Elastic coefficient analysis on planar S-shaped micro spring under high impact load

Planar spring adopted in micro inertial devices is usually in form of S-shaped and equal line-width. When the planar spring works under inertial loads, its elastic coefficient can't be easily calculated theoretically and was deduced based on mechanical energy method in this paper. And further, this paper proposed S-shaped gradient line-width spring and deduced its theoretical formula of elastic coefficient. The simulations were taken by ANSYS and verified the applicability of the formula. The analysis demonstrated that the relative error of the elastic coefficient formula is less than 3 % under a concentrated force, and the average relative error is less than 5 % under an inertial force. The analysis of spring structure parameters indicates that spring line width and length of the straight beam are two main influence factors on the elastic coefficient. The other structure parameters, such as thickness, line-width increment, spring section number and bending radius, have less influence on the elastic coefficient. The planar S-shaped gradient line-width spring has abilities of the uniform deformation, optimized stress distribution, high impact resistance. Results in this paper provide a certain theoretical reference for the optimal design of micro inertial devices.