SPIE Proceedings [SPIE Smart Structures and Materials - San Diego, CA (Sunday 26 February 2006)] Smart Structures and Materials 2006: Industrial and Commercial Applications of Smart

Piezoelectric-Based Power Sources for Harvesting Energy from Platforms with Low Frequency Vibration

J. Rastegara, C. Pereirab and H-L., Nguyenb

aOmnitek Partners, LLC, Bay Shore, New York 11706 bU. S. Army Armament Research, Development and Engineering

Center (ARDEC), Picatinny Arsenal, New Jersey 07806

ABSTRACT

This paper presents a new class of highly efficient piezoelectric based energy harvesting power sources for mounting on platforms that vibrate at very low frequencies as compared to the frequencies at which energy can be efficiently harvested using piezoelectric elements1. These energy harvesting power sources have a very simple design and do not require accurate tuning for each application to match the frequency of the platform vibration. The developed method of harvesting mechanical energy and converting it to electrical energy overcomes problems that are usually encountered with harvesting energy from low frequency vibration of various platforms such as ships and other platforms with similar vibratory (rocking or translational) motions. Omnitek Partners has designed several such energy harvesting power sources and is in the process of constructing prototypes for testing. The developed designs are modular and can be used to construct power sources for various power requirements. The amount of mechanical energy available for harvesting is obviously dependent on the frequency and amplitude of vibration of the platform, and the size and mass of the power source. Keywords: Piezoelectric ceramics, energy harvesting, power sources

1. INTRODUCTION

Harvesting energy from the environment to power various devices is not new. The earliest such

devices can probably be said to be windmills. The first windmills were developed to automate the tasks of grain-grinding and water-pumping [1]. The earliest-known design is the vertical axis system developed in Persia about 500-900 A.D. The first known documented design is also of a Persian windmill, this one with vertical sails made of bundles of reeds or wood which were attached to the central vertical shaft by horizontal struts [1].

In recent years, particularly following the development of low-power electronics, sensors and wireless communications devices, electrical energy generators that harvest energy from the environment have seen renewed attention. In this area, piezoelectric materials have been used widely to generate electrical energy from the ambient vibration. Such electrical energy generators and methods of collecting, regulating and storing the generated electrical energy have been the subject of numerous studies (e.g., see [2-7]). For a review of the published literature on energy harvesting and related areas, the reader is referred to [8].

In this paper, a new class of highly efficient piezoelectric based energy harvesting power sources for

mounting on platforms that vibrate at relatively low to moderate frequencies is presented. In particular, platforms that rock through relatively small angles such as ships, trains or trucks, in which the platform is expected to rock at frequencies in the order of 0.2-0.5 Hz are of interest. The maximum amount of available 1 U. S. Patent is pending.

Smart Structures and Materials 2006: Industrial and Commercial Applications of Smart Structures Technologies,edited by Edward V. White, Proc. of SPIE Vol. 6171, 617101, (2006) · 0277-786X/06/$15 · doi: 10.1117/12.657464

Proc. of SPIE Vol. 6171 617101-1

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mechanical energy during each cycle of platform oscillation (rocking motion) is obtained and is proportional to the inertia of the oscillating element of the power source. The amount of mechanical energy available for harvesting is obviously dependent on the frequency and amplitude of vibration of the platform, and the size and mass of the power source. The present work is at its early stages of its development. A number of prototypes of the presented power sources have been designed and are planned to be constructed for testing.

