OBRABOTKAMETALLOV Vol. 25 No. 1 2023 technology where 0 ρ – some minimum value of the coefficient ρ; µ – the coefficient showing the increase of the value ρ to some maximum value; 1 α – the steepness coefficient of the value drop ρ; c dz V dt − – instantaneous cutting speed. Taking into account expression (17), as well as relying on equation (1), the cutting force will be interpreted as: 1 0 1 ( ) c v dz t V dt p f t T dx F e t y V dt dt −α − − = ρ + µ − − ∫ , (18) where ( ) p t y − – instantaneous cutting depth, v t f t T dx V dt dt − − ∫ – real feed. Based on the feed transformation presented in the equation (18), we obtain the equation for calculating the feed in the following form: [ ] 0 ( ) ( ) (1 ) v v t jT f f v v t T dx V dt V T x t x t T S x e dt − ω − − = − − − = − − ∫ , (19) where 0 S – the technological feed set by the CNC program, а (1 ) v jT x e− ω − – the deformation motion of the cutting tool along the feed axis transformed through the delay link. Equation (18), taking into account (19), will describe the cutting force, which after the linearization procedure in the vicinity of the equilibrium point, will take the following value: 0 0 0 0 1 0 (1 ) c v c V jT V p p dz F y S x e t t S dt − ω = − ρ − − ρ + ρ µα , (20) where ( ) 0 0 1 1 (1 ) c V c V ρ = ρ + µ − α . Fy, kgF Q, oC 30 40 50 8 60 70 100 9 80 90 110 120 10 11 12 13 14 15 Fig. 9. Results of the experiment on Steel 45
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