The aim of this article is mathematical modelling and investigation of chosen parameters of a small energy harvesting system designed for energy harvesting from car tire mechanical vibrations to provide power supply for various sensors, e.g., in tire pressure monitoring system. The energy harvester consists of three permanent magnets inserted into a tube made from polyamide material. Comsol program has been used to calculate the force between the magnets, the stiffness of the magnetic spring, and the natural frequency of the system. MATLAB program has been used to simulate the movement of the moveable magnet to compare it with the measurements. Finally, the parameters of the mathematical model of the energy harvester were investigated and validated on a specially prepared laboratory test bench.

The aim of this paper is to establish mathematical modelling and simulation for the voltage induced during movement of the moveable magnet in a double-sided magnetic spring, being part of the energy harvesting system. For various configurations of the set of permanent magnets, the repulsive forces of magnetic spring and induced voltage in energy harvester winding will be calculated. Changing the geometrical dimensions and shape of permanent magnets allows one to control the stiffness of the so-called double-sided magnetic spring, and furthermore, allows one to change the natural frequency of the energy harvester system. Properly chosen stiffness in the energy harvester system is the crucial issue for high efficiency in energy recovery. In a given case, the energy harvester consists of three permanent magnets inserted into a tube with coils wound on it. To calculate the force between the magnets and the magnetic flux in the coils, the ANSYS program was used. The voltages induced in coils for various configurations of the magnets were simulated in the MATLAB program.

In this paper, an original mathematical model and experimental results for the vibration generator and the magnetic spring prototype that converts mechanical energy to electrical energy are proposed. The magnetic spring model is developed by a robotic approach based on Denavit–Hartenberg’s notation and designed by the 2-degrees of freedom kinematic chain for determination of its motion and estimation of several resonance frequencies useful in many energy harvesting applications. The vibration generator that moves the magnetic spring is modeled by neural networks and the magnetic spring potential energy is calculated by the finite elements method (FEM). Furthermore, the magnetic spring and the vibration generator are designed by the Simulink block diagram. Testing results of the magnetic spring and vibration generator displacement conducted in laboratory have shown good agreement with simulation results.

Magnetic springs are widely investigated as energy converters alternative and energy harvesters by converting mechanical vibrations into electricity at low frequencies. In this article the design methodology of novel magnetic spring is proposed to improve the dynamic performance and electrical...