to power output and harvesting bandwidth in vibration-based piezoelectric energy harvesting. It evaluates electrical damping's impact on bandwidth and power using an impedance-based unified model. Analytical formulas are systematically developed to quantify the electrical damping and change in system stiffness for harvesters interfaced with various circuit topologies. The relationship between the electrical damping and power is elucidated through both analytical analysis and numerical examples. This electrical damping approach allows for analyzing power and bandwidth simultaneously.
The Asian citrus psyllid (ACP), Diaphorina citri Kuwayama (Hemiptera: Liviidae), is a citrus pest that vectors the bacterium that causes huanglongbing (HLB) disease between citrus trees. It has become a very large problem to the US citrus growers. Male ACP find females by vibrating the substrate (branch) to call them. The females vibrate a response and the males track these responses to find them in a citrus tree. We have created three ACP call recognition systems: one using Matlab, one using TensorFlow implemented on a Raspberry Pi, and one using Edge Impulse implemented on a RP2040 microcontroller. All three systems recognized calls with an accuracy greater than 79.5%. A demonstration on a single, long recording of two ACP vibrating to each other using the RP2040 system shows that it would be useful in a live implementation.
Traffic signal support structures are slender, highly flexible, and lightly damped. Therefore, they are particularly susceptible to wind-induced vibrations, which result in repeated load stresses and fatigue failures. A tuned energy harvesting inerter damper (TEHID)is proposed to reduce wind-induced vibrations of traffic signal support structures and convert the wasted vibration energy into electricity. The TEHID creates a large inertia mass by converting the low-frequency vibration motion of the light head to a high-speed rotation thereby eliminating the need for a large physical mass and accommodation space required by the conventional tuned mass damper (TMD). This paper focuses on the nonlinear dynamics modeling of the wind-induced vibration control and energy harvesting system for traffic signal support structures. The traffic signal structure is modeled as an L-shaped beam with multi-segments and the TEHID is simplified as a three-element device consisting of a spring, a damper, and an inerter. The nonlinear equations and the boundary conditions governing the motion of the integrated vibration control and energy harvesting system are derived from the energy method and presented herein. Modal analysis is conducted and the derived natural frequencies and mode shapes are compared with the finite element simulation results to validate the analytical model.
Vibration-based piezoelectric energy harvester (VPEH) has received significant interests in the last couple of decades. In recent years, more emphasis has been given to the understanding and modeling the effect of nonlinearities introduced by mechanical and electrical aspects of the system, while the nonlinearity induced by the piezoelectric material is usually ignored. However, it has been experimentally found that this material nonlinearity can have a significant effect on the system behavior even at low to moderate excitation level. This paper is motivated to consider this piezoelectric nonlinearity in the system model, and study how the nonlinearity affects the power characteristics of the system, most importantly, the power limit and electromechanical coupling. Through a harmonic balance analysis, an approximated model is developed from a nonlinear model proposed in the literature, and allows for deriving closed-form expressions of important power characteristics. The approximated model elucidates the effect of piezoelectric material nonlinearity, which is represented by a nonlinear damping term and a nonlinear stiffness term. It is revealed that the addition of piezoelectric material nonlinearity results in interesting power behaviors that are largely different from that of a VPEH without piezoelectric nonlinearity. For instance, the power limit is reduced by the nonlinear damping induced by the piezoelectric nonlinearity. In addition, the critical electrical coupling, also known as the minimum electromechanical coupling for the system to possible reach the power limit, increases with the base excitation. A strongly coupled VPEH with piezoelectric nonlinearity under low excitation could become weakly coupled under large excitation.
Galloping-based piezoelectric energy harvesters (GPEH) connected with various interface circuits are usually analyzed by treating their advanced structures and circuits separately, and a general model is missing to gain insights at a system level. To tackle this issue, this paper proposes a unified framework that enables an integrated view of the physics of linear GPEHs in multiple domains at the system level. In addition, it elucidates the similarities and differences among power behaviors of GPEHs connected with various interface circuits. It is based on two major elements: an equivalent circuit representing the entire system, and an equivalent impedance representing the interface circuit. Firstly, the electromechanical system is linearized and modeled in the electrical domain by an equivalent self-excited circuit with a negative resistive element representing the external aerodynamic excitation, and a general load impedance representing the interface circuit. Then, a closed-form, analytical expression of the harvested power is obtained based on the Kirchhoff’s Voltage Law, from which the optimal load, maximum power, power limit, and critical electromechanical coupling (minimum coupling to reach the power limit) are determined. In this unified analysis, the exact type of energy harvesting interface circuit is not assumed. After that, the power characteristics of a GPEH connected with five representative interface circuits are analytically derived and discussed separately, by using the particular equivalent impedance of the interface circuit of interest. It is shown that they are subjected to the same power limit. However, the critical electromechanical coupling depends on the type of circuit.
