Parametrical optimization of compression helical springs against instability

Abstract

In the present paper, the parametrical optimization problem of helical springs against instability is considered. Such an initial distribution of a helix angle and radius of a spring is sought in the assumed class of functions which ensure maximal value of the critical axial compressive force under equality and inequality constraints. The volume of the spring material, the initial compression rigidity and also the slenderness ratio of the spring are considered as the equality constraints. The inequality constraints are connected with: a strength condition, a condition of closing up of neighbouring coils, and geometrical conditions in the initial and compressed state.