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The dynamic behavior of a vibrational electromagnetic generator using a magnetic levitation architecture was theoretically and experimentally studied in great detail, when operating under a wide range of three-dimensional excitations. We developed a complete rigorous physical model from first principles based on the theory of electrodynamics of continua, centered on the laws of electrodynamics and balance of mass, linear momentum, angular momentum, energy and entropy. Local electromagnetic and gravitational body forces, couples and powers were considered, and the surface tractions were divided into constraint and friction components, as well as those due to external mechanical energy sources. The balance of linear momentum, angular momentum and circuit equations resulted in up to 13 non-linear differential equations describing the dynamics of the levitating-magnet and container, relating input forces and torques with output displacement, constraint forces and voltage. The balance of energy yielded a consistent equivalence between the time rate of change of the internal kinetic and potential energies of the generator and the output power, associated with the external circuit, Ohmic losses and friction losses, as well as the input mechanical power being supplied to the system by the environment. Both the input and output powers were proven to tend to increase equally when operating the generator under resonant conditions. The levitating generator was shown to be sensitive to axial translational and centrifugal inertial forces, each one effectively resulting in a uni-stable or bi-stable system. The dynamical response yielded multiple initial conditions dependent steady-states, hysteretic frequency output and chaotic characteristics. Relevant guidelines to optimize the energy conversion efficiency of energy harvesters are provided. This model was validated by experimental tests, including general 3D motions combining translations and rotations: cross-correlations exceeding 90% were achieved. Such Newtonian and Langrangian modelling approaches hold great potential to be easily adapted to a wide range of other electromagnetic generators, with multiple degrees-of-freedom and operating under various environments, such that significant advances in energy technologies can be supported. • A complete wide-reaching physical 3D model of electromagnetic generators was developed. • 13 non-linear differential equations were deduced to describe their dynamics. • Cross-correlations exceeding 90% were achieved for general 3D mechanical excitations. • Such model holds great potential to be adapted to a wide range of other generators. [ABSTRACT FROM AUTHOR]

• Electromagnetic energy harvesting holds potential for small and large-scale devices. • Twenty-one designs were found and differentiated in four categories. • Four modelling approaches were distinguished to model the transduction mechanisms. • Electric power densities of up to 8 mW/cm3 (8 kW/m3) were already achieved. • No multivariable performance optimization was already performed. Motion-driven electromagnetic energy harvesters have the ability to provide low-cost and customizable electric powering. They are a well-suited technological solution to autonomously supply a broad range of high-sophisticated devices. This paper presents a detailed review focused on major breakthroughs in the scope of electromagnetic energy harvesting using magnetic levitation architectures. A rigorous analysis of twenty-one design configurations was made to compare their geometric and constructive parameters, optimization methodologies and energy harvesting performances. This review also explores the most relevant models (analytical, semi-analytical, empirical and finite element method) already developed to make intelligible the physical phenomena of their transduction mechanisms. The most relevant approaches to model each physical phenomenon of these transduction mechanisms are highlighted in this paper. Very good agreements were found between experimental and simulation tests with deviations lower than 15%. Moreover, the external motion excitations and electric energy harvesting outputs were also comprehensively compared and critically discussed. Electric power densities up to 8 mW/cm3 (8 kW/m3) have already been achieved; for resistive loads, the maximum voltage and current were 43.4 V and 150 mA, respectively, for volumes up to 235 cm3. Results highlight the potential of these harvesters to convert mechanical energy into electric energy both for large-scale and small-scale applications. Moreover, this paper proposes future research directions towards efficiency maximization and minimization of energy production costs. [ABSTRACT FROM AUTHOR]

• Automated electromagnetic generators with self-adaptive coil switching are proposed. • A transduction model from first principles was developed and validated. • The generator performance was improved up to 26% using self-adaptation. • Complex dynamics of the resonant non-linear system were investigated. • Promising generator design combining energy transduction and automation engineering. Self-powered electronic devices have been widely sought after in the last few years demanding efficient harvesting of locally available forms of energy. Electromagnetic generators are suitable contenders for powering both small-scale and large-scale devices due to their widespread availability and customizability. New promising magnet levitation architectures for mechanical vibration energy harvesting offer low production and maintenance costs, as well as a wide array of designs. They also exhibit complex non-linear and hysteretic resonant behaviors. Nonetheless, their performance is typically optimized towards external excitations with very specific characteristics. In this study, we theoretically and experimentally prove the concept of an instrumented self-adaptive levitation generator with on/off coil switching employing an accelerometer, transmission gate switches and a processing system. This adaptable system is able to periodically turn off coils not contributing to the generated electromotive forces for certain frequencies and amplitudes of the input excitations. Taking the power consumption of instrumentation into account, power gains up to ≈ 26% were achieved for harmonic inputs with randomly time changing frequencies and amplitudes. Using a prototype generator with 140.7 cm3, output average powers of up to 1.79 W (i.e., 12.7 kW/m3) were extracted for optimal electrical loads under non-linear resonant conditions. Significant increases in electric power efficiencies were achieved as well. These promising results should pave the way towards intelligent self-adapting energy generators. [ABSTRACT FROM AUTHOR]