Nonlinear Effect

From Fig. 18.10, it can be seen that the working bandwidth is about 10 Hz, 18.5% of the central frequency, compared with 2.1 Hz (Ferro Solution VEH360) or 3.5% of the central frequency, for a typical linear oscillator harvester. The major reason for the large bandwidth is that the magnetic coupling is not linear to the displacement of the oscillator, so that the nonlinear effect provides the system with a wider working bandwidth [16]. As shown in Fig. 18.11, compared with the elastic potential energy, the magnetic potential energy curve has two potential wells distributed right next to each other, resulting in a wider total potential well. As long as the acceleration is larger than its threshold value, or when the cantilever is supplied with enough energy to get over the potential barrier, it can vibrate between the two shallow potential wells. Thus a relatively wide oscillation region at a particular driving frequency is obtained. However, if the oscillator is not supplied with enough energy or the damping is so strong that it is not able to overcome the potential barrier, the oscillation is limited in one well, instead of two. In this case, the behavior of the oscillator is more like that of a linear one, with a narrow working bandwidth.

Both the calculated and measured curves in Fig. 18.10 exhibit unsymmetrical peaks about the central frequency. This is because the performance of the oscillator at lower frequencies differs from that at higher frequencies. At lower frequencies, the oscillation behavior is dominated by the nonlinear effect. The output power decreases slowly as the frequency reduces due to the mismatch between the intrinsic and driving source frequency. Even at a frequency as low as 30 Hz, oscillation between the two potential wells was still observed. However, at a higher frequency range than 54 Hz, the performance is dominated by the linear effect and the

Fig. 18.11 Elastic potential energy (dotted line), magnetic potential energy (dash line), and total potential energy (solid line) of the oscillation system as functions of the free end displacement of the beam

oscillator was observed to be trapped in one well, leading to one sided narrow peaks in the voltage signal. This is because in the higher frequency range, a larger dynamic speed results in a larger damping force, so that the cantilever does not have enough energy to climb over the potential barrier. This single well oscillation dramatically decreases the harvesting efficiency, because the cantilever beam cannot reach flux reversal.

Updated: December 18, 2015 — 12:33 am