Calculation of radial material removal and the thickness of the layer with the current roughness when grinding brittle non-metallic materials

OBRABOTKAMETALLOV Vol. 23 No. 3 2021 technology ( ) + ± ρ = − × 2 ç ç 0.677 0.073 ( ) f u f c k u e f u t V t K V V n D H t V ( ) +χ+β       + ± ρ       × + − −           θ       2 2 ç ç ( ) 0.677 0.073 ( ) 1 1 exp x f u f c k u e m u t V t K V V n D V . (10) Example . Calculate the thickness of the layer with the current surface roughness during internal grind- ing of the hole − = ⋅ 3 150 10 d m the workpiece АS-370. At the same time, the grinding head is selected as the tool AW 60×25×13 63C F90 M 7 B A 35 m/s with the value of the transverse feed D = 5 si A μm per revolution of the workpiece and the speed of rotation of the workpiece V u = 0.25 m/s. Increments of elastic deformation of the tool and the workpiece, as well as temperature deformations of the system elements, are not taken into account. Current system status is t f = 14.65 μm. For the specified conditions = 1 c K , n 3 = 15.866·10 6 m, ρ 3 = 7.31 ·10 –6 m, θ = 0.5, β = 2 , m x = 0.7 and χ = 1.3. We determine the value of the radial removal of the material obtained by mechanical cutting, m: ( − − D = ⋅ ⋅ ⋅ + ⋅ ⋅ ± × 6 6 2 1 (0.677 14.65 10 0.25 0.073 (14.65 10 ) 1(35 0.25) 0.25 p r ) − − × ⋅ ⋅ ⋅ = ⋅ 6 6 6 15.866 10 0.1 7.31 10 ) 7.458 10 . Then calculate the amount of removal due to the brittle destruction of grains, m: ( − − D = ⋅ ⋅ ⋅ + ⋅ ± × 6 6 2 1 (0.677 14.65 10 0.25 0.073(14.65 10 ) 1(35 0.25) 0.25 x r ) ( − − + +   × ⋅ ⋅ ⋅ − − ⋅ ⋅ ⋅ +    ⋅   2 6 6 6 (0.7 1.3 2) 1 15.866 10 0.1 7.31 10 ) 1 exp 00.677 14.65 10 0.25 0.25 0.5 ) ) − − −  + ⋅ ± ⋅ ⋅ ⋅ ⋅ = ⋅  6 2 6 6 6 0.073(14.65 10 ) 1(35 0.25) 15, 866 10 0.1 7.31 10 4.603 10 . So the thickness of the layer with the current roughness will be equal to, m: − − − − = − D + D = ⋅ − ⋅ + ⋅ = ⋅ 6 6 6 6 14.65 10 7.458 10 4.603 10 11.795 10 . f p x H t r r Acomparison of the values of the radial removal of the material and the layer with the current roughness, calculated from the dependencies (8) and (9) for the case of internal grinding of the hole d = 150·10 –3 m of the workpiece made of AC-370 is given in Table 1. At the same time, the conditions of the above example with the initial state of the system are preserved; t f0 = 0; V k = 35 m/s; V u = 0.25 m/s. For most grinding modes, the deviation of the values of the radial removal and the layer with the current roughness of the material, calculated according to simplified models, does not exceed 1 %. Only for modes 4 and 6, these deviations are 1.17 and 1.19 % respectively. Thus, the accepted approximations provide a sufficiently high accuracy of calculations and allow to evaluate analytically the impact on the radial removal of the material and the layer with the current surface roughness of the elements of the grinding mode and the characteristics of the abrasive tool. The radial removal and the layer with the current surface roughness depend on the actual depth of micro-cutting, the speed of the workpiece, the dimensions of the workpiece and the wheel, the geometry of the abrasive grain, the number of cutting edges on the surface of the wheel. With an increase in the depth of micro-cutting, the radial removal of the material and the thickness of the layer with the current surface roughness increase for all values of the wheel speed and the workpiece speed (Fig. 5 and 7).