OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 4 No. 1 2022 For a surface section passing through the zone of contact between the workpiece and the wheel, the instantaneous depth of microcutting by single abrasive grains, taking into account (1) and (2), can be described by the function: 2 ( ) cos i i f i yi i e u z z t k t A D V . (3) To describe the patterns of material removing in the contact zone, the authors of [20] proposed the concepts of material removing probability ( ) P M and material not removing probability ( ) P M . The fi rst indicator ( ) P M is determined by the probability of an event in which the material at the point of the treated surface is removed. The second indicator ( ) P M is the probability of an event in which the material is not removed from the treated surface. The sum of the probabilities, as the probabilities of opposite events, is equal to one, and its values depend on the position of the point in the contact zone. For the processing of workpieces with abrasive tools, the probability of material removal is calculated from the dependence: ( ) ( , ) ( ) 1 exp a y a y P M , (4) where ( ) a y is an indicator that determines the probability of material removal at the level y before the surface enters the zone of contact between the workpiece and the wheel; ( , ) a y is an indicator that characterizes the change in the areas of dimples formed by the sum of the profi les of abrasive grains passing through the considered section of the workpiece after the corresponding contacts of the grains with the surface of the workpiece. During time turns through an angle and a section passes through it with an arc length ( ) k u V V or taking into account that u z V we get ( ) k u u z V V V . Of the total number of grains that have passed through the section, the width of the profi le g b will have grains whose vertices are located in the layer of the wheel ( ) k u u V V z u V . The number of such vertices is calculated from the density of its distribution over the depth of the tool ( ) f u ( ) ( ) k u g u V V n f u z u V . (5) In the presence of vibrations, the width of the vertex contour corresponding to a given level is nonstationary, it does not remain constant, but changes over time. Its value can be described by a power dependence [1], which, taking into account the fact that u z V , is calculated by the equation: 2 ( ) ( ) cos m m m g b b b f y e u z z b y C h C t k y u C t y u A D V . (6) To describe the distribution density of the abrasive grains vertices, O. Coyle suggested using a following dependence [17]: 1 ( ) h f u C u 1 ( ) h f u C u , (7) where h C – distribution curve proportionality factor:
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