CC BY
45
y^K 681.11.031.1
AN ACCURATE METHODOLOGY FOR DETERMINING THE EFFICIENCY OF ENERGY HARVESTING BY PZ ELEMENTS Frank Wornle1, Steven Grainger2, Andrei Kotousov1
The University of Adelaide, School of Mechanical Engineering,
Adelaide, 5005, Australia (1);
Glasgow Caledonian University, School of Engineering, Science and Design, Cowcaddens Road, Glasgow, G40BA, UK (2)
Represented by a Member of Editorial Board Professor V.I. Konovalov
Key words and phrases: energy harvesting; mechanical vibrations;
piezoelectric elements; Structural Health Monitoring.
Abstract: This paper describes a new experimental methodology for accurate measurements of the efficiency of energy conversion in PZ (piezoelectric) elements. These elements are often used to monitor on-line the progressive structural damage of engineering structures, such as bridges, aircrafts and pipelines. Harvesting energy from small amplitude mechanical vibrations of such structures can revolutionize these monitoring techniques by increasing their reliability, reducing the maintenance cost and making them fully autonomous. As the quantity of electrical energy that can be harvested from vibrations is rather low, it is important to ensure that the piezoelectric elements are operating at the best possible efficiency.
1 Introduction
Much of the world’s infrastructure (aircrafts, bridges, pipelines, etc.) has been around for many years and is becoming increasingly prone to structural damage and failures. Most administrative authorities have come to recognize the significance of this problem. To prevent the catastrophic consequences of such failures, large armies of staff are employed to inspect the potentially hazardous structures. However, as the number of aged structures needing placed under surveillance is steadily increasing, this approach will soon become unsustainable. Structural Health Monitoring (SHM) offers an alternative solution to this problem by automating the monitoring, detection, assessment of extent and location of on-setting structural damage. A network of small sensors can be placed onto a structure to assess its integrity and to monitor long-term changes of key structural parameters necessary for safe operation. SHM system can act as an early warning system, allowing the administrative authorities to schedule repairs before it is too late [1, 2].
A common problem of all SHM systems is that each sensor node requires electrical power. At present, most SHM systems need to run a pair of cables from a central power unit to each node. However, for many aged structures this is either not possible or not economically viable and very vulnerable to acts of vandalism. Battery powered systems are no alternative, as the typical lifespan of even the most recent high performance batteries only ranges from 2 to 5 years; this is insufficient for the long-
term monitoring of large-scale engineering and civil structures [3] whose lifespan may exceed 50 years. It is therefore promising to use the waste energy of structures to power the monitoring systems operating in difficult environments such as inside the walls of a building, on underground structures, at the bottom of the ocean or inside a car tyre; this often rules out conventional renewable energy sources such as solar and wind power.
To be truly autonomous, such a system would require a maintenance-free power supply which provides enough energy for all required functions, including the actual measurement(s), data processing as well as the occasional wireless transmission of data to a nearby base station. The driving force behind energy scavenging is the development of wireless sensor and actuator networks. A related project of particular interest is the PicoRadio project [4], which aims to develop a small, flexible wireless platform for ubiquitous wireless data acquisition that minimizes power dissipation. The PicoRadio project researchers have developed some specifications that affect the exploration of energy scavenging techniques that will be used by their devices. The most important specifications for the power system are the total size and average power dissipation of an individual node in the PicoRadio system. The volume of a node must be no larger than 1 cm3, and the target average power dissipation of a completed node is 100 ^W.
Most man-made structures are subject to varying levels of vibration, e.g. flow induced vibrations of pipes, vibrations due to automotive traffic in bridges or vibrations caused by rotating elements in machines and engines. These vibrations are often one of the main causes of structural damage accumulation or lifetime reduction. It is therefore logical to seek to harvest some of the vibrational energy, which is waste energy, converting it into a useful power source for the SHM system. This is an extremely challenging problem as the levels of vibration are often very small, requiring the generators to be exceptionally efficient to be useful. A number of solutions have been proposed, ranging from electrostatic generators (output: a few |jW) to self-winding rotary mechanisms (|mW to mW) and piezoelectric patches (hundreds of |mW to tens of mW). As piezoelectric elements offer the possibility of producing the required levels of power to operate a smart sensor system considerable effort has been spent on the efficient rectification of the A/C voltage produced by a piezoelectric generator [5 - 7]. Ideally the rectification scheme employed should allow the piezoelectric element to operate as a power source most of the time and work as a sensor collecting information for a small fraction of the total time.
