# Energy Harvester Based on a Rotational Pendulum Supported with FEM
## 2 The Concept of Pendulum-Based Electromagnetic Energy Harvesting Systems  
In recent times, energy harvesting systems using rotational movement have been receiving attention to scavenge energy from the environment [34; 35; 36; 37]. Very often, pendulums are used in electromagnetic energy harvesting systems because they allow versatility in their configuration. Electromagnetic transduction of vibration energy in the standard magnet-coil generators is based on the electromagnetic induction phenomena. In this, electromotive force is induced in an induction coil, which cuts the magnetic flux of a core during its relative displacement. For improving the electromagnetic coupling with the strongest flux density, permanent magnets made from an alloy of neodymium, iron, and boron (NdFeB) are most suitable. These magnets are also available in various configurations based on the direction of polarization, shapes, sizes, grades of neodymium, and thermal resistance. Historically, many concepts of electromagnetic energy harvesting systems with pendulums have been proposed among the other types of low-frequency energy harvesting systems based on cantilevers, mechanical springs, magnetic springs, and spiral springs [38]. Electromagnetic pendulum-based harvesters can depict both oscillations and full rotation of the pendulum depending on the character of excitation. In real applications, a particular design faces challenges such as sustaining rotational motion under random excitations, and sizing of the system based on constraints or power supply requirements [39]. In order to overcome such challenges and optimize the system for a particular application, several modifications were introduced. These modifications were based on the research on mechanical couplings [40; 41], using sub-harmonic resonance for the broadband power output [42], and using nonlinearities as an additional source of energy [43]. One of the analysis approaches used to study the dynamics of EH systems is comparing the experimental results with the results of mathematical modeling. Simplified mechanical models based on spring-mass systems have provided fairly good results in many studies [44; 45; 46]. Another approach is using the FEA for analyzing the electromagnetic interactions in such systems [47; 48; 49]. Currently, several commercial FEA software packages are available for analyzing electromagnetism problems including 2D axis-symmetric problems and advanced 3D problems. Some of the popular FEA programs are NEC (Numerical Electromagnetics Code), FEKO (Altair Engineering), COMSOL Multiphysics (COMSOL Inc.), and Momentum (Keysight EEsof EDA). Referring to the study on electromagnetic energy harvesters using rotational movement [7], we propose a rotational pendulum concept with an improved approximation. The originality of this system is the variable potential introduced by the pairs of additional adjustable magnets whose strength can be changed. The dynamic response of this system, depending on the system's configuration, provides full rotation or oscillations of the pendulum, which in turn influences the output power. In our analysis, we studied the magnetic interactions and the dynamics of a system using the FEA and mathematical models. In our previous work [7], the effect on performance was analyzed through magnetic interactions with a simplified FEA model. In this study, the effect of magnet positioning on potential modulation and on attaining complete rotational response is explored using numerical simulations. To avoid magnetic interaction with the housing, the system was realized using the 3D printing technique. The originality of the concept lies in the incorporation of adjustable additional magnets to modulate the magnetic potential, allowing a customizable system configuration that improves both pendulum dynamics and output power. This article is organized in the following way. In the next section (Section 3), the proposed concept of the rotational VEH system with the pendulum is described.