Presetting and Residual Stresses in Springs

In this chapter, the method for calculating residual stress and permanent deformation of helical springs is developed. The method is based on the deformation formulation of the plasticity theory and general kinematic hypotheses (SAE AE-22, §8.3.33). Two main types of helical springs—compression springs and torsion springs—are studied. For the first type (axial compression or tension springs), the spring wire is twisted. The basic approach neglects the pitch and curvature of the coil and replaces the helical wire with a straight cylindrical rod. The helical spring is in the state of screw dislocation; accordingly, the wire is twisted. The elastic–plastic torsion of the straight rod of circular section is studied. In the second type (torsion helical springs), the helical wire is in the state of edge dislocation, so the wire is in the state of bending. The elastic–plastic deflection of the straight bar with rectangular and circular cross section is studied using Bernoulli's hypothesis. The material for both types of springs is nonlinearly hardening elastic–plastic with elastic unloading. The hyperbolic, Ramberg–Osgood, Ludwik–Hollomon, Swift–Voce, and Johnson–Cook laws for the material are studied. For both problems, the elastic–plastic active deformation and the elastic spring-back allow the closed-form solutions. In addition, this chapter examines the calculation of residual deformation and residual stress for helical springs after a prolonged prestressing process. The article extends the model for the immediate prestressing process by considering the creep deformation of the spring. The method is based on the plasticity theory for the instantaneous flow, which is overexposed by the relaxation over the long-term prestressing. In this article, the following method is used. The plastic deformation of the circular section helical spring occurs instantaneously. As the spring continues to shorten in the tool holder, the stress relaxes and the force of the spring decreases. As a result, after the elastic relaxation of the long-term presetting, the residual stress of the spring also gradually decreases with the compression time. The final length of the springs decreases significantly as the presetting time increases. The advantage of the discovered closed-form solutions is the calculation without the necessity of complex finite element simulation of spring length loss and residual stresses after prestressing. The analytical expressions are proposed and the exact calibration is applied for evaluation of factors for presetting processes. This chapter is the final section of the second part, which studies the manufacturing processes of helical springs.