Dimensional analysis and ANN simulation of chip-tool interface temperature during turning SS304

OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. No. 4 2021 Ta b l e 4 Physical quantities along with dimensional formula Physical quantity Symbol Dimensional formula Temperature (degree Celsius) Θ D Cutting speed (m/min) V c LT –1 Chip cross-sectional area (m 2 ) A 0 L 2 Speci fi c cutting pressure (N/m 2 ) S p ML –1 T –2 Thermal conductivity of work material (W/m-K) k MLT 3 D –1 Volumetric speci fi c heat of work material (a product of density (  ) and speci fi c heat of work material ( C )) ([kg/m 3 ][J/kg-K])  C ML –1 T –2 D –1 Then four basic variables out of six physical quantities are selected in such a way that it does not make any dimensionless group in themselves. Those variables are V c , S p , k, and  C . One non-basic quantity is grouped with all the four basic variables to give one dimensionless number. Let Q 1 and Q 2 are the two di- mensionless groups, which are expressed as follows: ( ) 1 ( ) ( , ) ) ( a b c d c p Q V S k C   = (4) ( ) 2 0 ( ) ) . ) ( ( e f g h c p Q V S k C A  = (5) We write these Eqs. (4) and (5) in terms of fundamental measurements as, 2 3 2 1 ( )( )( )( ) , a a b b b c c c c d d d d Q L T M L T M L T D M L T D D - - - - - - - = (6) 2 3 2 2 2 ( ) ( ) . ( )( ) e e f f f g g g g h d h h h Q L T M L T M L T D M L T D L - - - - - - - - = (7) After the rearranging and since Q 1 and Q 2 are dimensionless quantities, the index for each term should be zero. Therefore, equating index for each term to zero and solving equations simultaneously, we get, a = 0, b = –1, c = 0, d = 1, e = 2, f = 0, g = –2, and h = 2. Substituting these values of constant in Eqs. (6) and (7), we get, 1 / , ( ) p Q C S   = (8) ( ) 2 2 2 2 ( ) . / c o Q V C A k  = (9) Let expressing chip-tool interface temperature as a function of the two dimensionless groups Q 1 and Q 2 that includes dependent variable ‘ θ ’. Cutting temperature equation using dimensional analysis (Eq. (8) and (9)) can be expressed as shown in Eq. (10). ( ) ( ) 2 2 2 0 0 / ( ) / ( ) , n m p c C S C V C A k    = (10) where C 0 , m , and n are constants, and its values are determined based on the experimental results. Eq. (10) can be used for determining the cutting temperature during the turning of SS304 steel using uncoated and coated inserts. The values of the constants in Eq. (10) are obtained using experimental results of cutting temperature (Table 2) and by knowing the cutting force, chip thickness, and chip width for the given cutting conditions (Table 5).