Deformation-based accurate geometric model of stranded wire helical spring

As a kind of cylindrical spring structured with a helically wound strand, the stranded wire helical springs are widely employed as reset components in engineering fields. The accurate description of the spring geometry is critical for its design, manufacture, and further theoretical and finite element method (FEM) analysis. However, the outside wires of the spring were assumed to be double-helixes in commonly used geometric model without considering the interwire contact interactions, which introduced non-negligible geometric error. To cope with this problem, a deformation-based accurate geometric model considering the interwire contact interactions is presented in this paper. By combining the geometry constraints between wires with the thin rod theory and an elastic–plastic contact model, a novel algorithm is established to determine the interwire contact behaviors and the coordinates of the nodes on the wire centerlines iteratively. The FEM simulations and the experiments are performed to verify the effectiveness of the proposed model. The results show that the accuracy of the proposed model is similar to that of FEM but much higher than that of the commonly used geometric model. The effects of the strand curvature and the outside wire pitch on the spring geometry are analyzed with the presented model as well.