Piezoceramic Unimorphs for Energy Harvesting Applications
HWAN-SIKYOON, GREGORYWASHINGTON* ANDAMITADANAK Mechanical Engineering, The Ohio State University, Columbus, OH 43202, USA ABSTRACT: The piezoceramic, lead zirconate titanate (PZT), is capable of producing large voltages with relatively minimal currents in response to an applied mechanical load when employed in initially curved laminates. This study addresses the issue of optimizing design parameters of a curved PZT unimorph to maximize charge generation due to mechanical loading. A horizontally placed PZT unimorph structure generates surface charge when vertically loaded and the charge can be collected using charge-collecting circuitry. In order to identify and optimize the variables fundamental to the design process, an analytical model of the curved PZT unimorph was developed using shallow thin shell theory and linear piezoelectric constitutive equations. An expression for charge generation was then derived in terms of geometrical dimensions, material properties and applied loading. The model was experimentally verified with samples consisting of different geometries and loadings. Finally, the analytical model was used to generate optimal design characteristics or ‘rules of thumb’
necessary for optimum design. It is envisioned that these ‘rules of thumb’ will be used by practitioners to design efficient charge generating devices.
Key Words: PZT unimorph, charge generation, energy harvesting, shoe insert.
INTRODUCTION
A
S consumer reliance on portable electronic devices such as cellular phones and PDAs (personal digital assistants) increases, so does the need for a reliable, efficient and cost-effective means for supplying electrical energy to those devices (Starner, 1996). As an alternative to supplying steady electrical power satisfying perfor- mance, volume and weight constraints, various energy harvesting technologies have been developed recently (Hausler and Stein, 1984; Starner, 1996; Amirtharajah and Chandrakasan, 1997; Kymissis et al., 1998; Shenck, 1999; Gonzalez et al., 2001; Kasyap et al., 2002; Ottman et al., 2002; Sodano et al., 2002). When properly scaled for consumer use, these strategies produce devices that can generate tens of microwatts to hundreds of milli- watts. This amount of power is not sufficient for consumer use at this time since most devices consume power measured in watts. However, in the near future, power requirements for signal processing will fall to low levels, measured in milliwatts (Westervelt et al., 2000).Power requirements divided by a factor of 100 are expected in commercial off-the-shelf (COTS) technology within the next five years. This stems from the fact that power consumption in integrated circuits (IC) will continue to decrease as IC processing moves towards
smaller feature sizes. For example, gate lengths (L) are being halved every three years. Since power consump- tion is proportional to (L3), power consumption is currently being halved every year. Further evidence of this fact can be seen by the latest rendition of the International Technology Roadmap for Semiconductors.
The International Technology Roadmap for Semicon- ductors is the result of worldwide consensus building among 800 experts from the USA, Europe, Japan, Korea and Taiwan. This roadmap is produced every three years and was last produced in 2001. The current rendition of the map states (ITRS Committee, 2001):
Today’s state-of-the-art semiconductor chips feature technology nodes of 180 nanometers with 130 nano- meter technologies just beginning to reach the market- place. In the previous roadmap released in 1999, it called for the future generations of dynamic random access memories to feature critical dimensions of 100 nano- meters in 2005, then 70 nanometers in 2008, 50 nanometers in 2011 and 35 nanometers in 2014. Now the industry plans to deliver 90 nanometers (2004), 65 nanometers (2007), 45 nanometers (2010), 32 nano- meters (2013) and 22 nanometers (2016). This 2001 schedule translates to smaller chip dimensions earlier in time than previously thought.
Fifteen years into the future, gate lengths are projected to be mere 9 nm. A reduction in this size will reduce power demands by 4 orders of magnitude.
As power consumption continues to be reduced, the
*Author to whom correspondence should be addressed.
E-mail: [email protected]
JOURNAL OFINTELLIGENTMATERIALSYSTEMS ANDSTRUCTURES, Vol. 16—October 2005 877
1045-389X/05/10 0877–12 $10.00/0 DOI: 10.1177/1045389X05055759
notion of a small smart material generator producing enough power to operate a personal digital assistant (PDA) or cell phone is not far fetched. However, these smart material generators need to be optimally designed, which is the topic of the research in this manuscript.
This research focuses on the possibility of harnessing energy parasitically from daily activities (i.e., walking, typing, breathing, etc.) to generate usable electric power (Hausler and Stein, 1984; Starner, 1996; Kymissis et al., 1998; Shenck, 1999). Among various potential sources of energy in body motion, collecting energy from walking has been reported to be the most efficient and feasible method (Starner, 1996; Gonzalez et al., 2001) and it can be accomplished using piezoelectric materials (Kymissis et al., 1998; Shenck, 1999; Gonzalez et al., 2001). Accompanied experiments have revealed that the material could be successfully used in harvesting several microwatts to milliwatts of usable power. Other researchers have successfully demonstrated that an initially curved piezoceramic unimorph can be used as shoe implants to generate enough power to supply electric energy to RFID tags (Kymissis et al., 1998;
Shenck, 1999).
