# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1901.04757