OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 1 2 h u C H , where u H – thickness of the tool working surface layer in contact with the workpiece. Taking into account the above, dependence (7) can be represented as: 1 ( ) u f u u H , (8) where – density function parameter. The change in the parameter ( , ) a y is determined by the increment of the sum of the transverse dimensions of the abrasive grains profi les: ( , ) ( ) ( ) ( ) c g g k u a y K n b f u u V V , (9) where c K – chip formation coeffi cient, which takes into account that not all material is removed from the volume of the scratch mark, but part of it is displaced and forms piles along the edges of the scratch mark. After integrating (9), we obtain an integral equation for calculating the parameter ( , ) a y z in the contact zone ( ) 0 ( , ) ( ) y t k y z k u c g g u L V V a y z K n b f u dudz V , (10) where y L – the distance from the main plane to the intersection of the level with the conventional outer surface of the tool is determined from the equation ( ) yi ki e L t y D . (11) The models of grain tops and densities of its distribution over depth considered above make it possible to establish functional relationships between the probability of material not removing with technological factors. When substituting the obtained expressions g b and ( ) f u from equations (6) and (8) into equation (10), the last one takes the following form: 2 ( ) 1 0 ( ) ( , ) cos y m t k y z c b k u g f y e u L u u K C V V n z z a y z t y u A u dudz D V V H . (12) After integrating the resulting equation with respect to u, we obtain 2 ( 1) ( ) ( ) ( , ) cos ( 1) y m z c b k u g f w y e u L u u m K C V V n z z a y z t y A dz D V m V H , (13) where ( 1) m , ( ) , ( 1) m – corresponding gamma-functions. Дальнейшее интегрирование уравнения (13) возможно только при известных значениях показателей , m и значениях y характеризующих начальную фазу отклонений. Вид зависимостей определяется их суммой. При 1, 5 , 0, 5 m и 2 2 b g C . Further integration of equation (13) is possible only when values of indicators , m, and values y characterizing the initial phase of deviations are known. The type of dependencies is determined by its sum. When For = 1.5 , = 0.5 m and = 2 2 b g C p :
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