OBRABOTKAMETALLOV Vol. 26 No. 1 2024 TECHNOLOGY For these dependencies, an equation of the infl uence of temperature on the yield stress can be compiled: Δ τ 20 , h T p b S e ¢ - = ⋅ (2) where Sb20° is the value of the actual ultimate strength at room temperature; ∆Т ′ is the increment of the homological temperature; h is the empirical coeffi cient of temperature softening. Taking into account the experience of other researchers and based on experimental data (fi gure 1), it is possible to write the equation for the dynamic coeffi cient, taking into account temperature and strain rate, in the following form: Δ ε ε ε 0 , k T K ¢ æç ö÷ = çç ÷÷ çè ÷ø (3) where ε is the current value of the strain rate; ε 0 is the minimum value of the strain rate; k is an empirical constant. From the above stated, it is possible to make a defi ning equation for the change in yield stress, taking into account the infl uence of deformation, strain rate and temperature: Δ Δ τ ε ε ε ε 0 0 ; m k T p h T u A e S ¢ ¢ - æ ö æ ö ÷ ÷ ç ÷ ç ÷ = ç ÷ ç ÷ ç ÷ ç ÷ ç ç è ø è ø (4) Δ ε τ ε , p m h T p u A K e S ¢ - = (5) where εm p is the multiplier responsible for the deformation hardening of the material; ε K is the dynamic coeffi cient; Δ h T e ¢ - is the multiplier responsible for the temperature softening of the material; A is the deformation coeffi cient; Su is the ultimate true strength. However, in equation (5), deformation, strain rate and temperature act as three independent factors [21]. For example, a variation in the homological temperature can be achieved by heating the material being processed, and a modifi cation of the deformation can be achieved by changing the geometry of the cutting blade (front angle). Therefore, using such a formula will lead to errors. In connection with this, it is necessary to move from the defi ning equation (5) to the specifi c work. Specifi c work for the process of cutting materials in general and in particular for milling aluminum alloys is the most convenient parameter, since it combines the dependence of yield stress and the increment of homological temperature [19, 25]: ε τ ε 0 , u W p p A =ò (6) where τp is the current value of the yield stress; εp is the current value of the deformation; εu is the fi nal value of the deformation. In the mathematical apparatus, it is most convenient to use diff erential equations to approximate calculations, and therefore it is necessary to replace the yield stress in equation (5) with the derivative of the specifi c work on deformation: τ ε . p W u p dA S d = (7) To simplify calculations, we assume that heat transfer conditions close to adiabatic occur in the chip formation zone. Then, taking into account this approximation, the specifi c work of the deformation can be written as:
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