# Simulation Analysis and Experimental Testing of Spin-Magnetic Piezoelectric Generators

Authors: Xiaochao Tian; Hu Wang; Jiaying Lin; Zhicong Wang; Jinlong Liu; Shenfang Li; Jun Hou; Jinzhi Zhu; Qing Lei
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

In order to investigate the optimal power generation performance of piezoelectric materials, a spin-magnetic piezoelectric generator was designed and the relationship between output voltage and speed and external force was derived through theoretical analysis. The maximum deformation and resonant frequency of the piezoelectric oscillator under magnetic drive are derived from simulation analysis. Finally, the relationship between output voltage and magnet size, distance between two magnets, and speed was tested experimentally, and the experimental data agreed with the theoretical analysis. The results show that when the speed is 312 r/min, magnet pitch is 12 mm, and magnet size is 10 mm∗ 35 mm∗ 4, the maximum output voltage is 54 V. This can meet the power supply needs of micro and small electronic products.


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## Body

## 1. Introduction

With the rapid development of portable micropower electronics and remote sensing and monitoring systems, research related to microminiature generators has become a research hotspot, and piezoelectric generators have attracted much attention from scholars because of their simple structure and green advantages. Piezoelectric generators have been successfully used to generate electricity in various environments, such as vibration energy [1–4], rotating body kinetic energy [5–8], and fluid energy [9, 10], using the piezoelectric positive effect principle. Each type of generator has its own characteristics and areas of application. Rotating piezoelectric generators are mainly used to construct self-powered monitoring systems for rotating bodies such as shafts, bearings, car tyres, propellers, or microwind turbines. The first is the inertial excitation type, which uses the piezoelectric oscillator to bend and deform during the rotation of the piezoelectric oscillator by changing the direction of the force [6, 11]. The second is the toggle drive type, using the rotating mechanism to toggle the piezoelectric oscillator, which will produce a large impact noise at high speed [12]. The third is the impact drive type, using the rotating falling steel ball to hit the piezoelectric oscillator; this method is only applicable to low-speed occasions, but this way, there is a large impact and possibility of impact damage [13]. Obviously, there are some insurmountable drawbacks in the structure and principle of piezoelectric generators along the rotational direction of the rotating body, which seriously restrict their application, especially not for high speed and restricted space applications. There are also various types of indirect excitation. Noncontact excitation generator, through the noncontact force (piezoelectric vibrator additional mass of inertia force [14, 15], or relative rotation of the magnetic coupling force), forces the piezoelectric vibrator deformation power generation, its advantages are simple structure, no contact shock and noise, but the effective band width is narrow, low reliability, the inertia excitation generator is only suitable for low-speed environment and high-speed piezoelectric vibrator due to excessive inertia force cannot be used. The piezoelectric oscillator is only suitable for low-speed environment, and at high speed, the piezoelectric oscillator will be destroyed due to the inertia force is too large to produce reciprocal bending deformation or too large one-way deformation.In order to address the problems of existing rotating piezoelectric generators and the need for self-powering of high-speed rotating body monitoring systems, this study proposes a rotating piezoelectric generator and investigates the factors and laws affecting the power generation capacity of rotating piezoelectric generators from both theoretical simulation and experimental testing.


## 2. Structural Design and Working Principle

A schematic diagram of the structure of a rotating magnetic piezoelectric generator is shown in Figure1. The structure consists mainly of a rotating shaft, bearings, piezoelectric vibrators, permanent magnets, and a turntable. The piezoelectric oscillator consists of a piezoelectric ceramic and a metal substrate on which the piezoelectric ceramic is mounted on both sides. The permanent magnet and the turntable are bolted together to form a rotary drive. The permanent magnet is fixed at the free end of the piezoelectric oscillator, and there is a gap between the permanent magnet on the disc and the permanent magnet at the free end of the piezoelectric oscillator.Figure 1
Schematic diagram of the structure of a spin-magnetic piezoelectric generator.Working principle: when the permanent magnet on the turntable is close to the permanent magnet at the free end of the piezoelectric oscillator, a repulsive force is formed between the two magnets and the piezoelectric oscillator is bent and deformed by the repulsive force. Due to the positive piezoelectric effect, the surface of the piezoelectric ceramic generates an electric charge to form electrical energy, thus realising the function of the system to generate electricity.


