A number of researchers have devoted their research efforts to investigate helical springs under static loads. However, most of these studies have been limited to circular cross-section springs where only a few of them have focused on elliptical cross-section springs.
Studying elliptical cross-section springs has been done previously, but with no elaborate analytical support. However, there has been found that for the same free height, elliptic cross-section helical springs can enable larger stroke than the circular ones. Therefore, it is possible to reduce the mounting height. In addition, for elliptical cross-section helical spring, shear stress distribution can be made uniform along the section by choosing a particular aspect ratio. Moreover, maximum shear stress can be reduced across the wire compared to equivalent circular cross-section helical spring. This would allow for supporting larger loads for the same spring dimensions.
These advantages are particularly important in view of the recent advances in materials and manufacturing methods promoting downsizing of machines. Finite Element Analysis has been adopted in some spring applications including leaf springs and helical springs with round wire. This has been in a move to establish the spring rate and stress distribution in the cross-section. It has also been founded in quest to validate analytical approaches. Unfortunately, no published application of Finite Element Analysis was available at the time this study was conducted.
Majdi Gzal (currently a PhD student) and Professor Oleg Gendelman at Technion, Israel Institute of Technology in collaboration with Professor Morel Groper at University of Haifa in Israel developed an analytical expression for the stresses in an elliptical cross-section helical springs while considering the helix curvature effect as well as the aspect ratio of the elliptical wire cross-section. The proposed expression eased the design process of these useful springs. Their research work is published in International Journal of Mechanical Sciences.
The authors, with an objective of analyzing the shear stresses in an elliptical cross-section helical spring with a small helix angle, they developed an analytical expression based on the theory of elasticity. They validated the accuracy of this expression by comparing their results with existing numerical studies and consistent with circular cross-section springs. In addition, they also conducted finite element as well as experimental analyses in a bid to analyze the spring in terms of shear stresses and spring rate.
The research team observed that the proposed expression of stress distribution based on small helix angles was accurate in view of the observed finite element analysis and experimental results obtained from a real automotive valve spring with a 6° helix angle. The results can then be adopted for the design of elliptical cross-section helical springs with small helix angle as well as circular cross-section helical springs as a unique case.
The outcomes of their study provided an explicit straightforward expression for the actual location of the maximum shear stress as a function of the aspect ratio as well as spring index. The results also enabled the obtaining of maximum shear stress analytically.
Above the analytical expression, the designer can accurately obtain spring’s rate as well as shear stresses by conducting a real experiment implementing strain gauges and applying finite element analysis.
Majdi Gzal, Morel Groper, Oleg Gendelman. Analytical, experimental and finite element analysis of elliptical cross-section helical spring with small helix angle under static load. International Journal of Mechanical Sciences, volume 130 (2017), pages 476–486.