Design and performance analysis of a mechanically coupled spring compliant to out-of-plane oscillation

In this paper, a spring system symmetrically arranged around a circular plate compliant to out-of-plane oscillation is proposed. The spring system consists of single serpentine springs mutually coupled in a plane. Three theoretical mechanical models for evaluating the stiffness of the spring system are built, which are based on the flexural beam, Sigitta, and serpentine spring theories and equivalent mechanical spring structure models. The theoretically calculated results are in good agreement with numerical solutions using the finite element method, with errors less than 10% in the appropriate dimension ranges of the spring. Compared to similar spring structures without mechanical coupling, the proposed mechanically coupled spring shows advantage in suppressing the mode coupling.