There are three main components to a piezoelectric harvester: the piezoelectric themselves, a housing unit for the stacks, and an energy harvesting circuit. The PZT stacks used in this harvester consist of three layers of PZT-5H material with a diameter of 10 mm and thickness of 4.75 mm per layer, totaling a stack thickness of 14.25 mm. Five of these stacks are then housed in a polycarbonate unit with a 1018 AISI low carbon steel base plate. The stacks themselves are held in place using a small 3D printed stack holder made of PLA plastic. The purpose of this module is to maximize the stress distribution of the vehicle through the asphalt to the piezoelectric. The stacks are then wired in parallel and connected to an energy harvesting power electronic.

Table 1 illustrates the materials used for each component of the harvester. Figure 2 shows expanded view of harvester module with part name and material identified.

Polycarbonate Plastic:

The Top and Base Plates are both made from polycarbonate plastic. This material has several desirable material properties for this design. Some of these advantages are high resistance to impact force, high electrical insulator capability, easy machinability, and high stiffness.

It is critical for these parts to be rigid. Any deflection in these parts will result in a loss of harvested energy. Therefore, a material with high stiffness is needed. Vehicles will be passing over the Top Plate at potentially high speed. This can create a high impact on our module, so the material must be impact resistant to prevent damage. To prevent possible electrical shorts from the piezos, an electrically insulating material is desired. Not only is polycarbonate a good insulator, but it is less expensive and lighter than the same-sized steel. Since both the Top and Base Plate need to be CNC machined, machinability is a quality crucial for success which Polycarbonate is. Table 2 details the numerical values of polycarbonate material properties.

PLA Plastic:

The Stack Holder is made of Polylactic Acid (PLA) Plastic. This material was selected because of its use in 3D printing manufacturing. The Stack Holder does not have any applied forces to it, so its structural integrity is not critical. The piezo stacks will be housed in the Stack Holder, so to prevent potentially electrical shorts, a material that is an electric insulator is desired.

1018 AISI Low Carbon Steel:

The Support Plate is made from AISI 1018 low-carbon steel. This type of steel offers a good balance of toughness, strength, and ductility. The main function of the Support Plate is to add rigid support to the Base Plate and enclose the

wires/fasteners. The Support Plate is also CNC machined, so machinability is crucial.

PZT-53HD:

The Piezo Stacks are the most essential component of the harvester. The stacks are made of zirconate titanate piezoelectric (PZT) ceramics. The specific material used for these stacks is PZT-53HD, manufactured by He-Shuai in China. PZT ceramics are preferred for their physical strength, chemical passivity, as well as their high operating temperature. These are highly desirable properties when considering the working conditions of the harvester. The properties of this material are specified in Table 3.

Neoprene Rubber:

The Spacer is made of neoprene rubber. Neoprene was selected due to its high elasticity, low stiffness, high fatigue life, and water resistance. High elasticity and low stiffness are desired to allow the Top Plate to “float” and return to its original position without permanently absorbing energy. The neoprene Spacer functions like a return spring. High fatigue life is important, so the Spacer does not wear out over time when loaded. Another function of the Spacer is to act as a gasket to prevent water from entering; therefore, high-water resistivity is desired.

Manufacturability:

The materials used to construct the harvester were chosen not only for their desired properties but their easy manufacturability. The 1018 AISI steel used in the support plate of the harvester provides a good balance of toughness, strength, and ductility. Additionally, steel was easily manufactured to the design specifications using a CNC (Computer Numerical Control) machine. This is the same reason why polycarbonate plastic was used for the toplayer and base plate. Polycarbonate is a strong, tough, and lightweight material and is easy to work with. A CNC machine was used to machine this plastic as well, shaping the material to the design specifications.

For the stack holder, PLA plastic and a 3D printer were used to manufacture the part. PLA plastic allows for a quick, cheap, and easy way to manufacture a part. This allows for easy redesigns if the part does not properly fit the PZT stacks, which have variations from the manufacturing process.

