This paper describes the operation of a vacuum packaged resonant accelerometer subjected to static and dynamic acceleration testing. The device response is in broad agreement with a new analytical model of its behavior under an applied time-varying acceleration. Measurements include tests of the scale factor of the sensor and the dependence of the output sideband power and the noise floor of the double-ended tuning fork oscillators as a function of the applied acceleration frequency. The resolution of resonant accelerometers is shown to degrade 20 dB/decade beyond a certain characteristic acceleration corner frequency. A prototype device was fabricated at Sandia National Laboratories and exhibits a noise floor of 40 g/ Hz for an input acceleration frequency of 300 Hz.

The authors present modeling approaches to describe the coupling of modes in a resonant vibratory rate gyroscope. Modal coupling due to off-diagonal stiffness and damping terms is considered. Three analytical modeling approaches are presented in the context of a z-axis micromechanical vibratory rate gyroscope fabricated in an integrated polysilicon surfacemicromachining process. The first approach is based on frequency-response analysis of the gyroscope output. The second approach takes the route of state-space-based system identification to identify the modal-coupling parameters. A third approach based on measured vibration data identifies the coupling parameters due to stiffness and damping. These three methods are then applied to predict the extent of displacement and force coupling between the drive and the sense axes of an existing device as a function of varying degrees of matching between the resonant frequencies associated with the drive and the sense modes. Experimental data show that as the resonant frequencies of the drive and sense modes are brought closer together, an improvement in overall resolution and scale factor of the device is obtained at the expense of an enhanced coupling of forces to displacements between the two axes and the onset of instability for an open-loop sensing implementation.

The present work deals with the optimization of a compliant force amplifier mechanism in a surface micromachined resonant accelerometer. Figures of merit including noise floor and scale factor are critically dependent on the gain of the force amplifier mechanism, and hence optimization of the force amplifier mechanism is necessary. The optimization is constrained by limitations imposed by the manufacturing process and the device geometry. The force amplifier mechanisms in this work are initially designed using continuum topology optimization. The results of topology optimization are seen to depend strongly on the size of the design space, output and input stiffnesses and boundary conditions. The results of the topology optimization are converted to beam element models that are used for a further shape and size optimization. Single-stage force amplification factors greater than 100 are obtained from the results of the optimization process.

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