Static response of stranded wire helical springs to axial loads: A two-state model

Stranded wire helical springs are fundamental mechanical components used in high-end vibration absorption systems. The static axial response model is an important tool for the design and manufacturing of the spring. The wires within the spring have been assumed to be in contact with each other when the spring is unloaded by commonly used models for modelling the static axial response; hence, significant error has been introduced. To improve the estimation accuracy of the static axial response, this article proposes a two-state model by assuming that the spring possesses two states during the loading process. Moreover, in this model, the friction between adjacent wires is neglected and the spring is unwound to be a straight strand in the initial step of the analysis. The model is almost piecewise linear and is able to model the nonlinearity of the load–strain relationship of the spring. Adopting the proposed model, the dependence of the stiffness of the spring on the spring geometries is analysed. To evaluate the presented model, the compression experiments are carried out. Compared to a commonly used static response model, the proposed two-state model features better accuracy that is validated by the experimental results.