Design of Limit-Switch Sensors Based on Discontinuity-Induced Nonlinearities

Limit-switch sensors are input-output devices that switch operating state in reaction to the crossing of a threshold value of their input. These are used to monitor and control critical values of temperature, voltage, pressure, etc. in both consumer and industrial settings. This paper argues for exploiting nonsmooth fold bifurcations in the design of ultrafast and robust, resettable, electromechanical limit switches. Specifically, the discussion emphasizes the dramatic changes in system response associated with the onset of near-grazing, low-velocity contact in vibro-impacting systems. These include rapid transient dynamics away from a pre-grazing, periodic, steady-state trajectory following the onset of impacts and post-grazing steady-state trajectories with distinctly different amplitude and frequency content. The results reported here include an experimental and computational verification of the ultrafast transient growth rates that show a significant potential for dramatic improvement in sensor performance. Moreover, two novel candidate sensor designs are discussed that rely on the post-grazing response characteristics for device function. In the first instance, transduction of a change in the response periodicity following grazing in a mechanical device is detected in a coupled electromagnetic circuit. In the second instance, a snap-through post-grazing response forms the operating principle of a capacitively-driven circuit protection device.