A novel piezoelectric energy harvester of noncontact magnetic force for a vehicle suspension system

The vehicle suspension system is considered to have tremendous potential in energy harvesting and to be applicable for improving the efficiency of energy use of the vehicle. A novel piezoelectric energy harvester (PEH) with noncontact magnetic force has the feature of low friction loss and is designed based on the vibration characteristic of the suspension system. The research comprises two main components: the motion conversion component and the energy conversion component. A screw‐nut mechanism that can convert linear vibration between the vehicle body and the wheel into rotational motion is used as the motion conversion component. The energy conversion component is a core component of the PEH; its function is to convert rotational energy into electrical energy through noncontact magnetic force and piezoelectric effect. The magnetic excitation model's credibility and the modeling method's feasibility are verified by experiment and simulation. Through vehicle field tests, the influence of the driving speed, road surface roughness, and cargo state on the harvested power is obtained. Driving on a random road, the maximum of the generated power is 24.28 W, at 60 km/h, under the laden state. Driving on a pulse road, the harvested power is 3346 W, at 30 km/h, under the unladen state. It is indicated that the PEH is a promising and practical option for harvesting energy for the vehicle's suspension system.


| INTRODUCTION
Obtaining energy from sustainable alternatives plays a vital role in solving the energy crisis, saving energy, and protecting the environment from hazardous emissions. 1 In recent years, more and more studies are concentrating on energy collecting, and the use of environment friendly energy alternatives has become one of the most essential and popular research topics, 2 such as sound energy, 3 vibration energy, 4 wave energy, 5 solar energy 6 and wind energy. 7,8 The results show that vibration energy has a considerable overall efficiency compared with other energy sources, in the range of 20%-40%. 9 Simultaneously, mechanical vibration energy recycling is one of the most efficient energy collection methods with the advantages of convenient realization, high energy density, and high recovery efficiency, so it is extensive use in commercial applications. Harvesting energy into power batteries is significant for power supply and environmental protection. [10][11][12] The vibration of a vehicle suspension system is one of the crucial sources of mechanical vibration energy. 13 In vehicle driving, the damper installed in the vehicle suspension system will be compressed or stretched due to different perturbations, such as road roughness, braking force, acceleration, and centrifugal force. 4 The undesired vibration is released via conventional dampers. However, it could be converted into valuable energy and be reused in vehicles in multiple ways, such as transforming it into electrical energy, storing it back in batteries, or powering different electrical microsystems. Therefore, considering the energy storage potential of each damper, the application of energy collection technology in vehicles has a great prospect. 14 Generally, piezoelectric, electromagnetic, electrostatic, and triboelectric conversion principles have been essentially considered to harvest the unexploited but abundant mechanical energy from the vehicle's suspension system. 15 In electromagnetic energy collection technology, the electromagnetic induction principle is used to convert vibration energy into electrical energy. Currently, the research on vehicle regenerative shock absorbers primarily uses electromagnetic materials to generate electrical power from vibration. 14 However, electromagnetic materials have outstanding defects in energy conversion efficiency. Electrostatic transduction performance is better in conversion efficiency, but external power is needed to produce an electrostatic field while harvesting energy. 16 Recently, a new type of energy harvesting technology named triboelectric nanogenerator has been developed to harness ambient mechanical motions from vibrations. 17 In addition, the cantilever-structured piezoelectric energy harvester (PEH) can be targeted as an efficient alternative for gathering the vibration energy of cars running on rough ground to substitute the battery in tire pressure monitoring systems. 18 In contrast with the above mechanisms, the PEH is characterized by better power generation efficiency and larger generating capacity. 15,19 On the other side, piezoelectric transduction has three times more energy density than the other transductions. 20 Furthermore, the PEH can be easily fabricated into multiple structures because of its configuration's simplicity and flexibility without requiring additional tools. As an extra energycollecting element, the piezoelectric material can be installed in numerous positions in the vehicle suspension system, such as springs, 21 tires, 22 and dampers. 