Spring amplification and dynamic friction modelling of a 2DOF/2SDOF system in an electromagnetic vibration energy harvester – Experiment, simulation, and analytical analysis

A cantilever beam-based vibration energy harvester is generally preferred due to its simplicity and effectiveness as compared to a spring mass system. This paper analyses the use of a spring to amplify the performance of a conventional single degree of freedom (SDOF) cantilever beam-based vibration energy harvester. A spring was introduced to modify the conventional SDOF design into a two single degree of freedom (2SDOF) system and a two degree of freedom (2DOF) system. The motion of the spring was restricted in the vertical motion using a slider and a linear guide rail fixed to the vibrating base, hence introducing a dynamic friction into the system. Both designs were analysed under three different cases to observe the effect of natural frequency reduction on the frequency bandwidth and power harvested by each design. The vibration-friction interaction in the designs was modelled based on the concept of relative motion. Two different friction theories were applied and verified with simulation and experiment. It was shown that the stick condition would not occur in a SDOF system with a dynamic friction interaction. It was also found that it is possible to tune the friction force of a dynamic friction surface to induce a favourable output at the isolation frequencies of a 2DOF system. Analysis shows that the 2DOF design displayed a larger power density than the conventional SDOF design below a certain natural frequency value, being 78.1% higher at 9.5 Hz. The power densities of the 2SDOF design were almost similar to the SDOF design. However, the 2SDOF design displayed a significant drop in power when under the condition of matched natural frequencies. Nevertheless, the frequency bandwidth of the 2SDOF design can be improved by tuning its two resonant peaks closer to each other.