Design and Non-Linear Analysis of a Parabolic Leaf Spring

Abstract

Tapered cantilever beams, traditionally termed as leaf springs, undergo much larger deflections in comparison to a beam of constant cross-section that takes their study in the domain of geometric nonlinearity. This paper studies response of a leaf spring of parabolic shape, assumed to be made of highly elastic steel. Numerical simulation was carried out using both the small and large deflection theories to calculate the stress and the deflection of the same beam. Non-linear analysis is found to have significant effect on the beam's response under a tip load. It is seen that the actual bending stress at the fixed end, calculated by nonlinear theory, is 2.30-3.39% less in comparison to a traditional leaf spring having the same volume of material. Interestingly, the maximum stress occurs at a region far away from the fixed end of the designed parabolic leaf spring.

Keywords: Parabolic leaf spring, End-shortening, Geometric nonlinearity, Equilibrium Configuration Path, Varying Cross-section.

doi:10.3329/jme.v37i0.819

Journal of Mechanical Engineering Vol.37 June 2007, pp.47-51