OBRABOTKAMETALLOV technology Vol. 25 No. 4 2023 based on digitized reference literature. It is currently impossible to test cutting modes for compliance with the requirements of process design and production charts using CAM systems in a virtual environment. Manufacturers are thus forced to carry out trial processing of workpieces according to the cutting modes set by the process engineer. At the same time, cutting modes are often diminished to a safe level in order to sequentially meet the drawing requirements in the manufacture of a batch of parts, which undoubtedly leads to lost productivity. Experimental verification increases the duration of the preparatory production stage, additional time and material costs. This problem has not yet been solved due to a lack of a wide-range analytical engineering model that reliably establishes the mathematical relationship between cutting force and cutting depth, the volume of metal being removed, cutting modes, the characteristics and geometric parameters of the grinding wheel, the physical and mechanical properties of the material being machined, etc. S.N. Korchak [1] established the relationship between the cutting force of a single grain of an abrasive wheel and the physical and mechanical properties of the material being machined through shear and compression stresses, taking into account the temperature in the cutting zone. Similarly, Yu. M. Zubarev et. al. [2] and Filimonov [3] obtained calculation dependencies to find the cutting force for grinding operations, taking into account friction (internal friction coefficient, friction angle, etc.). The dependences obtained in [1] were used to develop models to calculate the cutting force for flat grinding [4–5]. Several authors have presented force dependences that take into account the processes of blunting and wear of the abrasive grains in models of the cutting force occurring during grinding [6–14]. Others have considered the impact of dynamic loads on the cutting force arising from the “contact stiffness” of manufacturing, the non-stationary nature of abrasive machining, the variable stiffness of manufacturing, etc. [15–23]. In studies by Leonesioa et. al. [15] and Li and Shin [16], the cutting force is calculated with consideration to the rigidity of the technological system and dynamic loads. Patnaik et. al. [17] calculated the cutting force by taking into account the friction coefficient of flat grinding. The papers do not present engineering formulas, which complicates its practical application in mechanical engineering. We can highlight a number of papers on the development of a cutting force model for flat grinding operations. Voronov and Veidun [24] proposed a mathematical model of flat grinding with a disk with abrasive grains distributed over a cylindrical surface with random geometric characteristics. Nosenko et. al. [25] presented a dynamic mathematical cutting force model taking into account the wear of the working wheel surface during flat grinding. Danilenko [26] studied the components of the cutting force that occur during flat grinding for a narrow range of materials (mainly various titanium alloys). Li and Yang [27] experimentally assessed changes in cutting force and roughness for flat grinding of several grades of steel. Liu et. al. [28] experimentally assessed the impact of cutting speed on cutting force and wear of a grinding wheel. An analysis of the literature showed that, despite the abundance of analytical models linking cutting forces to the depth of cutting by single cutting grains, there are still no adequate engineering models for calculating the cutting force for a given cutting depth during grinding for the wheel as a whole. The proposed models calculate a certain cutting depth and force when metal is cut with a single grain of an abrasive wheel, depending on the number of grains and other factors, in the absence of reliable a priori information on the number of cutting grains and the volumes of metal removed. These formulas cannot be used to calculate the cutting depth of a grinding wheel and the resulting cutting force or the allowance to be removed during the operation in several passes. Program depth feed changes tenfold in a stepped cycle of flat grinding (for example, from 0.05 mm/ stroke at the first stage of the cycle to 0.001 mm/min at the last stage). The number of cutting grains and the cutting depth should also be significantly reduced. However, this does not affect the cutting depth by the wheel grains in the considered force models. Considering that there are an excessive number of cutting grains on the working surface of the wheel [29], some grains pass through the contact zone without metal removing. With a tenfold decrease in the depth feed, the number of excess grains increases. There are no available methods for calculating the number of excess grains and the cutting depth with a tenfold decrease in the depth feed. In addition, it is not taken into account that the volume of the metal layer removed
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