Based on the equivalent impedance analysis, a method is proposed to realize a coupled-field simulation study of piezoelectric energy harvesters of rectified interface circuits through an equivalent linear circuit. The method opens up opportunities for finite element packages to analyze, design, and optimize energy harvesters at a system level, either adding the capability of simulating rectified circuit interfaces, or reducing a nonlinear circuit interface simulation into a faster and more stable linear simulation that can be solved more conveniently. The nonlinear rectified circuit is replaced with an equivalent external linear circuit of two passive electrical elements in series. The types and values of the passive elements are explicitly determined for the standard AC-DC (SEH) and synchronized switch harvesting on inductor (SSHI) circuit interfaces. For validation, this equivalent linear circuit is applied to a bimorph beam harvester in ANSYS, and a system-level analytical approach is introduced which integrates two established analytical approaches. The agreement between the ANSYS results and those of the integrated analytical approach validates this equivalent linear circuit method and the integrated analytical approach.
Due to its multidisciplinary nature, the power behavior of a piezoelectric vibration energy harvester depends on system properties in multiple domains such as material, mechanical and electrical. This paper presents a dimensionless maximum power equation that integrates these effects into a simple model, which serves as a convenience tool for the design and analysis of piezoelectric vibration energy harvesters. The model is given as a closed-form relationship between the dimensionless maximum power (maximum power normalized by the power limit) and the normalized electromechanical coupling coefficient with respect to the critical coupling coefficient, which is the minimum coupling to reach the power limit of a system. In addition, this integrated design equation can be applied to different energy harvesting interface circuit types such as resistive and standard AC-DC with a simple change of the critical coupling expression in the equation. The application of this equation is illustrated by a detailed design example of a bimorph beam harvester for fixed target natural frequency and length given a base motion excitation. It is found that under the same level of excitation, there is an optimal PZT thickness for maximum power. In addition, overall, it is beneficial to make the system of low damping to yield a larger structural response and more power. However, this also leads to a higher bending stress, which is an important design consideration due to the relatively brittle nature of PZT materials.
In the past decade, nonlinearity has been introduced into piezoelectric energy harvesters (PEH) for power performance enhancement and bandwidth enlargement. While a great emphasis has been placed on the structural design and the effect of electrical part on the nonlinear dynamics of the system, the maximum power and power limit, an important aspect for performance optimization of nonlinear PEHs, are rarely studied, especially their relationship with that of linear PEHs. To this end, this paper is motivated to investigate the maximum power and power limit of a representative type of nonlinear PEHs, i.e., monostable. An equivalent circuit is proposed to analytically study and explain the behaviors of monostable PEHs, and reveals the connection between linear and monostable PEHs. The effect of nonlinearity, e.g., due to the additional magnetic force, is modeled as a nonlinear stiffness element mechanically and a nonlinear capacitive element electrically, based on the harmonic balance method. Facilitated by this equivalent circuit and the impedance matching technique, clear closed-form solutions of power limit and critical electromechanical coupling, i.e., minimum coupling to reach the power limit, of monostable PEHs are obtained. Then the effect of excitation level and magnetic field on the power and electromechanical coupling of the system is investigated. Though this paper uses monostable PEHs as an example, the results and technique can be extended to other similar types of nonlinear PEH systems as well, for example, bistable.
Through an impedance plot obtained from the equivalent circuit modeling of linear energy harvesters, this paper provides explanations of their system behaviors such as power and efficiency. The impedance plot shows the tuning impedance and the matched source impedance in the same graph, providing a visualization of their relationship as the system parameters are changed or tuned. Using this relationship, the power characteristics of the system are clearly explained. In addition, the impedance plot is connected to the structural effects in stiffness and damping due to energy harvesting. Two types of efficiency are defined in terms of the electrically induced damping: the energy conversion efficiency and conventional energy efficiency. By using the impedance plot, it is shown that the maximum power and maximum efficiency are achieved almost simultaneously for weakly coupled systems. However, for strongly coupled systems, they cannot be achieved at the same time due to the significant reduction in structural energy associated with high efficiency. Though many relationships discussed in this paper are reasonably understood in the research community, a deeper and more direct understanding of these relationships are offered by this paper with the aid of this graphical and intuitive approach.
