1 Introduction

In recent years, many parts of the world have been suffering from energy shortage as a result of oil shortage and increased energy demand. Therefore, alternative energy technologies have been developed. One such technology is piezoelectric energy harvesting. This technology involves the use of piezoelectric ceramics and converts physical energy into electrical energy. Generally, piezoelectric energy harvesting is based on piezoelectric effect. Piezoelectric energy harvesting using the piezoelectric effect is a technology that converts physical energy into electrical energy. When a piezoelectric ceramics are stressed mechanically by a force, it can generate a voltage or potential energy difference and a current [1–4]. In particular, piezoelectric energy harvesting involves the use of waste physical energy. In our surrounding, physical energy is constantly generated through vibration of equipment and the movement of people and vehicle. The waste energy, such as pressure and vibration energy, can be converted into electrical energy. Thus, any method used for producing electrical energy from waste energy is expected to be very eco-friendly and valuable [5, 6]. Research for obtaining electrical energy from waste physical energy is actively in progress. The cross-shaped piezoelectric generator based on the above discussed theory is suitable for use in daily life. The generator has a simple shape, similar to a unimorph-type generator that has a piezoelectric ceramic on one side of the elastic body. In addition to having a simple structure that makes its fabrication easy, the generator has excellent output characteristics. Moreover, its resonance frequency can be varied by changing the leg length and material of the elastic body. In this study, we developed a new model of a piezoelectric generator, referred to as cross-shaped piezoelectric generator, and investigated the dependence of its output characteristics on the elastic body material and the length of the four symmetric legs of the elastic body.

2 Structure of the generator and finite element method (FEM) analysis

2.1 Structure of the cross-shaped piezoelectric generator

The structure of the cross-shaped piezoelectric generator is shown in Fig. 1. The piezoelectric generator has an elastic body with four thin symmetric legs. Four rectangular piezoelectric ceramics are attached to the upper part of the legs [7]. Vibrations are applied to the center of the generator, and they propagate equally along all the legs. Therefore, all four legs have the same vibration mode and resonance frequency. It is thus possible to efficiently generate electric power.

Fig. 1
figure 1

Structure of the cross-shaped piezoelectric generator

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2.2 FEM analysis

The resonance and output characteristics of the generator are simulated by using an FEM program. Vibration modes of the generator are verified by modal analysis. The output voltage of the piezoelectric ceramics is calculated by using harmonic analysis during the simulation. The modeling and the vibration mode of the generator are shown in Fig. 2. The result of modal analysis shows that the four legs have the same vibration mode.

Fig. 2
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Vibration mode of the cross-shaped piezoelectric generator

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PZT4 is selected as the piezoelectric ceramic, and elastic bodies made of brass, copper, aluminum, and SUS304 are used. The physical properties of the elastic bodies are presented in Table 1 [10].

Table 1 Physical properties of the elastic bodies
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An abbreviation is defined for each parameter of the generator for convenience in FEA and experiments. The parameters considered are the elastic body width (EW), elastic body thickness (ET), elastic body length (EL), elastic body material (EM), ceramic width (CW), ceramic thickness (CT), and ceramic length (CL).

Figure 3 shows the dependence of the analysis result on the elastic body material. The applied force is 0.1 [N] in the direction of the Z-axis, and the parameter values of the generator are as follows: EL, 80; ET, 0.2; CL, 30; CT, 0.5; EW, 10; and CW, 10. The resonance and output characteristics are determined for the different elastic bodies. Further, Young’s modulus of the elastic body material, which determines the output voltage and the resonance frequency are determined in the order of aluminum, SUS304, copper, and brass. For every material, the resonance frequency is proportional to the speed of sound in the material. The speed of sound in the elastic body materials is defined as

$$ {\text{v}} = \sqrt {{\frac{{\text{Y}}}{\rho }}} $$
(1)

Here, Y is the Young’s modulus of the material and ρ is the density of the elastic body. The output voltage is proportional to the Young’s modulus. Generally, the resonance frequency is directly proportional to the Young’s modulus of the material and inversely proportional to the density of the material [8].

Fig. 3
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Dependence of analysis results on the elastic body material

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Figure 4 shows the dependence of the output characteristics on the leg length. The applied force is 0.1 [N] in the direction of the Z-axis, and the parameter values of the generator are as follows: ET, 0.2; EW, 10; CL, 30; CT, 0.5 and CW, 10. Thus, with an increase in EL, the resonance frequency decreases while the output voltage increases.