23 Because of that, it is expected that the PHE technology can be applied for energy recovery in vehicles for greater efficiency and lower costs. Over the last decade, the research on harvesting energy from vehicle suspension based on different types and configurations of piezoelectric materials has received considerable attention. 24 To investigate the energy-collecting capacity of piezoelectric transducers in suspension systems, researchers often use MATLAB/Simulink to model mathematical modeling and simulation on the quarter-car and half-car models with built-in piezoelectric stacks. 25,26 Under the standard road excitation, Tavares et al. conducted a numerical simulation on the classic parameterized quarter vehicle suspension. 25 Furthermore, Xiao et al. studied the energy collected capacity using the piezoelectric material from a quarter of the vehicle model under sinusoidal input excitation with an amplitude of 1 g. 26 From the theoretical study, the highest output voltage, and generated power from the PEH on record was 274.62 V and 2.84 W, respectively. The above research finds that the harvested power of a piezoelectric energy-regenerative device is relatively small. The collected power can only be employed to power equipment with low power requirements, like an embedded wireless sensor.
To increase the harvested energy, researchers mainly studied where the piezoelectric material is installed on the power generation capacity. Lafarge et al. found that more energy was obtained by positioning piezoelectric material between two surfaces of the absorber than by setting it on the surface of the damper. 23 In the study by Anton and colleagues, 27,28 the piezoelectric stack and the spring of the suspension system are installed in series. The results show that the piezoelectric stack output voltage and generated power increase along with the road surface roughness and vehicle speed increase. To convert the fluid pressure change caused by piston vibration into electrical energy, in the study by Lee et al., 29 two parallel piezoelectric material plates were installed in the suspension shock absorber to realize a combination of cylindrical piezoelectric transducer and cylinder of the shock absorber. Arizti 24 installed a multiple-layer piezoelectric stack at the top of the shock absorber piston to increase the ability to harvest power. Hendrowati et al. 30 connected a piezoelectric stack in series with the springs in the suspension system of a quarter vehicle model, in which the piezoelectric stack is composed of 15 layers of piezoelectric patches.
In the study by Xie and Wang, 15 a double-mass piezoelectric rod harvester was designed, equivalent to a spring and damper in the suspension system; through theoretical analysis, the suspension system mathematical model was established. Meanwhile, a piezoelectric power harvested model was based, and the influences of piezoelectric rod width, the vehicle speed, and the road roughness level on the harvested power of the PEH were theoretically discussed. It can be found that the maximum power generation can reach 738 W when the piezoelectric bar's width and height are 0.015 and 0.1 m, respectively. In our previous research, to evaluate the potential of light electric logistics vehicles using piezoelectric materials for energy recovery, we proposed a novel PEH and modeled a vibration model with a dualmass suspension system. 31 Based on the field experiment and numerical simulation results, the influence of various parameters, such as driving speed, lever arm ratio, and piezoelectric ceramics' cross-sectional area on power generation capacity, was analyzed. Although the above research can enhance the energy-collecting power of the energy-regenerative device to a certain extent, the addition of the PEH significantly changes the original suspension system of the vehicle. Meanwhile, in the energy harvesting process, the excitation object directly contacts piezoelectric materials, resulting in mechanical impact and friction, leading to the PEH's direct conversion efficiency being low. 32 Different from the studies of Xie and Wang 15 and Zhao et al., 31 in this paper, the validity, and veracity of the model and the validity of the modeling method were verified. Based on the previous work on PEH, a new type of PEH is proposed to collect vibration energy for vehicle suspension systems, with the characteristics of noncontact magnetic force action and low friction loss. To ensure that the installation of PEH does not change the structure of the original suspension system, the PEH was installed in parallel with the damper of the vehicle suspension system. The PEH consists of two main components: (1) the motion conversion component is a screw-nut mechanism that can convert the linear vibration between the vehicle body and the wheel into rotational motion; (2) the energy conversion component is a core component of the PEH which can convert rotational energy into electrical energy through noncontact magnetic excitation action and piezoelectric effect.
The architecture and mechanical design of the PEH are described in Section 2. In Section 3, the PEH is modeled and analyzed. The bench tests of the PEH are presented in Section 4. Section 5 discusses the results. In the end, the conclusions are summarized in Section 6.

