Introduction

Turning and hard turning technology has become an important manufacturing process and is used in a great variety of industrial applications like shafts, cams, bearings, forged parts, molds and dies (Davim, 2011). In the machining process, in order to make the parts that will provide the correct functioning, it is necessary to reach the desired surface quality. According to Shihab, Khan, Mohammad, and Siddiqueed (2014a), the hard machining presents challenges to attain high-precision machining and improved tool life in terms of selection of tool insert. The process in hard turning differs from conventional turning basically because of the characteristics: cutting tool, mechanisms involved during chip formation, and workpiece hardness. Grzesik and Zak (2012) and Grzesik and Wanat (2006) also points some advantages of hard turning: the cutting of production costs, reduction of each operation’s processing time, and elimination of the need for cutting fluid.

Production cost and the performance of the overall mechanical system is greatly influenced by the surface roughness, so this characteristic is very significant as a quality measure. Ferreira, Řehoř, Lauro, Carou, and Davim (2016) analyzed the flank wear and its influence on the resulting surface roughness in hard turning processes of AISI H13 machined parts with ceramic tools and found that cutting speed exerted a significant influence on the flank wear, but there were no clear trends of surface roughness with tool wear, either with or without wiper tools.

According to Zhang, Liu, and Yao (2007), improved surface roughness can be achieved with wiper inserts or increased feed rates; so, it is possible to achieve better surface finish or increase the productivity with hard part machining. In Suleyman, Yaldiz, and Turkes (2011), the influence of tool geometry on the surface finish in hard turning was researched; the Response Surface Methodology (RSM) was applied and a prediction model was developed related to the Ra. The results indicated that the significant factor to determine Ra and Rt was the tool nose radius.

There is also an alternative hybrid approach, combining Response Surface Methodology (RSM) and Principal Component Analysis to optimize multiple correlated responses during a turning process (Paiva, Ferreira, & Balestrassi, 2007). Scandiffio, Diniz, and Souza (2016) investigated the free-form milling of hard materials employing a ball-end cemented carbide cutting tool and concluded that tool life shortens as the tool vibration levels grow, hard materials cutting stability is improved when the tool tip’s center is engaged, thus leading to better quality surface finishing and longer tool life. In addition, Chinchanikar and Choudhury (2015) present a systematic literature review on hard steels machining using coated tools, hard turning, cooling methods and modeling of machining processes.

In this study, RSM was used to find the optimum values of the cutting parameters on the turning of AISI 52100 steel with Al2O3/TiC tool with wiper geometry through the development of a mathematical model of T, Ra and Rt parameters.

Material and methods

The development of Design of Experiments (DOE) was done in the 1920’s and later has been enhanced and applied by leading researchers all around the world (Taguchi, 1987).

According to Montgomery (2008), DOE is a methodology used to assess the magnitude and direction of many sources of factors that influence a process, be it a manufacturing one, the design of a new product and/or of a new service. The practitioner should start with the identification of factors and their combinations that may contribute to changes in the model that attempts to describe the behavior of the dependent variables or outcomes. Once the experiments are performed, the analysis proceeds to estimate the main effects of each factor as well as the two-factor (or more) interactions’ ones using appropriate statistical methods, which ultimately leads to the screening of factors.

During the conduction of experiments, all the factors are, in general, changed simultaneously and the several ways to combine them are called arrangements or designs. The most general case is the complete or full factorial arrangement; the total number of experiments N is related to the number of factors k by the relation N = 2k. According to Montgomery (2008), all possible combinations of levels of the experimental factors are used in a full factorial DOE technique, thus covering the entire experimental space. The RSM is a specific type of DOE that incorporate optimization techniques. Myers (1999) presented a thorough discussion of the RSM and a historical review of the state-of-the-art of RSM, as well as some suggestions for future research.

Pontes et al. (2010), in their concern with surface roughness in hard turning, proved that DOE is an efficient predictive statistical tool when designing Artificial Neural Networks of Radial Basis Function architectures. Santhanakumar, Adalarasan, Siddharth, and Velayudham (2016) employed a grey-based RSM and Taguchi’s L27 orthogonal design on the study of the influence of cutting speed (Vc), feed rate (f) and depth of cut (ap) on tool’s flank wear and on roughness in rough machining of high-strength materials; at the same time they reduced their multi-response optimization case to a single-response one, they found that, even though the surface finish’s quality was improved by the increase of the cutting speed, as feed rate and depth of cut increase to elevated values the roughness also increased.

