A High Precision Lumped Parameter Model for Piezoelectric Energy Harvesters
15 Dec 2017-IEEE Sensors Journal (Institute of Electrical and Electronics Engineers (IEEE))-Vol. 17, Iss: 24, pp 8350-8355
TL;DR: In this paper, a high precision lumped parameter model for efficient prediction of the resonant frequencies and coupling of cantilevered piezoelectric energy harvesters in absence of tip mass is presented.
Abstract: We present a high precision lumped parameter model for efficient prediction of the resonant frequencies and coupling of cantilevered piezoelectric energy harvesters in absence of tip mass. Correction factors for the existing lumped parameter model are derived by comparing with the highly accurate distributed parameter model of cantilevered harvesters. First, a correction factor is defined for uncoupled lumped parameter model to predict the natural frequencies. Finally, the coupled lumped parameter model is subjected to a unified correction factor to accurately predict both the resonant frequencies and electrical outputs. The unified correction factor is derived by unifying the frequency and amplitude correction factors. The calculated outputs are in good agreement with the experimental results available in the literature.
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TL;DR: A complete system level coupling circuit model is established to predict the performance characteristics of the piezoelectric vibration energy harvester (PVEH) and can set up a reference to optimize system parameters for WSN powered by PVEH.
Abstract: This paper proposes a design of wireless sensor node powered by piezoelectric vibration energy harvesting system. A complete system level coupling circuit model is established to predict the performance characteristics. The piezoelectric vibration energy harvester (PVEH) is based on a PZT bimorph cantilever, in which a big proof mass is introduced to decrease resonant frequency and a shell served as a stopper to avoid overload. Lumped parameters of the model are identified by experiments and calculations. Electromechanical analogy model of PVEH is simulated in LTspice software. The power consumption of a temperature WSN is tested and the equivalent load model is simulated. A power management circuit (PMC) with LTC3588-1 is designed for rectifying and regulating output of PVEH. Electrical energy is stored in a capacitor. Finally, a system level coupling model is established. Time domain circuit simulation can provide the detailed parameters about the WSN powered by PVEH such as full charge time and sustainable time of the system. Test curves of capacitor charging and WSN power supply in prototype testification show good consistency with the simulation results in LTspice. An application for temperature WSN powered by PVEH is testified as an example. The method and model proposed in this paper can set up a reference to optimize system parameters for WSN powered by PVEH.
11 citations
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TL;DR: In this paper, the authors proposed an optimized design of PEH that outperforms the existing AlN-based design in terms of power density, where they analytically optimized the design of: 1) cantilever-to-harvester length and 2) cotileverto-harster width (proof mass width) ratios for the maximum output power.
Abstract: Optimization of piezoelectric energy harvester (PEH) to convert the ambient vibrational energy into maximum electrical energy has been of continued interest. The integration of the proof mass with the optimum cantilever width significantly enhances the output power of PEH. In this paper, we propose an optimized design of PEH that outperforms the existing AlN-based design in terms of power density. We analytically optimize the design of: 1) cantilever-to-harvester length and 2) cantilever-to-harvester width (proof mass width) ratios for the maximum output power. The optimized harvester is fabricated using a novel integration scheme for the bottom electrode with Au as an interlayer. The Au interlayer is used to grow a good quality of AlN film with piezoelectric coefficients, $d_{33} = 12$ pm/V and $d_{31} = -2.37 $ pm/V. It is found that in order to achieve the optimum output from PEH, the fractional length and width occupied by cantilever are 28%–40% and 38%–45%, respectively. The optimized designs are fabricated using a CMOS compatible process. The maximum power density measured from the fabricated PEHs is found to be 9.36 $\mu $ W/mm3, which is better than the similar reported data. The optimized and compact low-power PEHs reported in this paper have high potential to be integrated with the system on chip (SOC) and other wireless sensor applications.
8 citations
Cites result from "A High Precision Lumped Parameter M..."
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TL;DR: In this paper, a finite analysis is conducted using COMSOL multiphysics software to optimize the damping of the cantilever of a piezoelectric energy harvester.
