Study on the vertical stiffness of the spherical elastic layer bonded between rigid surfaces

The initial vertical stiffness of the bonded spherical elastic layer with Poisson’s ratio from 0 to 0.5 is formulated on the basis of two kinematic assumptions. The governing equations of the stiffness are solved by numerical method. The vertical stiffness is not only related to the load area and the thickness of the elastic layer, but also related to the shape factor and inner edge angle of the spherical elastic layer. The analytical method is verified by FE analysis with a 2D axisymmetric model with Poisson’s ratio within (0.49, 0.499999). Poisson’s ratio, radius–thickness ratio and edge angles will influence the stiffness error. The stiffness error increases as the radius–thickness ratio increases and tends to saturate when the radius–thickness ratio exceeds 50. When the inner edge angle is constant, the relative errors of the vertical stiffness will decrease as the outer edge angle increases. When the outer edge angle is constant, the errors will increase and reach a maximum value and then decrease as the inner edge angle increases. For a single elastic layer with the radius–thickness ratio of 20, the relative error of vertical stiffness is within (−10, 12%), which is acceptable in bearing design.