OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 26 No. 1 2024 Quantities of diff erent nature cannot be homogeneous.Applying dimensional analysis, surface roughness can be given by an equation of the following form, ( , , , , , , , , ) a p R f F V D K C θ σ ρ α = , (1) where the fundamental dimensions are ρ, L, T and Ɵ. Therefore, since the total number of variables is ten, there are four fundamental dimensions. The number of dependent and independent variables is n = 10, and the number of repeated variables is m = 4. Therefore, none of the π terms in the present study will be n−m = 6. Thus, 1 2 3 4 5 6 ( , , , , , ) 0. f π π π π π π = (2) Note that equation (2) can also be written as: 1 1 2 3 4 5 6 ( , , , , , ) f π π π π π π π = ; (3) 1 a R F π = ; (4) 1 2 2 a p C V θ π æç ö÷ ÷ = çç ÷÷ çè ø ; (5) 2 3 3 a K FV θ π ρ æ ö÷ ç ÷ = ç ÷ ç ÷ ç ÷ è ø ; (6) 3 4 a F αθ π æç ÷ö = çç ÷÷ è ø ; (7) Ta b l e 4 Units, dimensions and properties of the machined materials Variable Unit Symbol Dimensions Workpiece properties SS 316 EN 8 SAE 8620 Al 380 Feed mm f L – – – – Speed m/min Vc LT −1 – – – – Depth of cut mm d L – – – – Surface roughness μm Ra L – – – – Density kg/m3 Ρ M L−3 8,000 7,850 7,845 2,760 Specifi c Heat J/kg k Cp L 2 T−2 Ɵ −1 0.5 0.475 1.6 0.963 Thermal Conductivity W/mk K M L T −3 Ɵ−1 16.3 46.6 27 109 Yield Strength N/m2 σ M−1 T−2 240 560 450 159 Coeff . Of Thermal Exp. m/m×K α L Ɵ −1 16.18×10 − 6 12.2×10 −6 11.6×10−6 12.1×10−6 Temperature oC Ɵ Ɵ 1.371 2.600 1.400 650
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