This work investigates a novel awl-shaped serpentine microspring for a suspension structure, with a lower spring constant under the same unit layout area in out-of-plane motion. Using Castigliano's theorem, the spring constant of the microspring was theoretically derived and simulations were performed using COMSOL Multiphysics to verify the theoretical results. The proposed awl-shaped serpentine microspring was successfully fabricated using siliconbased micromachining. Experiments were conducted to compare the theoretical and numerical results, which were in close agreement. In addition, 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. Accordingly, the awl-shaped serpentine microspring has a lower K/A value than the traditional serpentine microspring with the same total effective length and folds. With a greater taper angle, more folds, a smaller beam width, and lower beam thickness, the awl-shaped serpentine microspring has a smaller K/A value. Using the proposed mathematical model, the spring constants of microsprings of various sizes and geometric structures can be calculated in out-of-plane motion before the microstructure is fabricated. Thus, it saves time when designing a microspring with a proper spring constant.
Even when made by brittle materials, awl-shaped serpentine microsprings (ASSMs) were found to have a nonlinear displacement–force relationship similar to springs made by ductile material. It is found that the nonlinear displacement–force relationship is due to the geometry and dimensions of the ASSMs. The geometric effect of the nonlinear force–displacement relationship of ASSMs for in-plane motion was investigated. A theoretical solution was derived to analyze this nonlinearity. By successfully fabricating and measuring an ASSM, the theoretical results agreed well with the experimental results. The results indicated that ASSMs have a nonlinear force–displacement relationship, which is similar to that of hardening springs. The taper angle has a significant effect on the nonlinear displacement of ASSMs. When the taper angle was small, no obvious effect appeared on the nonlinearity of the microsprings with different numbers of turns. When the beam length increased, the critical force for nonlinear deflection decreased.
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