A New Method for Generating Virtual Models of Nonlinear Helical Springs Based on a Rigorous Mathematical Model

Abstract

This paper presents a new method for generating nonlinear helical spring geometries based on a rigorous mathematical formulation. The model was developed for two scenarios for modifying a spring with a stepped helix angle: for a fixed helix angle of the active coils and for a fixed overall height of the spring. It allows the development of compression spring geometries with non-linear load-deflection curves, while maintaining predetermined values of selected geometrical parameters such as the number of passive and active coils and the total height or helix angle of the linear segment of the active coils. Based on the proposed models, Python scripts were developed that can be implemented in any CAD software offering scripting capabilities or equipped with Application Programming Interfaces. Examples of scripts that use the developed model to generate the geometry of selected springs are presented. FEM analyses of quasi-static compression tests carried out for these spring models have shown that, using the proposed tools, springs with a wide range of variation in static load-deflection curves can be obtained, including progressive springs with a high degree of nonlinearity in the characteristics. The obtained load-deflection curves can be described with a high degree of accuracy by power function. The proposed method can find applications in both machine design and spring manufacturing.

Effective Computational Model for Determining the Geometry of the Transition Zone of End Coils of Machined Springs, Enabling Efficient Use of the Spring Material

“…The spring can thus be used in compression, tension, bending, and torsion. The most common industrially used compression springs are made of wire with a round cross-section [10,11], which provides the most efficient use of material due to the tangential stress distribution caused by wire torsion. However, there are a number of applications where springs with a rectangular wire cross-section are preferable.…”