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 in parts made of brittle non-metallic materials. Such a technological operation is one of the most common and in terms of volume is not inferior to the processing of external surfaces. In addition, the processing of precise holes is among the most labor-intensive and is more complex than the processing of external surfaces, which is due to more severe process conditions and less rigidity of processing tools. The quality parameters of the products that determine its operational properties and functional features are finally formed at the finishing operations, which include the internal grinding process. In this case, the removal of material from the rough surface of the workpiece is carried out due to the presence of several simultaneously running random processes of shaping that occur when the grinding wheel and the workpiece are in contact. To simulate grinding operations, a probabilistic-theoretical approach is used. [1]. The idea of using such an approach in the study of surface roughness was first expressed by the American mathematician J. Rice (1937) and the famous Russian scientist-academician Yu. V. Linnik (1954). Later there were studies by A. P. Husu , Yu. R. Witenberg , I. V. Dunin-Barkovsky , which were paid attention to by domestic and foreign scientists. However, these studies were aimed only at studying the characteristics of rough surfaces, without taking into account the conditions of its formation [2]. The probabilistic-theoretical approach was further developed in the works of A. N. Reznikov , O. B. Fedoseev , N. I. Bogomolov , L. A. Glazer , P. I. Lizarditsyn , Yu. D. Avrutin , D. G. Evseev , A.V. Korolev , Yu.K. Novoselov and other authors who use various statistical-probabilistic methods to obtain calculated dependencies for specific schemes and grinding conditions. The authors show that any conclusions about the number of working grains, its percentage ratio with grains on the surface of the grinding wheel can have real meaning only in relation to specific conditions inherent in this process, which is associated with the non-stationary grinding operations. These works of domestic and foreign authors make a significant contribution to the development of the theory of polished surfaces shaping, but it does not allow taking into account the specifics of processing products made of brittle non-metallic materials, and therefore the scope of its application is limited [3-17]. Taking into account the above, the purpose of this work is to create a new probabilistic-theoretical model that allows calculating the radial removal of the material and the thickness of the layer in which the current roughness is distributed when grinding brittle non-metallic materials. The task is to study the regularities of removing particles of brittle non-metallic material by radial removal and to study the current (at this point in time) roughness formed after each radial removal in the contact zone. Simulation of the process The probability of removing the material for processing workpieces made of brittle non-metallic materials by abrasive tools is calculated according to the dependence [1]: ( ) = − − − τ − τ − − τ 0 1 2 ( ) 1 exp ( , ) ( , ) ... ( , ) , n P M b b y b y b y (1) where n b – a parameter that characterizes the change in the area of depressions due to the processes of mechanical cutting and brittle chipping, respectively; + = + 1 n n n b a a . In works [18, 19], dependencies were obtained that simulate indicators:   π ρ ± − − = − + + +       2 3 5 3 3 0 1 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   π ⋅ ρ ± − + + − + − +       4 9 7 5 3 3 3 3 2 3 2 2 2 3 2 ( )( ) 4 6 4 8 5 20 3 9 16 7 c k u f y y y y u u f y n K V V t y z z z z z L L L L H V t L (2)