OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 5 No. 2 2023 Fig. 5 shows the graphs of function q(x, t) at x = 0 for the milling cutter with parameters d = 30 mm, j = 90°, l = 20°and the angle of the milling cutter rotation ψ being equal to 0° (line 1) and 20° (line 2). Fig. 6 shows the results of modeling the milling cutter generating surface when it is rotated by the angle of y = 20° and the nominal machined surface. Fig. 5. Function graphs θ(x, t) at x = 0 We estimate the curvature of the surface machined by calculating its main curvatures (k1 и k2), which are the solution of the equation 2 2 0 k H k K − ⋅ + = , (7) where 2 2 2( ) LG FM EN H ÅG F − + = − , (8) 2 2 LN M K EG F − = − , (9) where E, F, G are the coefficients of the first quadratic form (g) of the machined surface (6), described by the equation: 2 2 2 g E dx F dx dt G dt = ⋅ + ⋅ ⋅ + ⋅ , (10) where 2 0( , ) r x t E x ∂ = ∂ ; 0 0 ( , ) ( , ) r x t r x t F x t ∂ ∂ = ∂ ∂ ; 2 0( , ) r x t G t ∂ = ∂ , (11) L, M, N are the coefficients of the second quadratic form of the machined surface (6), described by the equation: 2 2 2 q L dx M dx dt N dt = + + , (12) where 0 2 ( , ) ( , ) r x t n x t L x EG F ∂ = ∂ − ; (13) 0 2 ( , ) ( , ) r x t n x t M x t EG F ∂ = ∂ ∂ − ; (14) Fig. 6. Modeling of the milling cutter’s producing surface and the nominal machined surface
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