Transport of granular matter on an inclined vibratory conveyor with circular driving
Abstract
I present a theoretical model to investigate the transport properties of granular materials on an inclined vibratory conveyor driven by circular oscillations. My model treats the granular dynamics on a vibratory conveyor as a combination of sliding and oblique hopping of a granular block with specific inelastic and frictional properties. The calculations show optimal transport conditions for the transport velocity efficiency, with an extra transport velocity efficiency minimum when the inclination of the vibratory conveyor is non zero. The investigations also show a current reversal under a certain inclination angle which does depend on the friction force.
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Introduction
Vibratory conveyors, i.e., troughs that induce the motion of the material laying on them when they are oscillating, are extensively used in industry for the handling and transport of granular materials. They present many advantages such as the simplicity of their construction, the controllable feeding speed, the possibility of mixing and/or segregating different types of granular materials laying on them by tuning the right oscillating frequencies, and finally the self-cleaning operating
mode [1–4]. Consequently, extensive theoretical and experimental [3–15] studies were devoted to the properties and dynamic of granular materials on these devices using mainly two types of driving modes: linear and circular. The experimental investigations revealed the existence of optimal transport conditions, i.e., maximal and minimal transport velocity for special throw numbers Γ=amax /gcos (α), where amax is the maximal vertical acceleration, α the trough inclination angle, and g is the gravitational acceleration. Moreover, the transport velocity of granular materials using a circular driving mode showed a surprising current reversal as a consequence of a continuous variation of Γ. Previous theoretical investigations using macromechanical models for the hopping and gliding dynamics reproduced successfully the experimental findings [3, 11, 12], and explained the dynamical origin of the optimal transport conditions.
In this work, I investigate the effect of the tilt of a vibratory conveyor driven by circular oscillations on the transport properties of granular materials. More specifically, I investigate the effects of this tilt on the current reversal and on the optimal transport dynamics.
Conclusion
I have presented a model for the determination of transport velocity efficiency of granular materials on an inclined vibratory conveyor subject to a circular driving mode. My calculations show the persistence, under certain conditions of the major features of the transport found for a horizontal conveyor, in particular the current reversal and the optimal transport condition. Based on this model, we could explain the origin of the different behavior of the transport velocity and the underlying dynamics. The calculations show the existence of a new transport minimum due to the competition between the gravitational and the driving forces. This minimum is strongly friction dependent. The calculations also show that by increasing the inclination angle we obtain a suppression of the current reversal. This suppression does depend on the elastic as well as the friction properties of the granular block. Finally, I hope that experimental studies will be performed in the future to validate the model predictions.