Abstract
The awl-shaped serpentine microspring plays a important role in MEMS devices due to the advantages of unique deformation behavior and more effective spatial usage. The analytic solutions of spring constants of awl-shaped serpentine microspring for in-plane and out-of-plane motion are theoretically analyzed by using Castigliano’s theorem. Using the theoretical solutions, the spring constant of microspring can be calculated quicker and the awl-shaped serpentine microsprings be easierly designed in MEMS devices. Moreover, the effect of spring constant and layout area on deformation performance of awl-shaped serpentine microspring are discussed. A parameter of spring constant to layout area ratio (K/A) is defined to be used as the index for comparing spring constants under the same unit area. A smaller K/A value would induce larger deformation under the same applying force and layout area. From the theoretical results, the awl-shaped serpentine microspring has a lower K/A value than the traditional serpentine microspring for in-plane and out-of-plane motion with the same total effective length and folds. Hence, the awl-shaped serpentine microsprings can induce larger deformation than traditional serpentine microsprings under the same applying force and layout area. The effect of the size and geometry of the awl-shaped serpentine microspring on the spring performance was investigated. With a greater taper angle, a longer total effective length, more folds, a smaller beam width and lower beam thickness, the awl-shaped serpentine microspring will produce a smaller K/A to achieve a larger displacement under the same layout area.The proposed awl-shaped serpentine microspring was successfully fabricated for in-plane and out-of-plane motion. Experiments results were conducted to compare the theoretical and numerical results, which were in close agreement. The error was less than 10%. Furthermore, the spring constants for in-plane and out-of-plane motion are compared and discussed. As w∕h being >1, the spring constant of in-plane motion ky is always larger than that of out-of-plane motion kz. If w∕h is <1, the spring constant kz would be larger than ky. Moreover, the effect of geometric sizes on the nonlinear deformation of microspring is investigated too. It is found that the nonlinear deformation is easier found for more folds, a greater taper angle, a smaller beam width, and lower beam thickness of awl-shaped serpentine microspring. Using the linear regression method, the linear spring constant k1 and cubic spring constant k3 of the Duffing equation could be determined and expressed in terms of N, ϕ, w, and h by the regression equation. Therefore, a critical nonlinear point is defined as the beginning of nonlinear deformation behavior of the awl-shaped serpentine microspring. The effect of the maximum stress and geometric sizes on the critical nonlinear point of awl-shaped serpentine microspring is also discussed. The analytic results illustrate that the taper angle and beam width of awl-shaped serpentine microspring is the significant afactors on the nonlinear deformation behavior.