Abstract: Piezoelectric energy harvesters have been extensively researched for use with wireless sensors or low power consumption electronic devices. Most of the piezoelectric energy harvesters cannot generate enough power for potential applications. In this study, we explore the parameters, including gap and proof mass, that can affect the damping of the cantilever to optimize the design of the energy harvester. A finite analysis is conducted using COMSOL Multiphysics software. Usually, this type of simulation is performed using the loss factor. However, it is known that results from the loss factor produce models that do not fit the experimental data well. In fact, the result of output voltage using the loss factor is 50% higher than the real value, which is due to ignoring the adverse effect of a superimposing mechanical damping of different constituent materials. In order to build a true model, Rayleigh damping coefficients are measured to use in a simulation. This resulted in a closer fit of modeling and experimental data, and a 5 times better output voltage from the optimized energy harvester compared with using the smallest gap and mass.
4 citations
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TL;DR: In this paper, an electromagnetic vibration type energy harvester based on the diamagnetic levitation system is designed, fabricated and tested, which mainly consists of two pyrolytic graphite sheets, two permanent magnets two inductive coils.
Abstract: The use of vibration energy harvesters for supplying energy to wireless sensor nodes is becoming increasingly popular. In this paper an electromagnetic vibration type energy harvester based on the diamagnetic levitation system is designed, fabricated and tested. The system mainly consists of two pyrolytic graphite sheets , two permanent magnets two inductive coils. The device has been modeled using analytic equations to analyze the motion characteristics and induced voltage by MATLAB. The magnetic field intensity is simulated by FEA software COMSOL Multiphysics 5.2. Theoretical modeling and analyses are carried out to compare with experimental data utilizing the same vibration setup. Throughout the experimental results, the maximal RMS voltage is up to 70.85 mV and the output power can reach 46.5 μW at 4.6 Hz under horizontal excitation. Both theoretical and experimental results show that this energy harvester can capture low-frequency broadband vibration energy.
1 citations
References
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01 Jan 1928
TL;DR: In this article, the Probleme dynamique and Vibration were used for propagation of ondes reference records created on 2004-09-07, modified on 2016-08-08.
Abstract: Keywords: Probleme dynamique ; Vibration ; Propagation des ondes Reference Record created on 2004-09-07, modified on 2016-08-08
3,837 citations
"A High Precision Lumped Parameter M..." refers methods in this paper
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TL;DR: The goal of this paper is not to suggest that the conversion of vibrations is the best or most versatile method to scavenge ambient power, but to study its potential as a viable power source for applications where vibrations are present.
Abstract: Advances in low power VLSI design, along with the potentially low duty cycle of wireless sensor nodes open up the possibility of powering small wireless computing devices from scavenged ambient power. A broad review of potential power scavenging technologies and conventional energy sources is first presented. Low-level vibrations occurring in common household and office environments as a potential power source are studied in depth. The goal of this paper is not to suggest that the conversion of vibrations is the best or most versatile method to scavenge ambient power, but to study its potential as a viable power source for applications where vibrations are present. Different conversion mechanisms are investigated and evaluated leading to specific optimized designs for both capacitive MicroElectroMechancial Systems (MEMS) and piezoelectric converters. Simulations show that the potential power density from piezoelectric conversion is significantly higher. Experiments using an off-the-shelf PZT piezoelectric bimorph verify the accuracy of the models for piezoelectric converters. A power density of 70 @mW/cm^3 has been demonstrated with the PZT bimorph. Simulations show that an optimized design would be capable of 250 @mW/cm^3 from a vibration source with an acceleration amplitude of 2.5 m/s^2 at 120 Hz.
2,536 citations
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TL;DR: The field of power harvesting has experienced significant growth over the past few years due to the ever-increasing desire to produce portable and wireless electronics with extended lifespans as mentioned in this paper, and the use of batteries can be troublesome due to their limited lifespan, thus necessitating their periodic replacement.
Abstract: The field of power harvesting has experienced significant growth over the past few years due to the ever-increasing desire to produce portable and wireless electronics with extended lifespans. Current portable and wireless devices must be designed to include electrochemical batteries as the power source. The use of batteries can be troublesome due to their limited lifespan, thus necessitating their periodic replacement. In the case of wireless sensors that are to be placed in remote locations, the sensor must be easily accessible or of a disposable nature to allow the device to function over extended periods of time. Energy scavenging devices are designed to capture the ambient energy surrounding the electronics and convert it into usable electrical energy. The concept of power harvesting works towards developing self-powered devices that do not require replaceable power supplies. A number of sources of harvestable ambient energy exist, including waste heat, vibration, electromagnetic waves, wind, flowing water, and solar energy. While each of these sources of energy can be effectively used to power remote sensors, the structural and biological communities have placed an emphasis on scavenging vibrational energy with piezoelectric materials. This article will review recent literature in the field of power harvesting and present the current state of power harvesting in its drive to create completely self-powered devices.
