Probabilistic model of surface layer removal when grinding brittle non-metallic materials

OBRABOTKAMETALLOV Vol. 23 No. 2 2021 TECHNOLOGY After changing the variable  to u z V and integrating over, a dependence is obtained for  calculating the current value of the number of cutting edges, passing through the section at   1.5 :                        2 1.5 1.5 2 2 2 2 1.5 1.5 3 ( ) ( ) 2 4 ( ) y k u z y y u u L V V n t z L z z L z dD V H d D                         2 arcsin 2 y y z L L (11) The number of cutting edges that pass during the contact of the section with the circle is determined from equation (11) at the upper limit of integration  y z L :             0.5 Ã( ) ( ) ( ) ( 3 / 2) e k u z f u u D V V n t y à V H . (12) The width of the grain pro fi les in the working layer of the tool at the level y from the surface of the workpiece will be equal to:     ( ) m m z b b f b C h C t y u , (13) where b C , m – is the proportionality coef fi cient and the exponent, respectively, in the equation when the grain shape is approximated by a paraboloid of revolution; f t – is an actual depth of cut; u – is the position of the grain in the abrasive tool relative to its conditional outer surface (Fig. 4). Fig. 4. Scheme of interaction of abrasive grains with a ceramic workpiece After substituting expressions (9) and (13) into (6), the dependence for calculating the indicator   1 ( , ) a y is obtained:               1 ( , ) ( ) ( ) (1 ) c z z k u ck a y k n b f u u V V P . (14) We replace the variable with  on u z V and after substituting it into expression (14) we get:             ( ) 1 0 ( ) ( , ) ( ) (1 ) y t z y z k u c z z ck u L V V a y z k n b f u P dudz V , (15)