A Raindrop Energy Harvester for Application to Microrobots

Abstract

The limitations of traditional fossil fuels have prompted researchers to develop new renewable energy technologies. Raindrop impact energy has become a research hotspot in the field of energy harvesting due to its wide distribution and renewability, especially in the self-energy supply of microrobots. The energy harvester is installed on the robot, utilizing piezoelectric-energy-harvesting technology to achieve self-energy supply for the robot, but the efficiency of existing raindrop energy harvesters is unsatisfactory. In order to better collect the impact energy of raindrops and broaden the application of piezoelectric energy harvesters in the field of autonomous energy supply of robots, inspired by the vibration generated by raindrop excitation of plant leaves in nature, a raindrop energy harvester for autonomous energy supply for robots was proposed through the bionic leaf design, a mathematical model was established for numerical simulation analysis, and the effects of excitation position, excitation height, petiole length and excitation rate on the output performance of the harvester were analyzed. Numerical simulation and experimental test results show that the piezoelectric energy harvester has a higher output at the excitation position at the tip. The higher the excitation height of the water droplet, the higher the output voltage. Increasing the length of the petiole can significantly improve its performance output, and at the same time, the raindrop excitation rate will also affect its output to a certain extent.

1. Introduction

With the rapid development of modern industries, global energy consumption is increasing, and traditional fossil energy will be exhausted in the near future, and the shortcomings of traditional fossil energy such as small reserves, environmental unfriendliness, low power density and non-renewable nature do not meet the requirements of sustainable development strategy. In the context of global energy transition and green development, the development of new renewable energy technologies, especially innovations in the field of micro-energy harvesting [1,2], is of great significance to promote the optimization of energy structure and meet the energy needs of low-power devices. The wide range of miniaturization, portable electronic devices, and sensor networks presents new challenges and demands for miniaturized energy-harvesting technologies [3,4]. Vibrational energy is widely available in nature, and in recent years, the technology of capturing vibrational energy in the environment and converting it into electrical energy to power microelectronic devices through vibration harvesters has been considered a viable alternative to traditional battery energy supply, especially in the self-supply of microrobots [5,6], through the use of piezoelectric-vibration-energy-trapping technology to achieve energy self-sufficiency and system lightweight, which is of great significance for the development of microrobots. Vibration energy harvesters [7,8,9] are a very promising field of energy-harvesting study, which typically includes piezoelectric [10,11], electromagnetic [12,13], and electrostatic [14,15]. Among them, piezoelectric-energy-harvesting technology is the process of using the characteristics of piezoelectric materials [16] to produce distributed charges when they are subjected to pressure or vibration, and converting them into electrical energy. Piezoelectric vibration energy harvesters have the advantages of high energy density [17], simple structure and easy manufacturing, no heat generation, no electromagnetic interference, long life, environmental friendliness and easy to achieve miniaturization, etc., and thus various scholars are committed to developing new low-cost piezoelectric-vibration-energy-harvesting technology, and a large number of theoretical and experimental studies have been carried out on piezoelectric-vibration-energy-harvesting technology. Wu et al. [18] proposed a frequency conversion electromagnetic shock vibration energy harvester with an adjustable tuning fork structure, and the experimental results showed that the structure could easily adjust the energy harvester frequency of the energy harvester to match the environmental resonance frequency so as to achieve frequency conversion without reducing the energy conversion efficiency and output power of the energy harvester. With the further deepening of the research on energy-harvesting technology, in order to improve the environmental adaptability of energy harvesters, more and more scholars have begun to study the bionic structure [19,20].

In order to improve the directional adaptability of the energy harvester, Han et al. [21] proposed an adaptive energy harvester inspired by mosquito wings for multi-directional vibration and introduced an adaptive rotation structure to achieve directional adaptive rotation. Qian et al. [22] designed a non-magnetic, bistable piezoelectric energy harvester inspired by the bistable structure of Venus flytrap in nature, which used the mutual restraint of the free ends of two sub-cantilever beams with pre-displacement to enable the two sub-cantilever beams to bend in two directions and produce bending and torsional deformation at the same time so as to obtain high mechanical potential energy. When a leaf is subjected to an external force, such as wind or raindrops, it deforms to convert that force into its own motion, which can be used for mechanical to electrical energy conversion applications. Zhou et al. [23] designed a novel biomimetic Diptera energy harvester inspired by the flight movement of Diptera, and the study showed that the structure achieved nonlinear and broadband energy harvesting with high power output.

