Analytical modeling of an inclined folded-beam spring used in micromechanical resonator devices

Abstract

Accurate estimation of the mechanical behavior of springs is crucial for the proper design of Microelectormechanical systems (MEMS). The main objective of this study is to derive a closed-form equation for the calculation of the stiffness of an inclined spring in the form of folded-beamss. The energy-based method was used to calculate the displacements of a folded-beams that was fixed at one end and giuded at the other end. The analytical model was then compared with the finite element method using ANSYS for different inclination angles of the folded-beams spring, showing good agreement. The angle on inclination has changed from zero to 180 degress, and stiffness of folded-beams is detemined. The derived expressions of the compliances were checked for the case of serpentine springs with inclination angle of zero, and different length ratios against the literature. It is found that neglecting small lengths for calculating the stiffness of the folded-beams spring is not justified. The influential geometrical parameters, including different lengths of the spring and inclination angle of the spring, on the stiffness are studied. It is found that the angle of inclination of the principal axes of spring constants depends on the geometrical parameters, and the angle of inclination has more effect on the stiffness of a folded-beams spring than the number of folds.