Enhancing power generation of piezoelectric bimorph device through geometrical optimization

Abstract

In this paper, it is demonstrated that the power output of a bimorph energy harvesting device can be significantly enhanced through geometrical optimization. The results of the study show that the maximum power is generated when the length of piezoelectric layer is 1/3 and the length of proof mass is 2/3 of the total device length. An optimized device with a total volume of approximately 0.5 cm³ was fabricated and was experimentally characterized. The experimental results show that the optimized device is capable of delivering a maximum power of 1.33 mW to a matched resistive load of 138.4 kΩ, when driven by a peak mechanical acceleration of 1  g at the resonance frequency of 68.47 Hz. This is a very significant power output representing a power density of 2.65 mW/cm³ compared to the value of 200 μW/cm³ normally reported in literature.

Graphical abstract

Keywords

geometrical optimization / piezoelectric material / bimorph / energy harvesting / power

1 Introduction

Over the past decades, there has been significant reduction in size, cost and power consumption of complementary metal-oxide-semiconductor (CMOS) based devices, which has significantly spurred the recent upsurge in energy harvesting research efforts, particularly for the development of self-sufficient wireless sensor systems [1–3]. Traditionally, wireless sensor nodes are powered by onboard batteries. The finite energy stored in the batteries of these sensor nodes remains a limit on the large scale deployability of wireless sensor networks for applications in industry and places geographically difficult to access. Energy harvesting devices could typically scavenge energy from the environment and power the wireless sensor electronics for their entire life, possibly eliminating the need for conventional electrochemical batteries. Vibration energy harvesting is attractive because vibrations are one of the most ubiquitous energy sources present in the environment. Thus, vibrations are a guaranteed environmental friendly and clean source of energy [4]. There are three transduction mechanisms commonly used for converting mechanical vibrations into electrical energy, namely electromagnetic, piezoelectric and electrostatic. Due to their simplicity of design, piezoelectric energy harvesting devices have received substantial research interest [5,6]. Unlike electrostatic harvesters, piezoelectric harvesters require no external voltage source, and are compatible with CMOS and micro-electro-mechanical systems (MEMS) technologies [7–10]. Compared to electromagnetic harvesters that tend to be bulky and produce a very low output voltage, piezoelectric harvesters are much simpler and more compact in construction, and they generate a much higher voltage [1,2,6,11]. These comparative advantages of piezoelectric energy harvesting devices make them a subject of intense research.

A typical piezoelectric energy harvesting device is a bimorph cantilever with an attached seismic proof mass. Such a device configuration, working in the first bending mode with a lower stiffness, offers a lower resonant frequency which can be easily matched to the target ambient vibration frequency for maximum power generation [12,13]. The energy harvesting beam device is located at a vibrating host structure and the dynamic strain induced in the piezoelectric material due to base excitation results in an alternating voltage output across the electrodes. The electrodes covering the piezoelectric material are connected to an appropriate power conditioning circuit to enable it to drive an external resistive load.

Piezoelectric energy harvesting devices are capable of scavenging a power output of 1 to 200 μW/cm³ which is sufficient enough to power wireless sensor devices with average consumption levels in the order of 100 μW [4,6,14]. Nevertheless, the power delivered by these energy harvesting devices is still low compared to the levels currently compatible with the majority of low power electronic devices [4–14]. An improved power output of these devices is critical to widening the application scope of energy harvesting technology. While researches have focused on power increases through optimization of resistive loads [15,16] and switching techniques [17], enhancement of power through mechanical design optimization has been grossly neglected [18]. Due to lack of research on mechanical design optimization, critical questions remain unanswered concerning the geometrical design of piezoelectric energy harvesters. Furthermore, lack of general guidelines for proper energy harvester beam design and geometrical optimization procedures make the design of energy harvesters very challenging. The traditional approach often adopted by most researchers is to fabricate a piezoelectric composite beam and then add a proof mass to tune the device to the desired resonance frequency. Numerical techniques using analytical and finite element methods are employed to meet specified design constraints. While such approaches are popular, they are not reproducible under different design contexts and typically only result in limited specific designs that cannot be generalised. It is not enough to choose the proof mass for tuning the device to a particular resonance frequency; but the choice of the proof mass dimensions must be informed by the need to optimize power generation. What is needed is a mechanical design procedure that can offer general guidelines and, at the same time, meet specific engineering system constraints.

