OBRABOTKAMETALLOV TECHNOLOGY Vol. 26 No. 1 2024 To take into account for the heat transfer between the workpiece–environment–tool system, the milling process should be considered quasi-adiabatic. Therefore, the exponent in equation (11) can be written as: Δ 1; Pe W T K A A ¢ = ⋅ ⋅ (14) 1 . u V melt S A C T = (15) Taking into account the equations (14, 15) it is possible to write the defi ning equation of specifi c work for a quasi-adiabatic process: ( ) ε ε ε 1 exp . m W p q W Pe A A K B A A K d = - (16) Now it makes sense to determine the maximum yield stress values achievable with high-speed milling of aluminum alloys for specifi c deformation work. It can be determined after diff erentiating and integrating equation (16) of the specifi c work of deformation: ε τ 0 max ; 1 m u q q q S B A K m ⋅ ⋅ ⋅ ⋅ = + (17) ( ) ε 1 1 max 1 1 . m q q Pe m m J B A A K K + æ ö + ÷ ç ÷ = ç ÷ ç ÷ ç ⋅ ⋅ ⋅ ⋅ ⋅ ÷ çè ø (18) Formulas (17) and (18) are common for both the front and back surfaces of the cutting blade. The diff erence lies in the diff erent values of the dynamic coeffi cient due to the diff erent values of homological temperatures on the contact surfaces of the tooth. For the front surface, the dynamic coeffi cient Kq is accepted as equal to 1.8, and for the back surface it is accepted as equal to 1.25. Taking into account equations (7, 8), dependences (17, 18) can be considered to be heat sources on the front and rear surfaces of the cutting blade [20, 27]. The maximum values of contact temperatures on the front and back surfaces of the cutting blade were calculated numerically from these diff erent heat sources for the back and front surfaces of the cutting blade in the MS Excel software environment. Since the studied group of aluminum alloys obeys the general law of softening for this group (fi gure 2) and can be approximated by an exponential curve with a suffi ciently high accuracy (above 0.93), any of these alloys can be selected to calculate the temperature. So, for example, the calculation performed for milling aluminum alloy D16T. The milling parameters were as follows: a carbide milling cutter with Fig. 4. Changes in Volumetric specifi c heat of the studied group of materials depending on temperature changes
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