2. MECHANICAL ENERGY AVAILABLE FOR HARVESTING

Consider the mass-spring system mounted on a vibrating platform as shown in Figure 1. Assume that the platform is vibrating in the direction indicated by the vector Y(t), a simple harmonic motion with a frequency ω and amplitude A. If the natural frequency of the mass-spring system is well below that of ω and damping is negligible, then during each cycle of platform motion, the mass m is raised and then lowered a total maximum distance of 2A, i.e., its potential energy is varied by the maximum amount of 2Amg . Here, it is assumed that the inertia of the vibrating platform is considered to be significantly larger than that of the mass-spring system. This is the maximum amount of energy that a vibrating platform can transfer to the vibrating mass-spring system, considering that there are no losses, the natural frequency of the mass-spring system well below the frequency of vibration of the platform. This is therefore the maximum amount of energy that becomes available during each cycle of platform vibration for harvesting and transferring into electrical energy. In addition, if the frequency of vibration of the platform ω is indicated in cycles/sec (Hz), then the maximum amount of power that could possibly be harvested becomes (2Amg ω), where g is the gravitational acceleration. If the amplitude A is in meters, the mass m is in kg, g is in meter/second, and ω in Hz, the above power will have the units of Watts.

Figure 1: A mass-spring system mounted on a vibrating platform. As expected, the maximum amount of mechanical energy that is available for harvesting is

proportional to the amplitude of the platform vibration; the frequency of the platform vibration; and the inertia of the energy harvesting power source. Thus, given a vibrating platform, the only parameter that can be varied is the inertia of the mass-spring system of the energy harvesting power source. However, by increasing the inertia (mass) of the energy harvesting power source, its size is also generally increased. It can therefore be concluded that to minimize the size of energy harvesting power source for a specified power requirement, the vibrating mass has to be constructed with high-density materials, and attempt has to be made to mount most of the components of the power source system onto the vibrating mass.

m

k

Vibrating platform

Y(t)



2.1. Harvesting Energy from Low-Frequency Rocking Motions

If the oscillatory motion of the platform is rotational, such as the rocking motion of a ship, then the

simplest method of generating potential energy for harvesting is the use of a pendulum, Figure 2, or some other pendulum-like mechanisms. In Figure 2, a pendulum of length r and carrying a mass m is shown. If the amplitude of the platform rotational oscillations is α, a properly designed pendulum would undergo oscillations of the same amplitude. During each cycle of its oscillations, the pendulum mass m is raised twice a distance h above its vertical positioning, thereby giving it a relative potential energy mgh. The distance h = r (1-cos α) is proportional to the length r. Therefore, to increase the amount of mechanical energy available for harvesting, the power sources have to be constructed as tall pendulum, which is not considered to be practical. Alternatively, the device could be made wider to accommodate a series of parallel pendulums, or a traveling mass, which is in fact a pendulum with infinite arm length r.

Figure 2: A pendulum mounted on a rocking platform.

In general, most mechanical to electrical energy conversion devices, including those based on

piezoelectric elements, and their electronics are not efficient when operated at very low frequencies. The efficiency of such systems is also increased if the frequency of vibration is relatively constant.

3. TWO-STAGE ENERGY HARVESTING POWER SOURCES

The following class of two-stage energy harvesting power source concepts has been developed to address the aforementioned problems with platforms with low frequency oscillations. The first stage of the power source consists of an oscillatory system such the aforementioned pendulum, hereinafter called the “primary system”, which is attached to the vibrating platform. Mechanical energy is then transferred intermittently to one or more “secondary systems” with significantly higher natural frequencies, which are also attached to the vibrating platform. The mechanical energy is then harvested efficiently from the secondary systems.

hm

rα

Rocking platform



An example of the aforementioned two-stage energy harvesting power source is shown in the schematic of Figure 3. The primary system consists of a simple housing which is attached directly to the rocking platform. The rocking oscillation of the platform is considered to be about an axis perpendicular to the plane of the page. As the platform undergoes rotary oscillation, the traveling mass begins to slide from the side that has been raised, travels the length of the housing and ends on its opposite end. As the traveling mass passes the secondary vibratory elements, in this case beam elements, it engages their free tip and causes then to bend slightly in the direction of its travel. The traveling mass then passes under the engaged beam and moves to the second beam element (secondary vibratory element). The resulting potential energy stored in the released beam elements will then causes them to vibrate. A mechanical to electrical energy conversion means, in this case piezoelectric elements that are attached to the surface of the beam elements and are subjected to compressive and tensile strains, are then used to harvest the available mechanical energy. In Figure 3, mass elements are shown to be attached at the tip of the beam elements to allow the designer to achieve optimal beam size and natural frequency.

