Multidimensional vibrationally driven energy generation: State-of-the-art review and modelling generalization

Most real-world mechanical energy sources present significant dynamics in multiple degrees of freedom (DOF). As the performance of vibration-driven energy generators is highly anisotropic, and thus dependent not only on the time variation of the input mechanical excitation but also on its spatial orientation, a new era of multi-DOF generators has recently emerged to harvest energy from 6 DOF excitations. Up to date, literature reviews analyzing the conversion of mechanical energy from vibrational sources into electrical energy using electromagnetic, triboelectric and piezoelectric generators, have not addressed multi-DOF generators and their intrinsic characteristics. Instead, they have been focused on linear and/or rotational architectures, optimized only for unidirectional vibrations. Besides, a generalized modelling approach to effectively deal with the dynamic complexity of multi-DOF generators is still lacking. This study provides a multifaceted investigation that includes a review of the major breakthroughs carried out in the scope of multi-DOF generators, and the development of a generalized dynamic modelling approach based on Lagrangian mechanics. Thorough analyses were performed encompassing several design configurations, modelling approaches, electric outcomes, and real-world applications of 35 designs of multi-DOF generators incorporating electromagnetic and triboelectric and/or piezoelectric transduction mechanisms. Both electromagnetic and hybrid generators were already engineered comprising up to fourteen rigid free bodies and twenty-four DOFs. Three modelling approaches were used to predict the electromechanical dynamics of generators: analytical, finite element, and related hybridizations. However, the complexity of the electromechanical dynamics increases significantly with the number of internal DOFs, and thus no models reach a confidence level allowing their use to accurately predict the electromechanical behavior of generators under multidimensional excitations. A generalized model is proposed from first principles, which encompasses the balance of mass, linear momentum, angular momentum, and energy and a description of magnet-magnet potential energies and magnet-coil magnetic fluxes as a function of the DOFs between bodies. This allows prediction of the time evolution of the multiple DOFs, as well as electrical outputs from predetermined initial conditions and input forces/torques or prescribed trajectories. Power densities up to 5.44 mW/cm3 (5.44 kW/m3) and efficiencies up to 48.5 % were experimentally found in the literature. Nevertheless, no relationship has been widely explored yet between the increasing power density and the increasing sensitivity of the generators to mechanical excitations with a wide range of DOFs. Even though significant advances have already achieved in this field, our findings highlight that future research must focus on developing sophisticated generators with the ability to effectively couple all translational and rotational DOFs from both kinetic and potential energy, ensuring the minimization of coil Ohmic losses and maximization of the electromechanical coupling coefficient, and thus energy conversion efficiency, for multi-DOF excitations and loads.