Simulation of the stock removal in the contact zone during internal grinding of brittle non-metallic materials

OBRABOTKAMETALLOV Vol. 23 No. 2 2021 technology 2 3 5 0 1 3 2 3 2 ( ) (1 )( ) 2 8 ( , ) 5 15 3 8 c z k u z f y y y u u k V V n P t y z z a y z z L L L V H   π ρ ± − − = × − + + +       4 9 7 5 3 3/2 2 2 3 2 3 2 ( ) ( ) 4 6 4 8 5 20 3 16 9 7 c z k u z f y y y u u f y y k V V n t y z z z z z L L L V H t L L   π ρ ± − + × + − + − +         , (3) where z n – is the number of grains per unit area of the working layer of the tool; k V – peripheral speed of the tool; u V – the peripheral speed of the workpiece; u H – thickness of the layer of the working surface of the tool in contact with the workpiece; f t – actual depth of cut; y L – the length of the contact zone from the conditional outer surface of the tool to the main plane; 0 P – the probabilistic characteristic of chipping of brittle non-metallic chipping material; z – coordinate directed along the contact zone; z ρ – radius of rounding of the top of the grain. The dependence for calculating the indicator 2 ( , ) a y τ is as follows: 2 3 5 0 2 3 2 3 2 ( ) (1 )( ) 2 8 ( , ) 5 15 3 8 c z k u z f y y y u u k V V n P t y z z a y z z L L L V H   π ρ ± − − = − + + +       4 1.3 2 0.05 2 ( ) ( ) ( ) c z k u z f x u u f x k V V n t y r V H t r ρ ± − + ∆ + + ∆ 9 7 5 3 2 3/2 4 6 4 8 5 20 3 9 7 y y y y y z z z z z L L L L L   + − + − +       , ( 4) where x r ∆ – is the increment in material removal in the process of brittle cleavage of brittle non-metallic material. Results and discussion Let’s calculate the probability of non-removal and the probability of removing material when grinding holes with a diameter of 150 mm in workpieces made of glass (AC-370) with the AW 60 × 25 × 13 63C F90 M 7 BA tool 35 m / s (at a wheel speed of 35 m / s, workpiece speed – 0.25 m / s, longitudinal feed – 33 mm / s, cross feed – 0.008 mm / stroke). From the calculation of the balance of displacements [18], we determine that for the given processing conditions 6 9, 04 10 f t − = ⋅ , m. Based on the research data [17, 20, 21], we accept: 1, 0 c k = ; 6 7, 31 10 z − ρ = ⋅ mm; 15, 86 z n = grains / mm2. For the considered conditions 0, 002 y L = m, 0 0, 5 P = , 0,1 x f r t ∆ = ⋅ . The calculation is performed according to equations (2), (3), (4) for level 6 1 10 y − = ⋅ m at 0,1 2 y L z = − : 6 6 6 6 2 1 6 3/2 3 1, 0 2 7, 31 10 (35 0, 25)15, 86 10 (1 0, 5)(9, 04 10 1 10 ) ( , ) 8 0, 25(9, 04 10 ) a y z − − − − π ⋅ ⋅ ⋅ + ⋅ − ⋅ − ⋅ = × ⋅ ⋅ 3 3 3 5 3 3 3 3 2( 0,1 10 0, 001) ( 0,1 10 0, 001) 8 0,1 10 0, 001 0, 53 10 15 5 0, 53 10 3 0, 53 10 − − − − − −   − ⋅ ⋅ − ⋅ ⋅ × − ⋅ ⋅ − + + ⋅ ⋅ +     ⋅ ⋅ ⋅   6 6 6 6 4 6 3/2 6 2 3 1, 0 2 7, 31 10 (35 0, 25)15, 86 10 (9, 04 10 1 10 ) 16 0, 25(9, 04 10 ) (9, 04 10 ) − − − − − π ⋅ ⋅ ⋅ + ⋅ ⋅ − ⋅ + × ⋅ ⋅ ⋅ ⋅