Oussama Zerti
email: oussama_zerti@yahoo.fr

Mohamed Athmane Yallese

Abderrahmen Zerti

Salim Belhadi

Francois Girardin

Simultaneous improvement of surface quality and productivity using grey relational analysis based Taguchi design for turning couple (AISI D3 steel/ mixed ceramic tool (Al2O3 + TiC))

Keywords:

Current optimization strategies are based on the increase the productivity and the quality with lower cost in short time. Grey relational analysis "GRA" based on Taguchi design was proposed in this paper for simultaneous improvement of surface quality and productivity. The turning trials based on mixed Taguchi L18 factorial plan were conducted under dry cutting conditions for the machining couple: AISI D3 steel/mixed ceramic inserts (CC650). The machining parameters taken into account during this study are as follow: major cutting edge angle (χr), cutting insert nose radius (r), cutting speed (Vc), feed rate (f), and depth of cut (ap). Significant effects of machining parameters and their interactions were evaluated by the analysis of variance. Through this analysis, it have been found clearly that feed rate and cutting insert nose radius had a big significant effects on surface quality while depth of cut, feed rate followed by cutting speed had a major effect on productivity. The mathematical relationship between the machining parameters and the performance characteristics was formulated by using a linear regression model with interactions. Optimal levels of parametric combination for achieving the higher surface quality with maximum productivity were selected by grey relational analysis which is based on the high value of grey relational grade. Confirmation experiments were carried out to prove the powerful improvement of experimental results and to validate the effectiveness of the multi-optimization technique applied in this paper.

Introduction

Surface roughness represents an evaluation criterion of quality products and it plays an important role to estimate the manufacturing cost (Asiltürk & Akkus, 2011;Zerti et al., 2017a,b). On the other hand, the productivity is considered as a very important technological aspect that causes great effect on both product cost and series production rate [START_REF] Hassan | Experimental investigation of Material removal rate in CNC turning using Taguchi method[END_REF]. For this reason, manufacturers are always committed by the good quality and high productivity in short time with low cost, because ensuring those conditions represent an index of manufacturer's qualification. Consequently, the desired surface quality with the maximum productivity is a major constraint for the choice of the optimum machining parameters in the production process. In order to achieve the desired conditions required by customers, the use of grey relational analysis as a multi-objective optimization technique based on Taguchi design is found as an efficient solution for this optimization problem. This technique has been used in different applications in because of its ease of application and reliability.

There are a number of researchers in different fields who have used grey relational analysis based on Taguchi design for a simultaneous improvement of multi-performance characteristics in order to achieve at the desired objective. [START_REF] Bouzid | Simultaneous optimization of surface roughness and material removal rate for turning of X20Cr13 stainless steel[END_REF] optimized cutting parameters for determining the minimum surface roughness (Ra) which corresponds to the maximum material removal rate (MRR) in turning of X20Cr13 steel with mono and multi-objective optimizations based on the L16 OA of Taguchi. Taguchi's signal-to-noise ratio was used to accomplish the objective function. [START_REF] Wang | Parametric optimization on multi-objective precision turning using grey relational analysis[END_REF] selected the optimum cutting conditions through the application of grey relational analysis based on Taguchi design (L9 OA) with introducing of signal to noise ratio (S/N) to get the lowest surface roughness and tool wear that correspond to the maximum of material removal rate in precision turning. [START_REF] Lin | Use of the Taguchi method and grey relational analysis to optimize turning operations with multiple performance characteristics[END_REF] reported an improvement of tool life, cutting force, and surface roughness by using Taguchi method with grey relational analysis for optimizing cutting speed, feed rate, and depth of cut during turning operations of S45C steel bars using a P20 tungsten carbide. They found that optimization of complicated multiple performance characteristics could be greatly simplified through this approach. [START_REF] Balasubramanian | Grey Relational Analysis to determine optimum process parameters for Wire Electro Discharge Machining (WEDM)[END_REF] solved the problem of simultaneous optimization for wire electro discharge machining (WEDM) to obtain higher material removal rate (MRR) and lower surface roughness (SR) by the use of grey relational analysis. [START_REF] Hanafi | Optimization of cutting conditions for sustainable machining of PEEK-CF30 using TiN tools[END_REF] applied the method of grey relational analysis based on the Taguchi method for multiobjective optimization of power consumption and surface roughness when dry turning of the PEEK reinforced with 30% carbon fibers. The same technique was proposed in other several cutting process, for example: in the drilling process Noorul [START_REF] Haq | Multi response optimization of machining parameters of drilling Al/SiC metal matrix composite using grey relational analysis in the Taguchi method[END_REF] identified optimal drilling parameters namely: cutting speed, feed rate and point angle for multiple response characteristics such as surface roughness, cutting force and torque in the case of machining couple: Al/SiC metal matrix composite/TiN coated HSS twist drills under dry condition. The authors found that this technique is so reliable for improving the drilling process.

For another type of cutting process, [START_REF] Kuram | Multi-objective optimization using Taguchi based grey relational analysis for micro-milling of Al 7075 material with ball nose end mill[END_REF] performed an experimental investigation based on the L9 OA of Taguchi method for Micro-milling of aluminium material with ball nose end mill. The authors applied Taguchi method and grey relational analysis to achieve at mono and multi-objective optimization. The works accomplished by [START_REF] Jailani | Multi-response optimisation of sintering parameters of Al-Si alloy/fly ash composite using Taguchi method and grey relational analysis[END_REF] aimed to use grey relational analysis in order to optimize the sintering process parameters of Al-Si (12%) alloy/fly ash composite. The modelling of the cutting process has attracted the attention of many researchers for its great interest in the industry because it allows predicting the technological parameters without carrying out the experimental tests. An attempt was made by [START_REF] Gaitonde | Analysis of machinability during hard turning of cold work tool steel (type: AISI D2)[END_REF] to determine the link between cutting condition such as cutting speed, feed rate, and machining time and machinability aspects via response surface methodology. These considered aspects were machining force, power, specific cutting force, surface roughness, and tool wear. The study was carried out for the case of turning of high chromium AISI D2 cold work tool steel using CC650WG wiper ceramic inserts. Authors found through the response surface analysis that the surface roughness could be minimized at small values of feed rate and machining time with elevated values of cutting speed, whereas the maximum tool wear appear at Vc = 150 m/min for all values of feed rate. [START_REF] Al-Ahmari | Predictive machinability models for a selected hard material in turning operations[END_REF] formulated mathematical equations of surface roughness and cutting forces during turning of austenitic AISI 302 steel. The process parameters considered in this study were cutting speed, feed rate, depth of cut and nose radius in order to develop a machinability model. Additionally, response surface methodology (RSM) and neural networks (NN) were employed to assess the model. [START_REF] Zahia | On the application of response surface methodology for predicting and optimizing surface roughness and cutting forces in hard turning by PVD coated insert[END_REF] exploited the RSM methodology that helps to formulate a reliable statistical model for monitoring the evolution of surface roughness and cutting forces according to cutting parameters such as: cutting speed, feed rate and depth of cut during the hard turning (AISI 4140) (56 HRC) with using PVD -coated ceramic insert. [START_REF] Zahia | Turning roughness model based on tool-nose displacements[END_REF] developed a mathematical model of surface roughness that vary in function of cutting parameters, tool-nose displacements, spindle and machine tool frame. The study of [START_REF] Neseli | Optimization of tool geometry parameters for turning operations based on the response surface methodology[END_REF] presented an application of response surface methodology (RSM) for modeling the average surface roughness (Ra) obtained during the turning of AISI 1040 steel, to assess the effect of tool geometry parameters on the latter. They found that the tool nose radius was the most influencing factor on the measured surface roughness.

Ceramic cutting tool is a big utilization in the machining of high alloy steel, Davim and Figueira (2007a) made a comparison between the wiper and conventional ceramics inserts to determine the influences of cutting parameters on the obtained machinability parameters (cutting forces, surface roughness, and tool wear). They found after that the use of wiper ceramics inserts allow to reach at surface roughness values less than 0.8 μm with possibility of dimensional accuracy in a work-piece, IT < 7. [START_REF] Davim | Machinability evaluation in hard turning of cold work tool steel (D2) with ceramic tools using statistical techniques[END_REF] used ceramic inserts for surface finishing phase on the same material (cold work tool steel AISI D2). They revealed that obtaining surface roughness of less than 0.8 μm is feasible if the choice of cutting parameters is suitable and which also permit to eliminate cylindrical grinding operations. [START_REF] Aouici | Machinability investigation in hard turning of AISI D3 cold work steel with ceramic tool using response surface methodology[END_REF] examined the machinability behavior of cold work hard tool steel AISI D3 heat-treated (60 HRC) with a TiN doped ceramic cutting tool (SNGA120408) containing approximately 30% of TiC. The responses were estimated based on a (3 3 ) full factorial experimental design, where the quadratic effects were also determined. The desired optimum was set for minimum levels of surface roughness, cutting force, specific cutting force and consumed power via the statistical method (RSM) and the desirability function approach.

Singh and Dureja (2014) compared Taguchi method and RSM with a view for optimizing flank wear of tool and surface roughness during the finish operation of AISI D3 steel in hard turning. The results indicated that optimal levels of cutting parameters selected by both RSM and Taguchi method were nearly the same. [START_REF] Zerti | Taguchi design of experiments for optimization and modeling of surface roughness when dry turning X210Cr12 steel[END_REF] proposed a study with the application of Taguchi method to minimize some technological parameters (such as surface roughness, tangential force, specific cutting force, and cutting power) characterizing material machinability. They carried out 18 tests based on Taguchi design experiments during the turning of AISI D3 steel using mixed ceramic inserts (CC650) under dry cutting conditions. [START_REF] Bouchelaghem | Experimental investigation and performance analyses of CBN insert in hard turning of cold work tool steel (D3)[END_REF] examined the machinability behavior of AISI D3 hardened steel with CBN cutting tool for the evolution of surface roughness, cutting forces and tool wear in function of variation of cutting parameters. [START_REF] Bensouilah | Performance of coated and uncoated mixed ceramic tools in hard turning process[END_REF] conducted a comparative study to evaluate the performance of coated and uncoated mixed ceramic tools during hard turning of AISI D3 cold work tool steel. They determined the effects of cutting parameters on the machining performance through the use of ANOVA analysis of S/N ratio of the responses. The authors modeled the machining performance by linear regression for both ceramic tools CC6050 and CC650. [START_REF] Yallese | The effects of cutting conditions on mixed ceramic and cubic boron nitride tool wear and on surface roughness during machining of X200Cr12 steel (60 HRC)[END_REF] evaluated the effect of cutting parameters during the hard turning of AISI D3 steel with ceramic and CBN tool wear. They estimated the surface roughness by a power model deduced from experimental data and compared it with a theoretical model. [START_REF] Meddour | Investigation and modeling of cutting forces and surface roughness when hard turning of AISI 52100 steel with mixed ceramic tool: cutting conditions optimization[END_REF] performed a statistical study to determine the significant effect of cutting speed, depth of cut, feed rate and tool nose radius on surface roughness and components of cutting force during hard turning of AISI 52100 steel by mixed ceramic cutting tool. They developed mathematical models in order to estimate those two responses. Also, they recommended that the use of big nose radius and little feed rates could improve surface quality.

The present research paper shows an experimental investigation related to the simultaneous improvement of surface quality (Ra) and productivity (MRR) using the application of grey relational analysis (GRA) based on Taguchi design (L18 OA) during the dry turning of (AISI D3 steel/ mixed ceramic inserts). Response Surface Methodology (RSM) was exploited to obtain an empiric mathematical models by regression analysis for the surface roughness and material removal rate. The ANOVA analysis of S/N ratio described the degree of influence of each of the control machining parameters and their interactions on each response. Also Pareto chart and 3D plots with their contours based on S/N ratios of responses were used to confirm the results found by ANOVA analysis. 3D surface roughness profile was made to view visualizing its topography. Confirmation tests were carried out to ensure the effectiveness of the grey relational analysis based on Taguchi design in the simultaneous improvement of the performance characteristics considered in this study.