In this paper, we revisit the design of an energy harvesting shoe insert in order to illustrate performance gains that can be accomplished with a more analytically based design methodology. Many researchers have neglected the curvature in the device and very little research focuses on what parameters to minimize and maximize when designing energy generators. In order to develop a mathematical model, a set of governing equations are derived to describe the amount of charge
‘built up’ on the surface of an initially curved piezo- ceramic unimorph beam with respect to the applied force. The principal design metric here is the charge generationof the PZT unimorph and not the voltage or the power generated by the device. This is because of the fact that for rechargeable batteries, which the unimorph will eventually be attached to, the amount of charge stored in the battery, which is converted into current, determines the capacity of the battery. It also allows easy comparisons between model and experiment.
The approach for analysis presented here is based on shallow thin shell theory by Donnell-Mushtari, compo- site laminate theory, and linear piezoelectric constitutive equations (Reissner, 1946; Kraus, 1967; Jaffe et al., 1971; Andersen, 1989; Qatu, 1989; Halpin, 1992; Tzou, 1993). Once developed, this model can be used to design energy harvesting devices and to develop ‘rules of thumb’ for optimally sizing the actuator.
CHARGE GENERATION USING AN INITIALLY CURVED PIEZOCERAMIC UNIMORPH
A simply supported piezoceramic unimorph beam is shown in Figure 1. As an input force, a distributed pressure load is applied on the top surface and the piezoelectric layer experiences stress in the x(1) direc- tion. Since the electrodes are applied in the z(3) direction, the device is active in 31-mode.
The device consists of two major components:
the top PZT layer and the bottom stainless steel substrate. These two layers are bonded together by a thin adhesive layer, and a thin aluminum foil is applied on top of the PZT layer. The electromechanical behavior of piezoceramic can be described by the four quantities of concern in piezoelectricity: stress (T ), strain (S), electric field (E), and electric displacement (D). Piezoelectricity couples the mechanical and elec- trical components, which results in the constitutive relationships expressed as
Sj¼sEjiTiþdjmEm ð1aÞ Dm¼dmjTjþ"TkmEk ð1bÞ for the isothermal case, where s is the compliance matrix, d is the piezoelectric matrix, and " is the permittivity matrix (ANSI/IEEE, 1987). In the current development of a mathematical model of the PZT unimorph, the relationship between the applied force and the amount of charge generation will be derived.
Since the current or the generated charge measure- ment is conducted experimentally in a short-circuited
Figure 1. Curved PZT unimorph excited in 31-mode by a normal distributed force.
condition, the electric field, E, in Equations (1a,b) will be assumed to be zero in the subsequent derivation.
In reality, the electrical boundary condition depends on how fast the attached charge-collecting circuit draws the current from the electrodes. The process will be instantaneous in a short-circuited case and, in an open-circuit condition, the generated charge will migrate very slowly in the form of leakage current through PZT.
In most cases, the charge migration occurs somewhere in between those two conditions. However, different electrical boundary conditions affect only the time history of the beam deflection in the force–deflection diagram and the amount of charge developed and collected will be the same as long as the PZT unimorph is deflected to its maximum value and sufficient time is given such that the developed charge moves from the electrodes into the attached circuit. Therefore, a quasi- static beam deflection model will be considered in this study where the deflection of the PZT unimorph is assumed to occur slowly enough to ensure that the closed-circuit condition is always met throughout the process.
The charge developed on the surface of the piezo- ceramic, q can be expressed as the integral of electrical displacement over the effective surface area of the electrodes on the material (Tzou and Anderson, 1992).
q ¼ Z
A
D3 dA: ð2Þ
Utilizing the inverse relationship between stiffness and compliance, and substituting Equation (1) into Equation (2) results in
q ¼ d3jcEji Z
A
SidA, ð3Þ
where cjirepresents stiffness matrix component and A is the effective area of the electrode. The charge developed on a surface is now described as a function of the strain induced in the structure. In the next section, the relationship between the strain in the piezoceramic and the applied force is derived.
MODELING OF TWO-LAYER SINGLY CURVED PZT UNIMORPH
The mechanical behavior of the initially curved PZT unimorph beam is modeled using a laminated shell theory. Laminated shells are conveniently characterized by their neutral surfaces. The equations derived for generic thin shells can be reduced to those for curved beams by removing all transversely varying terms and derivatives (Kraus, 1967). A schematic of a differential element of a shell is shown in Figure 2. Notice here that the radius of curvature, R, is defined as a distance from the origin of the cylindrical coordinate to the neutral surface of the shell. In this development, Kirchhoff ’s hypothesis and Love’s assumptions are used where the normal to the neutral surface remains normal and unstretched during deformation (Reissner, 1946; Kraus, 1967).
For shallow shells, one can interchangeably use the curvilinear coordinate along the neutral surface with the rectangular coordinate (Qatu, 1989). Also, by invoking the additional assumption that the shell is thin, that is =R 1, where is the thickness of the shell, the strain in x(1)-direction, S, at an arbitrary point across the thickness can be denoted as
Sðx, zÞ ¼ SðxÞ þ zðxÞ, ð4Þ
Figure 2. Differential curved beam element of length (dx).
where S denotes the membrane strain of the neutral surface and represents the bending strain or changes in the curvature of the neutral surface during deformation.