Figure 3: Schematic of a two-stage energy harvesting power source.

The traveling mass and the sliding surfaces and the traveling mass and beam tip engagement mechanism must obviously be designed to minimize frictional losses. The spacing of the beam elements and the total deflection of the beams and their bending stiffness must also be selected to maximize the transfer of potential energy from the traveling mass to the beam elements and to ensure that the total potential energy stored in each beam element is harvested by the piezoelectric elements before the next strike of the traveling mass. As can be seen, during each cycle of oscillation of the rocking platform, each beam element is struck twice by the traveling mass.

The amount of mechanical energy available can be seen to be proportional to the width, L, of the power source housing and the mass of the traveling mass. Such energy harvesting power sources are relatively long but have fairly low profile. For example, if the traveling mass has a mass of m= 0.2 kg, the rocking frequency is ω = 0.3 Hz, the width of the energy harvesting power source is L=0.5 m and the rocking amplitude is α = 5 deg., the maximum mechanical power that is available for harvesting is

Pmax = 2 m g ω L sin(α) = 0.051 W or 51 mW

where g is the gravitational acceleration. The basic concept presented in this section can be developed into numerous different designs with the common characteristic of being designed with two stages, a primary stage that transforms the low frequency (and usually small amplitude) oscillations into potential energy that becomes available to a secondary stage of vibrating elements with significantly higher frequency of vibration appropriate for efficient energy harvesting utilizing various means such as piezoelectric elements. In this section, the present two-stage energy harvesting power source design was described with an example of its application to platforms that undergo rocking (rotary) oscillations. The oscillation may, however, be translational or be in the form of the combination of the two. The basic design of such a translational two-stage energy harvesting power sources is described below.

Rocking platform

Secondary vibratory (beam) elements

Traveling mass

Piezoelectric element



3.1. Harvesting Energy from Low-Frequency Translational Oscillations

Consider the mass-spring system shown in Figure 1. The platform displacement Y(t) causes the mass-

spring unit to vibrate. The mechanical energy transferred to the mass-spring system is obviously the largest if the motion is a simple harmonic with a frequency that is equal or close to the natural frequency of the mass-spring system. If the amplitude of oscillation of the vibrating platform is relatively large, enough energy could transfer to the mass-spring system during each cycle of platform motion to be harvested and transformed into electrical energy, e.g., by attaching the spring element via a piezoelectric stack to either to the moving platform or to the mass element.

However, if the frequency of vibration of the base platform is low, it is difficult to efficiently transfer

the aforementioned mechanical energy into electrical energy. For such applications, the present method provides the means to transfer the mechanical energy from the mass-spring system shown in Figure 1, i.e., a primary vibrating system, to a secondary system with high natural frequency. As a result, the mechanical energy transferred to the primary system is available for transformation into electrical energy at a significantly higher efficiency. It is noted that during each cycle of primary system vibration, the entire available mechanical energy does not have to be transferred to the secondary system since the transferred mechanical energy could accumulate in the primary system and be transferred to the secondary system in the consequent cycles of primary system vibration. Similarly, the entire energy of the secondary system does not have to be harvested during each cycle of primary system vibration since the remaining mechanical energy is accumulated in the secondary ad/or the primary system and would be harvested in the consequent cycles of the secondary system vibration.

The basic operation of such a two-stage energy harvesting power source is shown in Figure 4. In this system, the mass-spring system of the primary vibrating system is provided with certain means, in this case one or more engagement teeth, to intermittently transfer its mechanical energy to one or more secondary vibrating elements, in this case simple beam elements with piezoelectric strips attached onto their surfaces. Thereby, as the mass m of the primary system vibrates, the mechanical energy transfer teeth engage the tip of the secondary vibrating units (beams) and displace them until they are released. The initial displacement provided to the secondary vibrating units causes them to vibrate at their natural frequency, thereby generating charges on the piezoelectric elements, which are then harvested. The natural frequency of the secondary vibrating units relative to the primary vibrating system is preferably selected such that the potential energy imparted to each secondary vibrating unit is nearly completely transformed into electrical energy and harvested by the power source electronics before the next strike of the mechanical energy transfer teeth.

