Force Frequency Coefficient of Rectangle Quartz Crystal Resonators Based Load Sensor

AT-Cut quartz crystal resonators (QCRs) are widely used as load sensors in electron device and engineering machinery industry. The high thickness shear vibration frequency of QCRs is sensitive to the initial mechanical stresses. Therefore, based on this force frequency effect, we can obtain the external force by monitoring of the change of the frequency of QCRs. Here, we check and study the force-frequency effect of the rectangle QCRs, with two opposed concentrated external force on the middle of the rectangle crystal plate edge parallel and vertical to the x crystallographic direction respectively. The influences of the geometric dimension of QCRs on the FFE are investigated. In the parallel loading condition, the frequency increases with the increasing of external force. When edge is small, the slope of the force-frequency effect decreases with the increasing of edge length. When edge is large (about twice of the opposite edge), the slope is nearly a constant and not change. In this vertical loading case, the frequency decreases with the increasing of external force. The variation of the slope of the force-frequency effect is complicated first, and the slope keep as a constant when the variable edge is twice of the opposite edge. The related mechanism of the stress component distribution is discussed. This work is useful for developing the QCRs based load sensor.