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 In comparison with the process of metals grinding, the size and shape of the contact zone when grinding holes of bars made of sitall (Fig. 4) vary from those known from literary sources [17–19]. The actual size of the zone by coordinate z 75...80 % larger than the one accepted for comma-shaped slices and 10...15 % smaller than the one accepted for segment-shaped slices. The width of the zone differs from the maximum possible by the amount of the current radial removal of the material (Fig. 4). The radial removal of the material and the layer with the current roughness are determined by the grinding modes, the state of the tool surface, the dimensions of the workpiece and the wheel, the initial state of the processed surface after the previous contact. With a steady grinding process, to deduce the dependence of the radial removal on the elements of the grinding mode in an explicit form, taking into account the multi-pass process, we combine the origin of the coordinates with the level of the maximum vertices of the profile on ( − j n )-th touch, where n – the number of touches of the surface with the wheel required for a complete update. Then at − ≤ ≤ D 1 0 j p y r we will receive: − = + D − 1 ( 1) f p j t n r y . (7) It is known that with a sufficiently wide change in the elements of the cutting mode, the number of touches n , that are necessary to completely remove the initial surface roughness varies from 2 to 12 [18]. Taking into account the above, under the assumption, that n is a continuous value, based on the depen- dencies (6) and (7) after expansion into a series and convolution of the first 12 terms at the selected proba - bility value β m , we obtain an approximate solution for calculating the radial removal of the material ob- tained by mechanical cutting for the conditions of grinding workpieces made of brittle non-metallic materials (Fig. 7): ( ) + ± ρ D = 2 ç ç 0.677 0.073 ( ) , f u f c k u e p u t V t K V V n D r V (8) where e D – equivalent diameter. The thickness of the layer with the current roughness (Fig. 6), based on geometric considerations, can be calculated according to the dependence: = − D + D f p x H t r r . (9) After substituting the parameter values in expression (9), a mathematical model of the formation of a layer with the current roughness after grinding workpieces made of brittle non-metallic materials is obtained: Fig. 6. Pattern of abrasive grain contact with brittle workpiece material