| Architecture
When a vehicle drives in the city, the suspension system vibrates, and a large number of vibration energy is released in thermal energy. Thus, a PEH is proposed to recycle the suspension system vibration energy that could be wasted in this work. The architecture of the PEH is shown in Figure 1.
The PEH is connected with the damper of the original vehicle suspension system in parallel, and the upper and lower end is connected to the body and the wheels, respectively. The PEH consists of two main components: the motion conversion component and the energy conversion component. The rectilinear motion between the vehicle body and the wheel is converted to rotational motion, which is realized by the motion conversion component. The energy conversion component converts rotational motion into electrical energy via the alternant magnetic force and the piezoelectric effect. Electrical power is stored to power vehicle electrical equipment as an alternative energy source.

| Mechanical design
The general overview, composition, and assembling relation of PEH are shown in Figure 2. A ball screw and a screw nut mainly form the motion conversion component. One end of the ball screw is machined with a threaded hole and a keyway. The fixed connection between the ball screw and the rotor is realized through the rotor ring fixing bolts and flat key to achieve torque transmission. The energy conversion component consists of a stator ring, several piezoelectric patches, a rotor ring, and several magnetic slabs; the stator and the rotor are made of aluminum. Piezoelectric patches are inlaid in the inner ring of the stator evenly, and equivalent size magnetic slabs are installed on the piezoelectric patches' rectangular surface. The ring rotor is a wheel-like structure with spokes, and its outer ring has a tooth slot the same width as the magnetic slab, and the magnetic slab is embedded in the tooth slot. The magnetic slabs of the stator and rotor are relatively set, so the magnetic poles close to each other are of the same polarity to ensure that the magnetic force between the stator and the rotor is repulsive. The magnetic force affects the polarization directions of the piezoelectric patches, causing them to deform and generate charges, thus realizing the energy conversion from mechanical energy to electric energy. Unlike the direct contact impact phenomenon between piezoelectric ceramics and lever described in, 15,29 in this design, the magnetic slabs on the stator and rotor have no direct physical contact in the interaction and can effectively reduce the friction energy loss during the power generation process.
The general overview, composition, and assembling relation of piezoelectric energy harvester.
The inner radius of the stator ring is r 1 , the outer radius of the rotator ring is r 2 , and the gap between the rotator ring and the stator ring is d = r 1 − r 2 . l and w denote the axial length and the width of the magnetic slabs and the piezoelectric patches, respectively. The thickness of the magnetic slabs and the piezoelectric patches is t 1 and t 2 , respectively.
To conveniently lead out the electrical power harvested by the piezoelectric patches, the leads are welded at the positive and negative plates of one end of the piezoelectric patch, respectively, and the leads are connected with the external circuit through the wire hole on the end shield. A thread connects the stator and the end shield. The outer surface of the rotor is processed with grooves of the same size as the magnetic slab to ensure that the magnetic slab can be perfectly inlaid on the rotor. In Figure 3, an actual size prototype was manufactured to validate the feasibility of the design.
Specifically, the width of the mounting groove on the stator, piezoelectric patches, and magnetic slabs are consistent, and the number of magnetic slabs installed on the stator is twice that of the rotor. This ensures that the magnetic force acting on the piezoelectric patch, along with its polarization direction, changes periodically when the rotor rotates continuously. PZT-4 (lead zirconate titanate) is selected to be the piezoelectric material, and the chosen magnet type is NdFeB-N50. Table 1 lists the dimensions and material characteristics of the prototype.

| Dynamic analysis of PEH
In this study, we assume that the ball screw and the rotor are rigid; the clearance between the various connecting parts and the friction during motion is ignored. The dynamic model of PEH is shown in Figure 4, the direction of rotation and linear motion is represented by the black arrow, and the direction of torque and force is represented by the red arrow. θ ω ω , ,̇represent the angle, angular velocity, and angular acceleration of the rotating part, respectively; z z z ,,̈represent the displacement, velocity, and acceleration of linear motion. The mutual transformation equation of linear motion and rotational motion is as follows: The rotator ring's rotational speed is n 1 ; the ball screw's lead is l d .
The mutual transformation equation of force and torsion is as follows: where T M is torque, F l is the linear force. The dynamics equation of the PEH is given by: where, the output torque of PEH is T out , the rotating component's output inertia torque is T , the energy conversion component's output torque is T p , the moment of inertia of all screw is J b , the moment of inertia of rotor ring is J p .
From Equations (4)-(6), it can be obtained that the axial output force is as follows: where, F z is the axial output force of the PEH; F p is the resisting force of energy conversion component; is proportional to the acceleration z̈, which represents the inertia force of the rotating parts. Furthermore, the PEHs' inertial mass can be defined as:

| Magnetic force excitation model
As shown in Figure 5, the research is conducted in magnet slab B on the stator ring; according to the structure size of the PEH and the material properties of the magnetic patch, the characteristics of the magnetic force F acting on the piezoelectric patch along the polarization direction can be obtained. According to Al-Ashtari et al., 33 an empirical formula is introduced to research the interaction force F M between two identical rectangular magnets: where the magnets' residual flux density is B r , and the value of the empirical corrective exponent n is 1/3. The rectangular magnet magnetics' flux density field   B d ( ) is defined as Equation (9), and the attenuation function of the repelling force f d ( ) based on experience is given by Equation (10). The value of d 0 is 1 mm. Figure 5A-C is the diagram of the magnetic interaction force. Figure 5A shows that the magnetic interaction force between the magnets A and B is 0; at this moment, the line connecting the centers of the N poles of the two magnets is perpendicular to the surface normal of magnet A. As demonstrated in Figure 5B, the rotor ring rotates at a certain angle, . From Figure 5C, we can see the magnetic force F is at its maximum, and the magnitude of the force is F M . In summary, it can be approximately considered that the normal component force F t ( ) of the magnetic force, acting on the piezoelectric patch, is a sinusoidally varying force with the rotor ring rotation.
The normal magnetic force versus time is shown in Figure 6. The expression of period T and F t ( ) is as follows: T π n πn nn = (2 / )/2 = 1/ , is the amplitude, f n n = 1 2 is the frequency, n πr w = / 2 2 represents the number of magnetic slabs installed on the rotator; 2n 2 is the number of piezoelectric patches installed on the stator. It can be found that the rotational speed n 1 increases with the increase of the input stroke speed ż, which makes the excitation frequency f of the magnetic force acting on the piezoelectric patch increase significantly.

| Power generation model
According to the magnetic force excitation characteristics acting on the polarization direction of the piezoelectric patch, the piezoelectric equation is obtained as follows: where Q t ( ) is the quantity of electric charge produced by the piezoelectric patch, d 33 is the piezoelectric constant along the rolling direction.
Piezoelectric material is a dielectric material. A piezoelectric device can be equivalent to the following circuit, as Figure 7 shows, because the piezoelectric device is a kind of capacitive device that can store charge. Where C p is the internal equivalent capacitance, R L is leakage resistance, and load, u t ( ) is open-circuit voltage. According to Kirchhoff 's current law, we have: where the piezoelectric induced current is i t ( ) 0 , the capacitor charging current is i t ( ) C , the output current is i t ( ) R , the specific expressions are as follows: The first-order linear differential equation of magnetic excitation force F t ( ) and open-circuit voltage u t ( ) circuit voltage can be deduced from Equations (15)- (17): The general solution of expression of the first-order linear differential equation dy dx P x y Q x / + ( ) = ( ), as follows: The general solution of the u t ( ) was deduced based on Equations (12) and (19) as follows: In the period from 0 to t, the root mean square (RMS) value of the harvested power of the piezoelectric patches is as follows: where P τ dE dt ( ) = / is the piezoelectric patches' harvested power, at time τ τ t (0 < < ) , and E C u t = ( ) /2 p 2 . The period t is divided into j equal time steps to estimate the harvested power. Thus, Equation (21) can be rewritten as:

| BENCH TESTS OF THE PEH
To verify the rationality of the PEH structure and the validity of the research method, the PEH bench tests were performed to evaluate the magnetic force model and voltage output characteristics.

| Experimental setup
To explore the response of the PEH under reciprocating motion input, the prototype is installed on the amplitude vibration loading device, as shown in Figure 8. The amplitude vibration loading device is controlled by a computer. Adopting different constant-speed input excitations to simulate the suspension system vibration. An oscilloscope recorded the output open-circuit voltage. In this part, to test the PEH harvested power performance, the output voltage waveforms were observed under different excitation speeds v (v = 5-30 mm/s).

| Bench test analysis
The same input with a uniform excitation is used in experiments and simulations to test the prototype.  Figure 9 shows the open-circuit voltage of each piezoelectric patch in the device response to uniform excitation (v = 5 mm/s) compared to the simulation analysis result. A total of 30 magnetic slabs (n 2 = 30) are installed on the rotor of the prototype, and the screw lead l d is 5 mm. Combined Equations (2) and (11), the fluctuation period of the theoretical output voltage is 33.3 ms, which is consistent with the test results. It shows that the peak voltage of the output open-circuit from the experiment and simulation is 1.05 and 0.76 V, respectively. Next, the causes of voltage peak deviation are analyzed from the following aspects: First, there is an error between the simulation setting value and the actual value of the material performance parameters. Second, due to the welding lead at the end of the piezoelectric patch, the above part of the piezoelectric patch solder joint cannot be subjected to magnetic force, so the actual area of the piezoelectric patch involved in power generation is less than the simulation setting value. Third, the gap and friction between the connecting parts are ignored in the simulation modeling. Finally, the collection method, accuracy, and processing of test data will make the experiment value deviate from the simulation value. Therefore, it is concluded that the error between the calculated output voltage and the actual test value can meet the accuracy and engineering practical needs and verify the  magnetic excitation model and the feasibility of the modeling method.
To determine how the uniform excitation speed affects the output voltage, an extra experiment was conducted at different excitation speeds (5-30 mm/s), and Table 2 shows the specific simulation and experimental results.
It can be found from the above table that the output peak voltage rose as the excitation speed was increased, and at 30 mm/s, the value of the peak voltage was 5.07 V. The reason for this result is that with the increase in excitation speed, the rotor rotation speed, that is, the frequency of magnetic excitation, increases. Under the excitation of magnetic force, the piezoelectric patches produce a charge, and the other part of the charge is stored in the piezoelectric equivalent capacitance, and part of the charge is dissipated by the leakage resistance. The lower the loading frequency, the more the charge leakage, and the lower the voltage at both ends of the

