Modelling, Fabrication and Characterization of a Piezoelectric Vibration Energy Harvester

Modelling, Fabrication and Characterization of a Piezoelectric Vibration Energy Harvester

Prasanta Kumar Samal,

Indian Institute of Science, Bangalore

Pramod Kumar Malik,

Indian Institute of Science, Bangalore

Premanjan Sethy,

Indian Institute of Science, Bangalore

Dr. Rudra Pratap

Indian Institute of Science, Bangalore

Abstract

In the immediate surroundings of our daily life, we can find a lot of places where the energy in the form of vibration is being wasted. Therefore, we have enormous opportunities to utilize the same. Piezoelectric character of matter enables us to convert this mechanical vibration energy into electrical energy which can be stored and used to power other device, instead of being wasted. This work is done to realize both actuator and sensor in a cantilever beam based on piezoelectricity. The sensor part is called vibration energy harvester. The numerical analyses were performed for the cantilever beam using the commercial package ANSYS and MATLAB. The cantilever beam is realized by taking a plate and fixing its one end between two massive plates. Two PZT patches were glued to the beam on its two faces. Experiments were performed using data acquisition system (DAQ) and LABVIEW software for actuating and sensing the vibration of the cantilever beam.

1. Introduction

   There are so many technologies have been developed in energy harvesting, such as solar, wind, geothermal, and hydraulic power plants or farms. Since vibration exists everywhere, such as the vibration of floor and wall, machines, pumps, vehicle chassis, railway train or tracks, and human motions, etc. it becomes a good

   alternative energy source and receives more and more attention in recent years.

   The process of converting the wasting vibration energy into useful one is known as vibration energy harvesting. When piezoelectric materials are used for conversion, this is termed as piezoelectric vibration energy harvesting. And also the present world scenario is such that, the big things are becoming bigger and bigger and small things are becoming smaller and smaller. An alternative for batteries for small machineries is to create energy while working. Using piezoelectric materials (e.g., PZT) is one way we can accomplish this. This is another application of piezoelectric transducer. Transducer is a device which converts one form of energy into other. In electromechanical system, the electrical energy is converted into mechanical energy and vice versa. They are of two types one is actuator, and another is sensor. When the electrical energy is converted into mechanical one to excite any structure, is called actuation. And when the mechanical vibration energy is converted into and represented in terms of electrical energy, is called sensing.

   Piezoelectricity is the property of certain materials called piezoelectric materials. By virtue of which if the material is subjected to mechanical stress it generates charge distribution and thus there is voltage difference between two electrodes. This is known as direct piezoelectric effect. The reverse piezoelectric effect causes mechanical strain on the material by the application of electrical voltage. When an AC voltage is applied, it will cause it to vibrate and thus generate

   mechanical or pressure waves at the same frequency of applied AC voltage. This reverse piezoelectric effect is usually used as actuator which converts electrical energy into mechanical energy. Similarly, the direct piezoelectric effect can be used in sensing the mechanical displacements by measuring electrical voltage produced due to the resulting mechanical stress. Both actuators and sensors are the transducers which convert one form of energy into another [1].

   A significant number of journal papers and conference proceedings develop accurate models and discuss the numerous applications of the field in great detail.

   First, the piezoelectric constitutive relations and the corresponding matrices are defined in section Fundamentals of Piezoelectric Materials. Then, finite element analyses and their results are shown in section Numerical Analysis. In section Fabrication and Setup, the procedure followed in realizing the device and the experimental setup is discussed. Experimental procedure and the results are plotted in section experimental result. The concluding discussion including future research directions are presented in section conclusion.

2. Fundamentals of Piezoelectric Materials

   The piezoelectric effect was first mentioned in 1817 by the French mineralogist Rene Just Hauy1. It was first demonstrated by Pierre and Jacques Curie in 1880. Their experiments led them to elaborate the early theory of piezoelectricity. This theory was complemented by the further work of G.Lippman2, W.G.Hankel3, Lord Kelvin and W. Voigt (beginning of 20th century).