According to Bouacha, Yallese, Khamel, and Belhadi (2014), the AISI 52100 hardened steel (the same material used for the experiments in this paper) is highly recommended for the manufacture of various profiling rollers, balls, dies and bearing cages. It is also recommended in cold working, for profiling cylinders, forming matrices and for wear coating purposes.

The dimensions of the steel rod used in this research were: diameter = 49 and length = 50 mm. The chemical composition of the AISI 52100 steel (in wt. %) is described in Table 1.

A CNC machine was used in the turning process, with maximum power of 7.5 HP axis; maximum speed of 4,000 rpm; maximum torque of 200 kgf m^-1 and a turret with eight positions.

The inserts are of mixed ceramic (Al2O3 + TiC) coated with titanium nitride (TiN), GC 6050 class with wiper geometry ISO CNGA S01525WH 120408. The tool holder is ISO DCLNL Model 1616H12; position angle of 95°, rake angle of -6° and clearance angle of 7°.

The tool wear was monitored using an optical microscope with a digital camera at 40x magnification. The permissible flank wear was established at VBB = 0.3 mm. Measuring Ra and Rt a tool tip was used. Roughness measurements were made using a portable stylus-type profilometer, Surtronic 3+ stylus-type instrument manufactured by Taylor Hobson. The roughness measurements were taken at three different points of the piece and four values per point were measured, totaling twelve measures for each run accomplished.

The criterion for tool change, especially roughness values (Ra < 0.5) µm, was flank wear VBB < 0.3 mm. This criterion was adopted according to the risk of breakage of the mixed ceramic insert and each piece machined was removed so the roughness could be measured. Moreover, the insert was removed from toolholder for monitoring the flank wear (VBB). Figure 1a shows the tool wear mixed ceramic and Figure 1b the hard turning process of AISI 52100 steel used in the experimental study.

In the 2k full factorial design, each input factor has two levels; the total of experiments are related to the total possible combinations between factors. After the full factorial analysis, the design was augmented through the addition of axial points, to form a central composite design (CCD) of the RSM. All the analysis was based on Minitab^® numerical results.

In running a two-level factorial, the practitioner may start by fitting the first-order model with interactions of Equation 1-2 for exploratory reasons; however, the second-order model of Equation 3 is frequently more adequate. There is the possibility of replicating certain points in a 2k factorial that gives useful information about the curvature in the experimental region. The method consists of adding center points to the 2k design. The important reason for including the center points at the design is that they do not affect the effect estimates in a 2k design (Gheshlaghi, Scharer, Moo-Young, & Douglas, 2008). Based on that, the turning tests were evaluated in a way to provide accuracy when studying the correlation of cutting parameters on machining tool life and workpiece roughness through the application of factorial and response surface designs. Table 2 lists the setup of the experiment.

The guidelines, hardness of the workpiece material and the chemical composition provided by the cutting tool manufacturer inspired the selection of these levels.

The most used response surface experimental approach is the CCD. As stated, it consists of a factorial design with center points, allowing an efficient estimation of first and second-order terms augmented with a group of axial points (Montgomery, 2008). Table 3 presents the experimental matrix using the levels defined in Table 2 and the measured responses.

It is of crucial importance to confirm the adequacy of each fitted model; the criteria to select the most adequate model are based on the lack-of-fit test and the adjusted coefficient of determination, R²adj, which is a modified R² that is adjusted for the number of terms in the model (Ohale, Uzoh, & Onukwuli, 2017). Four types of models have been employed in this study using Equation 1-3: (a) linear, (b) linear + interactions, (c) linear + squares and (d) full quadratic models were specified.

When unnecessary terms are included, R² can be artificially high. Unlike R², R²adj may get smaller when unnecessary terms are added to the model. Table 4 shows the results for the four models that were fitted to T, Ra and Rt; see also Figure 2, which illustrates the average response surface for Ra using Equation 1-7; the analysis of the response surface for the average roughness as a function of Vc, f and ap presents evidences that the factor that most influences the Ra of the machined surface is f. In this way, it is also possible to verify visually by analyzing the surfaces that the increase of f impacts on the increase of Ra; the increase of Vc impact to increase Ra.

Residual analysis aims to assess the quality of results, in other words, show whether the results are real or whether they are coincidental. In addition, it serves to identify discrepancies or errors, such as inversion of values, misspellings, inadequacy of the experiment result, and so on. According to Montgomery (2008), when a model is properly formulated, the residual should not be correlated (independent) and should be normally distributed.