One of the principal challenges of piezoelectric power generation is to produce a good coupling between the mechanical and electrical oscillations. This requires a good, ideally broadband, impedance match of the capacitive piezoelectric element and the voltage rectifying circuitry. Ottman et al. [5, 6] have suggested an interesting approach using an adaptive control system for a step-down converter, which maximises the power flow from the piezoelectric device to the load. Their results are very promising: an increase in output power by a factor 4 has been achieved. Potential areas of improvement include the rectification stage, where synchronous rectification might offer a higher degree of efficiency [8], as well as the better integration of all system components into a flexible and robust single-chip device.
To determine the overall efficiency of a piezoelectric power generator, the electrical output power has to be compared to the power of the vibration, which provides the mechanical excitation. Most piezoelectric generators make use of a cantilever beam with a proof mass to induce strain to the piezoelectric material. The resonant frequency of the oscillating beam is tuned to the most dominant frequency of the exciting vibration, thereby maximising the energy that can be harvested by the generator. With this type of generator, the input signal is essentially uni-modal. An
accelerometer is commonly used to measure the acceleration of the free end of the beam; from this, the amount of energy the generator is subjected to can be inferred. However, this approach makes a number of assumptions and approximations, which may reduce the accuracy of the conversion coefficients thus determined. For example, it is assumed that the curvature of the piezoelectric element can be derived from the motion of the tip of the beam. Furthermore, it is assumed that the deformation of the beam is perfectly uni-modal. Both of these assumptions may not always be fulfilled.
The problem of the assessment of the efficiency of PZ elements is very difficult for analytical or numerical modelling as many important parameters of the structure, such as the properties and effect of the adhesive layer, bonding technique and dynamic response of the whole structure cannot be accurately determined from such models. The proposed methodology is based on the direct measurement of the deformation of the piezoelectric element, as opposed to an indirect characterisation via the acceleration of the tip of the beam. A scanning 3D laser vibrometer (Polytec PSV-400-3D) is used to record the transversal bending modes of the piezoelectric element. From this data, the average curvature can be determined, leading to a highly accurate estimate of the mechanical energy which enters the generator. The automated setup and the high visibility of the obtained measurement data make it very easy to compare and experiment with different configurations of piezoelectric generators. The experimental setup is described in section 2. A variety of selected results are presented in section 3 with a discussion in section 4 and conclusions drawn in section 5.
2 Experimental setup
The experimental setup used for this paper is shown in Fig. 1. Only one of the three laser heads is used to measure the 3D displacement of a grid of 9 x 5 = 45 test points, evenly distributed across the surface of the PZT-5 piezoelectric patch, bonded to a 550 x 40 x 5 mm mild steel cantilever beam near the clamped end.
Small rare earth magnets attached to the beam along its longitudinal axis allow the beam to be excited using a small electromagnet. A heavy base plate on vibration absorbing foam ensures good isolation from most external disturbances (Fig. 2).
Fig.1 Experimental setup: Scanning 3D laser vibrometer
mounting
bracket
electro-magnet
heavy base plate on isolating foam
incident and reflected laser beam
rare earth permanent magnet
output voltage measurement
excitation control
Fig. 2 Schematic of the experimental setup
Once calibrated, the laser beam of the PSV-400-3D can be used to record the displacement, velocity and acceleration of the specimen under investigation at each of the previously defined measurement grid points. Noise reduction is achieved by averaging subsequent data records. This process is carefully controlled so that the phase information between different grid points is preserved.
The recorded information is stored as a Universal File Format (UFF) record, which can be loaded into MATLAB for further processing and analysis. Cycling through all data records allows a vivid picture to be drawn of the motion of the piezo patch across all points of the measurement grid. This makes it very easy to separate transversal vibration modes from non-transversal modes, such as torsional modes and mixed vibration modes. Being able to associate individual modes with their respective mode shapes provides useful insight into the contribution of each of the modes to the total generated electric output power. This information can then be used to optimize the mechanical design of the piezoelectric power generator.
3 Selected Results
A MATLAB m-file script has been written to automatically extract the sought for information from the collected data records. The all-important deformation of the piezo patch can be computed from the relative motion of neighbouring grid points (Fig. 3). From this, the overall curvature in X- and 7-direction is derived. The latter is then used to calculate the amount of mechanical energy, which enters the piezoelectric power generator.
y, mm x, mm
Fig. 3 Measured deformation of the piezo patch (fundamental mode)
Fig. 4 Averaged displacement spectrum: very little energy outside the fundamental
The fundamental resonance of the beam is approximately 10 Hz. Driving the electromagnet with a sinusoidal oscillation at this frequency induces the beam to resonate at this frequency with only very little energy spread across higher order harmonics. This is evident from the displacement spectrum (averaged across all measurement points, Fig. 4).
