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   π ρ ± − − = − + + +       2 3 5 3 3 0 2 3 2 3 2 ( )(1 )( ) 2 8 ( , ) 5 15 3 8 c k u f y y y u u n K V V P t y z z a y z z L L L H V   ρ ± − + D + + − + − +   + D     4 9 7 5 3 3 3 1,3 2 2 3 2 0, 05 2 ( )( ) 4 6 4 8 5 20 3 ( ) 9 7 c k u f x y y y u u f x y y n K V V t y r z z z z z L L L H V t r L L , (3) where 1 ( , ) a y z – an indicator that characterizes the change in the area of depressions formed due to the process of mechanical cutting; 2 ( , ) a y z – an indicator that characterizes the change in the area of depressions formed due to the brittle chipping process; D x r – the value of the increment of material removal in the process of brittle chipping of brittle non-metallic material; 3 n – the number of grains per unit area of the working layer of the tool; k V – peripheral speed of the tool (wheel); u V – peripheral speed of the bar; u H – the thickness of the working surface layer of the tool in contact with the workpiece; f t – actual cutting depth; y L – the length of the contact zone from the nominal external surface of the tool to the main plane; 0 P – probabilistic characteristic of a brittle non-metallic material chipping; c K – chip formation coefficient; z – the coordinate directed along the contact zone; ρ 3 – the radius of rounding the grain top. Dependencies (1), (2), (3) allow considering the method of analytical calculation of the radial material removal and surface roughness according to the input technological variables of the grinding process. As noted in [18], the “material – medium” boundary region can be specified by levels of equal probability of material removal. Figures 1 and 2 shows illustrations of material removal during grinding holes in sitall blanks (AS-370) by a tool AW 60×25×13 63C F90 M 7 B A 50 m/s (at the speeds of the grinding head – 35 and 50 m/s, the workpiece speed – 0.25 m/s, longitudinal feed – 33 mm/s, transverse feed – 0.008 mm/stroke). When passing the surface of the contact zone, the levels are shifted to the center of the workpiece (Fig. 1). By observing the change in the position of the level = β ( ) m P M limiting the transition area “material- medium” from the medium side, it is possible to follow the dynamics of the removal of the allowance in the contact zone of the workpiece with the tool. The distance between the radius vectors of the initial surface and the surface after contact will determine the radial removal of the material D r per touch, and the position Fig. 1. Changing the radius vectors of equal probability levels