Results and discussion

Table 5 lists the measurements considering a full factorial design with eight corners and five center points. Analysis of variance (ANOVA) was applied to investigate the main effects, interactions and curvature effects of T, Ra and Rt (see Table 6, 7 and 8, respectively).

The non-significance of the various terms was assessed on the basis of the resultant P-values: (a) in the case of T, the three-way interaction Vc * f * ap (p = 0.558), (b) in the case of Ra, both the main effect ap (p = 0.710) and (c) the three-way interaction Vc * f * ap (p = 0.057). In the case of Rt, that just the main effect f and two-effect f * ap were significant (p = 0.000 and 0.025, respectively).

Curvature tests indicate that the center points added to the experimental matrix provided statistical evidence of curvature for the response surfaces T and Ra. In addition, Figure 3 shows graphically the main and curvature effects for each response and Figures 4, 5 and 6 shows the effect of interactions of controllable variables on responses.

It is essential to realize that the factor f has the greater main effect in each response, due to the steeper slope than the other factors. In Figure 3a, the difference (ycorner - ycenter) is small, that is the reason why the center points are lying near the plane passing through the factorial points. The almost horizontal behaviors for factors ap in Figure 3b as well as Vc and ap in Figure 3c show that there is no significant impact on the responses when the levels are changed from the low to the high.

According to the results in Table 4, the full quadratic model is the most appropriate approach to fit the response surfaces for T, Ra and Rt: R²adj = 99.74, 97.69 and 91.26%, respectively. Table 9, 10 and 11 present the ANOVA results for each response. Despite the fact that some terms are not significant, mainly for Rt, if any one of them is removed, either R²adj or the lack-of-fit test indicates a worsening of the model. As stated, removing these terms of Rt, the new R²adj = 82.00% and the lack-of-fit = 0.021. The lack-of-fit P-value indicates that there is 17.2% chance that a ‘lack of fit F-value’ of 2.78 could occur due to noise, as show in Table 9 (Shihab, Khan, Mohammad, & Siddiqueed, 2014b).

Taking into account Table 4 and the abovementioned analysis, response surfaces and contour plots were generated for T, Ra and Rt, using the full quadratic model in Equation 7-9 (see Figure 7); only the most significant variables were generated in the graphs.

The hessian matrix was constructed from the quadratic models of the responses. Using the Minitab^® software, the eigenvalues were calculated and analyzed. According to the eigenvalues, the T function is convex; Ra and Rt are saddle. So, with the eigenvalues and calculated stationary points from Table 12, it is possible to verify that the stationary point from T is a minimal point and Ra and Rt are border points.

In this study, it was found that the residuals of the models obtained for the surface roughness and tool life have normal distributions. According to the recommendations (Taguchi, 1986), Myers (1999) conducted a residual analysis of the responses. Residuals are the differences between two or more observations and their average.

The normal probability plot was drawn for residuals as shown in Figure 8a, b and c. It was observed that the points are distributed over the line and P-value of normality test was more than 5%, but the residuals are normally distributed; and the residues shown to be independently and random. Thus, it can be seen that the models were satisfactory. In the P-value hypothesis test, the null hypothesis could not be rejected, so proposed models are adequate.

In order to perform a multiobjective analysis on the controllable variables (Vc, f and ap), the Desirability method was used; with the main objective of maximizing T and minimizing Ra and Rt. The desirability is a multiobjective method capable of evaluating a set of responses simultaneously, and allowing the determination of the most desirable set of conditions for the studied properties (Derringer & Suich, 1980). The optimal points achieved by desirability method for each variable are shown in Figure 9.

With the achieved results, it is possible to verify the robustness of the method to define optimal points for the tool life, minimizing the roughness. The use of desirability is very useful in the optimization processes, as well as in the practical application of this work focusing on the production in industry.

Conclusion

The complete models obtained by RSM provided excellent (97.69%) explanation for the adjusted parameters of the responses, which demonstrates that the breakthrough factors, ap and Vc, as well as their interactions, have a considerable influence on surface roughness Ra and Rt and T parameters. As they exert significant influence on T, an increase in any of them contributes to the reduction of the cutting tool’s life.

Thus, the methodology presented herein proved to be adequate for a turning process optimization. Also, this approach can be applied in experiments with cutting parameters as well.

Acknowledgements

The authors would like to thanks Capes, CNPQ and Fapemig for the support in this research.

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Author notes

viniciuspaes@gmail.com