Optimal phase difference between longitudinal and normal oscillations with piecewise constant acceleration during vibratory conveying

Abstract

The paper is dedicated to researching vibratory conveying with longitudinal harmonic oscillations and normal oscillations with piecewise constant acceleration (two-component vibration) of conveying track in non-hopping modes of moving when particles slide without detachment from the surface when maximal normal acceleration that does not exceed the gravitational acceleration. The optimization criterion is the maximal value of dimensionless conveying velocity (the mean conveying velocity divided by the product of amplitude and frequency of longitudinal oscillations), depending on several dimensionless parameters, first of all, on the phase difference angle between longitudinal and normal oscillations. The study considers several non-hopping modes of moving, distinguished by stages of movement during the oscillation period: forward (or upward on an inclined track) sliding, backward (or downward) sliding, and relative calm of particle’s movement. The maximal conveying velocity is achieved in different modes, depending on the values of several dimensionless parameters: the inclination angle parameter – a ratio of an inclination angle tangent to a frictional coefficient), the intensive vibration parameter – a ratio of the amplitudes of normal and longitudinal oscillations, divided by the frictional coefficient) and the index of asymmetry n – a ratio of the maximal acceleration of the track when moving down to the acceleration of gravity. The conditions for the existence of optimal conveying modes in dependence of values of dimensionless parameters are researched. The equations describing the various conveying modes are considered, and the equations for optimal phase difference angles between longitudinal and normal oscillations are obtained for the various conveying modes. The graphs of optimal phase difference angles dependent on several dimensionless parameters are constructed.