The electrical performance comparisons of the PZT-5H bimorph cantilever with and without the tip mass are given in this section. Table 4.7 shows the detailed performance results for the maximum power output (along with the respective values of the optimum load resistance), the maximum voltage (for Rl ^ to), and the maximum current (for Rl ^ 0) outputs at the fundamental short – and open-circuit resonance frequencies. The maximum power density and specific power values are also given. It is observed that the maximum power output for resonance excitation increases by a factor of more than two with the tip mass attachment. For both resonance frequencies (short circuit and open circuit), the optimum load that gives the maximum power output increases considerably in the presence of the tip mass. As will be seen in Chapter 5, the optimum load is inversely proportional to the undamped natural frequency for resonance excitation. Therefore the increase in the optimum load due to the reduction in the resonance frequency is expected. It is worth noting that the increase in the maximum values of the current output is not as substantial as the increase in the maximum voltage. The power density calculation accounts for the additional volume of the tip mass and it exhibits an increase of about 61% (from 2.1 mW/(g2 cm3) to 3.4 mW/(g2 cm3)). The specific power calculation includes the additional mass of the tip attachment and it exhibits an increase of 59% (from 0.27mW/q(g2 g) to 0.43mW/q(g2g)). For the purpose of comparing various
Table 4.7 Electrical performance comparisons of the PZT-5H bimorph cantilever with and without a tip mass of 0.239 g
energy harvester designs and materials, it is convenient to use these expressions normalized with respect to base acceleration (as well as the device volume and/or mass). However, it is extremely important to note that the amount of power output is completely dependent on the source of energy, that is, the frequency and the amplitude of the acceleration input. For instance, although the resonance performance of the configuration with the tip mass is better in Table 4.7, one should prefer the case without the tip mass for excitations around 500 Hz since the fundamental short-circuit resonance of the case without the tip mass is 502.5 Hz whereas that with the tip mass is 338.4 Hz.
It is important to recall that these FRFs are based on linear electromechanical modeling and the experiments are conducted under excitation levels less than 0.1g. For high acceleration levels, piezoelastic nonlinearities as well as nonlinear dissipation become effective and the linear predictions tend to overestimate the experimental results. For the device tested here, the linear predictions overestimate the experimental results for excitation levels higher than a few hundreds of milli-g acceleration (see Section 4.5). For instance, the power density of
2.1 mW/(g2 cm3) in Table 4.7 accurately estimates the power output as 84 pW/cm3 for 0.2g acceleration input. However, the prediction of 8.4 mW/cm3 for 2g acceleration input will likely overestimate the experimental power output significantly (see Figure 4.35). Nevertheless, the valid range of the linear electromechanical model presented in Chapter 3 (up to a few hundreds of milli-g acceleration) covers the acceleration levels available in most ambient vibration energy sources .