Enhancement of power output by a new stress-applied mode on circular piezoelectric energy harvester Open Access

Energy harvesting technology is developing rapidly. As a kind of transducer with excellent performance and convenient utilization, piezoelectric energy harvester has attracted much attention.^1–10 It is a potential candidate when collecting surplus mechanical energy. A novel bi-directional piezoelectric energy harvester is introduced by Su and Jean,¹¹ which can harvest vibration energy bi-directionally due to its composition of two sub-systems. Shen et al. changed the form of PZT diaphragm into the double-sided spiral shape and tested its displacement and resonance behaviours.¹² Erturk and Inman built a distributed parameter electromechanical model based on cantilevered piezoelectric energy harvesters,¹³ presenting the exact analytical solution of a cantilevered piezoelectric energy harvester with Euler-Bernoulli beam assumptions.

In recent years, researches on circular piezoelectric energy harvester have been in the ascendant.^14–17 The key performance of the energy harvester is power output. There are a lot of scholars studying how to increase the power output. J Palosaari et al. presented a unique measurement setup with tailored input force, adjustable mechanical pre-stress, and simultaneous measurement to show that pre-stressing technique is an effective method to improve the efficiency of piezoelectric harvester.¹⁸ K. Sunghwan managed to optimize the output by changing the electrode pattern of circular piezoelectric harvester.¹⁹ The moment equation of clamped circular plate to calculate the curvature is obtained from the elasticity solution.²⁰ 

where W_r is the deflection of the plate in the z-direction, r is the distance from the center of the plate to the point of deflection, ν is the Poisson’s ratio, P_o is pressure, and a is the radius of the plate. D is a constant related to the structure property. For the common unimorph plate, there is only one neutral surface which depends only on the cross section of the device, therefore, the strain–curvature equation for the unimorph plate is described as:

where z_c is the distance between the neutral surface and the centroid, z is the distance from the centroid to the location of strain, ρ is the curvature, ε is the strain, and subscripts r and θ indicate direction.

However, there are a few reports for circular plate harvesters. Sheng Wang reported a piezoelectric drum transducer, under a pre-stress of 0.15 N and a cyclic stress of 0.7 N, a power of 11 mW was generated at the resonance frequency of the transducer (590 Hz) across an 18 kΩ resistor.²¹ Recent progress was performed by Chen and Yang. They manufactured a piezoelectric diaphragm with a dimension of Φ25 mm. At 113 Hz, a maximal power output of 12 mW can be obtained from its piezoelectric disc across a resistive load of 33 kΩ.²² 

In our previous researches, Xiao and Yang fabricated a piezoelectric generator with multiple circular diaphragm piezoelectric harvesters array. The frequency range of energy harvesting can be widened to meet the broadband vibration.²³ Liu and Yang raised the output power of a single piece of ceramic to 11.3 mW when the stress-applied is 0.3 N by changing the bonding shape of the mass and ceramic sheet.²⁴ 

In this article, in order to reduce the size of the device and increasing the power output, a new shape of mass is designed to change the stress distribution. This new structure increases the power output of the single piezoelectric film by ∼100% and the volume decrease by ∼57% when the weight of mass is 30 g, which means greater potential applications in MEMS by this energy harvester.

As shown in Fig. 1, the testing platform consists of four main equipments, the function generator (33220A, Agilent Technologies Inc., Santa Clara, ca) supplies arbitrary vibration signals, which is amplified by the amplifier (YE5871A, Sinocera Piezotronics Inc.) and converted to the mechanical shaker (JZK-5, Sinocera Piezotronics Inc., Yangzhou, China), then the shaker will vibrate at the corresponding frequency.

As the fixture clamping piezoelectric disc was screwed on the shaker, piezoelectric disc will vibrate along with it and generate electricity. The output voltage is measured by the digital oscilloscope (TDS1012B, Tektronix Inc., Beaverton, OR), then the computer integrates all data and produces the final graph. A single-axis MEMS accelerometer (BW 14100, BW sensing Technologies, Inc., Shanghai, China) is used to control the acceleration amplitude by readouts, it is assembled on the shaker together with the device, and then is connected to NI-9233. The vibration acceleration of shaker is fixed during the whole experiment (a=9.8 m s^-2 when the vibration frequency is 400 Hz). As the piezoelectric energy harvester generates Ac voltage originally, a kind of rectifier circuit is used to transform the Ac into Dc. The harvester is modeled as a sinusoidal current source in parallel with its internal capacitance Cp, The full wave rectifying bridge circuit was made up with four signal Schotty diodes (1N5711), the filter capacitor was assumed to be large enough that the output voltage was essentially constant, in this experiment a capacitor of 100 F was used. We detected the voltage with the multimeter (Keithley 2000) and calculated the output power through the usual formulation: p = V² R⁻¹. R is equal to the matching impedance of the piezoelectric ceramic sheet. The impedance matching is measured by precision LCR meter(TH2816A, Tonghui). This instrument applies an AC signal to the ceramic and the frequency of the AC signal is equal to the resonance frequency of the energy harvester. The impedance of the ceramic at this frequency is the impedance matching.²⁵ 