Fig. 4
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Dependence of analysis results on the leg length

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3 Fabrication and experiment

A total of seven cross-shaped piezoelectric generators were fabricated for use in experiments that were to be performed for verifying the analysis results; these generators had elastic bodies with different leg lengths and made of different materials. The generators were fabricated by using the four materials—brass, copper, aluminum, and SUS304—and with leg lengths of 50 [mm], 60 [mm], 70 [mm], and 80 [mm]. The thickness of the elastic bodies was 0.2 [mm]. All the ceramics used were of the same size: CL, 30; CT, 0.5; and CW, 10. Four rectangular ceramics were attached to the elastic body legs after the elastic body was cut to have a cross-like shape. PIC 151 manufactured by PI Ltd. was used as the piezoelectric ceramic and elastic epoxy was used as the adhesive material. For applying vibrations, the center of the generator was perforated so that the elastic body could be attached to the shaker. The fabricated piezoelectric generator is shown Fig. 5

Fig. 5
figure 5

Fabricated cross-shaped piezoelectric generator

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Figure 6 shows the experimental equipment used in the vibration experiments. The output characteristics were determined by using an oscilloscope, a function generator, a digital multimeter, a power amplifier, a shaker, an acceleration sensor, and a laptop. The function generator was used to set the frequency and amplitude of vibrations. The power amplifier received a signal from the function generator, and the signal was amplified and applied to the shaker. The shaker generated vibrations, and these vibrations were applied to the center of the piezoelectric generator. The frequency of the vibrations could be varied by adjusting the function generator, and the output voltage of the generator, which depended on the frequency, was measured at the output terminal of a half-wave-rectifier circuit by using the oscilloscope. The output current was measured with the digital multimeter by connecting a resistor of 100 [Ω]. Thus, the output voltage and current of the fabricated piezoelectric generators were measured by conducting vibration experiments. In addition, the resonance frequency was determined through a comparison between the analysis results and measured results.

Fig. 6
figure 6

Experimental equipment used in the vibration experiments

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Figures 7 and 8 show the dependence of the voltage characteristics and current characteristics of the elastic bodies on the elastic body material. The output voltage of SUS304 was the highest, 4.42 [V], and the output voltages of the other elastic bodies were measured in the order of brass, copper and aluminum. The output currents were 7.83[μA], 4.2[μA], 3.26[μA], and 2.1[μA], respectively. Thus, the output current was proportional to the output voltage. The resonance frequency was measured to be 28 [Hz], 25 [Hz], 22 [Hz], and 19 [Hz] for SUS304, aluminum, brass, and copper, respectively.

Fig. 7
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Dependence of the output voltage on the elastic body material

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Fig. 8
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Dependence of the output current on the elastic body material

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Figures 9 and 10 show the dependence of the voltage characteristics and current characteristics on the leg length for an elastic body. For leg lengths of 50 [mm], 60 [mm], 70 [mm], and 80 [mm], the voltages measured were 1.28 [V], 1.23 [V], 1.82 [V], and 1.85 [V], respectively; thus, the output voltage increased with the EL. The resonance frequencies corresponding to these voltages were 34 [Hz], 29 [Hz], 24 [Hz], and 19 [Hz], respectively. Further, the resonance frequency was found to be proportional to the speed of sound in the elastic body material. It is possible to change the resonance frequency by adjusting the EL [8, 9].

Fig. 9
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Dependence of the output voltage on the leg length

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Fig. 10
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Dependence of the output current characteristics on the leg length

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4 Conclusion

In this paper, piezoelectric energy harvesting is introduced as an alternative energy technology, and a new model of a piezoelectric generator with excellent output characteristics is proposed. FEA was conducted to simulate the output characteristics before the fabrication of the generator and to make a comparison between experimental results and analysis results. For determining the dependence of the output characteristics on the material and leg length of the elastic body, vibration experiments were conducted by applying vibrations to the center of the generator. Of all materials, SUS304 showed the highest values of the output voltage and current, 4.42 [V] and 7.83 [μA]. It appears to be possible for the generator to efficiently generate electrical power even when low-frequency vibrations are applied. In addition, the output voltage characteristics were determined for different leg lengths: 50 [mm], 60 [mm], 70 [mm], and 80 [mm]. In the case of the leg length of 80 [mm], the highest output voltage and current were 1.85 [V] and 3.26 [μA]. The resonance characteristics were determined in the low frequency range between 19 [Hz] and 34 [Hz]. The resonance frequency of the generator could be controlled by changing the leg length and material. Thus, the piezoelectric generator can be used in daily life. Electrical power can be efficiently obtained because of the resonance phenomenon. The piezoelectric generator is thought to be capable of replacing existing sources of power for small equipment.