Analytical and Experimental Investigation of Logarithmic-Spiral Conical Compression Springs

This paper introduces an analytical closed-form model for the comprehensive mechanical response of logarithmic-spiral conical compression springs in linear, progressive stacking, and near-collapse regimes, the correctness of which has not been verified. A unified mathematical formulation for the load–deflection response of fully telescoping springs is constructed using torsion deformation theory and geometric stacking requirements. Closed-form formulas have been developed for deflection, instantaneous stiffness, transition load, and collapse load. The model is numerically implemented, and experimental validation is performed using additively made ABS springs created by fused deposition modelling. The effective torsional modulus is determined by calibrating material properties against cylindrical reference springs. This theory has been empirically confirmed, yielding a mean percentage error of 2.59% and a coefficient of determination of 0.98 throughout all deformation phases. The observed deviations prior to collapse are minimal; the discrepancies are ascribed to geometric and manufacturing flaws in the material. This study presents the inaugural closed-form model of logarithmic-spiral conical springs, validated experimentally, and offers practical insights for enhancing nonlinear stiffness and energy absorption.