## 3. Theoretical and Simulation Analysis

### 3.1. Theoretical Modeling

According to the theoretical mechanics, the external forces acting on the piezoelectric beam consist of the piezoelectric vibrator’s own gravity, centrifugal force, and magnetic forces. The external forces acting on the piezoelectric beam can be expressed as(1)F=mg+Fmn,where m is the mass of the piezoelectric oscillator, g is the acceleration of gravity, and Fmn is the magnetic force acting on the piezoelectric oscillator.Consider the force between a permanent magnet on a turntable and a permanent magnet on a piezoelectric cantilever beam as a pair of permanent magnets interacting with each other. The magnetic force between two rectangular magnets in space can be described as follows:(2)Fmn=3bhBr241+3dβπ2tan−1bh2db2+h2+4d2−tan−1bh2l+db2+h2+4l+d2,where I is the length of the magnet, b is the width of the magnet, h is the height of the magnet, β denotes the magnetic permeability, Br denotes the magnetic flux density on the polar surface of the magnet, and d is the distance between the two magnets magnet.The equation for the open-circuit output voltage under an external excitation forceF is as follows:(3)V0=31−a2g31lp4cWp2d+dmF,where a=dm/2d+dm, b=Em/Ep2, c=1−a3+a3b, g31 is the piezoelectric voltage factor, dm is the thickness of the substrate, d is the thickness of the piezoelectric ceramic, Em is Young’s modulus of the substrate, Ep is Young’s modulus of the piezoelectric ceramic, lp is the length of the piezoelectric beam, and Wp is the width of the piezoelectric beam.Substituting (1) and (2) into (3) gives(4)V0=31−a2g31lp4cWp2d+dmmg+3bhBr241+3dβπ2tan−1bh2db2+h2+4d2−tan−1bh2l+db2+h2+4l+d2.As can be seen from the equation, the output voltage of the piezoelectric oscillator is directly related to the amount of external force and the speed of rotation.


### 3.2. Simulation Analysis

The piezoelectric ceramic used is PZT-5 and the metal substrate is beryllium bronze, with a rectangular structure for the piezoelectric ceramic and the metal substrate. The material parameters of the piezoelectric ceramic, permanent magnet, and beryllium bronze are given in Table1. the stiffness coefficient matrix (unit  ×  109 Pa), piezoelectric coefficient matrix (unit  ×  10−12 C/N), and dielectric constant matrix (unit  ×  10−9 F/m) of PZT-5 are(5)cE=114.2558.29458.52500058.294114.2558.52500058.52558.52598.18100000020.74700000020.74700000026.042,d=0000741000074100−274−274593000,ε=10.44300010.4430006.405.Table 1
Parameter table for piezoelectric ceramics, permanent magnets, and beryllium bronze materials.
Substrate materialModulus of elasticity,EGpaPoisson’s ratio,γDensity,ρ (kg/m3)Dimensions (L∗W∗H)Piezoelectric ceramics630.312755050mm∗ 30mm∗ 0.1 mmBeryllium bronze1280.35860070mm∗ 35mm∗ 0.1 mmPermanent magnets1.6 × 10110.28740010mm∗ 35mm∗ 4mmConsidering the service life of the piezoelectric oscillator and the speed problem in practice, only the first-order resonance mode analysis of the piezoelectric oscillator is carried out, and the simulation results are shown in Figures2 and 3.Figure 2
System simulation modal diagram.Figure 3
Vibration pattern of a single piezoelectric oscillator.The first-order resonance frequency of the piezoelectric oscillator is 5.1993 Hz and the maximum free end deformation is 6.282 mm, which is in line with the actual vibration pattern. The theoreticaln=60f optimum speed of 312 r/min can be obtained.The effect of the amount of external force and the speed of rotation on the output voltage can be calculated using equation (4), and the results are shown in Figure 4.Figure 4
Relationship between speed of rotation, external force, and output voltage.As can be seen from the graph, the output voltage increases with increasing angular velocity and with increasing external force.


