The Effect of Spin Upon the Rolling Motion of an Elastic Sphere on a Plane

Abstract

Abstract The motion and deformation of an elastic sphere rolling on an elastic plane are examined for the case when the sphere, in addition to its straight rolling motion, has an angular velocity of “spin” Ω about an axis normal to the plane. The action of spin is to twist the area of contact. Surface tractions resulting from this rotation are found, which demonstrate the necessity of partial slip in the area of contact. Previous investigations suggest that this slip cannot occur at the leading edge of the contact circle, so that a system of tractions is found which corresponds to zero stress at the leading point. It is shown that such a system of tractions gives rise to a transverse creep of the sphere in the direction of its rotation Ω. The magnitude of this creep is calculated for small values of Ω, when slip occurs to only a small extent. Experiments have been performed using a simple thrust bearing with plane parallel races. As the bearing rotates, the balls creep radially outward in the predicted manner. Quantitative measurements of this creep agree with the theoretical estimate over a wide range.