Determination of the stiffness of rolling kinematic pairs of manipulators

A method of determination of the radial and axial stiffness of rolling bearings and rolling kinematic pairs as a function of the external load and the kinematics of motion has been presented. In this method, an influence of the distribution of rolling elements during the bearing raceway motion (with respect to the direction the resultant vector of the radial load acts) on the coefficient of the load distribution angle and the coefficients of stiffness, has been taken into consideration. An algorithm, which allows for tracing on-line the stiffness as a function of external loads and the kinematics of kinematic pair, has been proposed. A contact between the rolling element and the raceways has been modeled, as an example, by classical Hertzian formulas. In these considerations, low-speed (low-acceleration), short-period motions of rolling bearings have been assumed as a characteristic type of motion of kinematic pairs of manipulators.