Nonlinear load-deflection and stiffness characteristics of coned springs in four primary configurations

Abstract

Even though coned disk springs have been used as preload or isolation elements in mechanical design for over a century, prior research has used several simplifying assumptions in determining their static load-deflection relationships and their stiffness properties have been largely ignored. Accordingly, the entire displacement range is considered in this article, from fully unloaded height to flat height under quasi-static loading conditions. Friction is accounted for at the face-to-face disk spring contacts and at the disk spring edge-to-surface contacts, but is ignored in edge-to-edge contacts. New experimental results for a single coned disk element, the primary parallel stack configuration, and two primary series stack configurations are presented. Measured load-deflection characteristics are analyzed in the context of newly defined nine distinct regimes that are motivated by the physics. Hysteresis curves are also examined and compared with a refined load-deflection relation with interfacial and edge friction coefficients. Finally, a continuously nonlinear stiffness expression is analytically derived, which matches well with measurements but only over a limited range of displacements.