The disks used in this experiment were made using commercially available PZT piezoelectric ceramics produced by three different manufactures nicknamed M1, M2, and M3 (The names of the manufacturers were omitted to prevent commercialism.). The PZT piezoelectric materials are in the broad category of soft-hard ferroelectric piezoelectric ceramics and their basic constants, as measured in the laboratory, are listed in .

Table 1 Averaged measured values of d_{33eff} and ε_{33T}/ε_{o}.

First, disks from the three various manufacturers were cyclically loaded at four stress values, with an amplitude of 25, 50, 75, and 100 MPa and a frequency of 5 Hz, and the output power was measured on various values of external resistors connected in parallel to the PZT disks. The number of disks used for the first two manufacturers was 12, each having a diameter of 10 mm and a thickness of 4 mm, whereas, for M3, the manufacturer used was made of eight disks with a diameter of 15 and 4 mm thickness. The applied axial compression load was adjusted to yield the required stresses of 25, 50, 75, and 100 MPa to enable a comparison among the three manufacturers. The results are presented in Figures 6–8 for the M1, M2, and M3 manufacturers, respectively. All the graphs show a maximal power output for a given external resistor. The value is about 3 MΩ for manufacturer M1 (Figure 6), 2.8 MΩ for M2 (Figure 7), and 2.8 MΩ for the last manufacturer, M3, as shown in Figure 8. These values can be considered to be the optimal parallel external resistor to be connected to the PZT disks to yield the maximum electrical power for the generator.

Figure 6 Power versus external resistance for various applied stresses, 12 disks, thickness 4 mm, and diameter 10 mm (M1).

Figure 7 Power versus external resistance for various applied stresses, 12 disks, thickness 4 mm, and diameter 10 mm (M2).

Figure 8 Power versus external resistance for various applied stresses, 8 disks, thickness 4 mm, and diameter 15 mm (M3).

Taking into account Equation (7), one would have expected that increasing the stress would increase the electric power measured on the external resistor. Figures 6 and 7 show that, up to a value of 75 MPa, an increase in the applied mechanical stress would lead to a higher electrical power. However, when the stress is increased to 100 MPa, there is a drop in the electrical power for piezoelectric disks manufactured by M1 and M2. However, for disks manufactured by M3, there is a steady increase in the electric power up to 100 MPa. This shows that the quality of the PZT powder used to manufacture the disks is a prime factor to determine the ability to withstand high stresses. Also, it seems that there is a boundary stress, above which a given PZT disk would not increase its electric output power. For the first two manufacturers, this stress seems to be 50 MPa, whereas, for the third manufacturer, it is approximately at 75 MPa. This is clearly shown in Figure 9, where the output power nondimensionalized by the output power at a stress of 25 MPa is presented as a function of the applied compressive stress, for the various manufacturers and compared with the predicted output power, according to theory [Equation (7)]. As already stated before, only the disks manufactured by M3 are able to comply with the predicted output, up to a stress of 75 MPa, beyond which the electric output power ceases to follow the predicted output, and a large difference between the two is experienced (see also [17]).

Figure 9 Power versus external resistance for various applied stresses all three manufacturers, M1, M2, and M3 and theory.

Another factor to be taken into account is the effect of the repeated loading on the electric output power, or the number of cycles the disk experiences during his lifetime, without reduction in its electrical output. Figure 10 shows the electric power versus loading cycles, for disks manufactured by M2, and under a stress of 65 MPa. The power was supplied by 20 PZT disks having the diameter of 7 mm and a thickness of 4 mm.

Figure 10 Power versus loading cycles at stress 65 MPa, 20 piezoelectric disks, thickness 4 mm, and diameter 7 mm (M2).

After a relatively low number of cycles (6000), a sharp drop in the electric output has been experienced for the disks manufactured by manufacturer M2.

This is further emphasized in Figure 11, where the power output is measured as a function of the external resistor connected in parallel to a generator built of 10 PZT disks having a diameter of 100 mm and a thickness of 4 mm under a stress of 64 MPa and manufactured by M2. A clear reduction in the electric output has been measured for cycles up to 11 kilocycles.

Figure 11 Power versus external resistance at stress 64 MPa, 10 piezoelectric disks, thickness 4 mm, and diameter 10 mm (M2).

The same reduction in the electrical output was experienced by disks manufactured by another manufacturer, M3. In this test, 10 PZT disks with a diameter of 10 mm and thickness of 4 mm were tested under 50 MPa, and their electrical output was measured for various numbers of cycles (see Figure 12). A reduction of about 13% in the electric output was measured when the numbers of cycles was raised from zero cycles (output 0.068 W) to 9 kilocycles (output 0.060 W).

Figure 12 Power versus external resistance at stress 50 MPa, 10 piezoelectric disks, thickness 4 mm, and diameter 10 mm (M3).

Another issue investigated in the present test series was the sequence of loading and its effects on the electric output.

This is depicted in Figures 13 and 14 for disks manufactured by M3 and subjected to various compressive stresses. Figure 13 shows the averaged electric output produced by five PZT specimens when compressed by 50 MPa and then raised to 75 MPa and back to 50 MPa. The number of cycles at each point was very small (10–15 cycles). The applied axial compression load was 50 kN and the various stresses were accomplished by increasing or reducing the number of disks. One can clearly see the reduction in the electric output from 5.38 to 3.28 mW (64% reduction) due to the fact that the stress was increased by a factor of 1.5–75 MPa.

Figure 13 Output power versus applied compressive stress – the influence of the sequence of stresses: 50, 75, and 50 MPa (M3).

Figure 14 Output power versus applied compressive stress – the influence of the sequence of stresses: 50, 60, 50, 60, and 50 MPa (M3).

To further understand this issue, another sequence of loading was performed and the electric power was measured. This is shown in Figure 14, where the averaged electric output for the same five PZT specimens (as before) were compressed to 50 MPa and then to 60 MPa, back to 50 MPa, again raised to 60 MPa, and reduced to 50 MPa. This sequence of loading leads to improved results: a reduction of only 16% (from 5.38 to 4.64 mW) when doing the first part of the load sequence (50–60 MPa and back to 50 MPa) and no further reduction when performing the second part of the sequence (50–60 MPa and back to 50 MPa). This shows that the upper compressive stress for this type of PZT (manufactured by M3) is about 60 MPa.

According to Equation (7), to obtain a power above a given limit, one can either increase the mechanical stress or increase the volume of the piezoelectric material. In view of the stress limitations shown before, a test was carried out with eight layers of piezoelectric material, one on top of the other, while each layer consisted of 16 disks with a 10 mm diameter and 4 mm thickness, loaded at 50 kN, yielding a compressive stress of 40 MPa.

The results of the electric power for each layer are shown in Figure 15 as a function of the external resistor connected in parallel to each PZT layer. In general, the electric output is evenly distributed in each layer and the difference among the various layers was <10%. The total power was measured to be 0.43 W at 40 MPa having eight PZT layers. To obtain the same amount of power, the following configurations are feasible: a stress of 50 MPa with only five layers or a stress of 60 MPa with four layers. This shows that, to compensate for a relative low mechanical stress, one would have to increase the volume of the PZT material to obtain the same electric power.

Figure 15 Power versus external resistance at stress 40 MPa, eight layers, 16 piezoelectric disks, thickness 4 mm, and diameter 10 mm for each layer (M3).

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