Wang et al. [24] designed a triangular PVDF leaf-shaped piezoelectric energy harvester based on a plant leaf structure with a reticulated leaf vein distribution, and studied and compared the energy-harvesting performance of different leaf vein structures through wind tunnel experiments. Doria et al. [25] reported a new piezoelectric raindrop energy harvester, using a spoon cantilever energy harvester to study the output performance of the energy harvester when filled with water, and the experimental and simulation results showed that the structure can collect more raindrop energy than a simple cantilever piezoelectric energy harvester. In order to efficiently collect raindrop energy, Voon-Kean et al. [26] improved the design of a raindrop-energy-harvesting system, used the energy capture system to carry out experimental tests in the actual rainfall environment, and studied the effects of rainfall parameters including rainfall rate, rainfall amount, raindrop number and raindrop size distribution on the energy capture effect.

In this study, a raindrop energy harvester for autonomous energy supply for robots was designed based on the vibration generated by leaves in the natural environment. A mathematical model of the energy harvester under the conditions of basic excitation and raindrop impact excitation based on the Euler–Bernoulli theory was established, and the performance of the energy harvester in terms of environmental adaptability and output performance was explored by numerical analysis and comparison of experimental test results. The main contents of this study include the following aspects: the second section describes the structure and working principle of the energy harvester; Section 3 shows the process of establishing the mathematical model of the energy harvester; Section 4 shows the verification of mathematical models and experimental tests; Section 5 gives a potential application of the energy harvester; and Section 6 sets out the conclusions of this study.

2. Structure and Working Principle of Energy Harvester

2.1. Energy Harvester Structure

Inspired by the vibration of plant leaves by raindrops, this paper proposes a structural design of a piezoelectric energy harvester for the collection and conversion of raindrop energy, as shown in Figure 1. The main structure of the energy harvester is divided into two parts: the leaf surface is round and the petiole is rectangular. The leaf surface is integrated with the petiole, and when the basic excitation and the water droplet impact excitation, the leaf surface is equivalent to a mass block with a certain mass, the center is at the center of mass point of the leaf surface, and the raindrop excitation area can be increased at the same time. The blades and petioles are cut by electric spark, and the specific material and structural parameters are shown in

Table 1. Size parameters and material properties of piezoelectric energy harvesters.

Parts	Parameter	Symbol	Value	Unit
PZT	Length × width × thickness	Lp × wp × hp	50 × 10 × 0.2	mm
	density	ρp	7200	kg/m3
	Elastic modulus	Ep	58	GPa
	Piezoelectric parameters	e31	−11.6	C/m2
	Dielectric constant	ε33	13.29	nF/m
Petiole	Length × width × thickness	Ls × ws × hs	(80~96) × 15 × 0.4	mm
	Density	ρs	2700	kg/m3
	Elastic modulus	Es	70	GPa
Rounded blades	Radius	R	45~51	mm
Harvesterezoidal blades	Upper bottom	at	64.3~72.8	mm
	Below bottom	bt	77.1~87.4	mm
	Height	Ht	80~102	mm
Triangular blades	Hemline	as	141.4~160	mm
	Height	Hs	80~102	mm

.

As shown in Figure 2, the raindrop energy harvester is installed on the robot device, and the energy trapper is stimulated to produce electrical energy output so that it can realize self-power supply and drive the robot to work.

2.2. Work Principle

In nature, leaves will vibrate when they are excited by external vibration and raindrop impact, and the raindrop energy harvester proposed in this study uses the piezoelectric effect to convert the raindrop impact energy into electrical energy. As shown in Figure 3, when the raindrops hit the energy harvester, the energy harvester will produce sinusoidal attenuation vibration, the impact height and the size of the raindrop will affect the output performance of the energy harvester, and the vibration state generated by the energy harvester will change depending on the impact position.

