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

OBRABOTKAMETALLOV Vol. 23 No. 2 2021 technology 3 9 3 7 3 5 3 2 3 3 ( 0,1 10 0, 001) 4( 0,1 10 0, 001) 6( 0,1 10 0, 001) 0,1 10 0, 001 9(0, 53 10 ) 5 0, 53 10 7(0, 53 10 ) − − − − −  − ⋅ ⋅ − ⋅ ⋅ − ⋅ ⋅ × − ⋅ ⋅ + − + −  ⋅ ⋅ ⋅  ⋅  3 3 4( 0,1 10 0, 001) 8 0, 53 10 2, 701 20 3 0, 53 10  − ⋅ ⋅ − + ⋅ ⋅ =  ⋅  6 6 6 6 2 2 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 6 4 6 1,3 6 6 2 0.05 1, 0 2 7, 31 10 35, 25 15, 86 10 (9, 04 10 1 10 0,1 9, 04 10 ) 0, 25(9, 04 10 ) (9, 04 10 0,1 9, 04 10 ) − − − − − − − ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ − ⋅ + ⋅ ⋅ + × ⋅ ⋅ + ⋅ ⋅ 3 9 3 7 3 3 2 3 3 2 ( 0,1 10 0, 001) 4 ( 0,1 10 0, 001) 0,1 10 0, 001 9 (0, 53 10 ) 7 (0, 53 10 ) − − − − −  − ⋅ ⋅ ⋅ − ⋅ ⋅ × − ⋅ ⋅ + − +  ⋅ ⋅  ⋅ ⋅  3 5 3 3 3 3 3 6 ( 0,1 10 0, 001) 4 ( 0,1 10 0, 001) 8 0, 53 10 2, 701 20 5 0, 53 10 3 0, 53 10 − − − − −  ⋅ − ⋅ ⋅ ⋅ − ⋅ ⋅ + − + ⋅ ⋅ =  ⋅ ⋅ ⋅  To determine the index, profilograms were used, taken from a sample of the workpiece (sitall AS-370) after rough grinding [22]. The probability of an event characterizing the removal of the surface layer at the level 0, 004 y = of mm at the value of the indicator 0 0, 546 a = is calculated by the equation (2): 0 1 2 ( ) 0,546 2,7 2,701 ( ) 1 1 0, 997 a a a P M e e − + + − − − = − = − = . The probability of no material removal, as an opposite event, can be determined from the total probability formula: 1 ( ) 1 ( ) 1 0, 997 0, 003 P M P M = − = − = . For other levels of the considered example, the calculated data on the probability of material removal are given in Table and Fig. 1. Analysis of the data obtained (Table) provides a clear illustration of the regularities of material removal along the contact zone at various levels. Calculations by formula (2) show that the probability of removal at values 3, 38 z = − , 0, 8 f y t = ⋅ , 6 9, 04 10 f t − = ⋅ m is equal to 0.71. This means that 71 % will be removed, and 29 % of the processed material will remain on the surface in the form of microroughnesses. This is explained by the fact that in the process of grinding, single grains leave traces in the form of scratches, which are superimposed on each other, while some of the grains do not cut, as it fall into the trajectory of the previous grain. Some of the grains will partially contact the material being processed, that is, the contact will not extend over the entire width of the grain. Chipping can occur under the scratch when processing brittle non-metallic materials. With an increase in the number of grains in contact with the surface of the workpiece, the number of scratches overlapping each other increases. The proposed dependences make it possible to calculate changes in the probability of material removal when processing brittle non-metallic materials during grinding operations. The above analytical models can