At present, the centrifugal grinders are, practically, used for the fine grinding of the materials, in which the material failure is occurred, when rotating toward each other the two rotors [1]. The rotors are, constructively, arranged, in the form of the cylindrical grids with the slit-like grooves (e.g. channels), the width of which is decreased with further distance from the gratings rotation center to the periphery. This destruction is, practically, occurred, mainly, at the particles impact of the rotor elements, but there is also the material cutting by the channels edges [2,3]. The grille is not clogged with the shredded material, since it is being purified by the air flows, moving at the high velocity.              

            The great practical interest is presented itself the determination of the minimum width of the channel between the rotor’s elements of the centrifugal grinder. We will solve this challenge by identifying the characteristic size of the particle through dp.

   Let the particle is entered the channel to the depth, which is equal to dp. The particle can, either be entered into the channel freely (e.g. Option 1), or after its contact with the inner surface of the element row 2 (e.g. Option 2).    

             So, the particle is experienced a free, as it is not expected the cracking or layer’s shear of the object, having maximum size of 2 mm. The particle must, completely, be withdrew from the contact with the wall of the gap of the first grating, i.e. to be entered into the channel following the lattice not less, than the depth, which is equal to its diameter.      

            Then for the time, required for the particle to be entered into the channel to the depth dp, by the Option 1, the wall of the channel will be passed the distance , where  – is the minimum width of the channel:  

                              

where v12r  – is the radial velocity of the particle at the channel’s inlet;  u12 ,  u21 – are the circumferential velocities of the elements 1 and 2 cylindrical lattices, respectively; r11 and r12 –  are the inner and outer radii of the 1 – st lattice.  

              So, the expression has been obtained under the condition by the angular velocities equating of the lattices ω1 = ω2. The width of the channel, in case of the particles motion by the second Option, is defined as follows.      

              The relative velocity of the particle s equal to zero, so the particle, having come out of the contact with the wall, is being moved in the direction of the circumferential velocity.     

          Having based on this consideration, the minimum width of the channel can be defined:

                                                

             The numerical values substitution is given for the particle the diameter of 2 mm. = 6,67 mm. with the free inlet channel, and after the contact with the surface of the element (when it is entered tangentially to the circle) = 13,9 mm. Both sizes are quite feasible, constructively.