This paper presents a unified model of piezoelectric vibration energy harvesters through the use of a generalized electrical impedance that represents various energy harvesting interfaces, providing a universal platform for the analysis and discussion of energy harvesters. The unified model is based on the equivalent circuit analysis that utilizes the impedance electromechanical analogy to convert the system into the electrical domain entirely, where the model is formulated and analyzed. Firstly, the common behaviors of energy harvesters under this unified model are discussed, and the concept of power limit is discussed. The power limit represents the maximum possible power that could be harvested by an energy harvester regardless of the type of the circuit interface. The condition to reach this power limit is obtained by applying the impedance matching technique. Secondly, three representative energy harvesting interfaces, i.e., resistive (REH), standard (SEH), and synchronized switch harvesting on inductor (SSHI), are discussed separately, including their corresponding forms of the generalized electrical impedance and associated system behaviors. As an important contribution, a clear explanation of the system behavior is offered through an impedance plot that graphically illustrates the relationship between the system tuning and the harvested power. Thirdly, the effect of the system electrometrical coupling on power behaviors is discussed. As another important contribution, this paper derives and presents the analytical expressions of the critical coupling of the interfaces, which is the minimum coupling required to reach the power limit and also the parameter used to define the coupling state, i.e., weakly, critically, or strongly, of a system. In particular, the analytical expressions for the SEH and SSHI interfaces are presented for the first time in the research community. Lastly, the system behaviors and critical coupling of the three energy harvesting interfaces are compared and discussed. The SSHI interface has the lowest critical coupling, which explains its superior power harvesting capability for weakly coupled systems.
Power harvesting describes the process of acquiring the ambient energy surrounding a system and converting it into usable electrical energy. Much of the work over the past two decades has focused on the conversion of ambient vibration energy sources using piezoelectric, electromagnetic and electrostatic transduction. Attempts were made to obtain a general model that could be applied to any transduction mechanism. Of the most interest is an electromagnetic generator model that was used by many researchers to model piezoelectric power harvesters. Two major results from the model are the power limit expression and the equal relationship between the electrically induced damping and the mechanical damping to reach the power limit. However, piezoelectric power harvesters cannot be accurately modeled by this electromagnetic model due to the essential difference in physics. There have also been attempts to obtain the power limit expression based on piezoelectric relationships, but they either neglect the piezoelectric backward coupling to the structure, or assume the power limit occurs at the resonance of the system. This paper obtains the power limit expression based on the piezoelectric coupled equations without those assumptions. In addition, the relationship between the electrically induced damping and mechanical damping at the power limit is studied. Furthermore, a closed-form criterion is derived and proposed to define strongly and weakly coupling power harvesters, whose differences in power characteristics are explained through analytical and numerical analysis. While most of the discussion is focused on linear power harvesters connected to a resistive circuit, the aim of this paper is to provide a comprehensive and deep understanding of this simple configuration, answers to important questions, and a starting point to develop a more general theory on power harvesters because similar system characteristics are observed in power harvesters with more complexities.
A piezoelectric based energy harvesting scheme is proposed here which places a capacitor before the load in the
conditioning circuit. It is well known that the impedance between the load and source contributes heavily to the
performance of the energy harvesting system. The additional capacitor provides flexibility in meeting the optimal
impedance value and can be used to expand the bandwidth of the system. A theoretical model of the system is derived
and the response of the system as a function of both resistance and capacitance is studied. The analysis shows that the
energy harvesting performance is dominated by a bifurcation occurring as the electromechanical coupling increases
above a certain value, below this point the addition of an additional capacitor does not increase the performance of the
systems and above the maximum power can be achieved at all point between these two bifurcation frequencies.
Additionally, it has been found that the optimal capacitance is independent of the optimal resistance. Therefore, the
necessary capacitance can be chosen and then the resistance determined to provide optimal energy harvesting at the
desired frequencies. For systems with low coupling the optimal added capacitance is negative (additional power to the
circuit) indicating that a second capacitor should not be used for. For systems with high coupling the optimal
capacitance becomes positive for a range of values inside the bifurcation frequencies and can be used to extend the
bandwidth of the harvesting system. The analysis also demonstrates that the same maximum energy can be harvested at
any frequency; however, outside the two bifurcation frequencies the capacitor must be negative.
KEYWORDS: Energy conversion efficiency, Resistance, Energy harvesting, Energy efficiency, Systems modeling, Ferroelectric materials, Mechanical efficiency, Sensors, Aluminum, Power supplies
The concept of power harvesting works towards developing self-powered devices that do not require replaceable power
supplies. One important parameter defining the performance of a piezoelectric power harvesting system is the
efficiency of the system. However, an accepted definition of the energy harvesting efficiency does not currently exist.
This article will develop a new definition for the efficiency of an energy harvesting system which rather than being
defined through energy conservation as the ratio of the energy fed into the system to maintain the steady state to the
output power, we consider the ratio of the strain energy over each cycle to the power output. This new definition is
analogous to the material loss factor. Simulations will be performed to demonstrate the validity of the efficiency and
will show that the maximum efficiency occurs at the matched impedance; however, for materials with high
electromechanical coupling the maximum power is generated at the near open and closed-circuit resonances with a lower
efficiency.
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