Conventionally modeled as spring–damper system, the end-stops in vibration energy harvesters set a limit to the displacement of the proof mass at sufficiently high excitation levels. In some studies, it is seen that the end-stop parameters needed adjustment to fit the simulations to the measurements at particular operating condition. In this article, the discrepancy between the simulation and measurement results on varying the operating condition is investigated in detail. A check on sensitivity of an electrostatic in-plane gap closing energy harvester to the parameters end-stop stiffness, end-stop damping, and end-stop position at various biases and excitation levels is performed. The simulations at 3-V bias and root mean square (RMS) acceleration amplitude 0.6 g show a remarkable variation of 30 Hz in up-sweep jump-down frequency on varying end-stop position by 0.12 µm. The simulation results also show a significant increase in sensitivity of up-sweep jump-down frequency to end-stop damping on increasing excitation level at fixed bias. The article also discusses the sensitivity in jump frequencies to perturbations in the excitation signal due to the presence of noise, where the jump-down frequency becomes smaller as the noise level increases. The trajectories studied at 8-V bias and RMS acceleration amplitude 0.6 g with different end-stop parameters show a strong influence of the end-stop model parameters on the motion of the proof mass. A lumped model of the device is fitted to the measurements for a whole range of operating conditions with one fixed set of model parameter, where asymmetric end-stop positions and their effect on the device behavior are shown to be crucial. The results presented in this article show that in order to reproduce and analyze the measured behavior of the harvester over a range of operating conditions, very fine details in the model are significant.
Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems
