In the article an attempt to describe a stage of power interaction of knives is made at mill fibrous semi-finished products by means of the theory of discrete contact of knives sets. Time of a relaxation of fibrous semi-finished products is investigated. This time makes from 4-10-4 seconds for semi-finished products of low concentration up to tens seconds for wood. Pressure in a zone of contact of knives of a rotor and stator is theoretically investigated. Dependences of size of pressure on relative introduction of knives in a fibrous material and displacement of a rotor are received. Theoretical researches are confirmed experimentally. Deborah's number ξ for a ground fibrous material is investigated. Dependences of this number from knife backlash and speed of sliding of knives are received. It is investigated deformation by a component of factor of friction between sets. For reduction of a deformation component of factor of friction between sets (i.e. reductions of power consumption) at mill chips wood and weights of high concentration it is necessary to increase frequency of rotation of a rotor, and at mill weights of low concentration, on the contrary, to reduce it. © Published under licence by IOP Publishing Ltd.