Optimal design of a micromachined force gauge under uncertainty

Micromachined force gauges, like many microdevices, are subject to inevitable and inherent uncertainty in dimensional and material parameters that lead to variability in the gauge accuracy and reliability. This paper presents a methodology for the design of a micromachined force gauge under uncertainty, in which the measured force and the maximum stress in the beams in the gauge are related to five uncertain design parameters representing the dimensions of the beam, the material property and the deflection of the beam under the force being measured. A deterministic large-deflection beam model is combined with a sampling-based stochastic model to obtain the distributions of the measured force and the maximum stress corresponding to the interactive influence of the uncertainty in the five design parameters. An optimization problem is formulated to maximize the force measurement accuracy subject to a constraint on the maximum allowable stress. On the basis of the optimization results, design windows for the deflection and the force that maximize the accuracy are derived as functions of the uncertainties in the design parameters. The results provide directly usable information on the optimum geometric design of the force gauge for given uncertainties in the manufacturing and operation of the device.