Steady periodic regime of rotary motion of rollers in vibrating classifiers

The problem of dynamics of vibrating classifiers with rollers intended for sorting of loose materials is considered in the paper. The main goal of research consists in substantiation of a choice of such parameters of rollers and classifiers which provide a steady periodic mode of rollers rotation. Differential equations of rollers rotation under action of inertial forces are essentially nonlinear. These equations are transformed to equations concerning the value of delay of moving rollers concerning rotation of axles on which these rollers are freely suspended. As values of such delays is small, the equations of motion can be linearized with a sufficient degree of accuracy. The linearized equations represent the inhomogeneous Hill equations, which can be under certain conditions transformed into the Mathieu equations. Periodic solutions to these equations are obtained, and also stability of these solutions is investigated.