OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 3 2024 Let us limit ourselves to longitudinal turning of a shaft of constant diameter (D = const) in the following modes: L1(t) = L1(0) = const, L2(t) = V1t , L3(t) = V3t . Turning with a tool with a plan main angle φ = π/2 is considered (fig. 1). Auxiliary angle φ1→0. Orthogonal clearance angleα→0. Usually α < 6°. When turning at constant modes, subject to stability of equilibrium 1 2 3 { , , } const T X X X ∗ ∗ ∗ = = X , the following is true: (0) 1 2 3 (1 ); ; , P p P P P t t X k S V T V V ∗ ∗ ∗ ∗ = - - = ≈ (4) where (0) 1 ( ) ( ) (0) P t t R t L = - ; 2 2 ( ) ( ) X t X t T = - is true for equilibrium stability, so 2 P S V T ∗ = ; in (4) it is taken into account that 3 2 V V 〉〉 . Fig. 1. Formation of forces, deformations and trajectories of actuators Therefore, in steady state, the tool tip moves along the workpiece surface in the “A-B” direction. This direction is at an angle of φ = arctg(V3/V2). The trajectory is shifted by X * = const (fig.2). It is marked in red color. If a typical case is considered: (0) (0) P P t S . Then Φ1→0. For further analysis it is convenient to enter aggregated coordinates 2 2 3 3 ( / ) / ( / ) V dX dt V dX dt υ = - - ; 2 3 / V V ∗ υ = . (5) It has been shown earlier [24, 25] that the forces Φ2, Φ3 are represented as ( ) { } Ô Ô (0) 2 0 0 1 (0) 3 0 0 1 Ô ( ) exp ( ) ; Ô ( ) exp ( ) , P T T P k F t X t k k F k t X t ∗ ∗ = + ρ - ς υ - υ = + ρ - ς υ - υ (6) Fig. 2. Сhanging the direction of motion in the contact area between the rear edge of the tool and the workpiece
RkJQdWJsaXNoZXIy MTk0ODM1