The electromagnetic vibratory actuator load during the transport of a rigid body on a vibratory conveyor

During a vibrational transport of a rigid body on a vibratory conveyor having electromagnetic vibratory actuator, a rigid body exerts by equal, but opposite force to a surface’s reaction force. This paper covers research on a reactive force that the body exerts on the EVA during its relative motion. The reactive force is a vector sum of the surface's normal contact force and tangential force of friction, modeled with the Coulomb friction model. For a general case of vibratory transport, the friction force is defined and given as a piecewise function. Additionally, differential equations for the rigid body’s relative motion are defined and solved to find potential moments in time when the body starts and stops with relative motion. During the period of the relative motion, a dynamic friction force is used. Conditions for a special case of a no-hopping motion are defined and presented graphically. For a given vibratory conveyor and vibratory regime a graph for reactive force that acts as a load on the EVA is shown. Computer simulation using Solidworks® is performed and its results are compared to the previously obtained mechanical model.