3. Mathematical Modeling

In order to better study the power generation performance of the piezoelectric energy harvester of bionic blades, a mathematical model of electromechanical coupling was established according to the physical model of the energy harvester, and the mechanical coupling was numerically analyzed.

In this study, the area of the leaf surface of the energy harvester is expressed as follows:

$$S_y=\pi R^2$$

(1)

The leaf surface is equivalent to a tip mass; the blades are all thin slices with uniform mass distribution, and its center of mass is at the center of the circle, and the distance between the center of mass position of the circular leaf (L_y) and the fixed end is denoted as follows:

$$L_y=L_s+{\displaystyle \frac{R}{2}}$$

(2)

When the blades of the energy harvester are excited by the water droplets, the water droplets begin to fall from a certain height, and their speed increases, which will produce an impact force at the moment of contact with the energy harvester, and the piezoelectric beam will then produce a large displacement to do free attenuation vibration. Assuming that the water droplet acts perpendicular to the tip of the bionic blade energy harvester along the central axis of the piezoelectric beam, the bionic blade piezoelectric energy harvester is regarded as a simple cantilever beam mechanism, and the impact force of the water droplet is equivalent to a concentrated force acting at the length L from the fixed end. One end of the energy harvester is fixed to the base, and the other end is subjected to shock excitation and free attenuation vibration. Figure 4 shows a distributed dynamics coupling model and equivalent circuit diagram of a water droplet impact energy harvester.

The Euler–Bernoulli theory is used to establish the coupling equation of motion of the profiler vane piezoelectric energy harvester under the impact of water droplets, as shown in Equation (3), and the coupling circuit equation is as shown in Equation (4):

$$YI{\displaystyle \frac{{\partial }^4{u}_2\left(x,t\right)}{\partial x^2}}+c_{s}I{\displaystyle \frac{{\partial }^5{u}_2\left(x,t\right)}{\partial x^4\partial t}}+m_e{\displaystyle \frac{{\partial }^2{u}_2\left(x,t\right)}{\partial t^2}}+c_a{\displaystyle \frac{\partial u_2\left(x,t\right)}{\partial t}}-\mathsf{\Theta }\left[{\displaystyle \frac{d\delta \left(x\right)}{dx}}-{\displaystyle \frac{d\delta \left(x-L_i\right)}{dx}}\right]V\left(t\right)=F_d$$

(3)

$$C_{pu}{\displaystyle \frac{dV\left(t\right)}{dt}}+{\displaystyle \frac{V\left(t\right)}{R}}=i\left(t\right)$$

(4)

where δ(x) is the Dirac function, and F_d is the impact force of the water droplets. In the process of free fall of the water droplet from a certain height H to the surface of the blade, the water droplet is regarded as a sphere, and Rd is the radius of the water droplet. As a water droplet falls, it experiences an upward drag force and a downward gravitational force, both of which are shown below:

$$F_a={\displaystyle \frac{{\rho }_{a}A{c}_f{v}_d^2}{2}}+{\displaystyle \frac{4\pi }{3}}{\rho }_{a}g{R}_d^3$$

(5)

$$F_g={\displaystyle \frac{4\pi R_d^3{\rho }_{w}g}{3}}$$

(6)

where ρ_a is the density of air (ρ_a = 1.29), pw is the density of water (ρ_w = 1000), c_f (0.45~0.796) is the drag coefficient, which denotes the area of water droplets, as shown in Equation (7).

$$A={\displaystyle \frac{3c_f{\rho }_a}{8{\rho }_w{R}_d}}$$

(7)

When the two forces reach a certain equilibrium, the water droplet will gain its maximum velocity, the final velocity of the impact droplet, which is expressed as follows:

$$v_d\left(h\right)=\sqrt{{\displaystyle \frac{8R_d{\rho }_{w}g}{3c_f{\rho }_a}}\left(1-e^{-{\displaystyle \frac{3c_f{\rho }_a}{4R_d{\rho }_w}}h}\right)}$$

(8)

