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Research Papers

Limit-Switch Sensor Functionality Based on Discontinuity-Induced Nonlinearities

[+] Author and Article Information
Bryan Wilcox

Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

Harry Dankowicz1

Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801danko@illinois.edu

1

Corresponding author.

J. Comput. Nonlinear Dynam 6(3), 031004 (Dec 16, 2010) (8 pages) doi:10.1115/1.4002686 History: Received January 13, 2010; Revised August 27, 2010; Published December 16, 2010; Online December 16, 2010

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 a distinctly different amplitude and frequency content. The results reported here include a review of 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.

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Figures

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Figure 1

Schematic of a lumped-parameter model of the experimental apparatus (9)

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Figure 2

The sequence of points introduced in the derivation of Eq. 4 and the growth in order in ε of the value of hturning at successive impacts. Modified and reprinted with permission from Wilcox, B., Svahn, F., Dankowicz, H., and Jerrelind, J., 2009, J. Sound Vib., 324(4–5), Copyright 2009, Elsevier, Ltd.

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Figure 3

(a) Numerically simulated Δx2,i+1 versus Δx2,i at successive impacts, straight lines represent a linear regression fit. (b) Experimental Δx2,i+1 versus Δx2,i at successive impacts, straight lines represent the predicted relationship as obtained from Eq. 4. Modified and reprinted with permission from Wilcox, B., Svahn, F., Dankowicz, H., and Jerrelind, J., 2009, J. Sound Vib., 324(4–5), Copyright 2009, Elsevier, Ltd.

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Figure 4

A testbed for investigating post-grazing dynamics and signal transduction in a coupled electromechanical system

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Figure 5

Pre-grazing dynamics for ω=0.659; discrete points are experimental data and the solid line is numerical data. Here the large black dot corresponds to x4=0.

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Figure 6

Post-grazing dynamics for ω=0.659; discrete points are experimental data and solid lines are numerical data. Here the large black dot corresponds to x4=0 and the small black dots correspond to himpact=0.

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Figure 7

Pre-grazing dynamics for ω=0.527; discrete points are experimental data and the solid line is numerical data. Here the large black dot corresponds to x4=0.

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Figure 8

Post-grazing dynamics for ω=0.527; discrete points are experimental data and solid lines are numerical data. Here the large black dot corresponds to x4=0 and the small black dots correspond to himpact=0.

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Figure 9

Pre-grazing dynamics for ω=0.415; discrete points are experimental data and the solid line is numerical data. Here the large black dot corresponds to x4=0.

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Figure 10

Post-grazing dynamics for ω=0.415; discrete points are experimental data and solid lines are numerical data. Here the large black dot corresponds to x4=0 and the small black dots correspond to himpact=0.

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Figure 11

Plan (upper) and sectional (lower) schematic views of the proposed MEMS device for investigating grazing-induced snap-through behavior

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Figure 12

An operational schematic of the capacitively excited parallel-plate device shown in Fig. 1

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Figure 13

The steady-state pre-grazing response (dotted) and the transient post-grazing response (solid) with large black dots corresponding to himpact=0

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