Quality-productivity decision making when turning of Inconel 718 aerospace alloy : A response surface methodology approach

Article history: Received October 2 2016 Received in Revised Format October 28 2016 Accepted December 2 2016 Available online December 2 2016 Inconel 718 is among difficult to machine materials because of its abrasiveness and high strength even at high temperature. This alloy is mainly used in aircraft and aerospace industries. Therefore, it is very important to reveal and evaluate cutting tools behavior during machining of this kind of alloy. The experimental study presented in this research work has been carried out in order to elucidate surface roughness and productivity mathematical models during turning of Inconel 718 superalloy (35 HRC) with SiC Whisker ceramic tool at various cutting parameters (depth of cut, feed rate, cutting speed and radius nose). A small central composite design (SCCD) including 16 basics runs replicated three times (48 runs), was adopted and graphically evaluated using Fraction of design space (FDS) graph, completed by a statistical analysis of variance (ANOVA). Mathematical models for surface roughness and productivity were developed and normality was improved using the Box-Cox transformation. Results show that surface roughness criterion Ra was mainly influenced by cutting speed, radius nose and feed rate, and that the depth of cut had major effect on productivity. Finally, ranges of optimized cutting conditions were proposed for serial industrial production. Industrial benefit was illustrated in terms of high surface quality accompanied with high productivity. Indeed, results show that the use of optimal cutting condition had an industrial benefit to 46.9 % as an improvement in surface quality Ra and 160.54 % in productivity MRR. © 2017 Growing Science Ltd. All rights reserved


Introduction
Nickel and Cobalt base corrosion, temperature and wear-resistant alloys, such as Inconel 718, are typically used in high temperature applications despite their classification as moderate to difficult when machining.It should be emphasized that these alloys can be relatively machined using conventional production methods at satisfactory rates.The properties that make Inconel 718 an important engineering material are responsible for its poor machinability (Tebassi et al., 2016a;Tebassi et al., 2017;Sharman et al., 2006).These properties are commonly the strength maintained during machining, the highly abrasive carbide particles contained in the microstructure and the poor thermal conductivity (Sharman et al., 2001;Li et al., 2002), which leads to elevate the cutting temperature up to 1200 °C at the rake face (Kitagawa et al., 1997).Consequently, the requirements for any cutting tool material used for machining these alloys should include: good wear resistance, high hot hardness, high strength and toughness, good thermal shock properties and adequate chemical stability at high temperature (Ezugwu et al., 1999); such as ceramic tools recommended for machining of these alloys compared with coated carbide at high cutting speed (Darwish, 2000;Nalbant et al., 2007;Gatto & Iuliano, 1997).
Nevertheless, notch wear VN and flank wear VB of the SiC whiskers and the Si3N4 ceramics, become very large at high speed and/or high feed rate (Narutaki et al., 1993).This large wear at high cutting speed is caused by diffusion between Si in the insert and Inconel 718 (El-Wardany et al., 1996).In addition, tool wear can also be caused by an abrasive rather than by a thermally process, by considering its poor thermal conductivity, which leads to elevate the temperature at the rake face (Kitagawa et al., 1997).The minimum flank wear was observed when using the SNGN tools at low cutting speeds or the RNGN tools at high cutting speeds (Altin et al., 2007).In addition, cutting forces and different types of tool wear were reduced by increasing the feed rate when turning of Inconel 718 with ceramic tool (El-Wardany et al., 1996), this parameter is considered as the most relevant cutting parameter affecting ceramic tool stresses (Kose et al., 2008;Nalbant et al., 2007;Ezugwu & Tang, 1995;Gatto & Iuliano, 1997;Altin et al., 2007).
However, Zhuang et al. (2014) concluded that the tool failure having another form.Certainly, the main failure modes of ceramic cutting tools during machining of Inconel 718 are notch wear and flank wear.This damage may be caused by the hardened layer beneath the workpiece surface.Considering mechanical properties of workpiece, specific shearing energy which is a strong function of feed rate; was the largest at the lowest cutting speed (125 m/min) and reduces subsequently when the cutting speeds increases up to 300 m/min (Pawade et al., 2009).Regarding surface quality and productivity, Yadav et al. (2015) and Tebassi et al. (2016b) obtained that the most influencing factor on MRR is depth of cut, whereas spindle speed and depth of cut are the most influencing factors on flank wear.In the same way, at low feed rate; the tendency for built-up edge formation, is also higher than at a higher feed, due to an increase in the size of the plastic deformation area at the interface of the tool and workpiece (Zhou et al., 2012).
Regarding this cited problematic, the main objective of the present work is to investigate the influence of different machining parameters on surface finish and productivity when turning of Inconel 718 superalloy using the SiC Whisker ceramic tool.Consequently, the current study develops cutting strategies using a combination of the optimal parameters in the goal of part functional requirements while keeping high level of economical and industrial competition.Response surface methodology design approach, has been adopted for the experimental planning during turning of Inconel alloy.The results were analyzed in order to determine the optimal machining parameters settings and achieve optimal surface roughness and productivity.ANOVA was performed to investigate the more influencing parameters on the multiple performance characteristics.Mathematical models have been developed based on the full quadratic model which is generally used in RSM problems (Choudhury & El-Baradie, 1999), it can be written as follow: (1) where, β0 is constant, βi ,βii and βij are the coefficients of linear, quadratic and cross product terms, respectively.(Xi), are the actual variables that correspond to the studied machining parameters.The surface roughness criterion Ra and productivity MRR are indicated as Y1 and Y2 respectively, and analyzed as responses.After modeling, normality is tested and proved using Box-Cox transformation (Osborne, 2010;Sakia, 1992), which defined a family of power transformations and includes any positive or negative power, as well as the log, power, square….etc.The Box-Cox power transformation on observations Yi (i =1, 2… n), is given by Box & Cox (1964) as: where lamda is the power transformation parameter and n is the sample size.Multi-objective optimization procedure is allowed for minimizing the roughness Ra combined with maximal productivity MRR, using desirability approach.