Taguchi design / Grey Relational Analysis (GRA)

Taguchi design

Taguchi design is a helpful technique that has a big contribution for the improvement of the performance of systems and solving complex optimization problems (settings) during production of the product by the implementation of the design experiments that is based on the use of the orthogonal arrays which are proposed by Taguchi for minimizing the number of trials and focusing just on the essential experiments for analyzing, which lead to win the time and reducing the cost [START_REF] Taguchi | Introduction to Quality Engineering[END_REF]. Also this method allows controlling simultaneously controllable and uncontrollable factors by converting the responses into signal-to-noise (S/N) for identifying industrial performance of the system [START_REF] Zhang | Surface roughness optimization in an end-milling operation using the Taguchi design method[END_REF]. S/N ratio is the essential criterion in the Taguchi method, it allows defining the degree of influence of the unwanted noise on the wanted signal [START_REF] Günay | Optimization of machining parameters in milling of Ti-6Al-4V alloy using Taguchi method[END_REF]. Whenever the characteristic is continuous, the S/N ratios are usually divided into 3 categories given by the following equations [START_REF] Nalbant | Application of Taguchi method in the optimization of cutting parameters for surface roughness in turning[END_REF]:

For (Nominal is the best): 2 / 10log y y S N s          (1)
For maximization (Larger-is-the better):

              n i i y n N S 1 2 1 1 log 10 / (2)
For minimization (Smaller-is-the better):

          n i i y n N S 1 2 1 log 10 / ( 3
)
where y is the average of results obtained, 2 y S is the variance of y, n is the number of repeat trials and yi is the result obtained.

Grey Relational Analysis (GRA)

Grey relational analysis is a technique proposed for solving the problem of complex optimization by converting the multi-objective to a single-objective to achieve at optimal combination of parameters levels for simultaneous improvement of multiple machining characteristics Dabade (2013). The use of this method contains the steps as follow:

Step 1: Grey relational generation According to the intended objective optimization to minimize or maximize experimental results, normalization of S/N ratio for the experimental results in the range between zero and one is necessary for grey relational generation. Depending on the objective function optimization, the normalization can be performed for two cases. If the smaller-the-better is the characteristic selected in the original sequence for minimization, then it should be normalized as given by Eq. (4).

)

) ( min( )) ( max( ) ( )) ( max( ) ( 0 0 0 0 * k x k x k x k x k x i i i i i    (4)
If the larger-the-better is the characteristic selected in the original sequence for maximization, then it should be normalized as given by Eq. ( 5).

)

) ( min( )) ( max( )) ( min( ) ( ) ( 0 0 0 0 * k x k x k x k x k x i i i i i    (5)
where xi*(k) is the value after grey relational generation (normalized value), and max(xi 0 (k)) and min(xi 0 (k)) are the largest and smallest values of xi 0 (k)) for the k th response. The larger value of normalized results indicates the better performance characteristic and the best-normalized results will be equal to one.

Step 2: Grey Relational Coefficient (GRC)

Grey relational coefficient describes the correlation between the ideal and the obtained experimental results. Mathematical formula of grey relational coefficient (ξi(k)) is given as following:

max 0 max min ) ( ) (           k k i i 1 ) ( 0   k i  (6) ) ( 0 k i  is the absolute difference between the reference sequence ) ( 0 k x k
and the S/N ratio of measured sequence ) (k

x k i . ) ( ) ( ) ( 0 0 k x k x k i i    (7) ) ( ) ( min min 0 min k x k x i k i j       (8) ) ( ) ( max max 0 max k x k x i k i j       (9) ψ is the distinguishing coefficient (ψ∈ [0, 1]).
In this study the value of ψ is 0.5.

Step 3: Grey Relational Grade (GRG) Grey relational grade represents the correlation among the series, it is given by the following formula:

   n k i i k n 1 ) ( 1   (10)
where n is the number of responses.

