Modelling of minor hysteresis loop of shape memory alloy wire actuator and its application in self-sensing

Shape memory alloy (SMA) wire actuators offer large force and displacement capabilities out of the stress and temperature-dependent martensitic phase transformation. Among the various modelling approaches in the literature, the one proposed by Boyd and Lagoudas (1996), is mostly used in analysing SMA based components. In practice, partial actuation is often required and is enacted by aborting and subsequently resuming the phase transformation; exhibiting minor hysteresis response. The existing models are found to be inaccurate in simulating such partial transformation cases. In this study, a novel yield parameter, which depends on the martensite volume fraction, has been proposed; enabling the model of Boyd and Lagoudas to simulate minor hysteresis loop accurately. The corresponding model parameters are derived, satisfying certain practical aspects of the SMA response. Using the modified model, pseudoelastic responses are simulated for different partial loading cases and are compared against the same obtained from the existing models, illustrating its efficacy. Following the proposed model, the discrete form of the system dynamics of a SMA wire actuator is formulated. Using this, an extended Kalman filter (EKF) has been developed, to estimate the output of the system from the change in electrical resistance of the SMA wire during actuation. This approach eliminates the requirement of external sensors for feedback control. Using the developed EKF, the response of an SMA wire actuated system is estimated from the experimentally measured electrical resistance data of the SMA wire and are compared with the corresponding measured responses. The results reveal that a significant level of accuracy can be achieved with the proposed approach.

Automated summary

A novel yield parameter has been proposed in this study, allowing the modifications of existing models to accurately simulate the pseudoelastic response of SMA wire actuators under partial loading conditions. The results demonstrate the efficacy of this approach and provide guidelines for deriving relevant model parameters.