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 Fig. 2. Influence of the micro-cutting depth on the radial mate - rial removal when grinding holes in silicon workpieces (hole diameter – 150 mm, tool AW 60×25×13 63C F90 M 7 B A 50 m/s 1 – = 0, 010 f t mm; 2 – = 0, 020 f t mm; 3 – = 0, 050 f t mm) of the line with probability = β ( ) m P M during the contact is the current value of the radial removal and the shape of the curve that limits the contact zone from the tool side (Fig. 2). The most intense decrease in the radius vector of the workpiece is observed near the plane passing through the center of the wheel and the center of the workpiece when the depth of micro-cutting ( ) t z is maximum and the largest number of cutting edges of the tool passes through the section. The equation of the line bounding the contact zone of the workpiece with the grinding head on the tool side (Fig. 3) is written as follows, if in equation (1) the probability of material removal is given the value β m : ( ) = β = − − − τ − τ − − τ 0 1 2 ( ) 1 exp ( , ) ( , ) ... ( , ) m n P M b b y b y b y . (4) Let us denote: π ρ ± − = 3 3 0 1 3 2 3 2 ( )(1 ) 8 c k u u u n K V V P G H V π ρ ± = 3 3 2 3 2 3 2 ( ) 16 c k u u u n K V V G H V ρ ± = 3 3 3 1,3 0, 05 2 ( ) c k u u u n K V V G H V . The amount of material removed for the j-th contact of the surface with the wheel is numerically equal to the displacement to the center of the workpiece with the accepted probability of material removal and is calculated from equation (4), which at can be written as: +χ+β +χ+β +χ +χ β β − − + D − − β = − + + − + + D 1 2 1 3 ( ) ( ) ln(1 ) ( ) ( ) . ( ) x m m f f x m m m f f f x f t y t y r G t y G G t y G t r t (5) Let’s replace the variables: − = + 1 j j y y H ; = + D f j t H r ; D = ζ ⋅ x f r t ,