The new designed piezoelectric energy harvester consists of a hollow ring mass but the old one consists of a solid mass. Fig. 2 shows the differences between them. These two kinds of harvesters usually contain two parts, a mass and a piece of circular piezoelectric diaphragm. Both of them have the same piezoelectric diaphragm, including a piezoelectric ceramic and a copper sheet. The experiment uses two kinds of circular piezoelectric diaphragm. Table I shows their specific parameters. As shown in Fig. 2(a)–(c), the biggest difference between the old and the new harvester is their different modes of stress-applied. The cross section between the old mass and diaphragm is a solid circle, so we call this central mass and we call the new mass annular mass. The height of the central mass is 14 mm, and the height of the annular mass is 6 mm. We change the weight of the mass by adjusting its height. So, compared with the old harvester, the new one has a smaller volume because of its greater space utilization. The shadows in Fig. 2(d) are screws, connecting the energy harvester and the shaker.

There are three important parameters which have been marked out in Fig. 2(d) that affect the power output of the piezoelectric energy harvester. They are m, d₁ and d₂. m refers to the weight of the mass; d₁ means the bonding diameter between the mass and the ceramic sheet; d₂ means the clamping diameter of the clamp.

The same idea is used to design the annular mass. Fig. 2(b) is the structural model of the annular mass. The top hole is designed to allow the wire to pass through. As shown in Fig. 2(d), the design of the annular mass is related to the m and d₂. So we fix d₁ to 6 mm to reduce the number of the variables in the experiment. We have prepared a variety of annular masses with different m and d₂. Their specific parameters are listed in Table II. The experiment used 19 kinds of such masses to explore the relationship among the power output, d₂ and m.

In order to compare with the central mass on power output, we also do a comparative experiment between the old structure and the new one. The experiment remains m unchanged to explore the difference between the output of the two structures when d₂ changes.

We first select the 0.1 mm thickness of the piezoelectric ceramic and the copper sheet to test. The resistance of the external resistor in each experiment is equal to the matching impedance of the piezoelectric ceramic sheet at the resonant frequency. Fig. 3(a) shows the power output with the stress-applied mode commonly used in previous researches. With the mass bonded at the center of the piezoelectric ceramic, the power output could reach to ∼10.5 mW at the frequency of ∼155 Hz with the optimal load of approximately 26 kΩ. Fig. 3(b) shows the power output with the new type of stress-applied mode, the power output arises to ∼20.8 mW with the annular hollow mass block at the frequency of 237 Hz with the optimal load of about 18 kΩ. The power output of the annular structure is nearly twice as high as that of the central structure when the thickness of the ceramic sheet and the copper sheet is 0.1 mm.

Then we use 0.2 mm thickness of the piezoelectric ceramic and the copper sheet to test. Fig. 4 shows the power output of the new structure. The power is almost linearly improved when the weight of the mass increases. Moreover, when d₂ increases, the power output will increase because larger d₂ means longer arm, and longer arm will produce greater bending deformation. Under this experimental conditions (m =50 g and d₂ =36 mm), we get the maximum power ∼23.3 mW.

We can see the comparison of the two structures in Fig. 5. When testing the old structure, the power output increases as d₂ increases when m is constant. This is similar to the result presented by the new annular structure. In comparison, the power output of the annular structure is ∼2 mW, higher than the central structure when m and d₂ are unchanged and the growth rate is ∼17%.

The ceramic sheet is a hard brittle material while copper is ductile. The deformation of copper sheet is larger than that of ceramic sheet during the vibration. Fig. 6 shows the vibration model of the two structures when the deformation is maximum. In the case of central structure (a), the mass is directly connected to the ceramic sheet, which results in a smaller intensity of pressure applied to the copper sheet because the area of the ceramic sheet is relatively large. However, in the case of annular structure (b), the mass is directly connected to the copper sheet and their bonding area is small. So the pressure on the copper sheet will be larger.

Based on the above argument, we can conclude that the value of h₂ will be larger than h₁. And a larger degree of the deformation of the copper sheet will lead to a bigger bending deformation of ceramic sheet. Thus the new annular structure has a higher power output. When the differences of hardness between the copper and ceramic sheet is larger, the difference between h₁ and h₂ will become larger. This is the reason why the power output of the new annular structure greatly enhances(almost two times) when the thickness of the piezoelectric ceramic and the copper sheet is 0.1 mm, but no obvious improvement(∼17%) was observed when the thickness of the piezoelectric ceramic and the copper sheet is 0.2 mm.

A new type of stress-applied mode is raised in this article, which could be realized by transforming the form of mass block into annular hollow. Compared with the previous structure, the annular structure’s volume decreased by ∼57%, and its energy output density is ∼2.63 mW/cm³. No matter how much the thickness of the piezoelectric diaphragm is, the power output of the new structure has improved. When the thickness of the ceramic sheet and the copper sheet are all 0.1 mm, and stress-applied is 0.3 N, the power output of single piezoelectric film can be increased by ∼100% to ∼20.3 mW. So this new stress-applied mode on circular piezoelectric energy harvester is a greater choice and can get more extensive applications.

This work was supported by the National Natural Science Foundation of China (No. 61761136004 and No. 51472181).