# Coupled Numerical Model of Vibration-Based Harvester
## 1 Introduction  
The extraction of residual energy (harvesting) has been a subject of scientific research in the latest decade. In many projects and publications [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19], the arrangement of a system generating electric power is sought as a suitable or optimized solution of design proposals. A very satisfactory tool of basic research is numerical modeling [2; 3; 4; 8; 17; 18; 19]. It can be very robust [2], but also can only be used as a tool for partially solving the hybrid modeling approach [8].  
One of the prerequisites for the design of the electromechanical system is a correct way of grasping the physical principle for maximum description of phenomena and processes; it is fundamental in harvesting extraction, as cases in the theses and works [17; 18; 19]. When comparing the majority of experimental methods and approaches [9; 20], including hybrid design methods [6; 7; 8] with numerically modeled coupled tasks, the realized design using finite element methods (FEM) [2] is difficult to process but it leads to results with significant parameters relative to other quick approaches, as reported in work [19], Table 1, column \"Effective power density [W/m\({}^{3}\)]\".  
In Figure 1, an example is shown of a principal design of a harvester model based on the principle of electromagnetic induction using the Faraday induction law in its full range [2; 19]. The analysis and results evaluation were based on the numerical model solved by the FEM.  
The critical parameter can be, for example, the boundary sensitivity of the generator to the minimum vibration amplitude. For the studied design the acceleration value is \(G=0.01\ g-0.05\)\(g\) (\(g=9.81\) m/s\({}^{-2}\)). Minimal external dimensions of the microgenerator (MG) had to be found and simultaneously, the expected volume was in the range of \(V_{\text{MG}}=(10-50)\times 0.10^{-6}\) m\({}^{3}\). Further, the range of expected output effective power (RMS) was \(P_{\text{out}}=\)10-100 mW, expected output voltage range \(U_{\text{out}}\) =2-20V and excitation frequency range \(f_{\text{s}}=\)15-35 Hz. The principle of resonant arrangement of the moving MG core was used to attain a high efficiency of the vibration transformation, Figure 1. For moving path selection as linear part with non-linear magnetic braking system (Figure 2a), this concept was fully numerically modeled using the associated FEM model (112) described below. It has been shown that the technical solution of the MG core conductor designed within our approach leads to an increase in the damping coefficient and it does not have sufficient sensitivity to lowest acceleration values in the range \(G=0.01\ g-0.02\ g\). Therefore, the concept of beam version (BV) in the arrangement, Figure 2b,c was approached in the solution. Thus the designed and tested MG achieved the expected parameters in the range \(G=0.01\ g-0.02\ g\).  
A swinging arrangement (BV, Figures 1 and 2b,c) based on bearings with a minimum achievable damping rate \(l_{\text{b}}\) has been proposed. The swinging arrangement was damped by a non-linear element-magnetic dampers at the extreme positions, Figure 2b,c. For maximum sensitivity, the electro-mechanical system was tuned to enter the resonance in the supposed frequency range \(f_{\text{s}}\) of mechanical vibrations.  
Figure 1: The principal configuration of the core of the minigenerator a beam version (BV).  
Figure 2: _Cont_.