# Non-Destructive Damping Measurement for MEMS Acceleration Switches

## Determining damping coefficients is important for categorizing how each sensor or switch operates.

Microelectromechanical systems (MEMS) three-axis acceleration threshold sensors have been developed to measure acceleration threshold levels using voltage switching when the threshold is reached. Switches with different damping coefficients result in different mechanical impedances and response times. Analytical and numerical methods to model damping coefficient values based on empirical data are needed to characterize three-axis acceleration sensors; traditional methods use the displacement of an underdamped system to calculate the damping ratio.

Mechanical switches are single-output devices that distinguish whether closure occurs or not, and lack a transduction mechanism to turn acceleration into a readable displacement signal. A more inventive technique to analyze a closed switch has been devised. A shock table and vibration testing produces a deterministic acceleration input to close an acceleration switch, which has a defined switch gap distance, and mathematical fitting using these deterministic values allows one to determine damping coefficients. By using both an analytical equation fit method and a numerical optimization program, the damping coefficients for MEMS three-axis threshold acceleration sensors were calculated from the results of the tests and design dimensions of the switches.

The two damping measurement techniques presented cover all damping ratio values: underdamped and overdamped systems. Damping characterization will benefit end users by allowing a framework for modeling acceleration switch response in their application, and help them correctly choose a closure-acceleration value for the MEMS switch.

A linear shock table was used to test the sensors, allowing the data acquisition device to plot acceleration and voltage change over time. An open switch indicated little or no voltage drop, but at switch closure, the short circuit caused a change in voltage. The voltage was measured against time, and the change in voltage corresponded to the g-force at the time of switch closure. The acceleration and voltage change was analyzed with the system modeled as a mass with a spring and damper in a second-order differential equation.

Two methods were developed that characterize the damping ratio for packaged MEMS acceleration switches. MEMS acceleration switches only provide a single point of information in an applied acceleration field — when switch closure occurs. The two methods discussed here are ways to measure damping when switch closure is all that is known.

During an impact event, typically all modes are excited resulting in a superposition of modal displacements. During harmonic excitation, a particular mechanical mode can be excited generating a very simple motion. Damping values determined from harmonic excitation will be very specific to the mode, whereas damping values obtained from impact tests will be generalized.

There were many different parts to the experimental system setup used to test the sensors, and two MATLAB programs were written to analyze the data. A linear shock table was used to produce a high-impact shock (see figure). Four channels were used to measure each sensor, one at a time. Six JFTP sensors were attached to the mounting plate and moved at high speeds into a cushion.

The harmonic excitation method used an inductive shaker with accelerometer feedback control to hold a constant acceleration value through the sine sweeps. Data acquisition records the time versus switch voltage data and correlates into frequency versus switch voltage. Switch closure is indicated by a non-zero voltage. MATLAB post-processing programs were developed to sort through each data set and obtain the relevant information needed to solve for damping and natural frequency.

The analytical method for calculating damping was too sensitive to input variations; the acceleration, closure time, and frequency produced impractical damping values when applied to the equation. The numerical method proved to be a better way of determining damping because the analytical method used many assumptions when solving the characteristic equation.

There is a general decreasing acceleration pattern over increasing closure time for both contacts. There are data points that show constant peak acceleration over different closure times. Similar patterns occur with damping as with acceleration.

*This work was done by Ryan Knight and Evan Cheng of the Army Research Laboratory. ARL-0181*

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