Note that the z-coordinate is measured from the neutral surface. The variables S and are related to the displacement by
S¼@u
@xþw
R, ð5aÞ
¼ 1 R
@u
@x@2w
@x2 @2w
@x2, ð5bÞ
where u and w represent the components of the displacement vector of a point on the neutral surface in x- and z-directions respectively. The approximation used in Equation (5b) was first advanced by Donnell (Kraus, 1967).
Considering only the x(1)-direction, the stress–strain equation for an element in the kth lamina can be written as (Halpin, 1992)
T1¼ ck11S1, ð6Þ where ck11 is the stiffness matrix component of the kth lamina. The normal force and moment resultants, N and M, shown in Figure 2 are the integrals of the stresses over the beam thickness:
N M
" #
¼bX2
k¼1
Zk
k1
1 z
" #
Tdz, ð7Þ
where b represents the beam width and k refers to the kth lamina. Note that, in Equation (7), the lamina index, k runs from 1 to 2 representing the two layers in the unimorph beam. Substituting Equation (6) into Equation (7), utilizing Equations (4) and (5), and performing the integration over the thickness leads to
N M
" #
¼ A B
B C
" # S
" #
, ð8Þ
where A, B, and C are the stiffness coefficients arising from the piecewise integration defined in Equation (7) and they are written as
A, B, C
½ ¼bX2
k¼1
ck11 ðkk1Þ,1
2ð2k2k1Þ,1
3ð3k3k1Þ
: ð9Þ In Equation (9), k is the distance from the neutral surface to the top surface of the kth layer. This approach can be found in Halpin (1992).
The equations of motion may be obtained by taking a differential element of a beam having thickness, , and neutral-surface length, dx (see Figure 2). From the force
and moment equilibrium condition, the following equations can be derived.
@N
@xþQ
R¼uu,€ ð10aÞ
N Rþ@Q
@xþpz¼ €ww, ð10bÞ
@M
@x Q ¼0, ð10cÞ
where Q represents the shear force resultant on the surface perpendicular to x-direction, denotes struc- tural density, and pzrepresents the normal pressure load on the PZT layer. Utilizing Q=R 1 for shallow shells and removing Q from the equations leads to (Reissner, 1946; Kraus, 1967)
@N
@x¼uu,€ ð11aÞ
N Rþ@2M
@x2 þpz¼ €ww: ð11bÞ Substituting Equation (8), with S and defined by Equations (5), into Equation (11), the equations of motion can be expressed in matrix form in terms of the neutral-surface displacements as
L11 L13
L31 L33
u
w
¼ 0 0
@2
@t2 u w
þ 0
pz
, ð12aÞ where
L11 ¼A @2
@x2, L13 ¼L31 ¼A
R
@
@xB @3
@x3, L33 ¼ A
R22B R
@2
@x2þC @4
@x4:
ð12bÞ
The first equation in Equation (12a) describes the longi- tudinal motion of the curved beam and the second represents the transversal movement. Note that unlike a symmetrically laminated beam case, the terms contain- ing stretching-bending coupling, B, do not vanish in this case.
Boundary conditions for the simply supported beam with length l can be written as
wðx ¼0Þ ¼ Mðx ¼ 0Þ ¼ 0 and ð13aÞ wðx ¼ l Þ ¼ Mðx ¼ l Þ ¼0, ð13bÞ where all terms are only considered with respect to the x(1)-direction for the case of a beam.
While an exact solution can be obtained for the dynamic equations of Equation (12a), the mechanical excitation frequency of 1 Hz assumed in this study is much slower than the electrical response of the developed charge and therefore it is considered that the quasi-static analysis is appropriate. Thus the time
derivatives in Equations (12) are dropped and the governing equations become static equations. In addi- tion, since there is no external force applied in the x-direction, it is assumed that the membrane strain of the neutral surface, Sin Equation (5a) is negligible com- pared to the bending strain. Thus, from Equation (5a),
w ¼ R@u
@x: ð14Þ
Using Equation (14), the second equation in Equation (12a), which describes the transversal motion of the curved beam, can be rewritten as
B R
@2
@x2w
þC @4
@x4w
þpz¼0, ð15Þ Solving Equation (15) for transverse deflection, w, leads to
wðxÞ ¼ G1exþG2exþG3x þ G4pzR
2B x2 ð16Þ where 2B=CR:After applying the boundary condi- tions in Equation (13) to solve for the constants, G, the transverse deflection of the beam can be described in terms of a distributed pressure input, pz, as
wðxÞ ¼pzR
B2coshðxÞ pzR B2
ðcoshðl Þ 1Þ
sinhðl Þ sinhðxÞ þpzRl
2B x pzR B2pzR
2B x2 ð17Þ
An experiment was conducted to measure the displacement of the PZT unimorph in response to the applied force and the result verified that Equation (17) is accurate (Danak et al., 2003).
Finally, to obtain an expression for the gener- ated charge due to the deflection of the structure, Equation (17) is differentiated twice and substituted into Equation (5b) and then Equation (4) resulting in the strain description in terms of the applied force.
When the resulting strain equation is substituted into Equation (3), it generates the following charge equation.
q ¼ bd31C211 1þ2
2
Zl
0
@2w
@x2 dx, ð18Þ Equation (18) is an analytical formula that links the dimensional parameters of the PZT unimorph beam and to its corresponding charge generation. It can now be used for finding the optimal design parameters.
PARAMETRIC STUDY
From a previous study (Danak et al., 2003), it was observed that increasing each of the geometric param- eters such as length, width, and thickness of the device, as defined in Figure 3, results in an increased genera- tion of charge in general. In order to obtain a clearer
understanding of how to optimize the design param- eters within a confined volume such as the heel of a shoe, these parameters are varied simultaneously in this study.
As shown in Table 1, beams having greater substrate thickness have a lower center height than their thinner counterparts. This is because of the manufacturing process, where the curvature is generated from the difference of thermal expansion coefficients, and in implementation the center height may not be a true design parameter. However, by modifying the manu- facturing process, i.e., by applying different curing temperatures or curing times, one may have some level of control over the final center height. Therefore, it is included here as a plausible design variable.
Figure 4 shows the effect of varying the substrate thickness and the beam width on charge generation, with the other design parameters kept constant at their nominal values. The applied force was adjusted to each case such that it makes the unimorph just about to be flattened. Increasing the beam width results in propor- tionately increasing charge generation. Additionally, as the substrate thickness increases, the generated charge increases accordingly. Although this is an expected result, the analysis reveals that this increase in charge stems from the shift of the neutral surface toward the substrate, which induces more strain in the PZT layer in bending and thus more charge. Note, however, Table 1. Dimensions of nine samples used in experi- mental validation.
Substrate
thickness Length (mm) Width (mm)
Center height (mm) 0.254 mm (10 mil)
1-a 71.00 8.45 4.1
1-b 42.30 11.50 2.8
1-c 25.80 11.90 1.5
0.305 mm (12 mil)
2-a 71.00 11.10 4.5
2-b 41.50 10.00 2.8
2-c 26.30 11.10 1.3
0.381 mm (15 mil)
3-a 69.60 10.90 3.1
3-b 43.00 10.30 2.0
3-c 25.70 9.21 1.4
Figure 3. Geometric design parameters.
that there is a certain limit on the range of substrate thickness where this predicted behavior is guaranteed, as it cannot be very thin or very thick without limit. Thus, the behavior shown in the next set of plots is understood to be accurate around some nominal (or baseline) design. It should also be considered that increased substrate thickness requires larger mechanical force to deform the structure, which may be undesirable in certain applications.
Figure 5 shows the effect of increasing stiffness (Young’s modulus) and beam length on the amount of charge generated, and Figure 6 shows the effect of varying the length to width ratio of the structure.
Figure 5 shows that increasing the stiffness of the substrate leads to an increased charge for the same reason as increasing substrate thickness. As can be seen in Figure 6, even though beam length and width are both the same order of magnitude, the effect of varying the width is more effective in generating charge than increasing length. The effect of simultaneously varying substrate thickness and beam length with respect
to the beam width as presented in Figures 4 and 6 were observed in the experimental results as well. The effect of changing the center height and the beam length on the generation of charge can be seen in Figure 7. The rationale for the odd shaped plot stems from the fact that shorter beams cannot have the center heights that longer beams are capable of achieving.
All these results can be summarized as the following design rules of thumb:
. Increasing the width of the unimorph is more effective in charge generation than increasing the length.
. Increasing the center height with a variation in manufacturing process is also very favorable for charge generation.
. Increasing thickness of the substrate is effective in charge generation, which may be restricted by the available input force to deform the curved unimorph.
Increasing thickness of the PZT does not necessarily increase charge generation. Instead, it may favorably or
Figure 4. Charge vs beam width and substrate thickness. Figure 6. Charge vs beam width and beam length.
Figure 5. Charge vs stiffness (Young’s modulus) and beam length. Figure 7. Charge vs center height and beam length.
adversely affect charge generation in an initially curved configuration depending on which direction the position of the neutral surface of the laminate moves. As the PZT is placed further from the neutral surface, the PZT layer experiences more in-plane strain during bending of the structure, which results in more charge generation.
Thus one needs to make sure that an increase in PZT thickness also accompanies an appropriate change in neutral surface. As a final remark, it should be noted that these design rules of thumb can also be applied to an initially flat, PZT unimorph beam under various bending loads.
