Simulation of the stock removal in the contact zone during internal grinding of brittle non-metallic materials

OBRABOTKAMETALLOV Vol. 23 No. 2 2021 technology characteristics and functional suitability. At the same time, the cost of grinding work increases significantly in comparison with the grinding of metals, reaching an average of 20...28%of the total cost of manufacturing products [1]. The complex stochastic nature of the grinding process [2] leads to a decrease in reliability and productivity, a scatter of product quality indicators, and a decrease in economic efficiency. The selection of the optimal parameters of the technological system based on the process simulation can improve reliability, productivity and economic efficiency. A large number of works [3–15] are devoted to the creation of dynamic models for grinding processes. However, all the obtained models have a limited field of application and are suitable only for simulation the processing of metal products. To describe the processing of brittle nonmetallic materials, empirical dependences are mainly used, and the existing analytical models do not take into account the stochastic nature of the grinding operation and the combination of microcutting and brittle chipping when removing particles of brittle nonmetallic material and wear of the surface of the grinding tool. The aim of the work is to simulate the stock removal in the contact zone during internal grinding of brittle non-metallic materials. The task is to study the features and regularities of change in the probability of material removal, when the treated surface comes into contact with an abrasive tool. Simulation of the process To describe the interaction of a grinding tool with the surface of a workpiece made of brittle non-metallic materials, the authors have developed probabilistic-theoretical models that make it possible to identify the regularities of material removal in the contact zone. The models make it possible to trace the regularities of the interaction of cutting and piercing grains on the surface of the workpiece and the process of stock removal in the contact zone due to a combination of the phenomena of microcutting and brittle chipping, considered as a random event. The probability of removal when grinding brittle non-metallic materials is calculated by the formula: 1 2 ( ) ( ) ( ) P M P M P M = ⋅ , (1) where 1 ( ) P M – is the probability at which the processed material is not removed due to the microcutting process; 2 ( ) P M – the probability, that the material to be processed is not removed by the brittle chipping process. Dependence (1) can be described by the following expression: ( ) 0 1 2 ( ) 1 exp ( , ) ( , ) P M a a y a y = − − − τ − τ , (2) where 0 a – an indicator, characterizing the initial state of the surface of the workpiece in a given section before the start of the grinding process; 1 ( , ) a y τ – an indicator, characterizing the change in the area of the depressions formed due to the mechanical cutting process; 2 ( , ) a y τ – an indicator, characterizing the change in the area of depressions formed due to the process of brittle chipping; y – distance from the outer surface of the workpiece to the current level; τ – the moment in time of the event. The previously accepted models of grain peaks and densities of its depth distribution [16, 17] allow us to proceed to the establishment of functional relationships between the probability of non-removal the material and technological factors. To calculate the indicator characterizing the change in the area of the depressions formed due to the mechanical cutting process, the expression is obtained: