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Advances in Mechanical Engineering

Volume 2013 (2013), Article ID 263614, 7 pages

http://dx.doi.org/10.1155/2013/263614

## Design and Experimental Characterization of a Vibration Energy Harvesting Device for Rotational Systems

^{1}Beijing Institute of Structure and Environment Engineering, Beijing 100076, China^{2}Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China

Received 31 August 2013; Accepted 2 November 2013

Academic Editor: Jia-Jang Wu

Copyright © 2013 Lutao Yan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents a new vibration based electromagnetic power generator to transfer energy from stationary to rotating equipment, which can be a new attempt to substitute slip ring in rotational systems. The natural frequencies and modes are simulated in order to have a maximum and steady power output from the device. Parameters such as piezoelectric disk location and relative motion direction of the magnet are theoretically and experimentally analyzed. The results show that the position that is close to the fixed end of the cantilever and the relative motion along the long side gives higher power output. Moreover, the capability of the energy harvester to extract power from lower energy environment is experimentally validated. The voltage and power output are measured at different excitation frequencies.

#### 1. Introduction

Recently, there has been a renewed focus on vibration energy harvesting, since it provides big possibilities for a new way of clean, reliable, and maintenance-free power source [1]. Some possible excitation sources for energy harvesters have been reported in the literature, which include seismic noise, fluid-structure interactions, ocean waves, vehicle motion, or even human walking [2–5]. These research groups have made many studies on design and fabrication of power generators for different environmental vibrations. Moreover, for vibration-based micropiezoelectric energy harvesters, the order of magnitude of the measured output power can reach tens of microwatt (* μ*W) [6].

Attempts to make the wireless sensors self-contained with their own renewable power supply, the electromagnetic vibration-induced generators have been reported in the literature. Zhu et al. [7] reported a tunable vibration-based electromagnetic microgenerator, which can produce a power of 61.6–156.6 * μ*W over the tuning range when excited at a constant low vibration acceleration level of 0.59 ms

^{−2}. Lu and Hwang [8] developed an electromagnetic power output model in a vibration-induced microgenerator. The results show that a power output of 490

*W at vibration amplitude of 0.05 mm can be obtained. These studies make the concept of producing power for structures that have no physical connection to the outside world feasible.*

*μ*Particularly, in rotating machine field, electrical and/or data power are required to pass across rotating interfaces. At present, slip rings are commonly used for the electrical transfer. Unfortunately, more often than not, brushes contact of the stationary brushes and rotating shaft requires some form of lubrication and causes many disadvantages, such as inconsistent parasitic torque, noise, and degraded performance of the slip ring [9].

This paper reports a new energy generator in order to transfer steady power. Supposedly, this may give a new electrical transfer technique to substitute slip rings, which can prolong the operational lifetime. Theoretical optimization of the system, feasibility study, experimental results, and discussions of the generator are presented.

#### 2. Experimental Set Up and Conditions

In order to investigate the feasibility of the power generator which can be used in rotational system, a prototype of piezoelectric power generator is set up as shown in Figure 1(a). As mentioned in the literature, vibratory energy harvesting system generally consists of a spring-mass frame, a cantilever beam and one or more piezoelectric patches. In the experimental system, a rotor and a beam are set to simulate the stationary to rotating equipment, as seen in Figure 1(b). Two magnets are bonded on the ends of the rotors. The other one is fixed on one end of the beam. The force between two magnets on the beam and the rotor leads to the deformation of the beam and the piezoelectric plate, which can provide electrically potential energy.

When in terms of the structure of the system, the rectangular shaped cantilever, circular piezoelectric plate, and structure with lower harvester resonant frequency can improve the efficiency of the harvester [6, 10], the magnetic attractive/repulsive force model between the two cuboid magnets can be found in [7]. It depends on the area where the two magnets face each other and the distance between them. When the two magnets sharing the different line along their thicknesses, the beam will be forced torsion. Moreover, Stanton et al. [11] applied an analytical formulation to describe these nonlinear forces in order to extend device bandwidth. Overall, the nonlinear magnetic interaction model is so complicated but the system is feasible.

Because the voltage delivered by the piezoelectric element is not DC but AC, the interface circuit is needed to be designed and fabricated [12]. As shown in Figure 1, the interface circuit includes a diode rectifier bridge, an equivalent load resistor and a capacitor. Moreover, a zener diode is added to protect the front-end circuit, which works as voltage regulator. The laser displacement sensor is used to detect the amplitude of the beam. The motor is driven by a DC stabilized voltage/power source in order to obtain the stable operation condition. The experimental conditions are given in Table 1.

According to the reports of [13, 14], when the input excitation frequency matches the designed resonance frequency of the generator, the system will produce the resonance. Meanwhile, the permanent magnet has the maximum displacement amplitude and the piezoelectric element will produce the maximum voltage. Therefore, find the resonance frequency is very important. Consequently, a thin and long beam is designed, and its main mode shapes and translational eigenvectors are shown in Figure 2.

#### 3. System Optimization

##### 3.1. Optimum Location of the Piezoelectric Disk

In the harvest system, the piezoelectric disk can be bonded on any position of the cantilever. However, in the case of piezoelectric generators, the energy conversion is maximized by a maximum deformation of the piezoelectric material [12]. Therefore, it is necessary to study the deformation of the cantilever and choose the best location. Figure 3 shows the schematic diagram of deformation mechanism. From the mechanics of materials, the displacement of any position on the cantilever under the concentrated force can be given by where is the displacement of the corresponding location, is the load in direction, is the Young’s modulus of the material of the cantilever, is the area moment of inertia and is the length of the cantilever, and is the distance from the fixed end.

The bending curvature, which can be a reflection of the deformation degree is given by where is the curvature and and are first and second derivative of with respect to , respectively.

Figure 4 shows the theoretical calculation results of displacement and curvature based on (1) and (2). Under static force, the displacement increases along the beam and reaches a maximum in the free end. Based on material mechanics knowledge, it is understandable that the displacement increases as the load on the beam increases. From Figure 4(b), as the location is near the fixed end, the radius of curvature decreases, which means a large bending degree. Consequently, at the same position, the radius of curvature decreases with the increase of the force. As mentioned above, when the position that is close to the fixed end and increased force are employed, the larger voltage output can be obtained.

In order to verify the aforementioned analysis, a series of experiments are conducted. The beam is fixed at a constant displacement and then is quickly released. The output voltages of piezoelectric disks on different locations are measured by the data acquisition instrument. Figure 5 shows the output voltage peak values and the initial maximum displacements (IMD) of the beam are 14 mm and 8 mm. It can be seen that the output voltage values decrease rapidly in 120 ms, and the maximum voltages is obtained at the initial time. This may be attributed to the energy dissipation by the damping, such as structural damping and air damping. As can be seen from the figure, position 1 gives a higher voltage output compared with the other positions, which indicates that the experimental results fit quite well with the theoretical results. Moreover, more electrical energy can be acquired under large deformation conditions. It can be explained that the harvested electrical power is approximately equal to the mechanical energy of the cantilever, which can be reflected directly by the maximum displacement of the beam. Moreover, the voltage discharged by the piezoelectric element will not be harvested unless it can surpass the threshold of the diode. Therefore, in order to improve the capability of the energy harvester, diode with lower threshold voltage should be considered.

##### 3.2. Relative Motion Direction Optimum

For the relative motion of magnets on the beam and the rotor, there are two directions: move along the long side (pattern 1) and move along the short side (pattern 2) as shown in Figure 6. The interactive forces under two conditions can be qualitatively plotted. Moreover, according to the physical knowledge, the momentum increment is equal to the impulse caused by the external excitation force, which is also equal to the area under the force curve. Obviously, area under the curve 1 is larger than that of the curve 2. It is reasonable to assume that the magnet at the beam end will obtain a higher velocity in moving pattern 1.

The experimental results of output voltages peaks under two conditions are shown in Figure 7. During the process, the two moving patterns have the same velocity and relative displacement. It is found that the relative motion along the long side brings longer duration time of power generation and higher voltage peaks. In another word, the moving pattern 1 can deliver more energy than that of relative motion along the short side.

#### 4. Results and Discussion

##### 4.1. Generator Driven with Low Level Excitations

Figure 8 shows the measured displacements of the cantilever beam tip. It is important to note that while obtaining this plot, the motion of the beam is affected by the ambient vibration. Here, the ambient vibration may be caused by air flow, air squeeze, seismic noise, vehicle motion, thermal, or even human walking [1, 15]. Moreover, the power distribution of this energy is lower and nonuniform, and, therefore, it is difficulty to eliminate the effect of the natural surroundings. Consequently, the curves and the attenuation of the amplitude are irregular. From Figure 8, it is can be found that larger initial displacement brings higher level vibration, which agrees with the above analysis.

The voltage output under lower excitation is shown in Figure 9. At the starting point, the output voltage impulsively increases from zero to the measured value in very short time. Moreover, the harvested power increases significantly in the initial period. Due to the higher reserved mechanical energy, the voltage is much higher when the beam is fixed at a higher IMD. The maximum output voltages that obtained under IMD 0.7 mm, 0.9 mm, and 1.6 mm are 64.3 mV, 93.1 mV, and 185.1 mV, respectively. It is found that the output voltage drops off when the vibration amplitude is lower than 0.5 mm as shown in Figure 10. It is can be attributed to the electrical losses in the interface, which can be found in [7]. In other words, the energy obtained at the amplitude of 0.5 mm approximately equal to the energy loss and threshold power of the diode. Moreover, the capability of the energy harvester to extract power from lower energy environment is validated. As shown in Figure 10, the amplitudes are almost the same corresponding to the maximum voltage point in Figure 9. The frequency remains actually between 8 Hz and 9 Hz in every case, which equal to the damped linear natural frequency of the system.

##### 4.2. Performance of the Energy Harvester under Different Frequencies

Figure 11 shows the output characteristics of the power generator, and the IMD of the beam is fixed at zero in this section. The output voltage depends on several parameters: threshold of the diode, deformation of the beam, excitation frequency, and energy loss. The two magnets will encounter more times in high frequency environment, however, this will also bring shorter action time and lower energy as mentioned above. The comprehensive effects of excitation frequency and the harvested energy in one cycle will determine the rising slope of the curve. The maximum AC output voltage is the dominant factor that effect on the storage capacity, which can be reflected by the flat segment of the curve in the end period.

From Figure 11, the maximum voltages output are 3.62 V, 5.18 V, and 5.59 V for frequencies of 28.6 Hz, 16.3 Hz, and 9.2 Hz. The results are very similar to that of reports in [6, 16], which can be summarized that the peak-to-peak voltage can reach the maximum at resonant frequency.

Detailed displacement waveforms of the beam tip are given in Figure 12. According to the vibration principle, the frequency of the vibrating beam is equal to that of the driving force during the steady state. If the frequency of the input vibration is near the resonance frequency, the displacement amplitude increases obviously. The increased displacement amplitude allows the structure to receive more power from the external driving force. Therefore, it is understandable that the harvested power increases as shown in Figure 11. The harvested powers at different excitation frequencies are plotted in Figure 13. The maximum power output is 23.3 * μ*W at frequency of 9.2 Hz, which is 1.5 times more than the power obtained at 28.6 Hz.

Although the system can transfer the power between stationary and rotating frames and harvest power from the vibration environment, such generated power is lower and the system is inefficient to be used. In order to implement this method, here are some advices as follows (1) Piezoelectric laminates layered along the beam above and below the beam is commonly referred to as a bimorph; therefore, two PZT laminates can be bonded on either side of the beam in order to improve the harvested power [6, 11]. (2) Increase the cantilever number and arrange the magnets around the rotating circle. Moreover, cantilevers with varying length can cover a wide band of external vibration frequency as reported in [15]. This may let the energy scavengers to generate power much more effectively in rotational system with different rotational speeds. (3) Increase the deformation degree of the beam to obtain higher voltage output, or place a number of storage capacitors in parallel on the premise of the maximum voltage output is fixed. (4) Since a larger capacitor usually brings larger loss, charge the battery instead of the capacitor may reduce the electric loss and improve the efficiency [17].

#### 5. Conclusions

In order to transfer the electric power from stationary to rotating equipment, a vibration based electromagnetic microgenerator has been presented. The first four natural frequencies of the system are 8.9 Hz, 80.1 Hz, 149.3 Hz, and 243.07 Hz, and the first mode of vibration is particularly dominant. It is found that when the piezoelectric disk is bonded close to the fixed end, the voltage output become much higher than the other positions. This is mainly because this place obtains the maximum deformation degree of the piezoelectric material. The experimental results show that the relative motion along the long side brings longer duration time of power generation and higher voltage peaks.

The capability of the energy harvester to extract power from lower energy environment is validated. Furthermore, the diode of the rectifier bridge can be conducted when the amplitude of the beam is larger than 0.5 mm. As the excitation frequency is close to the resonant frequency, the voltage output increases. According to the experimental results, the maximum voltage is 5.59 V, which is obtained at the frequency 9.2 Hz. Meanwhile, the power output is 23.3 * μ*W at this frequency. Although the generated power of this system is lower, some possible advices are given, such as placing two PZT laminates on either side of the beam, increasing the cantilever number, increasing the deformation degree, and charging the battery instead of the capacitor.

#### Conflict of Interests

The authors declare no conflict of interests.

#### Acknowledgments

The authors would like to acknowledge the support from the National Natural Science Foundation of China (51075223) and the Natural Science Foundation of Beijing (3102018).

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