On the use of impact-induced nonlinearities in limit switch design

Abstract

This dissertation explores the use of grazing bifurcations in impacting mechanical systems as a useful means of creating fast-acting limit switches. Using analytical, numerical, and experimental techniques, the transient and asymptotic responses of several example vibro-impacting systems undergoing the onset of low-relative-velocity contact are investigated. It is argued that the rapid transients and distinct asymptotic dynamics distinguishing pre- and post-grazing attractors provides an advantageous mechanism on which to base a limit switch design. Further, it is shown that these changes, which originate due to the mechanical interactions, can be detected in coupled electrical systems through both electromagnetic and electrostatic coupling mechanisms. The dissertation concludes with a realization in a prototype microelectromechanical systems (MEMS) design in which a grazing bifurcation may trigger snap-through in a parallel plate capacitive actuator. The results of these studies indicate that a switch based on the proposed nonsmooth fold scenario would outperform one that relies on a smooth bifurcation, such as the cyclic-fold bifurcation, in terms of switching speed and sensitivity.