Vibrotransporting of Bodies on a Surface with Non-Translational Rotational Oscillations
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ANICS OF MACHINES
Vibrotransporting of Bodies on a Surface with Non-Translational Rotational Oscillations I. I. Blekhmana,*, V. B. Vasil’kova, and Yu. A. Semenova a Institute
for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia *e-mail: [email protected] Received November 11, 2019; accepted March 27, 2020
Abstract—In this article we study the theoretical problem of vibrational transportation of bodies along a surface in the state of non-translational, in particular, rotational oscillations. Nonlinear differential equations of motion of bodies on such surface are obtained. It is shown that, in the case where the influence of centrifugal and Coriolis inertia forces can be neglected, when finding the local average speed of vibrational transporting, one can use the results of an existing theory if additional parameters are introduced. The essential features of the arising motions are established, and a number of possible applications are discussed. The discovered regularities are confirmed by a physical experiment on a vibration bench. Keywords: vibrotransporting, vibrotransporting velocity, non-translational vibration, theory, experiment, applications. DOI: 10.3103/S1052618820040032
The effect of transportation of solid and granular bodies over oscillating rough surfaces was the basis for a large number of technical applications. The theory of this effect is relatively well developed in the cases when the surface performs plane-parallel translational oscillations [1–6]. In this article we address the more difficult problem of vibrotransporting on a rough surface with nontranslational vibrations. Such a study could be the basis for expanding the possibilities of using the vibration technique. In the theory of vibrotransporting, the motion of a plane solid particle is considered as a basic model. Even in this form, the problem leads to essentially nonlinear “nonsmooth” differential equations. This is due to the presence of dry friction and a nonholding bond. The main task in this case is to find the average particle velocity for a period of oscillations in stable steady modes. More difficult is the problem of vibrotransporting along а non-translationally oscillating surface. Figure 1 plots the calculation schemes of particle movement along the surface performing translational (Fig. 1a) or non-translational (Fig. 1b) oscillations caused by turning the surface around a certain point O. In Fig. 1, ( x , y ) is a movable coordinate system rigidly connected with the oscillating surface, J is the inertia force, J t is the tangential inertia force of relative motion, J c and J k are the centrifugal and Coriolis inertia forces, mg is the force of gravity, N is the force of the normal reaction, F is the dry friction force, α is the surface inclination angle to the horizon, and β is the vibration angle. (a)
y
Asin(Zt) N J
O
mg
E F
(b)
y E
Asin(Zt + J) N
x
Jk
D = const
Jc O
Jt
E F
E x
D = D0 + D1sin(Zt + J)
mg
Fig. 1. Particle on a vibrating rough surface: (a) tra
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