Convergence analysis and mesh optimization of finite element analysis related to helical springs

Abstract

Helical springs are widely used in engineering applications. In order to reduce cost in “try and error” time consuming experimental campaigns, numerical simulations became an essential tool for engineers. Indeed, it saves considerable time in the ahead design phase of a project to ensure the feasibility of structures. However, these simulations run thanks to a lot of parameters, which all must be selected carefully to get access to reliable results. In this paper, ten main modeling parameters are presented. Thanks to a valuable literature statistical analysis, seven of them are settled. Three remain to be studied: the mesh density, the order of the elements and the integration method. Then, three convergence analyses are performed with ABAQUS about the circular geometry accuracy of the tessellated surface, the axial stiffness (and axial load) accuracy of the helical spring and the maximal Von Mises stress accuracy within the helical spring. The numerical campaign is led with 8 mesh densities along the circumference and 6 element types. After comparison, in order to get both fast and accurate results, a limited list of near-optimal combination of density and element type are proposed. The users are free to use any of the presented solutions in function of the desired admissible accuracy of their model.The proposed meshing technique can be exploited for any helical structure with circular cross section, mainly loaded in torsion and shear, such as extension and compression springs.