OBRABOTKAMETALLOV Vol. 25 No. 1 2023 technology where Aω – amplitude, µm; ω – cyclic frequency, rad/s; yy – the initial phase of vibrations; variable 0,5 0,5 ( ) f e u t y D V ω ⋅ - ⋅ γ = , where y – the level in question. At the initial phase of relative fluctuations yy = 0×(2p) and amplitude Aω = 0.2×tfi, ω = 628 rad/s material removal at the current speed, taking into account vibrations: 6 2 6 1 0,4 6 12 6 6 (15 10 ) 5.89 10 7 13 0, 25 15 10 0.17 10 15 3 0.85(35 0.25)15.866 10 0.1 7.31 10 r - - ω - - - ⋅ D = = ⋅ p p ⋅ + + ⋅ + ⋅ ⋅ ⋅ , m 5) Calculate the thickness of the surface layer, in which the roughness is located, according to: i fi i H t rω = - D , (5) When substituting parameter values into equation (5), we get: 6 6 6 15 10 5.89 10 9.11 10 i fi i H t r - - - ω = - D = ⋅ - ⋅ = ⋅ , m. 6) Calculate the cutting force as follows: max max 1 sin 3 2 0.055 0.061 sin yi k g g g i e i g g s P L n h H D H h b = r + r τ b , (6) where Lk – grinding wheel height, m; hgmax – grain wear, hgmax = 10·10 -6 m; b and b 1 – cutting angles of abrasive material, b = 22° and b1 = 34°; τs – shear stress, N/m2. The shear stress is defined as: 1, 5 s σ τ = , (7) where σ – ultimate strength of the material, σ = 2·109 N/m2, 9 8 2 10 13.33 10 1.5 s ⋅ τ = = ⋅ , N/m2 By substituting the data into equation (6), the cutting force is determined as: 3 6 6 6 6 1 3 2 25 10 15.866 10 7.31 10 10 10 9.11 10 0.1 y P - - - - = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ × 6 6 6 8 0.3746 0.055 9.11 10 0.061 7.31 10 10 10 13.33 10 2.899 0.5591 - - - × ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ ⋅ ⋅ = , N. 7) Clarify previously obtained calculated values Dtf1, Dr1, Py1. The value of the increment of elastic deformations is determined as: 9 8 1 1 0 ( ) 30 10 (2.899 0) 8.698 10 y TS y TS y y A P P P - - D = ω ⋅ D = ω ⋅ - = ⋅ ⋅ - = ⋅ , m. The micro-cutting depth’ increment and the micro-cutting depth values are calculated, respectively as follows: 6 8 6 1 1 1 15 10 8.698 10 14.91 10 f y t A A - - - D = D - D = ⋅ - ⋅ = ⋅ , m, 6 6 1 0 1 0 14.91 10 14.91 10 f f f t t t - - = + D = + ⋅ = ⋅ , m.
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