【正文】 ns:where x1 is the coded value of cutting speed (S), x2 is the coded value of the feed rate ( f ), x3 is the coded value of radial rake angle(α) and x4 is the coded value of nose radius (r). ExperimentationA high precision ‘Rambaudi Rammatic 500’ CNC milling machine, with a vertical milling head, was used for experimentation. The control system is a CNC FIDIA12 pact. The cutting tools, used for the experimentation, were solid coated carbide end mill cutters of different radial rake angles and nose radii (WIDIA: DIA20 X FL38 X OAL 102 MM). The tools are coated with TiAlN coating. The hardness, density and transverse rupture strength are 1570 HV 30, gm/cm3 and 3800 N/mm2 respectively.AISI 1045 steel specimens of 10075 mm and 20 mm thickness were used in the present study. All the specimens were annealed, by holding them at 850 ?C for one hour and then cooling them in a furnace. The chemical analysis of specimens is presented in Table 3. The hardness of the workpiece material is 170 BHN. All the experiments were carried out at a constant axial depth of cut of 20 mm and a radial depth of cut of 1 mm. The surface roughness (response) was measured with Talysurf6 at a mm cutoff value. An average of four measurements was used as a response value.5 Results and discussionThe influences of cutting speed, feed rate, radial rake angle and nose radius have been assessed by conducting experiments. The variation of machining response with respect to the variables was shown graphically in Fig. 1. It is seen from these figures that of the four dependent parameters, radial rake angle has definite influence on the roughness of the surface machined using an end mill cutter. It is felt that the prominent influence of radial rake angle on the surface generation could be due to the fact that any change in the radial rake angle changes the sharpness of the cutting edge on the periphery, changes the contact length between the chip and workpiece surface. Also it is evident from the plots that as the radial rake angle changes from 4? to 16?, the surface roughness decreases and then increases. Therefore, it may be concluded here that the radial rake angle in the range of 4? to 10? would give a better surface finish. Figure 1 also shows that the surface roughness decreases first and then increases with the increase in the nose radius. This shows that there is a scope for finding the optimum value of the radial rake angle and nose radius for obtaining the best possible quality of the surface. It was also found that the surface roughness decreases with an increase in cutting speed and increases as feed rate increases. It could also be observed that the surface roughness was a minimum at the 250 m/min speed, 200 mm/min feed rate, 10? radial rake angle and mm nose radius. In order to understand the process better, the experimental results can be used to develop mathematical models using RSM. In this work, a mercially available mathematical software package (MATLAB) was used for the putation of the regression of constants and exponents. The roughness modelUsing experimental results, empirical equations have been obtained to estimate surface roughness with the significant parameters considered for the experimentation . cutting speed, feed rate, radial rake angle and nose radius. The first order model obtained from the above functional relationship using the RSM method is as follows:The transformed equation of surface roughness prediction is as follows:Equation 10 is derived from Eq. 9 by substituting the coded values of x1, x2, x3 and x4 in terms of ln s, ln f , lnα and ln r. The analysis of the variance (ANOVA) and the Fratio test have been performed to justify the accuracy of the fit for the mathematical model. Since the calculated values of the Fratio are less than the standard values of the Fratio for surface roughness as shown in Table 4, the model is adequate at 99% confidence level to represent the relationship between the machining response and the considered machining parameters of the end milling process.The multiple regression coefficient of the first order model was found to be . This shows that the first order model can explain the variation in surface roughness to the extent of %. As the first order model has low predictability, the second order model has been developed to see whether it can represent better or not.The second order surface roughness model thus developed is as given below:where Y2 is the estimated response of the surface roughness on a logarithmic scale, x1, x2, x3 and x4 are the logarithmic transformation of speed, feed, radial rake angle and nose radius. The data of analysis of variance for the second order surface roughness model is shown in Table 5.Since F cal is greater than , there is a definite relationship between the response variable and independent variable at 99% confidence level. The multiple regression coefficient of the second order model was found to be . On the basis of the multiple regression coefficient (R2), it can be concluded that the second order model was adequate to represent this process. Hence the second order model was considered as an objective function for optimization using genetic algorithms. This second order model was also validated using the chi square test. The calculated chi square value of the model was and them tabulated value at χ2 is , as shown in Table 6, which indicates that % of the variability in surface roughness was explained by this model.Using the second order model, the surface roughness of the ponents produced by end milling can be estimated with reasonable accuracy. This model would be optimized using genetic algorithms (GA). The optimization of end millingOptimization of machining parameters not only increases the utility for machining economics, but also the product quality toa great extent. In this context an effort has been made to estimate the optimum tool geometry and machining co