According to the impulse principle, this force can be expressed as follows:

$$F_d\left(t\right)={\displaystyle \frac{\left(1-\epsilon \right)m_d{v}_d}{\tau }}$$

(9)

where ε is the influence coefficient, and τ is the theoretical time for the water droplets to interact with the contact surface, which is expressed as follows:

$$\tau ={\displaystyle \frac{2R_d}{v_d}}$$

(10)

The modal expansion method is used to solve the equation of motion of the energy-harvesting system under water droplet excitation, and the equation of the free vibration of the energy harvester is shown in Equation (11).

$$YI{\displaystyle \frac{{\partial }^{4}u\left(x,t\right)}{\partial x^2}}+m_e{\displaystyle \frac{{\partial }^{2}u\left(x,t\right)}{\partial t^2}}=0$$

(11)

The u(x,y) expansion is expressed as follows:

$$u\left(x,t\right)={\eta }_j\left(t\right)\phi \left(t\right)$$

(12)

Its dynamic–electromechanical coupling model is represented as follows:

$${\displaystyle \frac{d^2{\eta }_j\left(t\right)}{d{t}^2}}+2{\xi }_j{\varpi }_j{\displaystyle \frac{d{\eta }_j\left(t\right)}{dt}}+{\varpi }_j^2{\eta }_j\left(t\right)+{\chi }_{j}V\left(t\right)=f_2\left(t\right)$$

(13)

$$C_{pu}{\displaystyle \frac{dV\left(t\right)}{dt}}+{\displaystyle \frac{V\left(t\right)}{R_L}}={\displaystyle \sum _{j=1}^{\infty }{\vartheta }_j\frac{d{\eta }_j\left(t\right)}{dt}}$$

(14)

The unit pulse function is used to express the impact force of water droplets. Water drop excitation is expressed as follows:

$$f_2\left(t\right)=F_d\left(t\right)\left[X\left(t\right)-X(t-\tau )\right]$$

(15)

$$X\left(t\right)=\left\{\begin{array}{l}\beta \sin \left({\displaystyle \frac{\pi t}{\tau }}\right) 0\le \mathrm{t}\le \tau \\ 0 \mathrm{t}<0\cup \mathrm{t}>\tau \end{array}\right.$$

(16)

X(t) is the step function and β is the attenuation coefficient.

$${\chi }_j=\theta {\displaystyle \frac{d\phi \left(L_i\right)}{dx}}$$

(17)

After the water droplets excite the blade surface, some of the water droplets will produce splashes, and some will remain on the surface of the piezoelectric beam, which will produce additional mass and affect its frequency. The following expressions introduce additional mass m_d representations:

$$M_e={\displaystyle \frac{m_i{m}_d\left(1+\gamma \right)}{m_i+m_d}}$$

(18)

$${\omega }_j={\left({\displaystyle \frac{{\lambda }_j}{L_i}}\right)}^2\sqrt{{\displaystyle \frac{EI}{\rho A+m_d}}}$$

(19)

The additional mass also has an effect on the damping of the energy harvester, which is shown below:

$${\xi }_j={\displaystyle \frac{C_d}{2m_e{\omega }_j}}$$

(20)

$$C_d={\displaystyle \frac{M_e}{m_i}}={\displaystyle \frac{{\omega }_d^2}{{\omega }_j^2}}-1$$

(21)

where ω_d is the vibration frequency of the energy harvester after the mass of the water droplet is added.

Introducing state parameters X = [X₁ X₂ X₃]^T to solve the mathematical model, the equation of state is as follows:

$$\stackrel{·}{X}=\left[\begin{array}{l}\stackrel{·}{X_1}\\ \begin{array}{l}\stackrel{·}{X_2}\\ \stackrel{·}{X_3}\end{array}\end{array}\right]=\left[\begin{array}{l}\stackrel{·}{\eta \left(t\right)}\\ \stackrel{··}{\eta \left(t\right)}\\ \stackrel{·}{V}\left(t\right)\end{array}\right]=\left[\begin{array}{c}{X}_2\\ -2\xi {\omega }_j{X}_2-{\varpi }_j^2{X}_1-{\chi }_j{X}_3+F_d\left(t\right)\left[X\left(t\right)-X(t-\tau )\right]\\ {\displaystyle \frac{1}{C_{pu}}}\left({\displaystyle \sum _{j=1}^{\infty }{\varphi }_j{X}_2-\frac{X_3}{R_L}}\right)\end{array}\right]$$

(22)

The final equation of the state of the energy harvester is input into MATLAB (MATLAB R2022a) for solving; the dynamic response and output performance of the energy harvester can be obtained through parametric study, and the structure is optimized according to the numerical analysis structure.

