Design-oriented Modeling of SMA Actuated Bistable Tape Spring Rolamite (BTSR) Hinges
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There is significant interest in the utilization of multistable structures and shape memory alloy (SMA) actuators for creating active shape adaptive structures [1,2]. Multistable structures offer a method for designing mechanisms with predefined target shapes, while SMA actuators serve as an elegant means to generate forces necessary for reversible reconfiguration. The CMASLab at ETH Zurich is presently engaged in developing a reconfigurable smart hinge utilizing bistable tape springs and shape memory alloys (SMAs) for a debris collection satellite. In contrast to SMA-driven compliant mechanisms commonly employed on Earth, those designed for space applications confront significant fluctuations in ambient conditions. Space mechanisms experience notable variations in ambient temperature, introducing complexity to the design of systems that integrate nonlinear structural components and thermally driven actuators. In this study, a design framework is formulated to anticipate the reversible actuation of a hinge mechanism comprising cylindrical bistable composite shells actuated by an antagonist pair of SMA springs while considering the ambient temperature variation. The modular framework incorporates a nonlinear finite element model to simulate the snapthrough behavior of the composite tape springs [3], coupled with Brinson's constitutive law-based thermo-mechanical model [4] for the SMA springs. This design framework proves effective in selecting the attachment geometry and initial configuration of SMA springs, ensuring successful reversible reconfiguration across the entire spectrum of operating conditions. Additionally, it is possible to predict the safety margins of the thermal actuators in terms of both the actuation force and the actuation strains using the proposed framework. The established model has undergone validation through experiments. In addition to facilitating the design of intricate systems, the model can elucidate intriguing observations from experimental data. For example, within a particular range of ambient temperatures, it may be observed that the SMA springs can actuate the bistable hinge only once. Attempts at reversible actuation prove unsuccessful, as, at an elevated temperature, the actuated spring cannot return to the low-temperature martensite state. The model not only anticipates this phenomenon, coined "Austenite trapping" by the authors but also provides a theoretical approach approach to circumvent it.