Low-Speed Friction Torque on Balls Undergoing Rolling Motion

When rotated from rest, the frictional resistance in slowly rolling balls increases to an asymptotic value. This value, known as the free-rolling friction torque, plays a significant role in low-speed positioning accuracy of precision systems. An experimental apparatus was designed to determine Ts, the steady-state friction torque that occurs in rolling balls. A theoretical expression was derived to predict Ts, following similar work performed by Todd and Johnson (1). The steady-rolling torque was assumed to contain rolling and spinning components which are functions of ball geometry, normal load, and friction coefficient. Theoretical and experimental torque values were determined for two oil lubricants, for various speeds and normal loads. Excellent correlation was found between the experimental and theoretical results obtained for both lubricants. Several results are also presented for the low-speed friction torque values of unlubricated surfaces.