In the study of nonlinear bi-stable piezoelectric cantilever energy harvesting system, the accuracy of magnetic force’s calculation on which the potential function and dynamics of the system depend is essential to predict the output response and energy harvesting effect. In this paper, we built a shape function to calculate the trace of the end of the beam with the integral of the entire cantilever beam’s slope, and the magnetic force is consequently derived from the achieved magnets’ real-time position and posture using the magnetizing currents method. With the comprehensive consideration of axial magnetic force and lateral magnetic force, the change of both resultant magnetic force’s value and direction are achieved. The simulation results demonstrate that when the displacement of the magnet at the end of the beam is large enough, the axial and lateral magnetic forces change turn from repulsion to attraction, which leads to a large veer of the direction of resultant magnetic force across two quadrants. And the relationship between magnetic force and interval between two magnets is also achieved. The calculation results of this work are nicely consistent with experimental data. So, the accuracy of this calculation method has been proved to be much higher than the existing calculation method.
Magnetic force of piezoelectric cantilever energy harvesting system with an externally applied magnetic field based on magnetizing current method