# Identification Procedure for Design Optimization of Gravitational Electromagnetic Energy Harvesters
###### Abstract  
Energy harvesting is a promising technique for supplying low-power devices as an alternative to conventional batteries. Energy harvesters can be integrated into Autonomous Internet of Things (AIoT) systems to create a wireless network of sensor nodes for real-time monitoring of assets. This paper shows a design and optimization methodology for gravitational vibration-based electromagnetic energy harvesters (GVEHs) of different sizes considering the design constraints of its real application. The configuration, analytical model, and electro-mechanical coupling of these devices are described in detail. A numerical model is developed in the Ansys Maxwell FEM environment to derive the non-linear stiffness and damping of the asymmetric magnetic suspension. Experimental laboratory tests on three harvester prototypes are compared to numerical results of dynamic simulations in MATLAB/Simulink for the validation of the proposed model through error estimation. The fully-parametric validated model is used to perform sensitivity analyses on the device's mechanical characteristics of natural frequency and magnet equilibrium position by varying the fixed and moving magnets dimensions. The set of magnets composing the magnetic spring is chosen complying with the application design constraints of size and resonance frequency tuning. Coil parameters of length and number of turns are optimized for maximum output power generation. The optimized device simulated performances are compared to other devices in the literature in terms of NPD, a significant index that evaluates power density under different excitation amplitudes. The optimized harvester presents the highest NPD value of 2.61, achieving an improvement of 52% with respect to the best harvester amongst the three tested prototypes. vibrational energy harvesting; magnetic spring; numerical model; experimental tests; optimization; Autonomous Internet of Things +
Footnote †: journal: Applied Sciences  
electric power [4]. Vibrational electromagnetic energy harvesters (VEHs) can be classified by the transduction mechanism in piezoelectric (refs. [5; 6; 7]), electromagnetic, and triboelectric harvesters [8]. The electromagnetic energy harvester working principle relies on [PERSON]'s law of voltage induction thanks to a variable magnetic flux generated by the relative motion between a magnet and a coil [9]. The most common configurations for electromagnetic energy harvesters are spring-mass-damper 1 DOF (one degree-of-freedom) systems. The maximum power conversion happens at the resonance frequency of the system. Consequently, one of the relevant design issues is the correct tuning of the resonance frequency with the fundamental excitation frequencies of the ambient vibrations of the specific monitored system on which the harvester is installed. Linear generators using traditional mechanical springs show limited bandwidths for effective power generation, hence solutions to improve the conversion efficiency should be studied [10; 11]. An effective solution can be the introduction of non-linearities in the system dynamics, more specifically using non-linear magnetic springs. Magnetic suspensions have significant advantages with respect to the use of mechanical springs. The absence of mechanical systems leads to an improvement in durability and maintenance reduction. Magnetic springs show resonance conditions at a low-frequency range, thus being compatible with harvesting applications in industrial vehicles [4; 12]. In recent years, many researchers have studied different configurations of magnetically-suspended VEHs (MVEHs) to maximize generated power. [PERSON] et al. [13] have studied a multi-frequency MVEH consisting of an array of four generators to enhance power density and broaden the frequency band. [PERSON] et al. [14] developed a small-sized MVEH to harvest human body mechanical motion with an optimized design to maximize output power. [PERSON] et al.