Rotation of a Clamped Spherical Ball due to Linear Reciprocating Motion

Abstract

A perfect spherical ball, symmetrically clamped between two identical surfaces, was found to rotate due to linear reciprocating excitation. A plausible theoretical explanation of this phenomenon follows. The rotation of the ball is a combination of the magnification of the dynamic response of the ball in the clamping system, near its natural frequencies, with frictional stick-slip at the contact areas. The ball rotates when the system is excited by a reciprocating motion not collinear with the preloading direction. The theoretical analysis of such rotation was corroborated by testing. This rotation may result in wear because of the slip motion involved. This work is focused on balls clamped between spherical (concave) surfaces. However, such rotation can also be developed in cylindrical hinges and rolling bearings, naturally loaded between a pair of surfaces. Furthermore, rotation of balls may develop in a nonrotating ball bearing under dynamic environmental conditions.