Magnetic force analysis and performance of a tri-stable piezoelectric energy harvester under random excitation

Recently, harvesting energy from environment has attracted lots of researchers' interests. Ambient vibrations are deemed as a promising power supply since it can be found almost everywhere. Piezoelectric effect has been exploited to convert mechanical energy to electricity. Nonlinearity techniques are favorable for improving the performance of piezoelectric energy harvesters. This paper focuses on a tri-stable piezoelectric energy harvester (TPEH) with two fixed external magnets. The lumped-parameter method is used to investigate the large-amplitude and broadband voltage response. A method based on equivalent magnetizing current theory is first applied to calculate the magnetic force and the potential function with triple wells. We find that this calculation method for magnetic force is more applicable for different magnet intervals compared with the magnetic dipoles method used before. Once the system parameters are chosen appropriately, large-amplitude interwell motion among three wells can be achieved. In our study, a filtered Gaussian noise within the frequency of 0-120 Hz is selected as harvester's excitation, which is similar with the realistic low-frequency vibration in environment. Simulation and experimental results demonstrate that the TPEH enhances the output voltage significantly compared to the conventional bi-stable piezoelectric energy harvester (BPEH). Also, the TPEH's frequency bandwidth is further broadened. Besides, it has been proved that the corresponding optimum magnet interval only changes slightly when the excitation intensity varies, therefore there is no need of adjusting the system parameters to meet practical conditions.