This paper is dedicated to proposing a new optimized design for a piezoelectric bimorph energy harvesting device with a proof mass. The length of both the piezoelectric layer and the proof mass that optimized the power generated at a specified resonance frequency and device volume were studied using numerical analysis in MAPLE^® software. Using the NLPSolve command in MAPLE^®, the geometrical dimensions of the harvesting device were optimized. Finally, an optimized prototype device with a total volume of approximately 0.5 cm³ was fabricated and was experimentally characterized. The results demonstrate that the power generated by a series bimorph energy harvesting device is maximized when the piezoelectric coverage length is 1/3 and the proof mass length is 2/3 of the total device length.

2 System modelling

2.1 Structure of the piezoelectric energy harvesting device

The structure of a bimorph piezoelectric energy harvesting device with proof mass is shown in Fig. 1. The proof mass width is equal to beam width and is given by W. The piezoelectric layer length is L_b while the proof mass length is L_m. The piezoelectric layer thickness is represented by t_p while the substrate thickness by t_sh. The total height of the proof mass is h_m. Table 1 defines the parameters and material properties used in the mathematical development of the geometrical optimization.

2.2 Modeling the power output

The power (P) that can be extracted by an energy harvesting device and delivered to a normalised resistive load (ψ) can be modeled by Eq. (1) [19,20]

(1) P={\displaystyle \frac{m{A}^{\mathrm{2}}}{\mathrm{2}{\omega }_{\mathrm{r}}}}{\displaystyle \frac{{\mathit{\Omega }}^{\mathrm{2}}\psi K^{\mathrm{2}}}{{\left({\mathit{\Omega }}^{\mathrm{2}}-\mathrm{1}\right)}^{\mathrm{2}}+{\mathit{\Omega }}^{\mathrm{2}}{\psi }^{\mathrm{2}}{\left({\mathit{\Omega }}^{\mathrm{2}}-\mathrm{1}-K^{\mathrm{2}}\right)}^{\mathrm{2}}+\left[\mathrm{1}/Q_{\mathrm{m}}+\mathrm{2}\mathit{\Omega }\psi (K^{\mathrm{2}}+\mathit{\Omega }\psi /\left(\mathrm{2}{Q}_{\mathrm{m}}\right))\right]/Q_{\mathrm{m}}}},

where ω _r is the short circuit resonance; m, the effective mass of the device; A, the peak acceleration of the harmonic vibration; Ω, the normalized resonance frequency; K, the effective electromechanical coupling factor; and Q _m, the mechanical quality factor. The normalized resistive load can be related to the resistive load (R) by ψ = RC _p ω _r, where C _p is the capacitance of the piezoelectric device. For a device operating at resonance Ω =1, Eq. (1) can be reduced to

(2) P={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\displaystyle \frac{m{A}^{\mathrm{2}}R{C}_{\mathrm{p}}{K}^{\mathrm{2}}}{R^{\mathrm{2}}{C}_{\mathrm{p}}^{\mathrm{2}}{\omega }_{\mathrm{r}}^{\mathrm{2}}{K}^{\mathrm{4}}+\left[\mathrm{1}/Q_{\mathrm{m}}+\mathrm{2}R{C}_{\mathrm{p}}{\omega }_{\mathrm{r}}(K^{\mathrm{2}}+R{C}_{\mathrm{p}}{\omega }_{\mathrm{r}}/\left(\mathrm{2}{Q}_{\mathrm{m}}\right))\right]/Q_{\mathrm{m}}}}.

2.3 Modeling the resonance frequency

The short circuit resonance frequency (ω _r) is related to the open circuit resonance frequency (ω _a) by

(3) {\omega }_{\mathrm{a}}={\omega }_{\mathrm{r}}{\left(\mathrm{1}+K^{\mathrm{2}}\right)}^{\mathrm{1}/\mathrm{2}}.

The short circuit resonance is defined by

(4) {\omega }_{\mathrm{r}}=\sqrt{k/m},

where effective spring constant k and the effective mass m are defined by Eqs. (5 and 6) respectively [19,21]

(5) k={\displaystyle \frac{\mathrm{3}{c}_{\mathrm{e}\mathrm{f}\mathrm{f}}{I}_{\mathrm{e}\mathrm{f}\mathrm{f}}}{L_{\mathrm{b}}^{\mathrm{3}}\left(\mathrm{1}+\mathrm{3}{L}_{\mathrm{m}}/\mathrm{2}{L}_{\mathrm{b}}+\mathrm{3}{L}_{\mathrm{m}}^{\mathrm{2}}/\mathrm{4}{L}_{\mathrm{b}}^{\mathrm{2}}\right)}},

