OBRABOTKAMETALLOV technology Vol. 25 No. 1 2023 In the diagram shown in Figure 1, deformations are decomposed into three main axes: x-axis is the axial direction of deformations (mm), y-axis is the radial direction of deformations (mm) and z-axis is the tangential direction of deformations (mm). Along the same axes, the force response decomposes from the cutting process into the forming motions of the tool (Ff , Fp, Fc (N)), Vf and Vc (mm/s) feed and cutting speeds, respectively, ω is the angular velocity of the spindle (rev/s). The description of the cutting force is generalized, based on the point of proportionality of its area of the cut layer, in the form: i p i F a S = ρ χ , (1) where i χ – a certain expansion coefficient of the general vector of response forces on the i-axis of the tool deformation; it should be noted that this approach is widely used within the scientific school of V.L. Zakorotny [12], the depth of processing also depends on the deformations of the tool and the workpiece 0 p p a a y = − , where 0 p t technologically specified processing depth without taking into account deformations of the tool and the workpiece, the amount of feed per revolution – S. The feed value can be represented as the following integral: V t f t T dx S V dt dt − = − ∫ , (2) where TV – revolution period of the workpiece. The most important component of the cutting force is the force component, which is formed not in the zone of primary deformation and friction of the cuttings on the tool face, but on the tool flank, where the pushing force and friction force are formed in the direction of the primary motion. This component of the force depends on the wear of the tool along the flank, therefore, based on the approach proposed in the work of V.L. Zakorotny [22], we describe the force formed here as: h K x h h F S e − = σ , (3) where σ – compressive strength of the processed metal in (kg/mm2); h K – the coefficient of the increase steepness in force, h S – the contact area of the tool and the workpiece along the flank of the cutting wedge, which is defined as: 3 h p S h t = , h K – the coefficient determining the steepness of the nonlinear increase in the contact area of the tool and the workpiece when the tool and the workpiece approach. Through the side cutting edge angle – φ, we decompose the force reaction on the x and y axes of the formation, as follows: ( ) ( ) cos sin x h h y h h F F F F = ϕ = ϕ . (4) The force response in the direction of z coordinate is, in essence, nothing more than the friction force, which can be represented as: ( ) z h t h F k F = , (5) where t k – coefficient of friction. Using the approach proposed by A.D. Makarov [22], we identify the characteristic of friction coefficient by the following expression: 1 2 0 / 2 f f K Q K Q t t t k k k e e − = + ∆ + , (6)
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