Harvester Shape:

When conducting the literature review, it was apparent that most RPEHs are circular in design. This includes the harvester designs presented in [4] [5] [6]. The latter paper [6] tests both a square and circular harvester design. This paper concludes that a square design will produce more energy. However, this design was tested with the top of the harvester exposed and flushed with the road surface. When the harvester is installed under the asphalt, as is in this design manufactured for this project, the stress distribution from the tire through the road will be in a cone shape, this is discussed in a later section. Therefore, to maximize the harvested energy the harvester shape should be circular to match the conical stress distribution.

Burger’s Model Asphalt Simulation:

Simulating asphalt in SIMULINK proved to be a difficult challenge. Developing a realistic mathematical model of asphalt is a complicated problem due to the complicated nature of asphalt mixtures which are susceptible to time-dependency, temperature, plastic flow in the binder, friction among particles, and the coupling of all these effects [7]. To formulate a constitutive description of viscoelastic materials one can also use differential formulation based on mechanical models. Mechanical models consisting of springs and dampers provide some physical insight into the viscoelastic behavior of materials. A widely used model of viscoelastic behavior for asphaltic materials is the Burgers model, shown in Figure 3 [7]. The parameters of the Burger’s model are shown in Table 4, when simulating the model, the average values were used and multiplied by the thickness of the asphalt to obtain the N/m and N/(m/s) units needed to input in the SIMULINK spring and damper blocks.

Determining Optimal Harvester Dimensions:

It is essential to optimize the diameter of the RPEH module, so the maximum amount of stress is applied. The optimal harvester diameter is directly related to the thickness of asphalt. The process below was used to determine the optimal

diameter. Figure 4 shows a diagram of the stress distribution cone through a specified thickness of asphalt [8].

In this work, the values of t_A and D_T were selected as follows:

t A = 5   cm (1)

D T = 12.7   cm (2)

From Figure 4, (1), and (2), the stress distribution diameter, defined by D_B, can be computed as follows:

D B = 2 t A + D T = 22.7   cm (3)

Theoretical Stress on Stacks:

Once the optimal diameter was determined, the theoretical stress applied to the stacks can be determined using the process below. These calculations are important to make sure the piezos are not overstressed. The yield strength of the PZT-5H material is 150 MPa which is greater than the calculated theoretical stack stress of 1.45 MPa with a 1500 kg car input. The same calculations were made with a 36,000 kg car input, approximately the weight of a fully-loaded semitruck, this resulted in a 14 MPa theoretical stress, still underneath the 150 Mpa yield strength of the PZT-5H material.

Optimal Module Diameter = 22.7 cm (from (3))

Defining the following parameters:

Testing Capacity Diameter = 10.16 cm

A_tire = Tire footprint area = 0.0161 m²

W = average vehicle weight per tire

σ_T = Stress on top of asphalt

σ_B = Stress below asphalt

N_Stack = Number of stacks in module

F_Module = Resultant Force on top of Module

F_Stack = Resultant Force per Stack

σ_Stack = Stress Applied to Surface of Stacks

D_Stack = Diameter of Piezo Stack

A_Stack = Area of Stack

A_Module = Area of Module = 10.17 cm

Testing Module = 10.16 cm diameter:

Car Input (mass): 1500 kg

σ T = W A t i r e = 3679   N 0.0161 = 228.5   kPa (4)

σ B = σ T D T 2 D B 2 = 228500 0.127 2 0.2286 2 = 70.5   kPa (5)

F M o d u l e = σ B A M o d u l e = 70500 × π 4 × 0.1016 2 = 572   N (6)

F S t a c k = F M o d u l e N S t a c k = 572 5 = 114   N (7)

σ S t a c k = F S t a c k A S t a c k = 114 π 4 × 0.010 2 = 1.45   MPa (8)

Semi-Truck Input: 36,000 kg

σ T = W A t i r e = 35000   N 0.023 = 1.5   MPa (9)

