OBRABOTKAMETALLOV Vol. 25 No. 1 2023 technology 3 0 2 1 0 3 ( ) ( ) v jT h h Q p t t f f t p Q k h t k k K K k h t e V − ω + + ∆ + − ∆ σ − ñ 3 0 0 0 3 0 ( ) . c v V jT p t t dz S h t k k e dt − ω − χ ρ + σ + ∆ (28) The general system of equations describing the dynamics of the cutting system is given below. 1 0 2 11 12 13 11 12 13 2 2 21 22 23 21 22 23 2 2 31 32 33 31 32 2 1 ( ) , , , c v dz t V dt p f t T f p dx F e t y V dt dt d x dx dy dz m h h h c x c y c z F dt dt dt dt d y dx dy dz m h h h c x c y c z F dt dt dt dt d z dx dy dz m h h h c x c y dt dt dt dt −α − − = ρ + µ − − + + + + + + = + + + + + + = + + + + + + ∫ ( ) 1 2 33 ( ) 1 ( ) 2 ( ) 3 0 3 ( ) ( ) ( ) 0 2 1 2 1 2 2 ( ) 3 , , , , , cos , sin , , / 2, ( ) ( ), ( ) ( ) ( h f z f z c x f h y p h z c h K x F h Q h p x h h y h h z h t h K Q K Q t t t h h h v z v v h c z F F F F F F F F F F F k Q h t e F F F F F k F k k k e e d Q dQ T T T T Q kN t T dt dt N t T F t T F t T − − = = χ + = χ + = χ + = σ + = ϕ = ϕ = = + ∆ + + + + = − − = χ − + − ( ) ( ) ) . v v dz t T V dt − − ñ (29) The same system, but already in a linearized form, in the vicinity of the equilibrium point and after switching to the operator form of recording, will take the following form:
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