OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 1 5 0 1 , c dz V dt e µ −α − ρ = ρ + µ (7) where ρ0 is the lowest value ρ (the coefficient that depends on temperature and characterizes the chip pressure on the front edge of the cutting wedge); μ is a coefficient showing the curvature of the exponential decrease ρ as the contact temperature increases; αμ is a steepness coefficient of the characteristic ρ; c dz V dt − is a real cutting speed. Taking into account Equation (7), the cutting force can be expressed as the following: 1 0 1 ( ) c v dz t V dt p t T dx F e a y V dt f dt −α − − = ρ + µ − − ∫ , (8) where ( ) p a y − is a real cutting depth; v t f t T dx V dt dt − − ∫ is a real feed. The outward force originating from the cutting zone, which depends on wear of the tool along the back surface and the thermal expansion of the workpiece material, is expressed as: ( ) 0 3( ) h K x F h Q h p F k Q h a y e − = σ + − , (9) where σ0 represents the ultimate strength of the processed metal in compression, kg/mm2, depending on the temperature of the contact between the back surface of the tool Qh and the workpiece, °C; Kh, is a coefficient that characterizes a nonlinear increase in outward force when the back surface of the tool and the workpiece come closer. Through the main cutting edge angle φ, the resultant force can be resolved along the x and y axes of deformation as follows: ( ) ( ) cos ; sin . x h h y h h F F F F = ϕ = ϕ (10) The force component on the tool back face in the z-coordinate direction, representing the friction force, is: ( ) z h t h F k F = , (11) where ki is the coefficient of friction is interpreted as: 1 2 0 2 f h f K Q K Q h t t t k k k e e − = + ∆ + , (12) where k0t is minimum value of the coefficient of friction; Δkt is the incremental change in the friction coefficient with a change in temperature in the contact area; Kf1 and Kf2 are coefficients that determine the rate of decrease and increase, respectively, of the friction coefficient characteristic. The general expression describing the force reaction resolved along the axes of deformation takes the following form: ( ) 1 ( ) 2 ( ) 3 ; ; , x f h y p h z c h F F F F F F F F F = χ + = χ + = χ + (13)
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