On the compression of a stack of truncated elastomeric cones as a nonlinearly responsive spring

In an effort to construct a design tool for a mechanical spring featuring highly nonlinear spring stiffness, compression of truncated elastomeric cones has been studied using nonlinear finite element analyses involving neo-Hookean material law and contact elements. Series of finite element models of various geometric aspect ratios of truncated cones were calculated to form a fundamental database of the design tool. It was found that the compressive stiffness of the rubber cone can be non-dimensionalized with respect to the elastic modulus and a characteristic length of the cone. While the stiffness of the truncated rubber cone appears more linear between 0 and 5% of the compression ratio, the stiffness increases exponentially with progressing compression at higher compression ratios. Regression equations of the non-dimensional axial force and spring stiffness were obtained with reasonable accuracy, compared with the original finite element data.