Two-Dimensional Discrete Model for Buckling of Helical Springs

The classical theory of helical spring instability is based on the buckling of an equivalent column. Alternatively, more advanced methods are found in literature, involving the numerical solution of the displacement field of the helical wire. Those approaches turn challenging when the helix is non-uniform or there is the need to take into account contact between coils. In this work, the buckling behaviour of uniform helix springs is investigated using a 2D model with lumped stiffness, so that it can be compared to the previous modelling techniques. The aim is, after validation, to adopt the proposed technique to non-uniform springs. The spring is modelled as a planar structure made of rigid rods connected by nonlinear elastic hinges. Each rod thus represents half a coil, and each hinge lumps the stiffness of the adjacent two-quarters of a coil. Because of nonlinearity, the equilibrium is solved for incremental loads. At each step, the stability of the spring is evaluated from the eigenvalues of the tangent stiffness (geometric end elastic contributions).