“…As a result of this approach, there is a gap between the subsystems of the vibrational activity of the tool [ 1 , 2 , 3 , 4 , 5 ] and the thermodynamics of the cutting process [ 6 , 7 ]; however, experimental studies show that such a relationship exists [ 9 , 10 ]. The second direction is related to the modeling of the temperature field in the tool itself, this approach is very well presented in [ 8 ], and it should be noted that this approach quite accurately connects the development of wear of the cutting wedge with the temperature gradient in the same cutting wedge. However, this approach has low practical application, since it is practically impossible to measure the gradient of the temperature field in the cutting wedge during cutting, and the interrelated dynamics of the cutting process and its relationship with the temperature are also not taken into account here.…”