Step 4: Determination of optimal machining parameters Once grey relational grade is computed, the selection of the optimal levels combination is made based on the main effects plot for (GRG). The largest value of grey relational grade that is found close to the ideal normalized value corresponds to the optimal combination. Therefore, the optimal level of the process parameters is the level with the greatest GRG value.

Step 5: Confirmation tests Once the optimal levels are selected, the validation test occupied the final step in the optimization procedure to confirm the reliability of the optimal levels is proposed by grey relational analysis to improve system performance. This test is done by comparing the value of the S/N ratio of GRG obtained from the optimal test with that predicted  ˆ by the following formula with the use of optimal levels [START_REF] Nalbant | Application of Taguchi method in the optimization of cutting parameters for surface roughness in turning[END_REF]:

) ( ˆ1      q i m i m     , ( 11
)
where m  is the total average of S/N ratio, i  is the average of S/N ratio at the optimal level, and q is the number of the main input factors that have a significant effect on the output responses.

Grey Relational Analysis optimization based Taguchi design

Based on the above discussion, the use of the grey relational analysis coupled with Taguchi design in order to optimize the turning operations with multiple machining characteristics includes the following steps as shown in Fig. 1.

Experimental set-up

During this experimental investigation, turning operations were carried out on a conventional lathe of the check company "TOS TRENCIN" SN40 model, with 6.6 kW spindle power for the turning couple (AISI D3 steel/mixed ceramic inserts CC650) under dry conditions.

Work piece material, cutting inserts and tool holders

The work piece material used was a round bar of AISI D3 steel having 70 mm in diameter and 400 mm in length. This lather is a high alloy steel that have several designation such as: DIN 1.2080, JIS SKD1, GB Cr12, AFNOR Z200Cr12. It is a tool steel with high chromium minimum risk of deformation and alteration of dimensions to thermal treatments and it has excellent wear resistance. Its chemical composition is given as follow: 2% of carbon (C), 0.30% of Manganese (Mn), 0.25% of silicon (Si), 12% of Chrome (Cr), 0.70% of Tungsten (W).

All turning operations were carried out by three mixed ceramic cutting tools CC650 were manufacturing by Sandvik Coromant and its chemical composition is as follow (Al2O3 (70%) + TiC (30%)). Each cutting tool is characterized by a nose radius r = 0.8mm, 0.12mm, 0.16mm and ISO geometric designation SNGA120408T01020, SNGA120412T01020, SNGA120416T01020 respectively.

Two tool holders are used in this investigation designated by ISO as PSDNN 2525 M12 and PSBNR 2525 M12, respectively. Their geometry of the active part; as shown in Fig. 2 is the same for the following angles: clearance angle (α) = 6°, rake angle (γ) = -6°, and cutting edge inclination angle (λ) = -6°, but it is different to the major cutting edge angle (χr) = 45° and 75°, respectively.

Design Experiments and cutting conditions

Mixed factorial plan reduces of Taguchi L18 was selected as an experimental design to study the impact of different machining parameters (Vc, f, ap) which varies at three levels (3 4 ) and tool geometry (χr, r) which varies at two levels (2 1 ) on the performance characteristics (Ra and MRR). The levels of the parameters were selected in the range of intervals advisable by manufacturer of Sandvik Coromant. The cutting parameters chosen to study with their levels are shown in Table 1.

Measuring equipment

Surface roughness measure

The criterion measures of the surface roughness (Ra) are obtained instantly after each pass roughing by means of a Mitutoyo Surftest SJ-201 roughness meter. To prevent errors and recovery for more precision, roughness measurement was performed directly on the work-piece without dismounting it from the lathe. The measurements were repeated three times along three work-piece feed rate directions also placed at 120° (Fig. 2). The result is considered as the average of these values for each cutting condition. To properly characterize the surface roughness of the work-piece, three-dimensional topographic maps were made using an optical platform of metrology modular Altisurf 500.

Formula of material removal rate

Material removal rate can be defined as the volume of material removed divided by the machining time.

