Modelling, Simulation and Testing of Shape Memory Alloy Negator Springs As Long-Stroke Constant-Force Actuators

Shape memory alloys (SMA) are smart materials used for the construction of compact solid-state actuators with high power density. SMA elements based of conventional design (wires, helical springs) have the force-displacement curve which follows an elastic behaviour ranging from zero to the desired peak force. This characteristic does not match the external load in many cases, which is often nearly constant, causing an oversizing of the actuator. This paper aims at overcoming these drawbacks by exploiting  SMA Negator constant-force springs. A Negator spring is a spiral spring made of strip metal wound on the flat with an inherent curvature such that each coil wraps tightly on its inner neighbour. The unique characteristic of Negator springs is the nearly-constant force needed to unwind the strip for very large deflections. Another merit of the shape of the Negator spring is that the high area over volume ratio grants improved bandwidth compared to any solution with wires.  This paper validates the mathematical model of the mechanical behaviour of SMA Negator springs against ad hoc experimental tests on such a shape. The SMA martensitic phase is described by a non linear model based on three main experimental parameter: initial elastic modulus, post-elastic modulus and yield strain, while the austenitic phase is considered elastic. The developed model approximates well the martensitic curve, while the austenitic phase is considered perfectly elastic. The authors obtain a closed form solution for the payload of the spring which depends only on the material and on a non dimensional geometry parameter. The proposed material model is also implemented in a commercial finite element software, ABAQUS, and the Negator spring is simulated through FE analyses.  Both numerical and analytical models are compared with experimental data and good agreement is found for both of them.