Enhanced design parameters of a cylindrical helical compression spring using an optimization algorithm and a non-linear behavior model

Abstract

An optimization algorithm based on SLSQP solver was created to design helical compression springs. The goal is to reach the required behavior even when the standards formula is inaccurate. Indeed, it was already shown in previous works that the classic formula determining the global load-length behavior of the spring is not always accurate enough because it does not consider the effects of the spring’s ends, in particular for springs with low index and low number of coils. Based on a new tri-linear model, this algorithm finds optimized spring design which respects the required operative points. In order to test the algorithm, the first tests were carried out to optimize the design of a PLA 3D-printed spring. It was shown that the initial design stiffness is overestimated by over 28% by the formula extracted from the standards. Then, the design of the spring was implemented in the algorithm to optimize the pitch and the number of active coils. The experimental curve of the optimized design spring goes through the target behavior, with a non-linearity at the beginning of the deflection. The experimental error about the final stiffness is successfully reduced to 1.1%. It is hoped that this work will provide a valuable progress to assist engineers and manufacturers in helical spring design.