Enhanced formulae for determining the axial behavior of cylindrical extension springs

TL;DR

This paper develops improved analytical formulae for cylindrical extension springs, accounting for loop stiffness and initial tension effects, enhancing design accuracy and manufacturing efficiency.

Contribution

It introduces new analytical expressions for loop stiffness and initial tension effects, enabling precise calculation of spring behavior and manufacturing parameters.

Findings

Analytical definition of loop stiffness improves load-length predictions.

New methods allow quick calculation of initial tension and pitch.

Enhanced design range extends operational limits of springs.

Abstract

Cylindrical extension springs have been commonly exploited in mechanical systems for years and their behavior could be considered as well identified. Nevertheless, it appears that the influence of the loops on the global stiffness is not yet taken into account properly. Moreover, it would be of key interest to analyze how initial tension in extension springs influences the beginning of the load-length curve. The paper investigates these topics using analytical, simulation and experimental approaches in order to help engineers design extension springs with greater accuracy. As a result, the stiffness of the loops has been analytically defined. It enables to calculate the global stiffness of extension springs with more accuracy and it is now possible to determine the effective beginning of the linear load-length relation of extension springs and thus to enlarge the operating range commonly defined by standards. Moreover, until now manufacturers had to define by a try and error process the axial pitch of the body of extension springs in order to obtain the required initial tension. Our study enables for the first time to calculate quickly this key parameter saving time on the manufacturing process of extension springs.