Electrical and geometrical optimization for a 2DoF non-linear energy harvester

In this paper a non-linear model for a two degree-of-freedom (2dof) vibrational energy harvester is presented, together with its experimental validation. The device consists of two masses relatively oscillating one inside the other. The inner (lighter) mass comprises five NdFeB magnets, arranged in a Halbach configuration. The outer (heavier) mass is made of seven coils. Magnetic springs are placed on the top and on the bottom of the outside mass and of the inside mass respectively, in order to allow impacts between the two: this enables energy to be transferred from the heavier to the lighter mass, in order to amplify the velocity of the latter. In this way, a better ability to convert energy from small vibrations is reached using electromagnetic conversion, which is strongly affected by the relative velocity of the two masses. A finite element model is presented in order to simulate the magnetic field produced by the Halbach stack and the force of the springs as a function of the cap height. This results are then integrated in a numerical model built in Matlab, in order to study the electrical optimization for the harvester: the number of turns of the coils is varied, showing the power output produced at different frequencies. Finally, the same model is used with exponentially correlated noise as the input, and the effect of lowering the cap is introduced using the model of the springs. Experimental data are compared to the simulation results, demonstrating the effectiveness of the model.