PREPARATION OF SAMPLES
Since the cost of building or buying a charge amplifier with the accuracy necessary for actual charge compar- isons was prohibitive, the goal of the experiment is to verify the trends in charge generation as predicted by the parametric study experimentally. To achieve this, samples are prepared with two main parameters varied:
beam length and substrate thickness. The manufacturing process controls the curvature of the beam, which determines the center height. In addition, since the PZT-5A wafers are far more expensive than the stain- less steel shim stock used for the substrate, only the thickness of the substrate is varied. The thickness of the PZT is 0.254 mm (10 mil). The actual samples created are outlined in Table 1.
Figures 8–10 show the nine PZT unimorph samples used in the experiment. The samples are manufactured by Dominion Resources using the THUNDERÕprocess using PZT-5A wafers (with Nickel electrodes) for the piezoelectric layer, stainless steel shim-stock for the substrate, and a high temperature adhesive, LaRCTM-SI for the bonding layer. The bonding strength of this adhesive is what allows the development of pre-stress in the laminate during manufacturing, which enables ThunderÕ devices to have a high level of ruggedness and performance capability (Bryant, 1996; Henry, 1996).
The samples manufactured for the tests consist of a 0.0254 mm (1 mil) layer of aluminum foil placed on top of the piezoceramic layer using a sprayed adhesive to prevent cracking of the ceramic during testing. Since the thicknesses of the additional adhesive and aluminum foil layers combined are still an order of magnitude lower than that of the piezoceramic and substrate layers, respectively, it is not included in the model used to obtain predicted charge values. Since the adhesive must be cured at temperatures near to the Curie temperature of PZT-5A, it must be repoled after manufacture to restore the transversely isotropic configuration. Each device was repoled at 50 V/mil at a ramp rate of 50 V/s for 4-s intervals using a computer-operated poling amplifier.
The resulting samples have the dimensions and composition as shown in Table 1. The samples having the greatest substrate thickness (samples 3-a,b,c) have lower center heights than their thinner counterparts.
Figure 8. PZT-5A, 0.254 mm-thick substrate samples (1-a,b,c).
Figure 10. PZT-5A, 0.381 mm-thick substrate samples (3-a,b,c).
Figure 9. PZT-5A, 0.305 mm-thick substrate samples (2-a,b,c).
The length and width measurements are made using the dimensions of the aluminum foil layer, which is cut to fit inside the dimensions of the PZT layer to avoid shorting out the device if contact is made between the aluminum and steel layer. The surface area of the aluminum layer on the samples is taken to be effective surface area of the positive electrode.
The samples outlined above will be respectively referenced using the designation identified in the left-most column, where a, b, and c refer to the size categories in descending order within each set of samples having the same substrate thickness. It is important to note that as shown in Figure 9, sample 2-a is defective in that it was returned from the manufacturer with a tear in the aluminum foil layer covering the PZT. Therefore, results of only samples 1-x and 3-x will be discussed.
CHARGE MEASUREMENT
The charge developed on the aluminum cover and the stainless steel substrate can be measured by shorting the electrodes by placing a resistor across them, and measuring the voltage drop, V, across the resistor (Chopra, 2002). Since PZT is considered to be a high impedance source, the resistor should be fairly large as well, however, it cannot be greater than the input resistance of the measuring device. For this reason, the tips of a 10 : 1 oscilloscope probe are directly connected to the electrodes to make the voltage measurement, and the 10 M internal resistance (9 M from the probe and 1 M from the oscilloscope) is considered to be the resistor that is placed across the electrodes of the PZT unimorph.
Figure 11 shows that the voltage signal from a deflected PZT unimorph consists of a negative peak at the point in time where the beam is first deflected, and then a positive peak when the weight is lifted. However, the polarity of the voltage signal depends on how one connects the wires to the electrodes and the alignment of the polarization vector of the PZT. In an actual
application, the output signal should be rectified first before it is connected to charge collection circuitry.
The current drawn in this measurement can be calculated by integrating the voltage measurement with respect to time. Using this method, the generated charge can be calculated as
q ¼ Z
Idt ¼ 1 R Z
Vdt ð19Þ
where the resistance is the internal 10 M resistance of the oscilloscope probe.
It is important to note that the method used here is not the most accurate way to make charge measure- ments off of the high impedance, high voltage, and low current source (PZT unimorphs) used here. A better solution involves the development of highly sensitive charge amplifiers, where the signal from PZT device is amplified before being sent into an oscilloscope for display. The use of charge amplifier circuits has been demonstrated for charge measurements of PZT devices in dynamic applications where resonant peaks are observed (Danak et al., 2003). However, in order to obtain a near exact measurement of charge in quasi- statically excited PZT devices implemented here, the circuitry for appropriate charge amplification must be very precise and is, therefore very costly. For these reasons, a simple method using a resistor and an oscilloscope was adopted.
EXPERIMENTAL RESULTS
Two different mechanical loadings are applied in the experiment. In the first set of tests, the PZT laminate samples are placed on an insulated, flat steel plate and deflected using a 5 lb (22 N) weight (see Figure 12). This weight remains on the laminate until the current flow stops. The weight is then removed to obtain another signal from the device. The area under the voltage versus time curves is sized and averaged to calculate the charge developed in the device. Next, measurements are taken when a female of 100 lb steps on the sample with the heel (Figure 13). The full weight of the person is placed on it just as it occurs when one is walking. The heel is then removed in a similar manner.