It is noted that the design presented in the schematics of Figure 4 is merely for the sake of illustrating the method of operation of an energy harvesting power source that operates based on the present method. In practice, however, such two-stage energy harvesting power sources may be designed in a variety of different types.

4. DISCUSSION AND CONCLUSIONS

A novel class of highly efficient piezoelectric-based energy harvesting power sources for mounting on platforms vibrating at very low frequencies is presented. The energy harvesting power sources have a simple two-stage design in which the first stage is attached directly to the vibrating platform. Mechanical energy is then transmitted intermittently to a second vibrating system with high enough natural frequency suitable for efficient harvesting using piezoelectric elements. The developed method of harvesting mechanical energy and converting it to electrical energy overcomes problems that are usually encountered with harvesting energy from low frequency vibration of various platforms such as ships and other platforms with similar vibratory (e.g., rocking or translating) motions. Omnitek Partners has designed several such energy harvesting power sources and is in the process of constructing prototypes for testing.



Figure 4: Schematic of a typical energy harvesting power source based on the proposed method.

It should be noted that the basic designs presented in this paper are merely for the sake of illustrating the method of operation of such two-stage energy harvesting power sources. The primary challenge in the design of such energy harvesting power sources is the method and means of intermittently transferring mechanical energy from the primary to the secondary vibrating systems without losses such as from friction and impact. For this reason, mechanisms that transfer mechanical energy without contacting elements, for example, those using magnets that are attached to one or both vibrating systems are preferred.

5. REFERENCES

1. Dodge, D.M, “Illustrated History of Wind Power Development,” http://telosnet.com/wind/early.html. 2. Williams, C. B., and Yates, R. B., 1996, “Analysis of a Micro-Electric Generator for Microsystems,”

Sensors and Actuators, Vol. 52, No. 1–3, 8–11. 3. Sodano, H. A., Magliula, E. A., Park, G., and Inman, D. J., 2002, “Electric Power Generation from

Piezoelectric Materials,” in Proceedings of the 13th International Conference on Adaptive Structures and Technologies, October 7–9, Potsdam/Berlin, Germany.

4. Sodano, H. A., Park, G., Leo, D. J., and Inman, D. J., 2003, “Use of Piezoelectric Energy Harvesting Devices for Charging Batteries,” in SPIE 10th Annual International Symposium on Smart Structures and Materials, March 2–6, San Diego, CA, Vol. 5050, pp. 101–108.

5. Goldfarb, M., and Jones, L. D., 1999, “On the Efficiency of Electric Power Generation with Piezoelectric Ceramic,” ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 121, 566–571.

k

Y(t)

Vibrating platform

Piezoelectric elements

m

Mechanical energy transfer

teeth

Secondary Vibrating

units

Vibrating beams



6. Ottman, G. K., Hofmann, H., Bhatt A. C., and Lesieutre, G. A., 2002, “Adaptive Piezoelectric Energy Harvesting Circuit for Wireless, Remote Power Supply,” IEEE Transactions on Power Electronics, Vol. 17, No.5, 669–676.

7. Hofmann, H., Ottman, G. K., and Lesieutre, G. A., 2002, “Optimized Piezoelectric Energy Circuit Using Step-Down Converter in Discontinuous Conduction Mode,” IEEE Transactions on Power Electronics, Vol. 18, No. 2, 696–703.

8. Sodano, H. A., Inman, D. J., and Park, G., 2004, “A Review of Power Harvesting from Vibration using Piezoelectric Materials,” The Shock and Vibration Digest, Vol. 36, No. 3, 197–205.



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SPIE Proceedings [SPIE Smart Structures and Materials - San Diego, CA (Sunday 26 February 2006)] Smart Structures and Materials 2006: Industrial and Commercial Applications of Smart