2,223 citations
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TL;DR: In this paper, a vibration-based piezoelectric generator has been developed as an enabling technology for wireless sensor networks, where the authors discuss the modeling, design, and optimization of the generator based on a two-layer bending element.
Abstract: Enabling technologies for wireless sensor networks have gained considerable attention in research communities over the past few years. It is highly desirable, even necessary in certain situations, for wireless sensor nodes to be self-powered. With this goal in mind, a vibration based piezoelectric generator has been developed as an enabling technology for wireless sensor networks. The focus of this paper is to discuss the modeling, design, and optimization of a piezoelectric generator based on a two-layer bending element. An analytical model of the generator has been developed and validated. In addition to providing intuitive design insight, the model has been used as the basis for design optimization. Designs of 1 cm3 in size generated using the model have demonstrated a power output of 375 µW from a vibration source of 2.5 m s−2 at 120 Hz. Furthermore, a 1 cm3 generator has been used to power a custom designed 1.9 GHz radio transmitter from the same vibration source.
1,646 citations
"A High Precision Lumped Parameter M..." refers background in this paper
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TL;DR: In this article, the authors present a mathematical model of a piezoelectric energy harvesting system with a two-segment cantilever and a single-mode Euler-Bernoulli model.
Abstract: About the Authors. Preface. 1. Introduction to Piezoelectric Energy Harvesting. 1.1 Vibration-Based Energy Harvesting Using Piezoelectric Transduction. 1.2 An Examples of a Piezoelectric Energy Harvesting System. 1.3 Mathematical Modeling of Piezoelectric Energy Harvesters. 1.4 Summary of the Theory of Linear Piezoelectricity. 1.5 Outline of the Book. 2. Base Excitation Problem for Cantilevered Structures and Correction of the Lumped-Parameter Electromechanical Model. 2.1 Base Excitation Problem for the Transverse Vibrations. 2.2 Correction of the Lumped-Parameter Base Excitation Model for Transverse Vibrations. 2.3 Experimental Case Studies for Validation of the Correction Factor. 2.4 Base Excitation Problem for Longitudinal Vibrations and Correction of its Lumped-Parameter Model. 2.5 Correction Factor in the Electromechanically Coupled Lumped-Parameter Equations and a Theoretical Case Study. 2.6 Summary. 2.7 Chapter Notes. 3. Analytical Distributed-Parameter Electromechanical Modeling of Cantilevered Piezoelectric Energy Harvesters. 3.1 Fundamentals of the Electromechanically Coupled Distributed-Parameter Model. 3.2 Series Connection of the Piezoceramic Layers. 3.3 Parallel Connection of Piezoceramic Layers. 3.4 Equivalent Representation of the Series and the Parallel Connection Cases. 3.5 Single-Mode Electromechanical Equations for Modal Excitations. 3.6 Multi-mode and Single-Mode Electromechanical FRFs. 3.7 Theoretical Case Study. 3.8 Summary. 3.9 Chapter Notes. 4. Experimental Validation of the Analytical Solution for Bimorph Configurations. 4.1 PZT-5H Bimorph Cantilever without a Tip Mass. 4.2 PZT-5H Bimorph Cantilever with a Tip Mass. 4.3 PZT-5A Bimorph Cantilever. 4.4 Summary. 4.5 Chapter Notes. 5. Dimensionless Equations, Asymptotic Analyses, and Closed-Form Relations for Parameter Identification and Optimization. 5.1 Dimensionless Representation of the Single-Mode Electromechanical FRFs. 5.2 Asymptotic Analyses and Resonance Frequencies. 5.3 Identification of Mechanical Damping. 5.4 Identification of the Optimum Electrical Load for Resonance Excitation. 5.5 Intersection of the Voltage Asymptotes and a Simple Technique for the Experimental Identification of the Optimum Load Resistance. 5.6 Vibration Attenuation Amplification from the Short-Circuit to Open-Circuit Conditions. 