## 2 Theoretical Studies of the Process of Potash Ore Cutting by Cross Cuttings  
One of the advantages of the planetary-disk operating bodies is the creation of a grid of intersecting cuttings on the surface of the rock chips [6, 7]. There are scientific studies of employees of Perm National Research Polytechnic University (PNRPU), Karaganda Research and Development Coal Institute (KRDCI), Moscow Mining Institute (MMI) and Giprouglemash, where the results of researches of the cross cutting pattern of potash ore blocks can be found [8; 9; 10; 11; 12; 13]. Each next layer of the mass is cut in such manner that these cuttings intersect with the cuttings of the previous layer at a certain angle when the cross-cutting pattern is implemented. The layer that is destroyed by the cutters installed on one disk of the special planetary-disk element of the heading-and-winning machine is called operating layer of the rock mass [14; 15]. The theoretical basics of the rock-breaking mechanism of potash ore by cross cuttings is going to be described below (Figure 1). The implemented rock cutting element is a cutter with a rectangular edge and a flat front face (as the most efficient for cross-cutting) [16]. Figure 1: Pattern of the separation of successive elementary cleavages of the potash mass during the destruction by cross cuttings: (**a**)—cutting face by cross cuttings: 1—large elementary cleavage; 2—cutter; 3—intersecting cuttings; 4—zones of concentration of fractures; (**b**)—pattern of separation of elementary cleavages of potash mass during the cutter’s movement across the cuttings of the operated layer: 1—large elementary cleavage; 2, 3, 4—small intermediate cleavages; 5—zones of concentration of stresses and fractures. The cutter (cutting angle \(\alpha_{c}\), cutting edge width \(b_{c}\)) moves at the speed of \(V_{c}\) across the cuttings of the operated layer of the mass in the cutting plane \(Z\). The cutter is deepened in relation to the cuttings of the operated layer by the value \(h_{c}\). The total thickness of the cleavage \(h\) is determined be the Equation (1):  
\[h=h_{c}+h_{p}, \tag{1}\]  
where \(h_{c}\)--the value of the deepening of the intersecting cuttings in relation to the cutting of the operated layer, mm; \(h_{p}\)--height of a protrusion, mm. The cuttings of each layer form intersecting zones of concentration of stresses and localization of man-made fractures on the face surface. The practical location of the zones of induced fractures is determined by the value of the rational cutting step \(t_{r.s. }\) of the cross and co-directional cuttings. The cutter penetrates into the potash mass during the rock-breaking step, while crushing and plastic deformation of a certain volume of ore is realized. The zone of stressed state is formed in the pre-cutter space. The implementation of traditional cutting patterns [17] is characterized by the formation of large cleavages, which are obtained during the creation and development of main fractures in the zone of contact of the front edge of the cutter with the potash mass. A counter-propagation of the transverse shear fractures existing in the mass (<<starting>> fractures), concentrated along the perimeter of the base of the formed protrusion, is occurring during the potash ore cutting by cross cuttings, provided that the cutting step is less than or equal to the rational cross cutting step (\(t\leq t_{r.s.}\)). The formation of the fracture surfaces of elementary cleavages through the development of the induced fractures existing in the mass determines a decrease in the forces required for the cleavage. Moreover, it decreases the volume of the bulb of pressure (consists of the fine particles of crushed rocks) and the zone of inelastic deformation of the ore [18]. Therefore, practical shaping of the cutting face using cross cutting pattern with the rational step \(t_{r.s.