(6) m={\displaystyle \frac{\mathrm{33}{m}_{\mathrm{b}}\left(\mathrm{1}+\mathrm{91}{L}_{\mathrm{m}}/\mathrm{66}{L}_{\mathrm{b}}+\mathrm{21}{L}_{\mathrm{m}}^{\mathrm{2}}/\mathrm{44}{L}_{\mathrm{b}}^{\mathrm{2}}\right)/\mathrm{140}+m_{\mathrm{t}}\left(\mathrm{1}+\mathrm{3}{L}_{\mathrm{m}}/L_{\mathrm{b}}+\mathrm{63}{L}_{\mathrm{m}}^{\mathrm{2}}/\mathrm{16}{L}_{\mathrm{b}}^{\mathrm{2}}+\mathrm{21}{L}_{\mathrm{m}}^{\mathrm{3}}/\mathrm{8}{L}_{\mathrm{b}}^{\mathrm{3}}+\mathrm{3}{L}_{\mathrm{m}}^{\mathrm{4}}/\mathrm{4}{L}_{\mathrm{b}}^{\mathrm{4}}\right)}{{\left(\mathrm{1}+\mathrm{3}{L}_{\mathrm{m}}/\mathrm{2}{L}_{\mathrm{b}}+\mathrm{3}{L}_{\mathrm{m}}^{\mathrm{2}}/\mathrm{4}{L}_{\mathrm{b}}^{\mathrm{2}}\right)}^{\mathrm{2}}}},

where the quantities are defined by the expressions given in Tables 1 and 2.

3 Numerical study and optimization procedure

The power generated by the device and the resonance frequency can be written as functions of material properties and geometrical parameters defined in Tables 1 and 2. The thicknesses of piezoelectric material and substrate material are set in this paper as input design parameters. The total device length and the space envelop restrictions are determined by the application space of the particular device. A high density material is ideal for use as a proof mass since it implies that a greater mass value is achievable in a small space hence a small compact device is realized easily. The current study employs lead metal because it was the readily material available with a high density value available for experimentation, otherwise a more dense and environmentally safer material like tungsten alloy could have been employed. For microscale devices the total device volume (space envelope) is usually set at 1 cm³. In this study, the energy harvesting device is intended to be optimized within a total volume of approximately 0.5 cm³.

3.1 Optimization procedure

An overview of the design method used for geometrical optimization is illustrated in Fig. 2. The values in Table 1 are used to simplify the expressions defined in Table 2. The simplified expressions in Table 2 are then used to simplify Eqs. (4–6). This procedure is accomplished by using the computational power of the symbolic software MAPLE^® (Version 10 [22]). For this numerical study, the target short circuit resonance frequency is 65 Hz (or equivalently an open-circuit resonance frequency of approximately 68 Hz). The total length of the device is set to 28.08 mm which corresponds to the clamped length of the stainless steel substrate available for the design of the prototype device. The ratio of the piezoelectric length to the total device length (denoted by α ) is taken as the parameter of interest.

The different device geometries (i.e. different sets of L _b , L _m , h _m and α) that satisfy the condition of short circuit resonance of 65 Hz and total device length of 28.08 mm is obtained, as presented in Table 3. The next task is to find which of these device geometries can optimize the power generated by the device. To do so, each of the different geometries and their corresponding values of L _b , L _m , h _m and α are used in Eq. (2) in the MAPLE^® environment. An additional constraint is imposed that the overall device volume should be (0.50±0.01) cm³. Then, a plot showing variation of the power density as a function of the geometrical parameter α is established. The NLPSolve command in MAPLE^® is used to solve this constrained optimization for the range of α.

3.2 Optimization results

The different device geometries that satisfy the set resonance frequency and the total device length are presented in Table 3. It can be observed from the results in Table 3 that increasing the value of α can lead to a decrease in the length of proof mass (L_m) and an increase in piezoelectric layer length (L_b). The value of the total height of the proof mass (h_m) also decreases with increasing α to keep the resonance frequency value constant.

Using the different geometries in Table 3, the maximum power that could be delivered to a resistive load at resonance and under 1 g peak acceleration is determined as demonstrated in Fig. 3.

It can be observed from Fig. 3 that the power density is optimum in the region of 0.3<α <0.35. In this region, á should be such that the device volume fits into the space envelope set to (0.50±0.01) cm³ and that the open circuit resonance frequency remains at 65 Hz. The NLPSolve command in MAPLE^® is used to solve for this constrained optimization and results are tabulated in Table 4.

