Coiling of Helical Springs

In this chapter, the method for calculation of residual stresses and plastic bending and torsion moments for combined bending and torsion loading is developed. The Bernoulli hypothesis is assumed for the deformation of the beam. The analysis is performed using the deformation theory of plasticity with a nonlinear stress–strain law describing active plastic deformation (SAE AE-22, §8.3.33). The curvature and twist of the beam increase proportionally during plastic loading so that the ratio of curvature to twist remains constant. The complete solutions based on this approximate material law provide a closed analytical solution. The unloading is linear elastic. This chapter is the first section of the second part, which studies mechanical problems arising during the manufacturing of helical springs.