The electrical output is characterised by the voltage across the load (here a simple resistor, e.g. R = 330 kW). The predominantly sinusoidal nature of this output further confirms that, using a cantilever beam, most of the energy is generated by the fundamental oscillation (Fig. 5). Calculating the RMS power associated with the output spectrum yields an average of 99.4 mW.
Fig. 5 Averaged output voltage spectrum: predominantly sinusoidal
The maximum curvature, k, calculated from the experimental measurements was found to be k = 2.2 10-2 m1. The strain energy of the PZ, U, can be found using elementary beam theory and neglecting the thickness of the PZ element we have
2 H2 2
U = Ek2------V0 sin2 wt,
8 0
where E denotes Young’s modulus of the PZ, H is the thickness of the beam and V0 is the volume of the PZ. Note that the effect of the PZ on the vibration of the beam has been neglected. The peak power is given by
H 2
P peak = E k2-----V0 w
80
and the average power of the accumulated strain energy of PZ element is
(1)
(2)
Pav = E k2 Д= V0 w = pE k2 H
8л/2
4л/2
Vof,
(3)
where f is the first fundamental frequency of the observed voltage in Hz.
The material properties of the selected PZ element are as shown in table 1.
Table 1
Material properties of the mechanical stage
Property Symbol Value
Elasticity modulus E 65 109 N/m2
Beam thickness H 3 mm
Length, PZ element lPZ 50 mm
Width, PZ element Wpz 25 mm
Height, PZ element hPZ 0.25 mm
Voltage constant g31 —1.1510-2 Vm/N
Capacitance C 1.0510-7 F
By substituting the appropriate numbers into equation (3), the average mechanical power was found to be 490 |mW. The conversion factor, which is the ratio of the applied mechanical power to the generated electrical power, is 0.2. This, of course, may not be the maximally achievable conversion factor as no attention has been paid to the proper electrical termination of the highly capacitive source and the resistance value of 330 kW has been chosen arbitrarily. Simple variation of the load resistance, with values ranging from 39 kW to 330 kW produces varying power conversion factors between 5 % and 25 %. These values are expected to improve when a proper impedance match is employed.
4 Discussion
The presented method of determining the total energy conversion factor of piezoelectric power generators can be used to quantify the effectiveness of different PZ elements and generator designs. The highly automated measurement procedure lends itself to parametric studies under well-controlled conditions, minimizing the risk of bias due to systematic measurement error, thereby producing highly comparable results. Interesting candidates for a parametric study include the material constants of the PZ element (e.g. the voltage constant), the geometry of the cantilever beam and its mounting on the source of vibration, the influence of environmental variables such as the temperature and of course the structure and elements of the selected electrical voltage rectification scheme. Results of individual experiments can be compared to one another as the method provides an accurate measure of the mechanical input power. This is in contrast to previously published results, where the parameters of the vibration source are often estimated and, more importantly, assumed to be constant throughout the entire series of experiments, a fact, which is not true in general.
In addition, the method makes it very easy to optimize a chosen design. The data provided by the scanning 3D laser vibrometer gives great insight into the physical mechanisms behind piezoelectric power generation, leading to an increased level of confidence in the measurement results and the conclusions which are drawn from this. New insights can be obtained of less visible effects such as the loading of the mechanical oscillator stage by an improperly matched rectification stage. This will be particularly important when studying highly dynamic rectification schemes such as flyback converters or synchronous rectifiers.
5 Conclusion
In this paper an accurate method has been presented for quantification of the efficiency of energy harvesting devices such as piezoelectric power generators. The proposed method uses a scanning 3D laser vibrometer to obtain highly accurate estimates of the mechanical energy, which the generator is subjected to. This allows meaningful parametric studies to be undertaken, arriving at an optimal design of the mechanical resonator in conjunction with the best possible coupling to the associated voltage rectifier. The high level of automation of the presented measurement procedure reduces the risk of human error and biased results to systematic measurement errors. It is expected that the outcome of a currently ongoing parametric study will result in a highly optimized piezoelectric power generator for smart sensor applications and Structural Health Monitoring.
The authors gratefully acknowledge the support of ARC grant 10BZ3505, which provided access to the Polytec scanning 3D laser vibrometer.
1 Ko, J.M.; Ni, Y.Q.; [2005], Technology developments in structural health monitoring of large-scale bridges, Engineering Structures, 27. Pp. 1715 - 1725.
2 Blazewicz, A.; Kotousov, A.; Wornle, F.; [2005], Detection of cracks using piezoelectric wafer active sensors, Key Engineering Materials, Vol. 293. Pp.201 - 207.
3 Roundy, S.; Wright, P. K; Rabaey J.; [2003], A study of low level vibrations as a power source for wireless sensor nodes, Computer Communications, 26. Pp. 1131 -1144.
