Modeling and Numerical Simulation of Shape Memory Alloys in Robotics Applications

Abstract

Shape memory alloys (SMA) are uniquely alloyed metals that have the ability to change crystalline structure upon the application or removal of stress or upon heating or cooling. This change in crystalline structure gives SMA several properties that make them useful in robotics applications. For example, certain SMA can be used to create actuators that are simple, high strength, and inexpensive. However, poor electrical efficiency, a moderate lifetime, and complex mechanical behavior that makes them difficult to design into new applications and products have stymied the growth of these actuators as viable alternatives to more traditional actuators such as pneumatics or motors. In order to improve the integration of SMA actuators into modern mechanical applications, tools have been created that account for the complex thermal and mechanical behaviors of these materials under feedback controls. This was done through the development of thermo-electro-mechanical constitutive models which were then analyzed analytically and then solved numerically using routines present in multibody dynamics software ADAMS as well as through programs such as MATLAB. Models of varying complexity were implemented and compared to one another as well as to experimental results. The mechanical model utilizes 1-D constitutive equations that account for the material temperature and state of stress to determine the material state. The material state determines the electrical resistivity of the material, which drives Joule heating. Thermal cooling of the material is based on a heat transfer analysis of various geometries. These models contain information on material states that are very difficult to measure experimentally (such as crystalline phase fraction) and thus provide insight into the material behavior and design that experimental results cannot offer. The numerical models of material behavior also can then be used with a variety of control laws in order to test their stability and response time.