Analysis and Prediction of Spring-Back in Cylindrical Helical Springs Using Analytical and Numerical Models

This research focuses on cylindrical helical springs with circular cross-sections made from carbon steel (SH 0.82% C) and stainless steel (AISI 302). The transformation from a linear bar to a circular spiral involves numerous factors such as material mechanical behavior, stress–strain relationships and residual stresses. This research investigates the spring-back phenomenon, which affects the final diameter of helical springs post-manufacture, using analytical, experimental and numerical methods. An analytical model, derived from the mechanical bending process, was proposed to predict spring-back, and its accuracy was validated against experimental data. This study also employed finite element simulations to analyze elastic recovery, confirming the analytical predictions. Results indicated that the spring-back ratio k could be expressed as an exponential function of the spring index C (the ratio between the final diameter of the spring D2 and the diameter of the wire DW), with a maximum error of 4.80% for stainless steel and 3.62% for carbon steel. This study’s findings provide valuable insights into optimizing the spring manufacturing process, enhancing the precision of spring diameter predictions, and potentially reducing production errors and material waste.