## 3.1. Theoretical Modeling

According to the theoretical mechanics, the external forces acting on the piezoelectric beam consist of the piezoelectric vibrator’s own gravity, centrifugal force, and magnetic forces. The external forces acting on the piezoelectric beam can be expressed as(1)F=mg+Fmn,where m is the mass of the piezoelectric oscillator, g is the acceleration of gravity, and Fmn is the magnetic force acting on the piezoelectric oscillator.Consider the force between a permanent magnet on a turntable and a permanent magnet on a piezoelectric cantilever beam as a pair of permanent magnets interacting with each other. The magnetic force between two rectangular magnets in space can be described as follows:(2)Fmn=3bhBr241+3dβπ2tan−1bh2db2+h2+4d2−tan−1bh2l+db2+h2+4l+d2,where I is the length of the magnet, b is the width of the magnet, h is the height of the magnet, β denotes the magnetic permeability, Br denotes the magnetic flux density on the polar surface of the magnet, and d is the distance between the two magnets magnet.The equation for the open-circuit output voltage under an external excitation forceF is as follows:(3)V0=31−a2g31lp4cWp2d+dmF,where a=dm/2d+dm, b=Em/Ep2, c=1−a3+a3b, g31 is the piezoelectric voltage factor, dm is the thickness of the substrate, d is the thickness of the piezoelectric ceramic, Em is Young’s modulus of the substrate, Ep is Young’s modulus of the piezoelectric ceramic, lp is the length of the piezoelectric beam, and Wp is the width of the piezoelectric beam.Substituting (1) and (2) into (3) gives(4)V0=31−a2g31lp4cWp2d+dmmg+3bhBr241+3dβπ2tan−1bh2db2+h2+4d2−tan−1bh2l+db2+h2+4l+d2.As can be seen from the equation, the output voltage of the piezoelectric oscillator is directly related to the amount of external force and the speed of rotation.


## 3.2. Simulation Analysis

The piezoelectric ceramic used is PZT-5 and the metal substrate is beryllium bronze, with a rectangular structure for the piezoelectric ceramic and the metal substrate. The material parameters of the piezoelectric ceramic, permanent magnet, and beryllium bronze are given in Table1. the stiffness coefficient matrix (unit  ×  109 Pa), piezoelectric coefficient matrix (unit  ×  10−12 C/N), and dielectric constant matrix (unit  ×  10−9 F/m) of PZT-5 are(5)cE=114.2558.29458.52500058.294114.2558.52500058.52558.52598.18100000020.74700000020.74700000026.042,d=0000741000074100−274−274593000,ε=10.44300010.4430006.405.Table 1
Parameter table for piezoelectric ceramics, permanent magnets, and beryllium bronze materials.
Substrate materialModulus of elasticity,EGpaPoisson’s ratio,γDensity,ρ (kg/m3)Dimensions (L∗W∗H)Piezoelectric ceramics630.312755050mm∗ 30mm∗ 0.1 mmBeryllium bronze1280.35860070mm∗ 35mm∗ 0.1 mmPermanent magnets1.6 × 10110.28740010mm∗ 35mm∗ 4mmConsidering the service life of the piezoelectric oscillator and the speed problem in practice, only the first-order resonance mode analysis of the piezoelectric oscillator is carried out, and the simulation results are shown in Figures2 and 3.Figure 2
System simulation modal diagram.Figure 3
Vibration pattern of a single piezoelectric oscillator.The first-order resonance frequency of the piezoelectric oscillator is 5.1993 Hz and the maximum free end deformation is 6.282 mm, which is in line with the actual vibration pattern. The theoreticaln=60f optimum speed of 312 r/min can be obtained.The effect of the amount of external force and the speed of rotation on the output voltage can be calculated using equation (4), and the results are shown in Figure 4.Figure 4
Relationship between speed of rotation, external force, and output voltage.As can be seen from the graph, the output voltage increases with increasing angular velocity and with increasing external force.


## 4. Comparison of Experimental Tests and Theoretical Analysis

### 4.1. Test Set

The system test setup is shown in Figure5. The test system mainly consists of an oscilloscope, a rotating generator prototype, a support frame, and a motor. The motor is used to drive the rotation of the rotating disc. A permanent magnet with a magnetic polarisation strength of 1.2 T was selected.Figure 5
Experimental test setup.


