Toshiyuki Imaizumi

Shape Optimization of the Wire Cross Section of a Helical Spring. Study on Shapes of Inner and Outer Boundaries of Wire with a Hole.

One of the effective ways for reducing the weight of a helical spring is to make a hole in the cross section of the wire of the spring. This paper discusses the shapes of outer and inner boundaries of the wire cross section of the helical spring that has minimum weight. Stresses are calculated by FEM based on the stress function, and the optimization problem is solved by the steepest descent method used in the previous paper. In consequence, the converged solutions obtained from various initial shapes greatly differ in shape, but are almost equal in weight. The stresses around the outer boundary of the converged cross sections can nearly be made uniform. It is also found that there are many solutions whose weights are almost equal to those of the converged solutions. In comparison with a helical round wire spring, the weight has been reduced by about 50%.