OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 5 Σ + + = + 2 2 d X dX m h cX F (L, V, X, p) f(t) dt dt (1) where m = diag(m), h = [hS,k], c = [cS,k], S, k = 1, 2, 3 is positively definite symmetric matrices of inertial, velocity, and elastic coefficients; X = {X1, X2, X3} T∈ℜ X (3) is deformation vector; F ∑ = F + Φ is the vectorfunction of forces on the rake F and flank Φ faces; F = {F1, F2, F3}T∈ℜX (3); Φ = {Φ 1, Φ2, Φ3}T∈ℜX (3). Let us also consider deformation velocities = d / d = X t ∈ ℜ(3) ,1 ,2 ,3 { , , } T X X X X V V V X V . We represent forces F in the form = = χ χ χ (0) 1 2 3 1 2 3 { , , } { , , } T T F F F F F [47]. Here χ χ χ 1 2 3 , , are angular coefficients satisfying the condition χ + χ + χ = 2 2 2 1 2 3 ( ) ( ) ( ) 1. The given perturbations 0 1 2 3 ( ){ , , } T f t χ χ χ = ( ) f t are considered to be reduced to the coordinate system of the forces F . Furthermore, 0( ) f t is modeled as “white” noise. Based on prior studies, the model of cutting forces acting on the rake face of the tool (0) F is given by [47]: a b c Fig. 1. Examples of photographs of the worn tool part and wear evaluation scheme: a – flank wear of a 79 WC-15 TiC-6% Co insert during turning of AISI 301 steel; b – wear development of a 79 WC-15 TiC-6% Co insert during turning of steel 0.2 C-Cr; c – schematic of the matrix grid
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