Effective Computational Model for Determining the Geometry of the Transition Zone of End Coils of Machined Springs, Enabling Efficient Use of the Spring Material

This paper presents an analysis of the effect of the geometry of the end-coil transition zone on the material stress state of a machined compression spring with a rectangular wire cross-section. The literature relationships for determining the stresses in rectangular wire compression springs neglect the effects associated with the geometry of this zone. A series of non-linear numerical analyses were carried out for models of machined compression springs with a wide range of variation in geometrical parameters. The results of these analyses were used to develop a computational model to estimate the minimum value of the rounding radius , which ensures that the stresses in this zone are reduced to the level of the maximum coil stresses. The model is simple to apply, and allows the radius to be estimated for springs with a spring index between 2.5 and 10, a helix angle between 1° and 15°, and a proportion of the sides of the wire section between 0.4 and 5.