Equation (18) is used to obtain the predicted charge generation values for nine samples listed in Table 1.
These values are compared to those, which are obtained experimentally. Note that the predicted values shown correspond with the numerical value for the force necessary to fully flatten the beam as predicted from Equation (17) (i.e., force required to deflect the center of the beam by the value of its center height). Also, although a uniformly distributed load is assumed in the model, in the actual experiment, the load starts as a point load and then spreads to a uniform load as the
-40 -20 0 20 40 60
-2 0 2 4 6 8 10
Seconds
Volts
Figure 11. Voltage signal from deflection of PZT unimorph.
beam becomes flattened. Nonetheless, the uniform load approximation in the model does not cause any error because the generated charge depends only on the final strain distribution along the PZT and the loading condition in the experiment approaches to the uniform load as in the model.
Figures 14 and 15 show the charge generation data for beams with the same substrate thickness and Figure 16
is for beams with similar length but different substrate thicknesses. In the figures, experimentally obtained values for both the 5 lb (22 N) and 100 lb (445 N) tests are shown alongside the predicted values. Note that since 2-a was defective, no comparison was made including 2-a.
As can be seen in Figure 14, the relationships between charge generated in beams 1-a, 1-b, and 1-c follow the same trend for all three data sets – the 5 lb, 100 lb experimental tests, and the predicted charge values. It is noted that all three data sets show that charge generated in 1-b as the greatest, followed by the charge developed in sample 1-c, with the charge in 1-a being the least,
Figure 12. Deflection using a 5 lb (22 N) weight.
Figure 13. Deflection using a 100 lb (445 N) weight.
0.00E+00 2.00E-06 4.00E-06 6.00E-06 8.00E-06
5 lb 100 lb Predicted
Charge generated (C)
1-a 1-b 1-c
Figure 14. Comparison of predicted and experimental charge generated for 0.254 mm-thick substrate samples.
0.00E+00 2.00E-06 4.00E-06 6.00E-06 8.00E-06
5 lb 100 lb Predicted
Charge generated (C)
3-a 3-b 3-c
Figure 15. Comparison of predicted and experimental charge generated for 0.382 mm-thick substrate samples.
0.00E+00 2.00E-06 4.00E-06 6.00E-06 8.00E-06
5 lb 100 lb Predicted
Charge generated (C)
1-b 2-b 3-b
Figure 16. Comparison of predicted and experimental charge data for different thickness substrate samples.
despite having the greatest length. This predicted behavior can be attributed to the fact that sample 1-b is 36% greater in width than sample 1-a, and as can be seen in Figure 6, increasing width has a greater effect on increasing the charge generating capability of the device than does increasing length.
Figure 15 shows that the greatest charge is predicted and experimentally obtained in sample 3-c in both the 5 lb (22 N) and 100 lb (445 N) tests. The trend is the opposite of what is intuitively expected since generally, longer samples are expected to generate more charge, especially since even the width is greater in the longer samples. In this case, it is found that the greatest strain is still predicted to be experienced in the shorter samples, and therefore, these beams generate the greatest charge.
Unlike previous two cases, Figure 16 shows a comparison of predicted and actual charge generation for samples with similar size but substrates of different thicknesses. In the figure, a clear similarity is identified between the predicted values and those in the 5 lb case.
However, the magnitudes for 1-b and 2-b are switched in 100 lb case, which is accounted for by the error in our charge measurement process. As one can see, the predicted (analytical) case shows that while there is an increase in charge for the thicker substrate, the values of the predicted charge for samples (1-b and 2-b) are quite close. Thus a small amount of error in the measurement process can show the variation given in the figure.
In general, while the results show a significant difference between experimental and predicted charge values, the experimental results do verify the trends predicted by the mathematical model. This is important since it can be used in the development of an optimized charge generating device for placement in a confined volume, whether it is a shoe insert or otherwise.
Now, in order to use an optimized PZT unimorph as an energy generator, it must be coupled with appro- priate circuitry that can collect the generated charge from the unimorph, and distribute a constant voltage to a loading device.
CIRCUITRY FOR CHARGE COLLECTION
Optimally designed piezoceramic unimorphs can be connected to the charge-collection circuitry shown in Figure 17 to examine the performance of these energy generators.
This circuit is primarily based on the work of Shenck (1999), with modifications made to take into account the use of a unimorph having much lower source voltage, as well as other changes with wiring of the comparators and diode selection. The basic circuitry takes into account the issues of having a high voltage source with minimal source current. The circuit is designed to switch the maximum amount of power from the decaying
Figure 17. Energy harvesting circuit.
envelope of the source signal by sensing the source signal peak. As the PZT is depressed charge is stored.
This charge is then used to power the components of the circuit, thus no external power supply is needed.
Appropriate bootstrapping is included to prevent the active control components from turning on before enough power is available in the storage capacitor.