### 4.2. Relationship between Output Voltage and Speed for Different Magnet Sizes

When the magnet pitch is 12 mm, the output voltage versus speed curve obtained by changing the magnet size is shown in Figure6. The permanent magnet size parameters are given in Table 2.Figure 6
Relationship between speed and voltage.Table 2
Dimensional parameters of permanent magnets.
MagnetsLength (mm)Width (mm)Thickness (mm)Polarisation intensityMagnet I53541.2Magnet II83541.2Magnet III103541.2The graph shows that as the speed increases, the output voltage increases with the size of the permanent magnet, reaching a maximum output transient voltage of 52.6 V at a speed of 312 r/min.


### 4.3. Relationship between Output Voltage and Speed for Different Magnet Spacings

When the piezoelectric oscillator size is 70mm∗ 35mm∗ 0.1 mm and the magnet size is 10∗ mm∗ 35mm∗ 4mm, the output voltage versus speed curve is shown in Figure 7 when changing the magnet spacing.Figure 7
Output voltage versus speed for different magnet spacings.The graph shows that as the speed increases, the output voltage decreases as the magnet pitch increases, with a maximum output voltage of 53.7 V when the speed reaches 312 r/min.


### 4.4. Output Voltage versus Speed

When the number of piezoelectric oscillators is 8, the magnet pitch is 12 mm, and the magnet size is 10 mm∗35 mm∗4, the output voltage versus speed curve is shown in Figure 8.Figure 8
Rotational speed versus voltage.At a rotational speed of 312 r/min, the piezoelectric oscillator has a maximum peak open-circuit voltage of 54 V. The piezoelectric oscillator is in resonance at this point, meaning that the excitation frequency at the free end of the piezoelectric oscillator is equal to the first-order intrinsic frequency of the oscillator.


## 4.1. Test Set

The system test setup is shown in Figure5. The test system mainly consists of an oscilloscope, a rotating generator prototype, a support frame, and a motor. The motor is used to drive the rotation of the rotating disc. A permanent magnet with a magnetic polarisation strength of 1.2 T was selected.Figure 5
Experimental test setup.


## 4.2. Relationship between Output Voltage and Speed for Different Magnet Sizes

When the magnet pitch is 12 mm, the output voltage versus speed curve obtained by changing the magnet size is shown in Figure6. The permanent magnet size parameters are given in Table 2.Figure 6
Relationship between speed and voltage.Table 2
Dimensional parameters of permanent magnets.
MagnetsLength (mm)Width (mm)Thickness (mm)Polarisation intensityMagnet I53541.2Magnet II83541.2Magnet III103541.2The graph shows that as the speed increases, the output voltage increases with the size of the permanent magnet, reaching a maximum output transient voltage of 52.6 V at a speed of 312 r/min.


## 4.3. Relationship between Output Voltage and Speed for Different Magnet Spacings

When the piezoelectric oscillator size is 70mm∗ 35mm∗ 0.1 mm and the magnet size is 10∗ mm∗ 35mm∗ 4mm, the output voltage versus speed curve is shown in Figure 7 when changing the magnet spacing.Figure 7
Output voltage versus speed for different magnet spacings.The graph shows that as the speed increases, the output voltage decreases as the magnet pitch increases, with a maximum output voltage of 53.7 V when the speed reaches 312 r/min.


## 4.4. Output Voltage versus Speed

When the number of piezoelectric oscillators is 8, the magnet pitch is 12 mm, and the magnet size is 10 mm∗35 mm∗4, the output voltage versus speed curve is shown in Figure 8.Figure 8
Rotational speed versus voltage.At a rotational speed of 312 r/min, the piezoelectric oscillator has a maximum peak open-circuit voltage of 54 V. The piezoelectric oscillator is in resonance at this point, meaning that the excitation frequency at the free end of the piezoelectric oscillator is equal to the first-order intrinsic frequency of the oscillator.


## 5. Conclusion

A spin-magnetic piezoelectric generator power generation model is established and the piezoelectric oscillator is simulated and analysed using the simulation software. The relationship between the influence of rotational speed on the piezoelectric generator is analysed through experimental tests, and the theoretical analysis matches the experimental test results. The output voltage increases with the increase of permanent magnet size; the output voltage decreases with the increase of magnet spacing. When the rotational speed is 312 r/min, the magnet spacing is 12 mm, and the magnet size is 10 mm∗35 mm∗4, the best power generation capacity is 54 V.



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*Source: 9102625-2022-06-14.xml*