   Harvesting vibration energy from civil structures such as tall buildings, communication towers, and long-span bridges were dealt [2-4]. Harvesting power in regenerative vehicle suspensions [5-9]. Harvesting Bike Vibrations Energy [10]. Power- generating floor has been developed by Research & Development Center of JR East Group [11]. Energy harvesting potential from railway tracks [12-15]. Power generation from road bump vibrations [16]. Vibration energy harvesting using piezoelectric Materials [17- 20].

   As expected from any relatively new technology, the research in this field has been mostly in design and development. Numerous products have been designed and developed within research organizations and universities. However, only a few have been realized as commercially viable products. This paper includes not only design, and development, but also conducting experiments validating its intended function.

   1 First observation of the presence of electric charges on the surface of a stressed tourmaline crystal

   2Mathematical deduction of the inverse piezoelectric effect,

   confirmed experimentally by P. & J. Curie: 1881

   3W.G.Hankel introduced the term piezoelectricity

   Piezoelectricity is the coupling between electrical voltage and mechanical stress. It is the property of the material by which electricity is produced by the application of pressure and vice versa.

   Piezoelectric Relations: The electrical behavior at constant stress or of an unstressed medium under the influence of an electric field is defined by two quantities, the field strength (E), and the dielectric displacement (D). Their relationship is:

   D = E (2.1)

   Here ' is the permittivity at constant stress or of the (unstressed) medium.

   The mechanical behaviour of the same medium at zero electric field strength is defined by two mechanical quantities, the stress applied (), and the strain (). Their relationship is:

   = SE (2.2)

   Here SE' denotes the compliance of the medium (at zero electric field).

   Piezoelectricity involves the interaction between the electrical and mechanical behavior of the medium. To a good approximation this interaction can be described by linear relations between two electrical and mechanical variables ( and E):

   = SE + dTE (2.3)

   D = d + E (2.4) These two equations are known as the strain form of piezoelectric equations. The second set of piezoelectric equations (stress form) can be obtained from the first set (strain form) as follows:

   = CE-1 + dTE CE-1 = – dTE

   = CE – CE dTE

   = CE eE

   Where, e = CE dT= piezoelectric stress matrix, CE is the stiffness matrix which is th inverse matrix of compliance matrix SE and thus

   e = CE dT

   eT = (CE dT)T

   = (dT ) T (CE) T

   = d(CE) T

   = dCE

   As CE is a symmetric tensor. Substituting = CE – eE in equation 2.4, we have

   D = d + E

   = d(CE – eE)+ E

   = dCE + ( – de) E

   = eT + E

   Where, = ( – de) = permittivity at constant strain (clamped permittivity).

   Thus the stress form of piezoelectric equations

3. Numerical Analysis

   Modal and Harmonic analysis were performed in order to determine the fundamental frequencies and its frequency response, using finite element calculation in ANSYS. For the analyses, the physical dimensions of the beam are given in the Table3.1, and its properties are given in the Table 3.2.

   Table3.1: Physical dimension of system

   Material	Length (mm)	Width (mm)	Thickness (mm)
   Aluminum	150	25	1

   	= CE eE	(2.5)
   D	= eT + E	(2.6)

   is:

   Piezoelectric Matrices: Piezoelectric materials are transversely isotropic. Transversely isotropic materials are a special class of orthotropic materials having the same properties in one plane (e.g. the x-y plane) and different properties in its normal direction (e.g. the z- axis). Such materials are described by 5 independent elastic constants, instead of 9 for fully orthotropic materials.

   The only 5 independent elastic constants are: c11, c33,

   Table3.2: Properties of Beam Material

   Material	Elasticity (E) in GPa	Poissons Ratio ()	Density () Kg/m3
   Aluminum	70	0.33	2800

   c44, c12 and c13.