In addition, high frequency switching is implemented to allow efficient and effective use of the energy source by only loading it when necessary. Subsequent switching losses are minimized by keeping the oscillator on/off duty cycles low (approximately 50%), thereby reducing energy storage requirements. An in-depth explana- tion of the components of the circuit can be found in Danak (2003).
The circuit was tested and the results revealed that this circuitry could be combined with PZT unimorphs to produce a 3 V (1 mA) output as long as the uni- morph is being continuously activated in 31-mode at approximately 1 Hz.
ILLUSTRATIVE EXAMPLE
The rules of thumb developed in a previous section can be used in designing a more efficient energy generating PZT unimorph. Alternatively, Equation (18) can also be utilized directly in a numerical optimization algorithm with appropriate design constraints. In order to demonstrate how to optimize the parameters of a PZT unimorph that fits in a confined volume, an example is presented here. In keeping with the theme of energy generation using PZT devices in shoes, the optimized device is assumed to fit in the confined volume of an athletic shoe. The dimensions of the design (heel) space of a Men’s size 8.500 shoe is shown in Table 2.
Using the rules of thumb, the dimensions of an optimized generator to fit within the confined volume of a shoe as defined in Table 2 can be found as shown in Table 3.
The materials used are kept consistent with those used in this study. Since increasing the width is more effective than increasing the length, the unimorph needs to be placed across the heel area such that the width of the unimorph is the same as the length of the confined space.
Determining the center height is a matter of comfort due to the fact that while a large value is desirable for charge generation, increasing the center height leads to large travel of a heel and thus significant discomfort. The thickness of PZT is assumed to be 0.254 mm as was assumed throughout this study. Since a large substrate thickness is desired in charge generation, the maximum thickness that can be almost flattened by a weight of 160 lb (713 N) was selected for an optimal thickness of the substrate. Note that this is just an example of a way in which the knowledge acquired from this study can
be implemented for maximizing the charge generation capability of initially curved PZT unimorphs.
CONCLUSIONS AND FUTURE WORK
The main goal of this study was to develop a method- ology for the development of more efficient d31 mode charge generators. Inherent in this goal is the develop- ment of ‘rules of thumb’ to aid practitioners in the manufacture of a charge generating PZT device. Toward that end, charge generation and harvesting using an initially curved PZT unimorph structure was studied.
Using linear piezoelectric theory, composite laminate theory, and shell theory, an analytic expression for charge in terms of geometry, material properties, and input force was developed. This equation was then employed in numerical parametric studies to determine the effect of different variables on maximizing charge generation. To verify the theoretical model of the device, nine samples were made and tested for 5 lb and 100 lb mechanical loads. Experimental results showed that there exists a strong correlation between the theoretical prediction and the experimental data ensuring the validity of the derived model. Finally, the feasibility of the use of PZT unimorphs as charge generators was verified by incorporating a sample PZT unimorph in an energy harvesting circuit designed to distribute a steady 3 V output in response to mechanical excitation of the PZT device. It was successfully demonstrated that this type of device could be utilized for harvesting kinetic energy associated with human walking, which would be wasted otherwise.
Although the theoretical model could predict the general trend in charge generation, it was observed that there exists numerical discrepancy between experi- mental and predicted results. The primary source of Table 3. Optimization sample of PZT unimorph for confined volume of men’s size 8½ shoe.
PZT type PZT-5A
Substrate material Stainless steel
Substrate thickness 0.519 mm
Length 65.00 mm
Width 70.00 mm
Center height 3.50 mm
Predicted charge 60.49 106C
Table 2. Confined heel space of a men’s size 8.500shoe.
Men’s 8.500shoe
Length 7.0 cm
Width 6.5 cm
error is associated with the method used for the charge measurement. Also, the current model is based on the two-layer curved beam model, which includes the subs- trate and the PZT layers. In contrast, the actual samples contained a thin aluminum foil layer in addition to the ceramic and substrate, in order to help prevent cracking of the ceramic during testing. This was not included in the theoretical model since the foil thickness was an order of magnitude less than that of the PZT. However, other studies have revealed that removal of the foil layer results in an increase in the amount of energy generated (Mossi et al., 1998). The thin adhesive layer between the PZT and the substrate could also have decreased the induced strain in the PZT leading to lower charge values than predicted. Another possibility is that some of the mechanical and piezoelectric parameters such as the Young’s modulus of the substrate and the piezoelectric constants of PZT layer could be changed due to the high-temperature manufacturing process. All these possible error sources will be examined as future work in order to obtain a more accurate theoretical model.
Another issue, which will be considered further in the future investigation, is the energy harvesting circuitry presented in Figure 17, which was based on the work of Shenck (1999). This circuit was designed to collect the high voltage-decaying signal from a PZT unimorph excited at 1 Hz, and distribute a constant 3 V output.
During our investigation, a number of losses were inherent in the existing circuit, particularly in the high- frequency switching converters as well as in the ICs as they are switching from one state to another (Shenck, 1999). These losses cause the steady 3 V generated by the voltage regulator to decrease quite readily during pauses in the excitation of the unimorph. Therefore, an improved circuit needs to be designed to resolve these issues.
