Actuation Frequency Modeling and Prediction for Shape Memory Alloy Actuators

This article proposes a numerical model to predict actuation frequencies (strain-cycling frequencies) for 1-D shape memory alloy (SMA) actuators. The numerical model is designed by comprehensively considering the factors that significantly affect an SMA actuator's strain-cycling frequency, i.e., heat convection methods, constant or nonconstant bias loads, and Joule heating methods. For computing strain cycles of SMA actuators, we develop a computation framework that effectively integrates an SMA constitutive model, a phase transformation kinetic model, stress-strain models for different types of bias stress, and a heat transfer model of SMA wires. The strain and temperature rates are formulated by nonlinear ordinary differential equations. The strain and temperature cycles can be accurately approximated by numerical iterative methods. Experimental verification was conducted to investigate the effectiveness of the proposed model. By initially identifying the SMA characteristic parameters, we employed Latin hypercube sampling method to generate 30 sets of design parameters for comparing the predicted and measured actuation frequencies. In addition, we investigated how the uncertainty of premeasured SMA characteristic parameters affect the numerical prediction of actuation frequency by conducting sensitivity analysis. The experiments demonstrate
$0.7\%\text{--}9.03\%$
and
$2.65\%\text{--}17.57\%$
differences between predicted and measured actuation frequencies for constant bias loads and spring bias loads, respectively.