Static Modeling of Bending Characteristics on V-Shaped Beam Actuator Based on Flexible Substrate

Due to the unique properties of flexible electronic devices, various microelectromechanical systems (MEMS) devices based on flexible substrate have been proposed for miniaturization, lightweight, and intelligent applications. Obviously, the deformation of flexible substrate inevitably affects the performance of flexible MEMS devices. This article first investigates the static modeling of bending characteristics on the flexible V-shaped beam actuator, which is the most representative MEMS thermal actuator. This article focused on a comprehensive static analysis of bending mechanical property based on the flexible substrate. The innovation of static modeling is obtaining variation regularity of bending characteristics by establishing the deformation coupling model of V-beam structure and flexible substrate. The V-shaped beam thermal actuators are designed and fabricated on flexible liquid crystal polymer (LCP) substrate, and the influence of bending substrate on the actuation performance of the device is revealed by calculation, simulation, and experiment. The experimental results demonstrate that the actuation current of the V-shaped beam actuator rises up proportionally with the increase of angle and the decrease of beam length. When flexible substrate bends gradually from curvature 0 to 33.3 (1/m), the rates of measured actuation current change are 17.05%, 13.70%, and 10.24%, corresponding to different angles of 13°, 20°, and 27° at $600~\mu \text{m}$ length of V-shaped beams. Meanwhile, the rates of measured actuation current change are 9.22%, 13.22%, and 13.70%, corresponding to different lengths of 400, 500, and $600~\mu \text{m}$ at 20° angle of V-shaped beams. The experimental results are consistent with the theoretical calculation results of static modeling, and the error is less than 3.7%.