The results in Table 4 suggest that the value of \alpha =\mathrm{0.333}\approx \mathrm{1}/\mathrm{3} gives the optimum power output. This is an interesting result since it gives a clear guideline that the optimum power is generated when the piezoelectric layer is a third of the total beam length. The proof mass takes the remaining 2/3. If the length of piezoelectric material is set to values greater than 1/3, the additional material significantly reduces the power density of the device due to increased capacitance and reduced piezoelectric coupling. This is contrary to the common practice where the length of piezoelectric layer is made to dominate the total length of the energy harvesting device.

4 Experimental studies

4.1 Fabrication of energy harvester

A prototype energy harvesting device with a width W = 4 mm and the optimized dimensions presented in Table 4 was fabricated. The piezoelectric material model number PSI-5H4E with nickel-plated electrodes from Piezo Systems Inc. (USA) was bonded to the stainless steel substrate using conducting two part epoxy glue from Circuit Works (USA). Super Glue was used to attach the lead proof mass to the beam. Please note that the geometrical dimensions are to within ±0.01 mm as measured using a digital vernier calipers (Engo-HDCD01150). Figure 4 shows two photo shots of the device.

4.2 Experimental setup and procedure

Figure 5 displays the schematic diagram of the experimental setup. A simple low cost custom made electromagnetic shaker was driven by the signal from the function generator (Universal Test System MS9150-Metex Instruments) and the dual power amplifier (Philip Harris, England) to supply a sinusoidal force of desired magnitude and frequency used to excite the device. Screws were used to fasten the device to the aluminium fixture on the shaker. The acceleration level was measured using the ADXL202 accelerometer (Analogue Devices, USA), which has a typical sensitivity of 312 mV/g (where 1g = 9.81 m/s²) when operating from a 5 V power supply. The accelerometer output signal and the output voltage signal from the prototype device were monitored by a digital storage oscilloscope (ISOTECH-IDS-8062). A Fluke 116 multimeter (DMM) was used to measure the root mean square (rms) voltage across the load resistance R. The power output under different load resistances R were calculated using the formula P=V²/R , where V is the output rms voltage.

4.3 Experimental results

The resonance frequency was determined by measuring the open-circuit voltage of the device using the oscilloscope for different excitation frequencies. Figure 6 indicates that the first resonance frequency occurs at approximately 68.47 Hz. This value conforms very well with the open-circuit resonance predicted by the theoretical model as shown in Table 5. Figure 7 exhibits the typical open circuit voltage of the device and the waveform of the accelerator signal for excitation of peak acceleration, A = 0.5  g.

The plot of power and voltage as a function of load resistance (R) shows very good agreement between the model results and experimental results (Fig. 8 and Table 6). A peak power of 1.33 mW delivered to an optimum load resistance of 138.4 kΩ and excitation of 1 g was experimentally realized at resonance. This is a very significant power output especially in comparison to other designs reported [4,23–27] (see Table 5).

5 Discussion

The study presented a simple but effective geometrical optimization procedure that maximizes the power delivered to a resistive load. It is clear that power generated by a piezoelectric energy harvesting device is very dependent on first resonance frequency of the device, and the resonance frequency changes as the geometry is altered. The geometrical parameter α was employed as the control parameter that enabled different harvester geometries to be generated, with each geometry having a short circuit resonance frequency of 65 Hz and a total device length of 28.08 mm. The most interesting results were observed when examining the effects of piezoelectric layer and proof mass lengths on the energy delivered to the resistive load. An increase in piezoelectric length was not accompanied by a corresponding increase in the power generated. In fact, the results showed that there exists an optimum value of α (= 0.333) that maximizes the power output. This value of α corresponds to an optimum piezoelectric layer length of 1/3 and an optimum proof mass length of 2/3 of the total beam length. If the piezoelectric length is increased beyond this value, the power output reduces. This observation may be due to the increased capacitance of the devices and the corresponding reduction in piezoelectric coupling as the piezoelectric coverage is increased [28,29]. The device with the optimized dimensions was fabricated and was experimentally characterized. The experimental results agreed very well with the results expected from the model simulation. The predicted open circuit resonance frequency of the device differed by less than 1% from the value determined by the experiment (see Table 5). The power density of the device is 2.65 mW/cm³, which is a very encouraging value compared to the other values reported [4,23–27] as shown in Table 6.

6 Conclusions

This paper has presented a geometrical optimization procedure that can be used to enhance the power output of a series bimorph energy harvesting device. The fabricated optimized prototype device was experimentally characterized and showed that a maximum power density of 508 μW/cm³ could be delivered to a matched resistive load at resonance and under an ambient mechanical acceleration of 1  g. The design procedure proposed significantly simplifies the process of identifying the critical parameters and increases the power output while reducing the amount of piezoelectric active material employed.

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