Material and measurement
The aim of the current experimental work is to investigate the effect of cutting parameters on surface roughness and productivity with developing a correlation between them.In order to reach this objective, cutting speed (Vc), feed rate (f), depth of cut (ap) and nose radius (r) are chosen as process parameters.
where MRR is in (mm 3 /min), Vc, ap, f and r are respectively the cutting speed in (m/min), depth of cut in (mm), feed rate in (mm/rev) and nose radius in (mm).

Experimental design
The experimental approach was carried out in order to investigate the effects of the different factors and their interaction on surface roughness and productivity.Furthermore, three levels are specified for each factor (Table 1).The experimental tests are carried out according to the augmented small central composite design SCCD (16 basics runs with zero center points), replicated three times (48 runs) for reducing its mean standard error, 1 for alpha value was carried out.Because, thinking more broadly about what constitutes a good design is important (Anderson-Cook et al., 2009) and it makes imminent sense to compare these designs graphically (Jones, 2009).Two graphical techniques for comparing response surface designs are used (Khuri, 2009;Borkowski, 2009).The technique can be judged as it provides a very nice overview of methods for evaluating and comparing response surface designs (Piepel, 2009).For example, largest design can generate a better (lowest) error for a given design space (Christine et al., 2009).In order to evaluate our current design using graphical tool (FDS plot), Fig. 2 shows the fraction of design space plot for the small replicated design SCCD (48 runs).This graph presents a line graph showing the relationship between the "volume" of the design space (area of interest) and the amount of prediction error (Anderson-Cook et al., 2009;Khuri, 2009;Borkowski, 2009).The curve indicates what fraction (percentage) of the design space has a given prediction error or lower.In general, a lower and flatter FDS curve is better.Lower is more important than flatter.A lower curve translates to a higher Fraction of Design Space -more of the design has useful precision.Indeed, Fig. 2 shows that 78% of design space having a mean standard error inferior or equal than 0.997.

