The Squeeze Film Damping In Torsional MEMS Resonators With Coupling Effect Between Torsion And Bending

Quality factor is an important dynamic indicator of MEMS resonators, higher quality factor represents the energy loss of MEMS resonators is slower during their vibration and the sensitivity and resolution are higher. Damping in MEMS resonators strongly affects their quality factor and squeeze film damping is the most significant source of damping which makes founding a theoretical model of squeeze film in torsional MEMS resonators becomes very important. At present, predecessors have made a lot of research about the squeeze film damping of torsional MEMS resonators, but most of them just considered the torsional vibration of the support beam, while some of them considered the bending vibration of the support beam, however they just studied the static characteristics and ignored the coupling effect between torsion and bending. During the operation of torsional MEMS resonators, the bending vibration is inevitable because they are not excited by pure torque and the relationship between torsional vibration and bending vibration is coupled.Firstly, an analytical model for squeeze film damping in torsional MEMS resonators considering the coupling effect between torsion and bending is established based on previous studies in the case of gas incompressible and compressible. The pressure distribution in the gap is derived by using the double sine series and the squeeze film damping force and torque applied to the micro-plate are derived by integration. The analytical expressions for the damping and stiffness coefficients of the squeeze film are derived and the quality factor of the model is obtained. Then, the model considering the coupling effect between torsion and bending is compared with the model just considering the torsion and find that there is a certain relative error between damping coefficients, stiffness coefficients and bias displacements of two models, even while the relative error is small, the discrepancy between quality factors of two models may still be big. Finally, the accuracy of the model considering the coupling effect between torsion and bending is verified by comparing its results with the finite element method(FEM) results.