The phase difference between components of elliptical oscillations of vibratory conveyor providing maximum conveying velocity

The piece goods conveying by the vibratory conveyor with elliptical oscillations is considered. Elliptical oscillations of the conveyor track are realized when conveyor has independent drives of oscillations in the direction of conveying (longitudinal oscillations) and oscillations in the direction perpendicular to conveying plane (normal oscillations) with phase difference between them. Elliptical oscillations allow increasing conveying velocity and inclination angle of conveyor track in comparison with the simplest linear oscillations. Conveying velocity of parts moving along the track of conveyor varies with the change of phase difference angle and reaches a maximum with a certain angle, depending on several different parameters. This angle is called the optimal phase difference angle, and it depends on the amplitudes and frequency of the component oscillations, the track inclination angle, the frictional properties, impact parameters of conveying parts. As the experimental investigations have shown, the piece goods conveying is quite accurately described by the theory of a massive point particle moving on an inclined plane under the action of vibration. A system of nonlinear differential equations describing the conveying in continuous contact modes and in modes with hopping was composed. This system has been solved by gradual integration method with numerical calculation with any desired accuracy. This allowed us to study the dependence of conveying velocity on different parameters in the form of graphs. And for greater generality the study was conducted in dimensionless parameters. There were studied in detail the influence of dimensionless parameters on dimensionless velocity – the coefficient of velocity that is the ratio of conveying velocity to amplitude of longitudinal oscillations with a constant frequency. To verify the obtained dependences, the experimental investigations of conveying velocity were carried out on vibratory conveyor with removable tracks. The conveyor was fastened on the turntable, the inclination of which was varied by a screw jack. The amplitude of the component oscillations was varied by changing voltage applied to the electromagnetic drives, the phase difference between component oscillations was varied by the phase shifter. Waveforms of oscillations were recorded by vibration measurement equipment. The coefficient of friction was measured directly during conveying. The velocity was measured by the stopwatch. The comparison of experimental results with theoretical data has shown the excellent agreement in continuous contact modes and the acceptable match in modes with hopping. Based on the obtained graphs, the approximate formulas for calculating velocity and optimal phase difference angle were derived. The influence of frictional properties of the conveying parts, namely, the coefficient of friction on optimal in terms of velocity phase difference angle between the longitudinal and normal components of the elliptical oscillations is investigated. It is shown that the optimal phase difference angle decreases with the increase in the coefficient of friction. The approximate formula of optimal phase difference angle dependence on the coefficient of friction and track inclination angle is derived.