Synergetic approach to improve the efficiency of machining process control on metal-cutting machines

OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS ∈ ⊂ t (l) (0) l( ) Ψ Ψ (2) defines the requirement for the quality of the surface formed by cutting. This condition is considered to be achievable on a machine tool if the TEEs L(t) are controlled. However, in the case of evolution, the condition ⊂ (l) (0) Ψ Ψ may become unattainable. We will rely on the synergetic principle of “expansion-compression” of the state space dimension [6–8]. As applied to machining, it reveals the interaction between the tool and the workpiece through the medium formed by the cutting process. Let us limit ourselves to the mechanical interactions of the three tool faces ) , = + + Â F t t t t ( ( ) F( ) ( ) ( ) Σ Φ Φ (3) where (3) 1 2 3 { ( ), ( ), ( )} = ∈ℜ T F t F t F t F(t) – forces formed in the interface area of the front face of the tool, { } (3) 1 2 3 ( ), ( ), ( ) T t t t = Φ Φ Φ ∈ ℜ (t) Φ – forces formed in the interface area of the main back face of the tool and its auxiliary face { } ( ) ( ) ( ) ) 1 2 3 ( ), ( ), ( ) T B B B t t t = Φ Φ Φ ( (t) Φ Â . It is necessary to represent it in coordinates of state and control. In the areas of interface of faces, the work 1 2 3 { , , } T À À À = À(t) and power of irreversible Fig. 1. Scheme of interaction between the spindle rotation and feed drives of the slide, as well as the formation of a dynamic connection of the cutting process