Analytical, experimental and finite element analysis of elliptical cross-section helical spring with small helix angle under static load. (September 2017) - Gzal, Majdi; Groper, Morel; Gendelman, Oleg
Highlights: This study proposes novel, explicit and simple expressions for determining the stress distribution and the maximum shear stress location in an elliptical cross-section helical spring with small helix angle. The provided expressions support a firm understanding of the parameters affecting the stresses and ease the design process of those useful springs. Shear stresses and spring's rate can be accurately obtained analytically or by conducting an actual experiment using strain gauges as well as applying a FEA. The maximum shear stress location deviates depending on the aspect ratio and spring index. Abstract: This study aims in determining the stress distribution in elliptical cross-section helical springs with small helix angle (less than 10°, often termed as close-coiled springs) considering the effect of wire curvature, subjected to axial static load. We present both analytical and finite element analysis, validated by an experimental study conducted on an actual automotive valve spring. A novel analytical expression for the stress distribution in such springs is developed based on the theory of elasticity. In particular, this expression leads to the analytic formula for the maximum resultant shear stress and its location along the spring's cross-section as a function of the aspect ratio. Contrary to the case of the circular cross-section, this maximum shear stress location is not invariant. The proposed analytical expression agrees well with the computed FEA results and is in very good correlation with the experimentally obtained figures. As an additional outcome of this study, we describe a method to experimentally measure the shear stress in helical springs using strain gauges.