Shape Optimization of the Wire Cross Section of Helical Springs

This paper presents the discussion of the optimal shape for the wire cross section of helical springs. Since the stress at the inner side of a coil is higher than that at the outer side in a helical spring with a round cross section, the mass may be saved through stress equalization by the improvement of the cross sectional shape. Shape optimization is performed by the modification of the cross sectional shape so as to minimize the mass of the helical spring under constraints such as spring rate, coil diameter, applied load and maximum design stress.

In the present analysis, stress distributions are calculated by the finite element analysis based on a stress function. In consequence, the optimized shapes are found to be almost oval and the mass is reduced by about 10% for the springs of small spring index.