Compression of Rubber Disks Between Frictional Surfaces

Abstract

Abstract An approximate analysis is given of the axial compression and retraction of a rubber disk sandwiched between two rigid frictional surfaces. The rubber is assumed to be linearly-elastic and incompressible, and Coulomb's law of sliding friction is assumed to apply. The amount of interfacial slipping during compression is calculated and the distributions of normal and shear stress are determined. The overall compressive stiffness is then evaluated for disks with a wide range of aspect ratio a/h, where a is the radius and h is the thickness, and for several values of friction coefficient. Force-displacement relations during retraction are obtained and the energy expended in frictional sliding is calculated in some representative cases. It is found to be a large fraction (about one-half) of the input energy for disks of large aspect ratio, compressed between low-friction surfaces. Finite element analysis (FEA) was carried out for disks with various aspect ratios and friction coefficients. Stress distributions and force-displacement relations are compared with the analytical results. Agreement is generally good, even though the stress singularity at the edge of the disk is ignored in the analysis. It appears to have little influence away from the edge.