Mathematical modelling of cylindrical electromagnetic vibration energy harvesters

In this paper the first steps for the derivation of a mathematical model to describe the mechanical behaviour of a cylindrical electromagnetic vibration energy harvester, designed to extract energy from human gait to power biomedical implantable devices, are provided. As it is usual, in the modelling of such devices, the proposed mechanical model is also based on the solution of Newton's second law, but here a nonlinear closed-form expression is used for the resulting magnetic force of the system, unlike what has been done in previous works where, traditionally, that expression is a linear or is a nonlinear approximation of the real one. The main feature of this mechanical model is that it depends on several parameters which are related to the main characteristics of this kind of devices, which constitutes a major advantage with respect to the usual models available in the literature since these characteristics can always be changed in order to optimize the device.

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