Modified sigmoid based model and experimental analysis of shape memory alloy spring as variable stiffness actuator

The stiffness of shape memory alloy (SMA) spring while in actuation is represented by an empirical model that is derived from the logistic differential equation. This model correlates the stiffness to the alloy temperature and the functionality of SMA spring as active variable stiffness actuator (VSA) is analyzed based on factors that are the input conditions (activation current, duty cycle and excitation frequency) and operating conditions (pre-stress and mechanical connection). The model parameters are estimated by adopting the nonlinear least square method, henceforth, the model is validated experimentally. The average correlation factor of 0.95 between the model response and experimental results validates the proposed model. In furtherance, the justification is augmented from the comparison with existing stiffness models (logistic curve model and polynomial model). The important distinction from several observations regarding the comparison of the model prediction with the experimental states that it is more superior, flexible and adaptable than the existing. The nature of stiffness variation in the SMA spring is assessed also from the Dynamic Mechanical Thermal Analysis (DMTA), which as well proves the proposal. This model advances the ability to use SMA integrated mechanism for enhanced variable stiffness actuation. The investigation proves that the stiffness of SMA spring may be altered under controlled conditions.