σ B = σ T D T 2 D B 2 = 1500000 0.153 2 0.2286 2 = 0.7   Mpa (10)

F M o d u l e = σ B A M o d u l e = 700000 × π 4 × 0.1016 2 = 5.7   kN (11)

F S t a c k = F M o d u l e N S t a c k = 5700 5 = 1.1   kN (12)

σ S t a c k = F S t a c k A S t a c k = 1100 π 4 × 0.010 2 = 14   MPa (13)

The main factors that affect the power output of a piezoelectric transducer are the piezoelectric material properties, the applied force, loading frequency, and the resistance of the connected load.

It can be proven from [4] that the output voltage V_p and the energy W produced by the piezo stack are given by

V p = α F h d 33 n A p ε r (14)

W = d 33 2 α 2 F 2 h 2 n A p ε r (15)

where d₃₃ is the piezoelectric strain constant, α is the force attenuation coefficient of the road, F is the vertical load stress, h is the thickness of piezoelectric ceramics.

It is clear from (1) and (2) that V_p and W are altered by both mechanical and electrical properties of the piezoelectric material. Optimization is required to address the device parameters that produce the maximum energy and voltage.

SIMULINK and MATLAB were the primary programs used to simulate the RPEH. MATLAB was used to write a simple code that would allow the user to enter the harvester variables in the SIMULINK diagram. These input variables were then used in a SIMULINK block diagram, shown in Figure 5(a). SIMULINK also has a premade piezoelectric stack block in its library. This block allows the user to easily change the number of layers, layer thickness, and diameter of the PZT stack. The layers in the PZT stack are connected in parallel. The stacks themselves are also connected in parallel. SIMULINK allows the user to generate a mechanical pulse, which is then converted into voltage through the PZT stack block. The mechanical pulse simulates the car tires driving over the

harvester. The RPEH Block diagram uses the burgers asphalt model, shown in Figure 3, to simulate the asphalt layer above the RPEH. Inside the circuitry subsystem (Figure 5(b)) is a Synchronized Switch Harvesting on Inductor (SSHI) rectifying circuit. This circuit serves as a high-efficiency rectifier, which converts the AC voltage produced by the PZT stacks into a DC voltage. The SSHI technique is based on the resonant circuit that is created by the internal capacitor of the piezoelectric stack and an external inductor which flips the capacitor voltage instantly to nullify the effect of the capacitive term. In this way, the energy used to charge the internal capacitor to conduct the diode bridge, which would have been wasted, is now harvested [9].

In this simulation, the DC voltage is then sent to a storage capacitor (470 μF), where the energy harvested per car was measured using the SIMULINK oscilloscope. It was based on this parameter that the optimum size of the PZT stacks was determined.

When determining the optimum thickness and number of layers per stack, a standard 15 mm total thickness was used, as well as a static 10 mm diameter. Table 5 shows the results of the optimization after simulation. The highlighted values indicate the PZT stack size and layers that were used in this design.

Based off the SIMULINK results, the optimal stack dimensions are a diameter of 10 mm with 3 stack layers, each layer 4.75 mm thick. The resulting waveforms are shown in Figure 6. The voltage waveform was obtained by taking the voltage

across the load resistor and thus the parallel load capacitor. The harvested electrical energy W stored in the capacitance C was then calculated as follows:

W = 1 2 × C × V c 2 (16)

where V_c is the voltage across the capacitor.

The RPEH was tested using a Hamburg Wheel Tracking machine. This machine is used in AASHTO-T324 asphalt testing to simulate road loading conditions and to test the permanent deformation resistance of the asphalt layer. The wheel tracking machine applied a force of approximately 700N to the asphalt at a speed of 1.6 km/h. The 700N force would be divided amongst the five stacks to total an approximate force of 140N per stack.