4. Experimental Platform Construction and Result Discussion

4.1. Experimental Platform Construction

In Figure 5, a water droplet excitation experimental test system is shown. The test system is mainly composed of a fixed bracket, a slide rail bracket, a dropper, an experimental prototype, an external load resistor, a data acquisition card, and a computer. During the experiment, the experimental prototype was fixed to the fixed bracket to ensure that it remained stable when hit by water droplets. The dropper and slide rail bracket form the water drop impact device. The dropper is placed vertically above the energy harvester and the slide rail is positioned to control the height of the droplet impact to simulate raindrop impact at different speeds and sizes. Similarly, the experimental prototype is connected to an external load resistor and an NI data acquisition card (model NI-9229 (product of Hungary)), which is connected to a computer for data acquisition and output data acquisition through LabVIEW (2021) software.

4.2. Experimental Tests and Numerical Simulation Results Are Analyzed

Inspired by the different degrees of vibration produced by the impact of external wind and raindrops in leaves, the raindrop energy harvester proposed in this study was used to collect raindrop energy through bionic blades for autonomous energy supply, Firstly, in order to research the variation in the output power of the harvester with resistance more efficiently, the harvester was installed on the excitation test platform, the excitation acceleration was set to 2 m/s², and the frequency range was determined by sweeping; Figure 6 shows the variation in the output power of the harvester configuration used in the experiment with the resistance. It can be seen from the figure that the output trend of the captor increases with the increase in the external load value and decreases rapidly after reaching the highest point; the resistance value at the highest point is the optimal resistance, and the subsequent water droplet excitation experimental tests are carried out under this resistance value.

The centroid point and tip of the blade collinear with the petiole axis were selected as the impact points for experimental testing, and the excitation height was 30 mm. Figure 7 and Figure 8 show the output of experimental tests and numerical simulations for different impact locations. As can be seen from the figures, the voltage response output at the tip of the water droplet impact point is about twice as high as that at the central point of impact, and the attenuation curve is also denser. This is because the impact point is farther away from the fixed end and the action position becomes longer, while the resonance frequency is related to the action length, and the vibration frequency generated by the tip impact position is closer to the resonance frequency of the modified energy harvester; therefore, the resulting voltage response output is also larger.

Figure 9 shows the comparison and error analysis diagram of the experimental test and simulation analysis results. Comparing the experimental test results and the simulation analysis results, it can be seen that the output voltage obtained by the experimental test is close to the peak value of the output voltage of the simulation analysis, and the numerical simulation is consistent with the experimental test results without considering the human operation error and the prototype production error.

Figure 10 shows the experimental output results of the energy harvester at different excitation heights, H = 30 mm, H = 50 mm, and H = 70 mm, and the impact positions are all at the tip of the blade colinear with the petiole axis. The speed of the excited water droplet is proportional to the impact force of the water droplet; that is, the higher the height of the falling water droplet, the greater the instantaneous velocity before contact with the surface of the piezoelectric energy harvester of the bionic blade, and the greater the impact force generated, resulting in the increase in the output voltage.

Figure 11 shows a comparison of the experimental test and simulation results of the energy harvester at different excitation heights. It can be seen from the figure that when the excitation height of the water droplet is H = 30 mm, the difference between the experimental test and the simulation analysis curve is obvious, which may be due to the fact that when the excitation height is low, the deformation generated by the energy harvester is small, and the ideal state output cannot be achieved.

