VARIATIONAL OPTIMIZATION OF COMPRESSION HELICAL SPRINGS WITH RESPECT TO THEIR STABILITY

Abstract

In this paper, the optimization problem of helical springs against instability is considered. An initial distribution of helix angle and radius of a spring is sought which ensures maximal value of the critical axial compressive force under equality and inequality constraints. As the equality constraints a volume of a spring material, an initial compression rigidity and also a volume taken up by a spring are considered. The inequality constraints are connected with: a strength condition, a condition of closing up of neighbouring coils, geometrical conditions in initial and compressed state (7 inequality constraints). Variational optimization using the Pontriagin maximum principle is considered. It turned out that the main profit of optimization is connected with the optimal distribution of a helix angle. The influence of the optimal variable radius on the critical axial force is much lower: the profit reaches here a few per cent only whereas that obtained by optimization of the helix angle can be even over 100%.