Choose Design
The RSM applied in this work is considered as a procedure to identify a relationship between independent input process parameters and output data (process response).This procedure includes commonly six steps (Tebassi et al., 2016b;Gaitonde et al., 2009;Davim et al., 2008): (1) define the independent input variables and the desired output responses, (2) adopt an experimental design, (3) perform regression analysis with the quadratic model of RSM, (4) perform a statistical analysis of variance (ANOVA) of the independent input variables in order to find parameters which affect the most significantly response, (5) determine the situation of the RSM model and decide whether this model needs screening variables or not and finally (6) optimize, conduct confirmation experiment with verifying the predicted output parameters.

Fig. 2.
Fraction of design space plot for Small CCD with 48 runs

Results and discussion
The design of experiment was developed for assessing the influence of the cutting speed Vc, feed rate f, depth of cut ap and nose radius r on surface roughness Ra and productivity MRR.The statistical treatment of the data was made in three phases.The first phase includes the use of ANOVA, with the aim of studying the effect of factors and their interactions.The second phase consists of the choice of the best model transforms law to obtain the highest correlation between the parameters using Box-Cox Plot for Power Transforms (Osborne, 2010;Sakia, 1992).Afterwards, in the final phase, the results have to be optimized.

Statistical analysis
A variance analysis of the surface roughness and productivity was performed with the objective of analyzing the influence of cutting speed, feed rate, depth of cut and nose radius of cutting tool on the obtained outputs.This analysis was out for a 5% significance level, i.e., for a 95% confidence level.

Surface roughness
It can be shown in Table 2, that the surface roughness Ra was obtained in the range of (0.32-1.64) µm and the material removal rate MRR was obtained, in the range of (800 -7200) mm 3 /min.
According to Table 3, that shows ANOVA for Ra, it can be observed that the significant terms on roughness Ra were Vc, ap, f and r, the products Vc*ap, Vc*f, ap*f, f*r, ap*r and Vc*r and the square f 2 .The perturbation plot in Fig. 3 helps to compare the effect of all the factors at a particular point in the design space.Depth of cut has been found with the lowest contribution.In addition, it is clearly observed that the feed rate strongly affects the surface roughness parameter Ra.This input parameter has an increasing effect that should be expected.It is well known that the theoretical geometrical surface roughness is primarily a function of the feed rate for a given nose radius and varies with the square of the feed rate value.
This is in good agreement with the established following equation (Davim et al., 2008;Schultheiss et al., 2014).

32.
( where f is the feed rate in (mm/rev) and r is the nose radius of the tool in (mm).

Fig. 3. Perturbation plot for Ra
The Fig. 4 shows the Box-Cox plot for Ra.This plot provides a guideline for selecting the correct power law transformation (Osborne, 2010;Sakia, 1992).
A recommended transformation is listed, based on the best lambda value, which is found at the minimum point of the curve generated by the natural log of the sum of squares of the residuals.From this figure, we can see that the current lambda value for the chosen law transformation is equal to 1 and its recommended value is equal to 1.For this, the chosen law transformation is shown in Eq. ( 5).

Ra
= Ra a ∑ a X ∑ a X (5) The normal plot of residuals for the surface roughness Ra was plotted in Fig. 5.The data follows the straight line (Sahoo & Mishra, 2014), closely.This indicates that the transformation of the response provides a good analysis, and the model proposed in Eq. ( 5) is adequate.

