Flat problem to determine the forces of destruction of pieces n disintegrators while being grabbed in thick layer

Abstract

Purpose. Research on analytical dependences of destructive stresses, acting on a piece of non-isometric shape at quasi-static deformation of a relatively thick layer of rock mass in disintegrators, on parameters of the piece shape, the pieces spatial orientation, also on the relative piece size in layer, taking into consideration the discrete nature of contact force application. Methodology. The flat scheme of a non-isometric shaped piece contacts in a thick layer of rock mass is obtained by composition of the central rectangular piece and the round pieces of average size for the given layer. The distribution of stress components in the layer of loose rock mass is accepted on the basis of the classical theory of elasticity and the theory of loose medium. The geomechanics criterion showing relationship of equivalent destructive stress and ultimate compressive strength of rock is used as a criterion of piece destruction in complex stress state. All force schemes of the piece loading are reduced to three-point bending schemes and two-point shear schemes, both across the long and the short sides of the piece. The most dangerous loading scheme is determined from the analysis of the mentioned schemes for each particular case. Dimensionless parameterization is applied both to specify the geometric parameters of pieces and to analyze the resulting destructive stresses. Findings. Analytical dependences of equivalent destructive stresses for an oblong piece are obtained depending on the piece relative length, the relative piece size in the rock layer, the angle of piece orientation relative to the direction of the maximum main stress and the side thrust coefficient in the layer. It has been set that lamellar pieces, especially those smaller than the average size for the layer, are destroyed mainly from the implementation of bending schemes across the long side, the shape of their fragments is improved by reducing the pieces relative length. Increasing the uniformity of the force field in the working zone of disintegrator also leads to improvement in the shape of fragments. On the other hand, as the shape of the piece approaches the isometric one, as well as when the piece relative size in layer raises, the probability of implementing shear schemes increases and the probability of implementing bending schemes decreases, including with a deterioration in the fragments shape compared to the original piece. At the same time, larger values of destructive stresses for the lamellar smaller pieces are proved analytically compared to the isometric bigger ones, all other things being equal. Originality. The versatility of application of the three-point bending scheme of a non-isometric shaped piece in combination with the two-point scheme of its shear for analysis of its destruction in the thick layer of rock mass is substantiated. For the first time, the dependences of equivalent destructive stresses for the non-isometric piece on its relative length, its relative size in layer, the angle of deviation of the pieces main axis from the main stress direction and on the side thrust coefficient in the layer have been obtained. Practical value. The results obtained allow making reasonable choice of parameters of disintegrators operational parts for destruction of materials in the thick layer, as well as predicting the change in lamellar pieces fraction during disintegration process. They give the possibility to determine key parameters of operational parts for new designs of disintegrators. This creates the basis for the development of calculation techniques for operational parts of modern samples of crushing and grinding equipment.