Dynamic Illustration of Stranded Wire Helical Springs Using a Modified Bouc–Wen Model

Stranded wire helical spring exhibits a particular dynamic behavior of nonlinear asymmetry hysteretic characteristic due to its special structure. The hysteresis loops with hardening overlap phenomenon are observed through the cycle loading experiments. In recognizing the incapacity of the existing model, a phenomenology-modified Bouc–Wen model, which combines a nonlinear elastic component, a nonlinear amplifier and the pure hysteretic variable of the normalized Bouc–Wen model, is proposed to capture the dynamic behavior. A two-stage identification method is developed to obtain all the parameters of the mode: The parameters of the nonlinear elastic component and the nonlinear amplifier are identified firstly using linear least squares method, and then the IUKF (Iterated Unscented Kalman Filter) algorithm is applied to identify the parameters of the pure hysteretic component. The experiment results corroborate the validity and effectiveness of the proposed model and the identification method.