Mathematical Model for the Internal Grinding Process of a Non-circular Hole Machining

Abstract

An integral part of the optimization problem of intragrinding operations is the mathematical model of the process, establishing the necessary dependences between the wheel characteristics, processing modes, cutting force, properties of the processed metal, requirements to the processing surface and other grinding conditions. The necessity to account for the plurality connections between the different technological factors, affecting the productivity of processing parts and having a wide range of variation in the process model of intragrinding processing, forces to abandon the narrow-band, partial power-low empirical dependences, which present only the processing conditions similar to the conditions of the experiment. Considering that power limitations of regime parameters are at the basis of the intragrinding operations performance management, we have developed a wide-range analytical model of cutting forces which is required to establish the interrelations between the program and the actual infeeds through the elastic properties of technological system and coverage of the main technological factors, influencing the change of the cutting force. This model is the basis of the mathematical model of the metal removal process during the internal grinding.The model provided in the article describes the metal removal process during the grinding of non-circular hole in the midship along the length of the billet, considering peculiarities of the internal grinding kinematics (changing because of the complex functional connection of the elastic deformations with the parameters of cutting modes and technological parameters) and a variable contact area of the wheel and the billet during each tool progress.