REFERENCES
Amirtharajah, R. and Chandrakasan, A. 1997. ‘‘Self-powered Low Power Signal Processing,’’ In: 1997 Symposium on VLSI Circuits Digest of Technical Papers, pp. 25–26.
Andersen, E.H. 1989. ‘‘Piezoceramic Induced Strain Actuation of One- and Two-dimensional Structures, MS Thesis, Massachusetts Institute of Technology, Cambridge, MA.
Bryant, R.G. 1996. ‘‘LaRCTM-SI: A Soluble Aromatic Polyimide,’’
High Performance Polymers, 8(4):607–615.
Chopra, I. 2002. ‘‘Review of State of Art of Smart Structures and Integrated Systems,’’ AIAA Journal, 40(11):2145–2187.
Danak, A.D., Yoon, H.-S. and Washington, G.N. 2003.
‘‘Optimization of Electrical Output in Response to Mechanical Input in Piezoceramic Laminated Shells,’’ In: ASME International Mechanical Engineering Congress & Exposition, Washington, DC, November 15–21, 2003.
Danak, A.D. 2003. ‘‘Optimization of Harvested Energy in Piezoceramic Shells,’’ MS Thesis, Ohio State University.
Gonzalez, J., Rubio, A. and Moll, F. 2001. ‘‘A Prospect on the Use of Piezoelectric Effect to Supply Power to Wearable Electronic Devices,’’ In: ICMR 2001, Vol. 1, Akita, Japan, October 2001, pp. 202–207.
Halpin, J.C. 1992. Primer on Composite Materials, pp. 43–151, Technomic Publishing Company, Lancaster, PA.
Hausler, E. and Stein, L. 1984. ‘‘Implantable Physiological Power Supply with PVDF Film,’’ Ferroelectronics, 60:277–282.
Henry, K. 1996. ‘‘NASA Rolls Out Award-Winning THUNDER,’’
NASA NEWS, Release No. 96-154.
IEEE Standard on Piezoelectricity, 1987. ANSI/IEEE Std 176-1987.
ITRS Committee, 2001. ‘‘International Technology Roadmap for Semiconductors,’’ November 2001.
Jaffe, B., Cook, W.R. and Jaffe, H. 1971. Piezoelectric Ceramics, pp. 1–21, Academic Press, New York, NY.
Kasyap, A., Lim, J., Ngo, K., Kurdila, A., Nishida, T., Sheplak, M. and Cattafesta, L. 2002. ‘‘Energy Reclamation from a Vibration Piezoceramic Composite Beam’’ In: 9th International Congress on Sound and Vibration, Orlando, FL, July 2002.
Kraus, H. 1967. Thin Elastic Shells, John Wiley and Sons, Inc., New York, NY.
Kymissis, J. et al. 1998. ‘‘Parasitic Power Harvesting in Shoes,’’ In:
Proceedings of the 2nd IEEE International Symposium on Wearable Computers, October 19–20, Pittsburgh, PA, pp. 132–139.
Mossi, K.M., Selby, V.G. and Bryant, R.G. 1998. ‘‘Thin-Layer Composite Unimorph Ferroelectric Driver and Sensor Properties,’’
In: Materials Letters, Vol. 35, pp. 39–49.
Ottman, G.K. et al. 2002. ‘‘Adaptive Piezoelectric Energy Harvesting Circuit for Wireless Remote Power Supply,’’ IEEE Transactions on Power Electronics, 17(5):669–676.
Qatu, M. 1989. ‘‘Free Vibration and Static Analysis of Laminated Composite Shallow Shells,’’ PhD Dissertation, The Ohio State University, Columbus, OH.
Reissner, E. 1946. ‘‘Stresses and Small Displacements of Shallow Spherical Shells,’’ Journal of Mathematical Physics, 25:80–85.
Shenck, N.S. 1999. ‘‘A Demonstration of Useful Electric Energy Generation from Piezoceramics in a Shoe,’’ MS Thesis, Massachusetts Institute of Technology, Cambridge, MA.
Sodano, H. et al. 2002. ‘‘Electric Power Generation using Piezoelectric Devices,’’ In: 13th International Conference on Adaptive Structure and Technologies, Potsdam/Berlin, Germany, October 7–9, 2002.
Starner, T. 1996. ‘‘Human-Powered Wearable Computing,’’ IBM Systems Journal, 35(3,4):618–629.
Tzou, H.S. 1993. ‘‘Piezoelectric Shells: Distributed Sensing and Control of Continua,’’ In: Solid Mechanics and its Applications, Kluwer Academic Publishers, Boston, MA.
Tzou, H.S. and Anderson, G.L. 1992. ‘‘Intelligent Structural Systems,’’
In: Solid Mechanics and its Applications, pp. 75–167, Kluwer Academic Publishers, Boston, MA.
Westervelt, R. et al. 2000. ‘‘Power Sources for Ultra Low Power Electronics,’’ June 2002, JASON Report # JSR-98-130.