Productivity
The Table 4 shows ANOVA corresponding to the material removal rate MRR.This table shows that the effects of cutting speed Vc, depth of cut ap, feed rate f and the products Vc ×ap, Vc×f and ap×f are all significant.The perturbation plot in Fig. 6 shows a steep slope for depth of cut ap compared with feed rate f and cutting speed Vc.Consequently, the response is sensitive to these factors and the highest contribution comes with the depth of cut followed by feed rate and cutting speed.Fig. 7 shows the Box-Cox plot for MRR.Consequently, the chosen lambda value for the law transformation for MRR is to 0.85 as shown in Eq. ( 6).The normal plot of residuals for the productivity MRR was plotted in Fig. 8.The data follows the straight line (Sahoo & Mishra, 2014), closely.This indicates that the response transformation provides a better analysis, and the model proposed in Eq. ( 6), is adequate.

Mathematical models
The initial analysis of the responses obtained from RSM includes all parameters and their interactions.
The relationship between the factors and the process response were modeled by full quadratic model (Choudhury & El-Baradie, 1999).
Based on Eq. ( 5) and Eq. ( 6), the roughness Ra and material removal rate MRR models in term of actual factors are given below in Eq. ( 7) and Eq. ( 8), respectively.μ +0.According to the Eq. ( 7), the "Pred R-Squared" of 0.9885 is in reasonable agreement with the "Adj.R-Squared" of 0.9914; i.e. the difference is less than 0.2 "Adeq Precision" measures the signal to noise ratio.A ratio greater than 4 is desirable.The current ratio of 85.298 indicates an adequate signal.Consequently, this model can be used to navigate the design space.(8) However, from the Eq. ( 8), the "Pred R-Squared" of 0.9970 is in reasonable agreement with the "Adj R-Squared" of 0.9976; i.e. the difference is less than 0.2."Adeq Precision" measures the signal to noise ratio.A ratio greater than 4 is desirable.The current value of 208.932 indicates an adequate signal.Consequently, this model can be used to navigate the design space.Based on the model shown in Eq. ( 7) and from Fig. 9 (a), (b) and (c), that show 3D surface plot for Ra, it can be seen that for low feed rate, the surface roughness is highly sensitive to depth of cut (Fig. 9 (a)).An increase in the latter sharply degrades the surface finish.At highest values of feed rate, depth of cut has a contradictory effect, using middle values of cutting speed and radius nose.Nevertheless, this variation becomes smallest with highest values of cutting speed; using middle value of feed rate and radius nose (Fig. 9 (b)).In addition, it revealed that a combination of middle cutting speed along with lower feed rate, high radius nose and middle value of depth of cut is necessary for obtaining better surface finish.The highest value of surface roughness can be shown, when lower values of cutting speed and radius nose are used (Fig. 9 (c)).8), it can be observed from Fig. 10 (a), (b) and (c), that the highest MRR can be resulted with the combination of the highest Vc, higher ap and higher f.In addition, the lowest MRR value can be observed at lower values of Vc, ap and f.Depth of cut maintains the highest effect on productivity.The comparison between actual and predicted response for Ra and MRR is illustrated in Fig. 11(a) and (b) respectively.The results of comparison were proven to predict the surface roughness and material removal rate close to those readings recorded experimentally with a 95% confidence interval.According to those figures, it can be seen that points split is evenly by the 45 degree line.This reflects the good agreement between experimental values illustrated in Table 2 and predicted values obtained with models shown in Eq. ( 7) and Eq. ( 8).One of the main goals for the experiment is to investigate optimal values of cutting parameters.In order to obtain the desired value of the machined surface roughness Ra of the industrial product, which presents an agreement with higher productivity; using importance degrees for each output parameter (Table 5), the fixed value of 1.6 mm for tool nose radius r is given as an industrial constraint.
Joint optimization must satisfy the requirements for all the responses in the set.Optimization achievement is measured by the composite desirability which is the weighted geometric main of the individual desirability's for the responses on a range from zero to one.Value of 1.0 represents the ideal case and zero indicates that one or more responses are outside acceptable limits (Sahoo & Mishra, 2014;Myers, 2016).The optimum cutting parameters obtained with the importance degrees of 3 for Ra and MRR are chosen in term of highest desirability value (Fig. 12) to be cutting speed of 189.51 m/min, feed rate of 0.15 mm/rev and cutting depth of 0.3 mm using tool nose radius of 1.6 mm.The predicted responses are Ra = 0.30 µm and 8142.14 mm 3 /min for MRR with desirability value of 1.00 as shown in Fig. 13; which presents solution ramps of multi-objective optimization (Tebassi et al., 2016b).

