Investigation of energy harvesting efficiency in a magnetic rolling pendulum—report

Abstract This article presents a comprehensive analysis of the energy efficiency and dynamics of a nonlinear magnetic rolling pendulum (MRP). The pendulum consists of a rolling magnet on a cylindrical track, suitably positioned bumpers, and coils, which allow for virtually any configuration. In this study, we determine the magnetic interactions in the system using (Finite Element Method) FEM to determine the characteristics of the force change over the entire range of pendulum movement. The design we propose has features that allow for the analysis of systems with one, two, and three wells, depending on the configuration of the magnetic bumpers. Then, we create a dimensionless mathematical model, which is verified on a laboratory stand by testing a prototype pendulum for selected excitation characteristics. The system’s displacement and voltage output responses are analyzed using nonlinear dynamics tools. For the analysis, we use tools such as bifurcation diagrams, Lyapunov exponents, Poincaré sections, and the amplitude frequency spectra. This allowed for the identification of periodic and chaotic solutions and transient chaos in the system for more than 1000 analyzed configurations. The impact of individual settings on energy efficiency is determined based on the author’s fill factor for the power value in a wide range of excitation parameters. The advantage of the proposed system for harvesting energy from mechanical vibrations, despite its apparent simplicity, is the possibility of many different configurations in terms of dynamics and efficiency, only by simple construction changes. We have shown that for the configurations considered, up to 15 mW of (Root Mean Square) RMS power and 20 mW of peak power is achieveable. The results demonstrate that the harvester maintains high efficiency even at low excitation levels, highlighting its potential for engineering applications.