An accurate dynamic model for polycrystalline shape memory alloy wire actuators and sensors

Abstract

Thermal shape memory alloy (SMA) wires exhibit a mechanical hysteresis of which the shape depends on both temperature and loading rate. Commercially available actuator wires typically exhibit polycrystalline behavior, which also depends on training effects. Polycrystallinity may lead to complex hysteresis loops, differing substantially from standard box shapes often employed in modeling attempts. In addition, actuation often results in loading trajectories leading through the interior of the hysteresis, making accurate modeling and control of SMA systems a highly challenging task. In this paper, we present a novel dynamic model for polycrystalline SMA actuator wires based on a modified version of the Müller-Achenbach-Seelecke model. The model permits to predict time evolution of stress and resistance of a onedimensional SMA wire under arbitrary input strain and Joule heating profiles. The constitutive equations are developed by properly exploiting the concept of a representative single-crystal, resulting in an optimal trade-off between physical interpretation and computational efficiency. After developing constitutive model equations, experimental validation is performed by means of two case studies, given by a superelastic NiTi wire and a quasi-plastic NiTi wire, respectively. The experiments are intended to illustrate the model capabilities in predicting internal hysteresis loops, loading rate effects, as well as actuation and sensing behavior at the same time. A remarkable accuracy is observed in all of the investigated experimental scenarios, making the model particularly suitable for high-precision control and self-sensing applications.

A Self-Sensing Method for Electromagnetic Actuators with Hysteresis Compensation

“…A short review of different models is provided here, while the work [34] provides a detailed overview. Physical models like the Jiles-Atherton model [35], Carpenter model [36], Globus model [37] and the models described by Stoner-Wohlfahrt [38] and Müller-Aschenbach-Seelecke [39] provide a good physical description of the underlying microscopic effects and working principles. On the other side, phenomenological models proposed by Preisach [40], Bouc-Wen [41] and Coleman-Hodgdon [42] as well as the Prandtl-Ishlinkskii model and its modified form [32,43] provide better modeling and identification results.…”

A phenomenological model for thermally-induced hysteresis in polycrystalline shape memory alloys with internal loops

“…The prediction for partial transitions often requires computational efforts. Motivated by the scaling policy (Rizzello et al, 2019), the concept of density reassignment is introduced in this section to improve computational efficiency. Compared with the scaling policy, it should be highlighted that the proposed strategy of density reassignment not only comes from the geometrical consideration of the internal loops but also enriches the physical aspects of the prediction.…”

“…To facilitate the control of SMAs and improve the computational efficiency, a 1-D differential model is proposed to capture the hysteretic phenomenon in the thermally-induced transformation for the SMA polycrystal. Besides, motivated by the scaling policy for internal loops (Rizzello et al, 2019) that utilizes the geometrical similarity between the outer loop and the inner ones, a strategy is proposed to involve both geometrical and physical considerations for the prediction of incomplete transitions. The major contribution of this work is remarked as follows.…”

Mesoscopic free energy as a framework for modeling shape memory alloys

“…The most common example is polycrystallinity, but the term refers to any stress or strain fields at the mesoscopic scale, such as those caused by layer boundaries within a single crystal. Here, we present a phenomenological adaptation of the theory from Heintze and Seelecke (2008), Rizzello et al (2018), and Smith et al (2003), which is based on statistical mechanics principles. This is an optional set of equations that can be used to implement polycrystalline-type of stress–strain behavior in the model and we include it here (1) for complete presentation of the model and (2) because of the several experimental data sets examined in the “Simulations” section require it.…”

“…Experimental data showing additional types of single-crystal inner hysteresis loops along with discussion of the thermodynamics can be found in Müller and Seelecke (2001). Polycrystalline SMA specimens exhibit somewhat different inner-loop characteristics and these were addressed with variations of the M-A-S model in Heintze and Seelecke (2008) and Rizzello et al (2018).…”