Finite-element analysis of a quartz digital accelerometer

A detailed three-dimensional (3-D) finite-element analysis of a quartz digital accelerometer (QDA) is carried out to understand and determine the temperature behavior of the entire heterogeneous sensor consisting of quartz resonant elements, polyimide bonding material, and beryllium copper spacers. Of particular interest is the identification of factors that can degrade the temperature stability of the QDA´s output frequency. The calculated temperature dependence of a double-ended tuning fork (DETF) is reported and shown to be in good agreement with measured data. This relation differs from that calculated for a tine and demonstrates the influence of the end boundary conditions. Calculated results for the full QDA include: (1) natural frequencies and mode shapes, (2) the shift in the QDA´s output frequency with acceleration level, and (3) the shift in the QDA´s output frequency with temperature. The effect of varying the thickness of the adhesive bonds between the DETFs and the spacers is examined. These results suggest that variations in bond thickness can generate temperature dependent residual assembly stresses that degrade the thermal stability of the QDA´s output frequency.<>