Analytical and numerical modeling of shape memory alloy Negator springs for constant-force,long-stroke actuators

Abstract

This article explores the merits of shape memory alloy Negator springs as powering elements for solid-state actuators. A Negator spring is a spiral spring made of strip of metal wound on the flat with an inherent curvature such that, in repose, each coil wraps tightly on its inner neighbor. The unique characteristic of Negator springs is the nearly constant force needed to unwind the strip for very large, theoretically infinite deflections. Moreover, the flat shape, having a high area-over-volume ratio, grants improved bandwidth compared to any solution with solid wires or helical springs. The shape memory alloy material is modeled as elastic in austenitic range while an exponential continuum law is used to describe the martensitic behavior. The mathematical model of the mechanical behavior of shape memory alloy Negator springs is provided, and their performances as active elements in constant-force, long-stroke actuators are assessed. The shape memory alloy Negator spring is also simulated in a commercial finite element software, ABAQUS, and its mechanical behavior is estimated through finite element analyses. The analytical and the numerical predictions are in good agreement, both in martensitic and in austenitic ranges.