SHAPE OPTIMIZATION OF THE WIRE CROSS-SECTION OF HELICAL SPRINGS (STUDY ON SHAPES OF INNER AND OUTER BOUNDARIES OF WIRE WITH A HOLE)

One of the effective ways for reducing the mass of a helical spring is to make a hole in the cross section of the spring wire. In this paper , we discuss the shape of outer and inner boundaries of the wire cross section of a helical spring that has minimum mass. Stress is calculat ed by means of the finite-element method (FEM) based on the stress fun ction, and the optimization problem is solved by means of the steepest descent method used in the previous paper. In consequence, the conver ged solutions obtained from various initial shapes greatly differ in s hape, but are almost equal in mass. The stress around the outer bounda ry of the converged cross sections can be made nearly uniform. It is a lso found that there are many solutions whose mass values are almost e qual to those of the converged solutions. In comparison with a helical round wire spring, the weight of the present spring has been reduced by about 50%.