Another way, MRR is to imagine an "instantaneous" material removal rate as the rate at which the crosssection area of material being removed moves through the work-piece. This aspect of machinability is calculated using the following equation:

MRR=1000 × Vc × f × ap, ( 12
)
where Vc is the cutting speed (m/min), f is the feed rate (mm/rev), and ap is the depth of cut (mm) and MRR is the material removal rate (mm 3 /min).

Data analysis and results

The measured values of surface roughness (Ra) and the calculated values of material removal rate (MRR) using Eq. ( 12) with their computed S/N ratio in this experimental study which was carried out based on various combinations of machining parameters levels proposed by Taguchi design (L18 OA) are shown in Table 2. "The larger is the better" and "The smaller is the better" characteristics are used to calculate the S/N ratio in order to maximizing (MRR) and minimizing (Ra); i.e. Maximizing surface quality; using equations 2 and 3, respectively.

Analysis of variance (ANOVA)

ANOVA allows determining the significance of input parameters (χr, r, Vc, f, ap) and their interactions in order of influence on the responses (Ra, MRR). The model is based on the calculation of the sums of the squares of the (S/N) ratios of outputs. First we calculate the sum of squared deviations of the total (S/N) ratios of outputs. The sum of squared deviations SST represents the difference between each (S/N) ratio of a measured response ηi and the total mean S/N ratio ηm, which is given as follows [START_REF] Lindman | Analysis of variance in experimental design[END_REF]:

    n i m i T SS 1 2 ) (   (13)
where n represents the number of trials and ηi represents the mean S/N ratio for the ith trial. The total sum of squared deviations SST is the sum of two terms: variance explained by the regression model (SSd) and random residual variance (SSe) (not explained by the model) which is written as follows:

e d T SS SS SS   (14)
Another statistical tool that allows determining the significant effect of each input parameter on each output response, named (F test) by [START_REF] Ross | Taguchi techniques for quality engineering[END_REF].

The results of variance analysis (ANOVA) for S/N (Ra) are shown in Table 3 and the contribution of significant terms on Ra are presented in Fig. 3 (a). It is seen that the feed rate occupies the first position of influencing on the quality of surface with a contribution of 50.21%, because during the feed rate of cutting tool of work-piece in turning process, the tool shape generates helicoids furrows on surface of work-piece. These furrows are deeper and broader as the feed rate increases, therefore the surface quality decreases. The second influential machining parameter is the nose radius of the tool with an impact of 20.27%. A popular established model presented by [START_REF] Yallese | Usinage de l'acier 100Cr6 trempé par un outil en nitrure de bore cubique[END_REF] to predict the surface roughness, with a cutting tool that have nose radius different of zero, is:

r f Ra   32 2 , ( 15
)
where Ra is the arithmetic mean roughness (µm), f is the feed rate (mm/rev), r is the cutting tool nose radius (mm). Based on the Eq. ( 15) the uses of the largest tool nose radius with little feed rate improves the quality of surface. Similarly, [START_REF] Singh | A surface roughness prediction model for hard turning process[END_REF]; [START_REF] Makadia | Optimisation of machining parameters for turning operations based on response surface methodology[END_REF] found that the feed rate is the most significant factor followed by tool nose radius affecting the surface roughness. The interaction f×ap comes in third position with an effect of 12.69% on quality of surface, the same interaction significance found by [START_REF] Aslan | Design optimization of cutting parameters when turning hardened AISI 4140 steel (63 HRC) with Al2O 3 + TiCN mixed ceramic tool[END_REF] when turning hardened AISI 4140 steel with Al2O3 + TiCN mixed ceramic tool. The factors (χr, Vc, ap) and the other interactions are having a slightly effect on quality of surface. From the analysis of Table 4 and Fig. 3 (b), it can be apparent that Vc, f, and ap have a significant effect on (MRR). Nevertheless, ap is the most significant factor associated with MRR with 54.85%. The next largest factors influencing MRR is f followed by Vc. Their contributions are 21.84% and 21.64%, respectively. The rest of terms do not represent any significant effects on MRR. The same order of significant effect of machining parameters on the MRR was found by [START_REF] Bouzid | Simultaneous optimization of surface roughness and material removal rate for turning of X20Cr13 stainless steel[END_REF] when turning of X20Cr13 stainless steel.