Since the ratio k between the blade and the petiole length has an effect on the output voltage of the captive, experimental tests were carried out at different ratios k, and the experimental results are shown in Figure 12. As can be seen from the figure, the output voltage of the energy harvester increases significantly as the ratio of blade-to-petiole length decreases. This is because the change in the length of the petiole leads to a change in the frequency of the energy harvester, and the closer the water droplet excitation is to the resonant frequency of the energy harvester, the higher the voltage output generated.

Figure 13 shows a comparison of the experimental test and simulation results at different k values. As can be seen from the figure, the peak voltage of the simulated output voltage curve is slightly higher than that of the experimental output curve, and the attenuation is slower. This also indicates that the k value can be adjusted to adjust the voltage output of the harvester.

For the raindrop excitation in the environment, considering the amount of rainfall, the influence of the excitation rate of the excited water droplet on the output voltage response of the piezoelectric energy harvester of the bionic blade is further studied. Experimental tests were carried out at different water droplet excitation rates; the excitation position was the tip of the blade, the height was H = 30 mm, and the output results of the voltage response are shown in Figure 14. With the increase in the excitation rate, the voltage response of the energy harvester is improved, and the output of the voltage response of the energy harvester is higher than 1 V when the excitation rate is v₂. This is due to the fact that when the water droplets excite the blades rapidly, the vibration characteristics of the energy harvester are enhanced, which increases the strain inside the piezoelectric sheet and increases the output voltage of the energy harvester.

In nature, the leaves are stimulated by raindrops for multi-point random excitation, and the multi-point random excitation test was carried out to explore the change in its output response. Figure 15 shows the output voltage change in the piezoelectric energy harvester of the bionic blade. As can be seen from the figure, the output voltage of the piezoelectric energy harvester fluctuates between 0.5 V and 1.5 V at different excitation points, and the stress distribution of the blade when it is impacted by water droplets is different due to the different excitation positions of the water droplets, resulting in differences in energy transfer efficiency, and the closer to the resonance frequency point of the captive, the greater the stress generated.

5. Performance Comparison and Potential Applications

As shown in

Table 2. Comparison of the research status and performance of raindrop energy harvesters.

References	Piezoelectric Material	Output Voltage (V)	Physical Model
Wang et al. [24]	PVDF	1.094
Doria et al. [25]	PZT	1.03
This work	PZT	1.5

, the performance comparison between the energy harvester proposed in this study and the raindrop energy harvester proposed by various scholars clearly shows that the output voltage of the profiled blade piezoelectric energy harvester proposed in this study is higher, and the raindrop-energy-harvesting effect is better.

In recent years, the energy supply technology of robotic systems has received extensive attention. As shown in Figure 16, as an environmental vibration energy harvester, the raindrop energy harvester proposed in this study has shown broad application prospects in the fields of autonomous power supply of robots, power supply of Internet of Things nodes, and vibration-energy-harvesting of bridges. Through the bionic design and piezoelectric conversion mechanism, the technology can effectively collect the kinetic energy of raindrops in the environment, providing maintenance-free power support for distributed sensor networks. Despite the dependence on rainfall conditions and the constraints of limited power output, raindrop energy harvesters are expected to develop into an important part of environmental micro-energy systems through material optimization, array design, and synergistic integration with other renewable energy technologies.

6. Conclusions

Inspired by the oscillation of leaves and the impact vibration of raindrops in nature, this study proposes a new type of raindrop energy harvester, which can be applied to the self-energy supply of microrobots to achieve system miniaturization and broaden its application scenarios. In this study, a mathematical model of the energy harvester under water droplet excitation is established and analyzed. The experimental and simulation results show that the output voltage of the tip excitation is higher than that of the centroid point excitation. The output voltage of the energy harvester increases with the increase in the excitation height. As the length of the petiole increases, the frequency of the energy harvester changes, and the output voltage increases under the same excitation conditions. When the profiling blade piezoelectric energy harvester is excited rapidly and continuously, its output voltage is higher. Due to the difference in the stress distribution on the leaf surface, the output voltage of the random excitation is different. By comparing the experimental and simulation analysis results, ignoring the human error and production error, the experimental test results and the simulation analysis results can be well combined, which verifies the correctness and accuracy of the mathematical model, and proves the effectiveness of the bionic blade for raindrop energy harvesting.