5.7 Experimental Validation for a PZT-5H Bimorph Cantilever. 5.8 Summary. 5.9 Chapter Notes. 6. Approximate Analytical Distributed-Parameter Electromechanical Modeling of Cantilevered Piezoelectric Energy Harvesters. 6.1 Unimorph Piezoelectric Energy Harvester Configuration. 6.2 Electromechanical Euler-Bernoulli Model with Axial Deformations. 6.3 Electromechanical Rayleigh Model with Axial Deformations. 6.4 Electromechanical Timoshenko Model with Axial Deformations. 6.5 Modeling of Symmetric Configurations. 6.6 Presence of a Tip Mass in the Euler-Bernoulli, Rayleigh, and Timoshenko Models. 6.7 Comments on the Kinematically Admissible Trial Functions. 6.8 Experimental Validation of the Assumed-Modes Solution for a Bimorph Cantilever. 6.9 Experimental Validation for a Two-Segment Cantilever. 6.10 Summary. 6.11 Chapter Notes. 7. Modeling of Piezoelectric Energy Harvesting for Various Forms of Dynamic Loading. 7.1 Governing Electromechanical Equations. 7.2 Periodic Excitation. 7.3 White Noise Excitation. 7.4 Excitation Due to Moving Loads. 7.5 Local Strain Fluctuations on Large Structures. 7.6 Numerical Solution for General Transient Excitation. 7.7 Case Studies. 7.8 Summary. 7.9 Chapter Notes. 8. Modeling and Exploiting Mechanical Nonlinearities in Piezoelectric Energy Harvesting. 8.1 Perturbation Solution of the Piezoelectric Energy Harvesting Problem: the Method of Multiple Scales. 8.2 Monostable Duffing Oscillator with Piezoelectric Coupling. 8.3 Bistable Duffing Oscillator with Piezoelectric Coupling: the Piezomagnetoelastic Energy Harvester. 8.4 Experimental Performance Results of the Bistable Peizomagnetoelastic Energy Harvester. 8.5 A Bistable Plate for Piezoelectric Energy Harvesting. 8.6 Summary. 8.7 Chapter Notes. 9. Piezoelectric Energy Harvesting from Aeroelastic Vibrations. 9.1 A Lumped-Parameter Piezoaeroelastic Energy Harvester Model for Harmonic Response. 9.2 Experimental Validations of the Lumped-Parameter Model at the Flutter Boundary. 9.3 Utilization of System Nonlinearities in Piezoaeroelastic Energy Harvesting. 9.4 A Distributed-Parameter Piezoaeroelastic Model for Harmonic Response: Assumed-Modes Formulation. 9.5 Time-Domain and Frequency-Domain Piezoaeroelastic Formulations with Finite-Element Modeling. 9.6 Theoretical Case Study for Airflow Excitation of a Cantilevered Plate. 9.7 Summary. 9.8 Chapter Notes. 10. Effects of Material Constants and Mechanical Damping on Power Generation. 10.1 Effective Parameters of Various Soft Ceramics and Single Crystals. 10.2 Theoretical Case Study for Performance Comparison of Soft Ceramics and Single Crystals. 10.3 Effective Parameters of Typical Soft and Hard Ceramics and Single Crystals. 10.4 Theoretical Case Study for Performance Comparison of Soft and Hard Ceramics and Single Crystals. 10.5 Experimental Demonstration for PZT-5A and PZT-5H Cantilevers. 10.6 Summary. 10.7 Chapter Notes. 11. A Brief Review of the Literature of Piezoelectric Energy Harvesting Circuits. 11.1 AC-DC Rectification and Analysis of the Rectified Output. 11.2 Two-Stage Energy Harvesting Circuits: DC-DC Conversion for Impedance Matching. 11.3 Synchronized Switching on Inductor for Piezoelectric Energy Harvesting. 11.4 Summary. 11.5 Chapter Notes. Appendix A. Piezoelectric Constitutive Equations. Appendix B. Modeling of the Excitation Force in Support Motion Problems of Beams and Bars. Appendix C. Modal Analysis of a Uniform Cantilever with a Tip Mass. Appendix D. Strain Nodes of a Uniform Thin Beam for Cantilevered and Other Boundary Conditions. Appendix E. Numerical Data for PZT-5A and PZT-5H Piezoceramics. Appendix F. Constitutive Equations for an Isotropic Substructure. Appendix G. Essential Boundary Conditions for Cantilevered Beams. Appendix H. Electromechanical Lagrange Equations Based on the Extended Hamilton s Principle. Index.
1,292 citations
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