(a) 200 X (b) 400 X

Fig。 5。 Machined surface: transversal section microstructure

The Fig。 4 shows the main effects plot for residual stresses。 The main effects are the same as the showed on the cutting force analysis that means: the feed rate and the cutting depth。 So, it is possible to correlate the residual stresses with these parameters。

The factorial analyses relatively to the cutting forces, showed similarity results for the penetration force (Fz) and to resultant of the cutting forces (Res), with the variances, and in relation to the most significant factors of influence in the process。

As the non significant effects are zero or aleatory distributed around the zero, the respective normal pareto graph indicate that, for an confidenc level of 95% (± 1。96 。 ), the feed rate, cutting depth and it’s interaction are the most significant factors, for the penetration cutting and for the resultant force。

The penetration force (Fz) can be adopted as the cutting force component that is possibly correlated with the residual stresses。 The cutting speed and the tool nose radius do not have influence on the penetration force。 By other side, an increase in the feed rate and in the penetration force, increase the mean values of the penetration forces。

The increase on the feed rate induces a larger volume of the cut material in a same unit of time, besides establishing a dynamic effect on the cutting forces。 In the same way the increase on the

cutting depth make a larger volume of the removed material。 These facts explain the most significance of these factors under the penetration force。

The factorial analysis also indicates that the cutting speed do not affect the other factors with relationship to the influence on the penetration force。 In the same way it happens with the tool nose radius。 On the other hand, it is noticed that the interaction between feed rate and cutting depth has some influence in the penetration force。

Based on the experimental values and the respective factorial analysis, an empirical model was proposed to describe the dependence of the penetration force (Fz) with the feed rate (f), and the cutting depth (p), at a confidence level of 90 % on the identification of the significant factors of the process。

Being considered the estimate coefficients for the penetration force (Fz) obtained in the factorial planning, a multiple regression of this force can be predicted through Eq。 1:

Fz = 6。96 + 317。35 。 f + 375。73 。 p + 2515。42 。 f 。 p (1)

Another model that can be proposed, in agreement with the trend line of current researches, could be a power law, such as the pattern of Eq。 2。

Fz = x。 a y + z。 p w (2)

Where x, y, z and w are constants。

Through mathematical software the previous equations can bee optimized increasing this reliability。 The Eq。 3 shows the one that presents smaller deviation in relation to the experimental values, between the all analyzed equations:

Fz = - 12。37 。 f - 0,75 + 434 。 p - 0,35 (3)

The Fig。 6 shows the graphs of the Eq。 3。

Fig。 6。 Penetration force as function of feed rate and cutting depth The factorial analysis for the residual stresses revealed that,

the most significant factors of the experiment are the feed rate (f) and the cutting depth (p), as can be observe in the Fig。 4, and that to have high compression residual stresses is demanded to machining with low values of cutting depths, high feed rate values and low values for the tool nose radius。

Based on the experimental values and in the respective factorial analysis, the Eq。 (4) shows the dependence of the residual stresses with the feed rate (f) and the cutting depth (p),  a