Numerical Heat Transfer Modelling of SMA Actuators and Model Comparison

Shape memory alloys (SMA) can be used to create actuators for use in mechanical systems that carry pronounced benefits with their low weight, high strength, and low cost when coupled with advancements such as robust self-sensing. However, there exist drawbacks in the form of slow system response and complex material behavior. The design and implementation of controllers that drive SMA actuators successfully can pose a challenge, and accurate modelling of the material in software can help to optimize the system response time and power requirements. We have created a variety of tools to help implement these actuators into simulations that capture accurate thermal and mechanical responses of various SMA systems under a variety of control laws. In particular, thermo-electro-mechanical models of SMA behavior are implemented into software representations of mechanical systems such that the entire temperature, stress, and phase profiles of an SMA actuator can be accurately determined via simulation. Because analytical equations for modelling SMA behavior quickly become so complex to be untenable, we use stable numerical schemes to solve for these profiles. In particular, a finite difference scheme allows for spatial and temporally discretized temperature profiles along a shape memory actuator which can be solved for using empirically derived expressions for the heat transfer coefficient that dictated convective heat transfer. These types of models allow for a variety of boundary conditions to capture a number of SMA geometries, orientations, and applications. This paper presents the results of the numerical schemes for thermal cycling and a sliding mode controller used to drive a simple SMA actuator with varying boundary conditions and compares them to experimental results.