Modeling of an SMA actuator based on the Liang and Rogers model

Abstract

The purpose of this study is to develop a complete mathematical model of a thick shape memory alloys (SMA) actuator based on the Liang and Rogers model. Due to hysteresis and significant nonlinearities in the behavior of shape memory alloy actuators, the modeling of SMA actuators has been a great challenge in recent years, which limit the application of these actuators. In this paper, a new model is used to represent the major and minor hysteresis loops of SMA actuator based on the Liang and Rogers model. The modified Liang and Rogers model of SMA wire actuated by an electric current is derived and several experiments are used to validate the model and to identify the parameters. A key feature of the proposed model is to predict the martensite starting temperature of minor loops. This model can be used to develop a position control system for the SMA actuator. Simulation results for the model are found to be in good agreement with experimental data.

Modeling of partial transformation cycles of SMAs with a modified hardening function

“…To model internal sub-loops, the concept of memory points was considered along with an additional evolution variable which defines the evolution of the transformation after an incomplete transformation procedure. Finally, based on the model of Liang and Rogers [35], Li and Harada [36] developed an extension to predict the modified transformation temperature threshold for the initialization of martensitic transformation when the material undergoes PT, while Shirani and Kadkhodaei [37] applied a phenomenological approach to obtain enhanced initialization of transformation and an updated model for PE.…”

Effect of shape memory alloys partial transformation on the response of morphing structures encompassing shape memory alloy wire actuators

“…A rate-independent algorithm was developed by Šittner et al (2000) on the basis of thermodynamics phenomenology, to simulate history-dependent behavior of SMAs. Memory of reversal points was also considered by Chemisky et al (2011), while Li and Harada (2013) extended the one-dimensional model of Liang and Rogers (1990) to obtain modified critical temperature thresholds for the transformation onset when functioning under incomplete phase transitions.…”

Thermomechanically coupled analysis and experimental investigation of morphing structures with shape memory alloy actuators operating under partial transformation with a focus on active load control

“…In his work, he used a model based on the thermodynamics to explain the phenomena associated with the observed response. The model of Liang and Rogers [238] was expanded by Li and Harada [338] to predict the modified transformation temperature threshold for the initiation of Martensitic transformation when the material undergoes partial transformation. The original expressions for the calculation of MVF were simplified and modified based on normalized resistance polynomial expressions.…”