Analytical and Experimental Study of Conical Telescoping Springs With Nonconstant Pitch

TL;DR

This paper explores various types of conical telescoping springs with nonconstant pitches, providing mathematical models and experimental validation to expand design possibilities beyond traditional constant-pitch springs.

Contribution

It introduces new mathematical models for conical springs with different spiral geometries and validates them experimentally, broadening the design space for telescoping springs.

Findings

Mathematical equations for different spiral types

Formulas for initial stiffness and load-length relations

Experimental validation with 3D-printed springs

Abstract

Most research papers that exploit conical springs focus only on conical springs with a constant pitch. In order to increase the range of possibilities for designers, this paper proposes a study of conical springs with other types of spirals projected on the conical shape. This study is related to three other types of conical springs: with a constant helix angle, with a constant stress at solid and with a fully linear load-length relation. For each spring, we give the equation of the spiral, the formula of the initial stiffness, and formulae to calculate the nonlinear part of the load-length relation for fully telescoping springs. We also report an experimental study performed to analyze the accuracy of the proposed study based on springs made by fused deposition modeling.