Research on the Motion of Few Tooth Magnetic Gears with Given Initial Angular Velocity Based on Euler Method

Abstract This paper aims to investigate the motion patterns of magnetically interacting gears with a few teeth and given initial angular velocities. Based on Ampere’s molecular current hypothesis, an equivalent current model is utilized to solve the magnetic field generated by cylindrical permanent magnets. Comsol software is employed to simulate the distribution of the magnetic field, demonstrating that the magnetic field calculated by the equivalent current model is in good agreement with the actual situation. Vector analysis, field theory, and the symmetry of the magnetic field distribution are leveraged to simplify the calculations, thereby reducing the runtime of the program. The Euler method is adopted to numerically simulate the motion of the gears. Finally, a comparison with experiments shows that the motion patterns in the experiments are essentially consistent with those in the numerical simulations. It is concluded that the ratio of magnetic field intensity to resistance torque, initial magnetic potential energy, and initial angular velocity positively correlate with the motion duration; the ratio of magnetic field intensity to resistance torque and initial magnetic potential energy positively correlate with the intensity of motion; when the initial angular velocity is excessively high, the other gear exhibits slight vibrations in its original position, and only when the initial velocity decreases to a certain value do the two gears interact significantly.