Modeling the interrelation of the cutting force with the cutting depth and the volumes of the metal being removed by single grains in flat grinding

Introduction. The model for calculating the cutting force is the basis of the modules of CAM-systems related both to the predicting processing errors on metal-cutting machines for specified grinding conditions, and to the optimizing all parameters of the technological mode (parameters of cutting modes, cutting tools, etc.). However, due to the lack of an adequate model for calculating the cutting force presented in engineering form, such modules have not yet been developed not only for flat grinding operations, but also for all other types of metalworking. It is challenging to obtain an adequate cutting force model for flat grinding operations because it is necessary to establish the interrelation between the machine parameters of the macrocutting modes (feed, cutting speed) of the grinding wheel with the parameters of the microcutting modes — the sets of cutting grains of the wheel associated with the plastic deformation of the metal in the shear zone, microvolumes of the metal being removed and the geometry of the cutting part of the abrasive grains. The purpose of this work is to develop a force model establishing the interrelation of the cutting force with the cutting depth and the volumes of the metal being removed by single grains and the wheel as a whole on the basis of the integration of microvolumes and microforces when metal being removed by the wheel grains. Research methods. The subject of the research is the mathematical modeling of the interrelation between the cutting force and cutting modes with the parameters of microcutting by a group of single grains, based on the equality of work when metal being removed of the same volume. The methodological basis of the research is the connection between the work (energy) spent on the plastic deformation of metal by a single grain, the intensity of stresses, the intensity of deformation rates and the volume of the metal being removed by the wheel as a whole, established by S.N. Korchak. Results and discussion. The result of the study is an analytical model that reliably and adequately establishes the interrelation between the cutting force and the cutting depth, cutting modes, wheel characteristics, physical and mechanical properties of the processing material, and other main technological parameters. The field of application of the results is the possibility of using the cutting force calculation model, presented in this paper, as a basis for the development of a module for a CAM-system (a digital twin of the machining), which would allow to perform the calculation and design of optimal technological parameters of the flat grinding operation, as well as cutting modes testing according to the criterion of processing accuracy of a parts batch, considering the influence of various variable factors and real processing conditions within the manufacturing process.