| RESULTS AND DISCUSSION
As shown in Figure 10, the vehicle used for to experiment is a medium-duty urban electric transport vehicle (without PEH), and the test site is a Class B road. The relative velocity between the body and wheels can be easily obtained while the vehicle is in motion under various driving conditions.
On the random road surface, the driving test was conducted with a rate of 20-60 km/h, and the acceleration test was smoothly accelerated from a static state to 80 km/h. At the same time, considering the vehicle often encounters deceleration strips in the driving process, it is required to research the suspension system vibration response characteristics under the pulse road. In the pulse road test, the interval between the two groups of deceleration strips was set to 20 m, and the vehicles passed through at the speed of 10-40 km/h, under two cargo states (unladen state and laden state), respectively.
Combined with the test results and Equations (2), (11), (12), (13), (21) and (22), the RMS of the power harvested by the PEH can be calculated. At the same time, the influence of vehicle speed, road surface classification, and cargo states on the power harvested was considered. In the random road test, the vehicle drives on the road, at different speeds, under the same cargo states. The influence of the driving speed on the suspension system's relative velocity and the PEH harvested power is illustrated in Figure 11A-F. Figure 11A-E shows the relative velocity variation between the body and the wheels with different driving speeds. When the vehicle drives at the same speed, under the laden state, the relative velocity is greater than that under the unladen state. When the driving velocity is 50 km/h, the maximum relative velocity is 0.4204 and 0.1901 m/s, respectively. As shown in Figure 11F, under the unladen state and laden state, the harvested power rise with the increase of driving speed, and the increased speed increase along with speed. Specifically, the vehicle speed increases from 20 to 60 km/h, the harvested power increases from 0.18 to 13.32 W under the unladen state, while it rises from 0.28 to 24.28 W under the laden state. We can find the following two points: first, two curves have the same variation trend with speed; second, at the same speed, compared with the unladen state, the harvested power under the laden state is more prominent.
It takes 20 s for the vehicle to accelerate from the stationary state to 80 km/h on a random road surface. As shown in Figure 12, under the laden and the unladen state, the relative velocity between the body and the wheel in the suspension system versus time. It can be found that during the whole acceleration process of the vehicle, the relative velocity increases as the driving speed increases, and the maximum amplitude under the unladen state is more significant than that under the laden state. Under the two cargo states, the maximum amplitude is 0.5198 and 0.2103 m/s, and the harvested power is 33.876 and 2.955 W, respectively.
By comparing the curves in Figures 11 and 12, it is obvious to find that under the same cargo state and driving speed, the relative velocity during the acceleration process is lower than the relative velocity in the steady motoring condition. The primary reason for this phenomenon is that, during the acceleration process, the acceleration direction is consistent with the vehicle driving direction, making the load on the front axle in the vertical direction lighter than that in the uniform speed.
It is common to encounter deceleration strips for a vehicle in daily traveling, as shown in Figure 10. Therefore, studying the PEH harvested power under pulse road excitation is necessary. Figure 13 shows the F I G U R E 12 Relative velocity varies with time.
variation of relative velocity, relative displacement, and harvested power during vehicle drives on a pulse road, where the sample analysis duration is 10 s. In the analysis process, take the data collected within 10 s as the analysis object, so the phase and frequency of the relative displacement and the phase and frequency of the relative velocity will be inconsistent, which will not affect the final analysis result. Figure 13A shows that, under the unladen state, at a speed of 40 km/h, the vehicle passes two deceleration strips, and the maximum amplitude of relative velocity and displacement can reach 2.434 m/s and 0.0547 m, respectively. Under the laden state, the relative velocity and displacement vary with time, as shown in Figure 13B. Relative velocities' maximum amplitude is 2.356 m/s, and relative displacements' maximum amplitude is 0.0493 m. Figure 13C shows the variation of the harvested power with the vehicle speed. The variation trends of the RMS of the power harvested by PEH are the same in both conditions of the unladen state and laden state.
The harvested power is positively associated with the vehicle speed, and its maximum value, at the rate of 30 km/h, under the two cargo states, is 3346 and 2918 W, respectively. The main reason for this result is that when a vehicle drives on the pulse road at the speed of 30 km/ h, the excitation frequency of the road surface approaches the suspension system's natural frequency, which makes the suspension system vibrate violently. At this time, the suspension system has a larger relative velocity and displacement, so the harvested power of PEH is maximized.
Comparing and observing Figures 13C and 11F, it is evident that the harvested power on the pulse road is much larger than that on a random road. This is because on the pulse road, the suspension system vibrates more severely, and the relative velocity and displacement are more significant than on the random road.
In addition, as shown in Figure 13C, under the unladen state, the harvested power is always larger than that under the laden state, at the same driving speed. This is because, under the unladen state, the pulse road excitation frequency is more similar to the suspension system's natural frequency. Therefore, the PEH has better power generation capacity under the unladen state.
Compared with the results of Xie and Wang, 15 on a random road, the maximum of the generated power of the PEH is 24.28 W, which is much lower than 738 W. At the same time, the power generation of PEH, on a pulse road, that is, when the vehicle passes through deceleration strips, the power generation of PEH is much larger than 738 W.

| CONCLUSION
This research demonstrated a novel PEH that converts the suspension system vibration energy into electrical power with noncontact magnetic force and piezoelectric effect. The proposed device is composed of a motion conversion component and an energy conversion component. A screw-nut mechanism can convert linear vibration between the vehicle body and the wheel into rotational motion and is used as the motion conversion component. As a core component of the PEH, the energy conversion component converts rotational motion into electrical energy via the alternant magnetic force excitation and the piezoelectric effect, the generated power is stored to power vehicle electrical equipment as an alternative energy source.
A prototype was manufactured, and the accuracy and reliability of the magnetic force model were proved based on PEH bench tests. The results show that the output peak voltage increased as the excitation speed was enhanced. Moreover, based on the vehicle field test, the influence of the driving speed, the road surface, and the cargo states on the harvested power of the PEH is obtained. The maximum value of the harvested energy is 24.28 W when the speed is 60 km/h, under the laden state, on a random road. The maximum values of both loading conditions on a pulse road are obtained under the condition that the vehicle drives at 30 km/h, and its values are 3346 and 2918 W, respectively. A mediumduty urban electric transport vehicle can be equipped with at least four PEHs, and the collected electrical power can be utilized to power some auxiliary systems of the vehicle or be stored in a battery. Then, the energy utilization efficiency of the vehicle could be improved.
In future work, two key issues need to be further studied. On the one hand, there is an urgent need to optimize the structure of PEH to improve its energy conversion efficiency. On the other hand, the manufacturing cost significantly affects affecting the popularization and application of the novel PEH. The novel PEH's initial cost and economic analysis are essential to the subsequent research.