Calculation of radial material removal and the thickness of the layer with the current roughness when grinding brittle non-metallic materials

Introduction. The quality parameters of products, which determine its performance and functionality, are finally formed in the finishing operations, which include the internal grinding process. In this case, the removal of material from the rough surface of the workpiece occurs due to the presence of several simultaneously running random processes of shaping, occurring during the contact of the grinding wheel and the workpiece. A probabilistic theoretical approach is used to simulate grinding operations. However, for determination of radial material removal and thickness of layer with current roughness, the known models cannot be used, as it does not allow taking into account specific features of machining products made of brittle non-metallic materials. Purpose of the work. Creation of a new theoretical and probabilistic model allowing to calculate radial material removal and layer thickness, in which current roughness is distributed during grinding of brittle non-metallic materials. The aim is to investigate the regularities of brittle non-metallic material particles removal by radial removal and study the current (for the moment) roughness formed after every radial removal in the contact area. In the work, radial material removal and the layer with current roughness are determined by grinding modes, tool surface condition, workpiece and wheel dimensions, and the initial condition of the machined surface after the previous contact. The research methods are mathematical and physical simulation using basic probability theory, distribution laws of random variables, as well as the theory of cutting and the theory of deformable solids. Results and discussion. The developed mathematical models make it possible to trace the dimensions and shape of the contact zone when grinding holes in billets made of silicon, which are somewhat different from those known when machining billets made of metal. The proposed dependencies show that with an increase in the depth of micro-cutting, the radial material removal and the thickness of the layer with the current surface roughness increase for all values of wheel speed and workpiece speed. From the experimental values obtained, the maximum micro-cutting depth and the thickness of the layer with current surface roughness are calculated. The thickness of the said layer is compared with the experimental values obtained from the ground surface profilographs. A comparison of the calculated and experimental data indicates its compliance with almost all feed values, which confirms the adequacy of the obtained equations, which model the real process of grinding holes made of brittle non-metallic materials quite well.