   E Figure 3.1 through 3.4 show the four fundamental

   Here we use the notation c instead of c for convenience. We have

   c22 = c11, c55 = c44, c66 = 2(c11 – c12), c23 = c13,

   and other coefficients are zero. So we have c' matrix

   As per equations (2.3) and (2.4), the piezoelectric matrix (d3X6) is the coupling between mechanical stress (6X1) and electric field strength (E3X1). The only 3 independent piezoelectric coefficients are: d33, d31 and d15.We have

   mode shapes of the cantilever beam and its corresponding natural frequencies. The frequency response of the system was obtained from harmonic analysis as shown in Figure 3.5. This correlates the modal analysis showing the spikes at corresponding natural frequencies.

   d32 = d31 and d24 = d15,

   and other coefficients are zero. So we have d matrix

   Figure 3.1: First Mode

   Figure 3.2: Second Mode

   Figure 3.3: Third Mode

   Figure 3.4: Fourth Mode

   Figure 3.5: Frequency Response of the System

4. Fabrication and Setup

   The simplest structure, a cantilever beam is realized by taking an aluminium plate as per dimensions. Two PZT patches, as the piezoelectric material, for actuation and sensing of its vibration, were collected. The PZT patches were glued to the beam on both the flat faces of the plate. The plate with two patches glued to it was fixed between two massive plates to realize the fixed condition of cantilever beam as shown in Figure 4.1.

   In the actuation mode, when the AC voltage is applied, the (actuating) PZT patch deforms and thus the beam starts vibrating. Similarly the other (sensing) PZT patch deforms due to the vibration of the beam, and thus produces electric field between the electrodes as sensing signal. This is the application of piezoelectricity in actuation and sensing of the vibration of a beam.

   Figure 4.1: Actual Setup

5. Experimental Result

   The vibration of the beam was actuated and sensed by using DAQ and the LabVIEW software. This acts as a transducer, the application of piezoelectric effect.

   The beam was successfully actuated in different conditions and also corresponding vibrations were sensed. A LabVIEW VI was written for both acquiring and generating analog voltage. By running the VI the DAQ generates the voltage in the specific channel out of the two output channels available for the device. From the corresponding pins of the connector block, two wires were connected to the two electrodes of the actuating PZT patch. This AC voltage creates vibration of the beam according to the wave form of the signal. The generated voltage can be amplified using an Amplifier if the generated voltage is not sufficient to actuate the beam. Due to the vibration of the beam, electrical voltage difference is produced between the two electrodes of the sensing PZT patch. This voltage is now acquired by the acquiring part of the VI. Both the signals were seen on the graph indicators as well as stored in the measurement files. These measurement files were plotted in MATLAB.

   Following are some of the plots in different conditions of actuation and corresponding sensing signals:

   Figure 5.1 shows the actuation (Blue) and sensing (Green) of the beam vibration; initially no actuation i.e., noise, then it was continuously actuated at 58 V for around 700 milliseconds and the corresponding sensing voltage was 2.2 V. Then the beam was manually excited by just taping the beam as shown it is done for twice. Thus there was only noise in actuation part, and spikes were there in sensing part. Similarly, Figure 5.2 shows actuation and sensing of the beam (initially noise, excited first with high and then with low amplitudes.

   Figure 5.1: Actuation and sensing (noise, continuous sinusoidal signal and manual pulses)

   Figure 5.2: Actuation and sensing (noise, excited with first high and then low amplitudes)

6. Conclusion

   The simplest system for testing the vibration energy harvesting has been successfully fabricated. Its numerical analyses were performed by finite element calculation using ANSYS. The first four fundamental frequencies were determined to be 36.36 Hz, 227.635 Hz, 638.512 Hz, and 1255 Hz respectively. The frequency response for the same was obtained and correlated. Experiments of the system have been performed using data acquisition system and plotted in MATLAB. The system was actuated at various frequencies with various amplitudes. It is concluded that the vibration energy can be harvested by the use of simple structures like beams, frames, plates, etc. with piezoelectric patches glued to them. The energy developed can be utilized in some useful power requirements specifically in small power requirements.

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