Increasing of vibratory conveying velocity by optimizing the normal vibration

Abstract

The paper is dedicated to researching the influence of normal vibration on the vibratory conveying velocity of particles on an inclined track that performs independent longitudinal and normal oscillations (two-component vibration). The study considers the optimizing conditions of the conveying velocity for different laws of oscillating components (harmonic, polyharmonic, oscillations with piecewise constant acceleration) with a limited value of the longitudinal acceleration of conveying track and with maximal normal acceleration that does not exceed the gravitational acceleration (non-hopping modes of moving, when particles slide without detachment from the surface). The optimization criterion is the maximal distance, traveled by the particle during the oscillation period, or the maximal value of dimensionless conveying velocity, depending on several dimensionless parameters. The maximal conveying velocity with polyharmonic normal oscillations is achieved at a certain ratio of the amplitudes of harmonic oscillation, which essentially depends on the track’s inclination angle to the horizon. The ratios of the amplitudes of harmonic oscillation, which practically do not reduce conveying velocity at any inclination angles, are proposed. Two-component vibratory conveying under normal oscillations with piecewise constant acceleration is considered in optimal non-hopping modes of a particle moving with one forward (or upward on an inclined track) sliding stage and one backward (or downward) sliding stage during the oscillation period. The equations for determining the dimensionless conveying velocity are derived for different values of dimensionless parameters, such as the inclination angle parameter (a ratio of an inclination angle tangent to a frictional coefficient) and the intensive vibration parameter (a ratio of the amplitudes of longitudinal and normal oscillations, divided by the frictional coefficient). The effectivity of polyharmonic normal oscillations in two-component vibratory conveying is compared with the effectivity of normal oscillations with piecewise constant acceleration. Maximal conveying velocity is achieved at certain values of phase difference angles between longitudinal and normal oscillations, which are called optimal. The value of dimensionless conveying velocity V increases with the increase of asymmetry of normal oscillations, which is described by the ratio n of the maximal acceleration of the track when moving down to the acceleration of gravity. This ratio n corresponds to the number of harmonics for polyharmonic oscillations. A comparison of values of V for normal oscillations with piecewise constant acceleration shows an advantage in velocity compared to polyharmonic normal oscillations at the same number n of harmonics, especially with increasing inclination angles. The research was carried out by the numerical step-by-step integration method, which allows for performing calculations with any given accuracy. The obtained results are demonstrated in figures and comparative tables.