Industrial benefit
In order to summarize the industrial importance of this presented research, the benefits in surface quality and in productivity are illustrated.Indeed, Fig. 14 (a) and (b) show medium value, optimal value and the obtained benefit for Ra and MRR, respectively.From Fig. 14 (a) it can be seen that the medium value for Ra is equal to 0.565 µm and 0.30 µm for its optimal value.Consequently, from this approach, the benefit in surface roughness is equal to 46.9 %.For the productivity, it can be observed in the Fig. 14 (b) that the medium value for MRR was 3125 mm 3 /min and the optimal value was 8142.14 mm 3 /min.Consequently, the benefit obtained from this approach in productivity was 160.54 %.

Conclusions
The current investigation was based on RSM using fraction of design space (FDS) plot for design evaluation and Box-Cox plots for developing mathematical models and improving their normality.The desirability approach was followed for the optimizing surface roughness and productivity based on cutting parameters (cutting speed, feed rate, depth of cut and nose radius).The important findings can be summarized as follows: Based on the fraction of design space plot, 78 % of the current designs maintained a standard error mean inferior or equal to 0.997 representing the best effectiveness of design; 2. The Box-Cox transformation improved significantly the normality and provided a good correlation for models.Indeed, the R 2 for the surface roughness model was equal to 0.9936 and for the productivity model was equal to 0.9979; 3. The signal to noise ratios (Adeq Precision) of about 85.298 for surface roughness model and 208.932 for productivity model have indicated an adequate signal.Consequently, these models can be used to navigate the design space; 4. Cutting speed, feed rate and nose radius have the greatest influences on surface roughness; 5. Depth of cut has the greatest influence on the productivity; 6.It has been found for the tested material that the optimal combination of cutting parameters for the obtained roughness Ra (0.30 µm) and the productivity (8142.14mm 3 /min) was 189.51 m/min for Vc, 0.3 mm for ap,0.15mm/rev for f and 1.6 mm for r. 7. Using optimal cutting conditions, the benefit in productivity registered was about 160.54 % accompanied with an improvement in surface quality of 46.9 % Regarding the current investigation, the multi-objective optimization methodology proposed can be considered as a powerful approach based on graphical tool for design evaluation (FDS plot) and a design improved modeling step for the best correlation.It can offer to scientific researchers and industrial metalworking a helpful for choice, comparing designs, improvement normality of models used to navigate the design space, and multi-objective optimization procedure for various combinations of input (Workpiece hardness, tool material, tool geometry …) and output (surface finish, productivity, surface integrity …) parameters of machining process.

Fig. 11 .
Fig. 11.Comparison between predicted and experimental results (a) for Ra and (b) for MRR

Fig. 14 .
Fig. 14.(a) Improvement in surface quality and (b) industrial benefit in productivity

Table 1
Assignment for the levels to the factors

Measures Design layout Analysis of variance and effects Modeling with better correlation Optimization using desirability approach Transformation Cox - Using Box Technique Industrial Application Runs Execution Design Evaluation Using FDS plot Design Evaluation Yes No
Vc and r or curvature in a factors ap and f, shows that the response is sensitive to those factors.Indeed, from this figure, it can be seen that the most significant factors on the parameters Ra was the cutting speed Vc, feed rate f and radius nose r.Experimental results for surface roughness and productivity

Table 3
Analysis of variance for Ra

Table 4
Analysis of variance for MRR

Table 5
Goals and parameter ranges for optimization of cutting conditions