Investigation of body motion in the trough of a vibratory conveyor under harmonic oscillations in two mutually perpendicular directions

We developed a mathematical model for the motion of a body in the trough of a vibratory conveyor that undergoes harmonic oscillations in two mutually perpendicular directions. Modelling accounts for inertial forces, gravity, reactions from the bottom and side walls of the trough, and dry friction forces between contacting surfaces. Differential equations of motion are derived for the individual stages of the body's interaction with the trough elements, and the conditions for the transition from joint motion with the trough to sliding along its surfaces are determined. Based on the developed model, the patterns of influence of amplitudes, oscillation frequencies, and friction coefficients on the velocity and nature of the body’s motion are established. To verify the adequacy of the mathematical model, we conducted experiments on a laboratory setup capable of generating harmonic oscillations of the trough in two mutually perpendicular directions. The results obtained can be utilised in the design and optimisation of vibratory conveyors for various technological applications.