Shape optimization of the wire cross section of a helical spring.

This paper discusses the optimal shape for the wire cross section of a helical spring. In general, stress at the inner side of the coil is higher than that at the outer side in a helical spring with a round cross section. Therefore, weight may be saved through stress equalization effected by improving the shape of the wire cross section. Shape optimization is performed by modification of the cross-sectional shape so as to minimize the weight of the helical spring under the constraints of design stress, spring rate, coil diameter and applied load. Stress caused by torsional moment and shear force is calculated by means of FEM, taking the effect of coil curvature into account. The shape of the wire cross section is successively modified by changing γi, which represents the radius from the sectional center to each node on the periphery of the section. The optimized shapes are almost oval and are obtained independent of supposed initial shapes.