Application of finite element analysis to the design of quartz thickness-shear mode pressure sensors

Quartzdyne has been in the business of providing pressure transducers to the oil and gas industry for several years. These transducers are designed to withstand extreme environments present in oil and gas wells including high temperatures, high pressures, and high levels of shock and vibration loading. The transducer must survive these extreme conditions and provide a stable, precise pressure measurement over a broad range of pressures and temperatures with high resolution and low power consumption. The sensing elements employed in these transducers are thickness-shear mode resonators. Hollow cylindrical AT-cut quartz shells enclose the resonator isolating it from the pressure fluid. These shells or endcaps convert externally applied pressure to biaxial normal stresses acting in the plane of the resonator. The resonator frequency shifts in response to mechanical stress providing a measure of the applied pressure. Two critical parameters which strongly influence sensor performance are sensitivity and range. Both parameters may be accurately predicted for a given sensor design using mechanical stresses supplied by finite element analysis (FEA).