Dynamic Modeling of Spatially Varying Shape Memory Alloy Unimorph Actuators

Shape memory alloys are a class of soft actuators that can recover strain through a phase change and are capable of biomimetic motion. Despite the advantages of these alloys (e.g., high strength-to-weight ratios, inexpensive cost, and small form factor), their major drawbacks (e.g., limited deformation, complex modeling, and low operating frequency) have limited their practical use. Incorporating these alloys into morphing structures increases their deformation profile but also increases the complexity of modeling. Here, continuous shape memory alloy phase kinetic equations are used to calculate the state of the material and are paired with a dynamic beam model in order to model the dynamic response of these morphing structures. A constant cross section, varying cross section, and series combination actuators are experimentally tested in order to assess the model’s accuracy for varying actuator dimensions. The root mean square errors were 1.60 mm and 1.65 mm for a constant cross section and varying cross section actuator, respectively. Additionally, two unimorph actuators were combined in series and experimentally tested with a payload mass of 10 g and 30 g resulting in an average root mean square error of 1.00 mm and 0.73 mm with a displacement of 21.14 mm and 10.48 mm, respectively. This model proves to be accurate for a variety of actuator configurations and external conditions, which enables shape memory alloy morphing actuators to be more easily designed and implemented in soft robotics and other systems.