Figure 18.14 shows the measured open circuit voltage of the energy harvester with different springs and resonant frequencies. For spring #1, with resonant frequency of 27 Hz, the peak voltage is 1.18 V for an acceleration amplitude of 2 x g; for spring #2, with resonant frequency of 33 Hz, the generated maximum voltage is 1.64 V for an acceleration of 3 x g; spring #3, increased the peak voltage to
Fig. 18.14 Measured results of the open circuit voltage for the energy harvesting device with three different springs at respective resonant frequencies: spring #1 at 27 Hz; spring #2 at 33 Hz, and spring #3 at 42 Hz
Fig. 18.15 Measured maximum output power of the harvester with three different springs and their associated resonant frequencies
2.52 V, with an intrinsic frequency of 42 Hz and an acceleration of 5 x g. Increasing acceleration values were applied to maintain the same source vibration displacement amplitude. The maximum output power on a 2.6 £2 load is 133.88 mW, 258.62 mW, and 610.62 mW, respectively, as shown in Fig. 18.15. Considering that the total practical volume of the device 29.3 cm3, this device has good performance with a maximum power density of 20.84 mW/cm3 at 42 Hz (using spring #3). The Q factor of the harvester at 42 Hz is 16, which was obtained from the decay curve
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of output voltage when turning off the source . Almost all of the damping is generated by the mechanical collision between the spring supported magnets and the solenoid holder. That means a much lower input force or acceleration is needed and much higher Q factor could be reached by using a better manufacturing technique. A simple relation between frequency and power can be derived from Eq. (18.10), Pmax~(AM/AT)2~/2, if all other parameters kept constant, where AM is the flux change per period and AT is the period. In fact, the measured results agree with the parabolic curve fitting, as shown in Fig. 18.15. Clearly this vibration energy harvester design can accommodate different vibrating frequencies of the environment by changing the spring that is connected to the hard magnet pair. If the vibration amplitude of the testing stage is kept the same, the output power and power density are proportional to the second power of the vibration frequency. Hence, if this Pmax~/2 relationship can be extrapolated to higher frequencies, much higher output power density can be achieved on condition that the ambient vibration amplitude is constant. Note that a large working bandwidth could still be obtained at high frequencies due to the nonlinear effect. These exciting data prove a promising future of the high-permeability material-based energy harvesting mechanisms.
In order to construct the frequency response curve, testing data were collected at different values of the source frequency. As indicated in Fig. 18.16, output power shows a gradual rise below 42 Hz and a rapid decline above this frequency. The major reason for the asymmetrical curve is the nonlinear oscillation with increasing mechanical damping as the frequency increases, as explained earlier. The half-power bandwidth of the device with spring #3 was measured to be 6 Hz, 15% of the central frequency, which is relatively large.