The RPEH was embedded in “Aquaphalt” which is a cold compacting asphalt mix used in driveway repairs. Cold compacting asphalt was used in this test as the harvester cannot be embedded in a hot mix of asphalt. The embedding process is shown in Figure 10.

After the RPEH was embedded in the Aquaphalt, it was left to cure for 24+ hours to allow the mix to stiffen. Once the RPEH was installed into the mold and underneath “Aquaphalt” it was then put into the Hamburg Wheel Tracking machine. The wheel tracking machine, with the embedded RPEH, is shown in Figure 11. The RPEH then was tested with an open circuit and with a load R_L equals to 10 kΩ, 100 kΩ, 500 kΩ, 600 kΩ, 900 kΩ, 1 MΩ and 10 MΩ. The peak voltage V_L across R_L is recorded. Then, the peak instantaneous power P_L(peak) delivered to the load is given by:

P L ( p e a k ) = V L 2 R L (17)

After running the tests using the wheel tracking machine, Figure 12 shows the results. This includes the instantaneous peak voltage for each tested resistor, as well as the peak instantaneous power. These are visualized by the blue bar graph, and the orange line plot, respectively. Additionally, an estimated power curve was included on the graph in orange. During testing, connecting a 900 kΩ resistor to the RPEH yielded the highest power output; however, a value of 950 kΩ would most likely yield a slightly higher value, as predicted by the curve.

Additionally, the oscilloscope data obtained during the asphalt test was imported into MATLAB to calculate the transient energy harvested per one loading pass. This was accomplished by using the “xlsread” function to import the oscilloscope “.csv” files into MATLAB. Following that the “trapz” function was used to calculate the area under the power curve, energy. These values were then

plotted in Figure 13. The process was done to obtain results that could be compared more easily to the SIMULINK simulation results. The plot implies that at a resistor load of 600 kΩ a max energy of 45 uJ was harvested.

The SIMULINK simulation, used to optimize the PZT stacks, best represents the RPEH in actual road conditions because of the force applied to the harvester, as well as the Burger’s asphalt model. These results show an approximate 20 V collected in the storage capacitor, equating in 0.0949 J of energy. This simulation was run using the SSHI rectifier circuit as explained in Section 2.2.

The wheel tracking asphalt test was conducted to observe if the RPEH would function underneath asphalt, which it succeeded in. When testing the RPEH

with the wheel tracking machine, varying resistor loads where connected to the output of the RPEH, this was done to observe the power curve, and determine the optimum resistor load. This was determined to be 950 kΩ. Additionally, MATLAB was used to calculate the energy harvested by the RPEH with each resistor attached. A max energy for this test was obtained from the 600 kΩ resistor connected to the RPEH, totaling in 45 μJ harvested. This value is much lower than the simulated energy output of 94.9 mJ, however, there are varying factors

that could have affected this change. Chiefly, the force used in the simulation was much higher than that of the asphalt test, approximately 700N compared to approximately 140N, respectively. This force was also applied at a greater speed in the simulations, about 120 km/h compared to the 1.6 km/h of the wheel tracking machine.

Therefore, a second SIMULINK simulation was run with input variables to match that of the wheel tracking machine. This included a load of 140N per stack at a speed of 1.6 km/h. Figure 14 shows the stored energy inside the load capacitor after a single pass.

The results of this simulation show an output of 500 μJ per car pass, this value is still larger than the 45 μJ calculated energy output during asphalt testing. However, there are a few factors that could differentiate the two outputs. First, the simulation was once again conducted using an efficient SSHI rectifying circuit, while the actual asphalt testing only applied varying resistor loads to the RPEH. Secondly, the simulation does not factor in the material properties of the neoprene spacer, this is most likely the cause of differing outputs as some energy had to be lost through this part. And lastly, the simulation uses the Burger’s asphalt model to simulate asphalt, during testing “Aquaphalt” was used in place of traditional asphalt found in a road. It is unclear which of these factors contributed the most to this lowered output, but it is apparent that these are the reasons.