The article presents a method of calculating the parameters of the screw conveyor vibration exciter. The calculation scheme of the new design of the vibration exciter, which allows to determine the parameters of the vibrations excited by this device taking into account the structural novelty and the specifics of the vibration exciter, in particular, in the screw reloader is also given. A system of equations describing the harmonic oscillations of the auger shaft axis, including the amplitudes of horizontal and vertical oscillations, is presented. As a result, a system of parametric equations describing the external and internal envelope line is obtained. When solving the system of equations, the equations of the boundary curves of internal and external rotating bodies are derived. The equations allow to calculate the trajectory of any point by its given polar coordinates. Examples of rotating bodies for different types of displacements of the triangle center in the calculation scheme, which are described by harmonic oscillations, are shown. The dependences of the body shape on the direction of oscillations along the coordinate axes are illustrated. It is shown that the transition from horizontal to vertical oscillations leads to a loss of symmetry of the body. The amplitude and frequency of oscillations also have a significant impact on the shape of the body. The forms of the rotating bodies, giving the possibility of combining the rotation and oscillation when driving on rollers are determined. The problem is generalized to an arbitrary number of regularly arranged rollers. The given technique gives the principal opportunity to create designs of vibrators that combine vibrations with rotation on rollers.
Introduction. The paper analyzes contemporary methods of frame support design in permanent workings and reveals that contact grouting has received little attention. Contact grouting makes the tight contact between the hardened cement grout and the surrounding rock possible, whereas it is impossible when applying concrete lagging. The paper employs analytical method of arch support, grouting layer, and the surrounding rock calculation considering their softening. Analytical formulae determining support load has been obtained. The formulae take into account strain and strength characteristics of the surrounding rock, hardened cement grout, and support. Support load was calculated under various values of the grouting layer thickness and linear strain modulus and the depth of mining. The dependencies between the support load and the indicated parameters have been obtained, which makes it possible to select the cement grout composition for various mining and geological conditions. Research objective is to determine the effect produced by grouting layer thickness and strain characteristics on arch support load value in order to check its strength in various mining and geological conditions. Methods of research are built upon the physically based analytical methods of geomechanics to solve the problem of interaction between the support, grouting layer, and surrounding rock mass. Results. The results of arched support load calculation are presented for various values of grouting layer thickness, its strain characteristics, and depth of mining. Conclusions. The presence of the grouting layer in the void behind the support has a significant effect on the methods of arch support design. The developed methods take account of the fact that a layer of soft rock develops in the rock mass between the grouting layer and undisturbed rock. When the rock is being broken, its volume in this layer increases, which, in its turn, results in support load transfer growth through the grouting layer. It has been determined that the increase in the hardened cement grout strain and grouting layer thickness reduces support load.
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