4 Wang S.B.T.; Niknejad A.M.; Brodersen R.W.; [2005], A Sub-mW 960-MHz Ultra-Wideband CMOS LNA, Technical Report, Berkeley Wireless Research Center, Dept. of EECS, UC Berkeley, Berkeley, CA, USA.
5 Ottman, G.K.; Hofmann, H.F.; Bhatt A. C.; Lesieutre G.A.; [2002], Adaptive Piezoelectric Energy Harvesting Circuit for Wireless Remote Power Supply, IEEE Transactions on Power Electronics, 17(5). Pp. 669 - 676.
6 Ottman, G.K.; Hofmann, H.F.; Lesieutre G.A.; [2003], Optimized Piezoelectric Energy Harvesting Circuit Using Step-Down Converter in Discontinuous Conduction Mode, IEEE Transactions on Power Electronics, 18(2). Pp. 696 - 703.
7 Ben-Yaakov, S; Krihely N.; [2005], Resonant Rectifier for Piezoelectric Sources, IEEE Applied Power Electronics Conference, APEC-2005, Austin ,Texas. Pp. 249 - 253.
8 J. Han, A. von Jouanne, T. Le, K. Mayaram, T.S. Fiez, Novel Power Conditioning Circuits for Piezoelectric Micro Power Generators, Applied Power Electronics Conference and Exposition (APEC’04), February 22-26, 2004, Anaheim, CA, USA.
Точная методика для определения эффективности накопления энергии с помощью пьезоэлементов
Франк Уорнль1, Стивен Грейнджер2, Андрей Кутузов1
Университет Аделаиды, Механико-машиностроительный факультет, Аделаида, 5005, Австралия (1);
Каледонийский университет г. Глазго, Институт машиностроения, науки и дизайна, Каукадденс роуд, Глазго, Г40БА, Великобритания (2)
Ключевые слова и фразы: накопление энергии; механические вибрации; пьезоэлектрические элементы; структурный мониторинг повреждений.
Аннотация: Описывается новая экспериментальная методика для точных измерений эффективности преобразования энергии в пьезоэлектрических элементах. Эти элементы часто используются для непрерывного мониторинга прогрессирующих структурных повреждений инженерных конструкций, таких как мосты, самолеты и трубопроводы. Накопление энергии от механических вибраций маленькой амплитуды может революционизировать техники мониторинга с помощью увеличения их надежности, уменьшения затрат на содержание и придания таким конструкциям автономности. Поскольку количество электрической энергии, которую можно собрать с помощью вибраций, достаточно невелико, важно удостовериться, что пьезоэлектрические элементы работают с максимальной эффективностью.
Genaue Methodik fur die Bestimmung der Effektivitat der Energieansammlung mit Hilfe der Piezoelemente
Zusammenfassung: Dieser Artikel beschreibt die neue experimentale Methodik fur die genauen Messungen der Effektivitat der Transformation der Energie in den piezoelektrischen Elementen. Diese Elemente werden fur das stetige Monitoring der fortschreitend strukturellen Beschadigungen der ingeniermassigen Konstruktionen, solcher wie die Bracken, die Flugzeuge und die Rohrleitungen oft verwendet. Die Ansammlung der Energie von den mechanischen Vibrationen der kleinen Amplitude kann die Technik des Monitorings mit Hilfe der Vergroflerung ihrer Zuverlafligkeit, der Aufwandsverringerung auf das Erhalten und die Verleihung solchen Konstruktionen der Autonomie revolutionitisiert. Da die Menge der elektrischen Energie, die man mit Hilfe der Vibrationen sammeln kann, nicht genugend ist, ist es wichtig, beglaubt zu werden, dafl die piezoelektrische Elemente mit der maximalen Effektivitat arbeiten.
Methode precise pour la definition de l’efficacite de ^c^mulation de l’energie a l’aide de piezoelements
Resume: Cet article decrit la nouvelle methode experimentale pour les mesures precises de l’efficacite de la transformation de l’energie dans les elements piezoelectriques. Ces elements sont souvent utilises pour le monitoring des destructions structurelles progressantes des constructions d’ingenieur comme ponts, avions et conduites. L’accumulation de l’energie a partir des vibrations mecaniques d’une petite amplitude peut revolutionner les techniques du monitoring a l’aide de l’augmentation de leur fiabilite, la diminution des depenses sur l’entretient et l’attribution a ces constructions du caractere autonome. Puisque la quantite de l’energie que l’on peut a^umuler a l’aide des vibrations n’est pas assez grande, il importe de s’assurer que les elements piezoelectriques fonctionnent avec une efficacite maximale.