Pareto analysis

Pareto analysis is a creative statistical technique which aims to identify the important causes for resolving the most problems. It is based on the Pareto principle also known as 80/20 rule which in general means that 80% of problems may be caused by as few as 20% of causes [START_REF] Karuppusami | Pareto analysis of critical success factors of total quality management: A literature review and analysis[END_REF]. This technique was considered in this study to check and confirm the results obtained by ANOVA analysis (Fig. 4). This chart presents the ranking of the influencing machining parameters and their interactions in descending order on the Ra and MRR.

Main effect factors and their interactions on responses (3D plots and contours)

The main effect plots for S/N ratios of (Ra) and (MRR) are presented in Fig. 5 (a,b), respectively.

Response graphs show the evolution of S/N ratio of responses in function of variation of levels for each machining parameters. The values of the plotted points in Fig. 5 (a,b) of the S/N ratio for surface roughness and material removal rate which correspond to each level of machinability parameters are given in Table 5 (a, b) respectively. The influence of cutting parameters on the responses can be easily determined through delta value that represents the difference between max and min of S/N ratios of responses as shown in Table 5 (a, b). The higher the value of the delta, the more influential is the cutting parameter. It can be seen in Table 5 (a, b) that the significance of all main factors is ranking in descending order of influence on the responses.

It is notable from Fig. 5 (a) and Table 5 (a) that the most machining parameter affecting surface quality is the feed rate (f) followed by tool nose radius (r). The others factors represent less effects on surface quality. Also, it is clear that the surface quality deteriorates by increasing feed rate. By contrast, the increasing of cutting insert nose radius improves the surface quality (Ra).

From Fig. 5 (b) and Table 5 (b), it can be observed clearly that all main factors (Vc, f, ap) have a significant effect on material removal rate. The descending order of influence of all main factors on responses is as follow: depth of cut, feed rate followed by cutting speed. By increasing all main factors (Vc, f, ap) we can improve the productivity (MRR). It can be observed that the same ranking in descending order of influence of all main factors on responses are obtained by ANOVA analysis and is also confirmed by Pareto chart. In order to check the influence of interaction of the depth of cut and the feed rate on the surface quality (S/N ratio for Ra), 3D response surface for the effect of the interaction is drawn in Fig. 6 (a). Variables not represented in the figure are held constant at the middle level (χr = 60°, r = 1.2 mm, Vc = 330 m / min). This figure indicates that, for a given depth of cut, the surface quality is sensitive to the feed rate because the increase of this latter deteriorates quickly the surface quality. This is consistent with the conclusion of research work published by [START_REF] Bouzid | Mathematical modeling for turning on AISI 420 stainless steel using surface response methodology[END_REF] where they remarked that the surface roughness (Ra) rapidly increases by increasing feed rate. However, this decrease in surface quality becomes increasingly small with lower values of the depth of cut.

(

Fig. 6 (b) shows the response surface for S/N (Ra) in the form of a contour. It is remarkable after this figure that for any given values of depth of cut and which belongs to the interval of this study, the best surface quality is found for small values of feed rate in the study interval. Also, at higher depths of cut, better quality of surface is obtainable from 0.3 mm to 0.45mm. in Fig. 7 it is notable that that the use of large nose radius improves the surface roughness by the crushing of the asperities. When the nose radius of cutting tool increases, the contact languor between the beak of the tool and the machined surface is increased and this leads to crushing of the asperities and traces of advance of the tool as shown in Fig. 7 (c).

Regression equations

Regression analysis is a computational technique that enables to found the functional relationship between the machining parameters (control factors) and the performance characteristics. The predictive equations for the performance characteristics were formulated by linear regression model with interactions given by Eq. ( 16).

i j i k ij ij k i i i X X b X b b Y        1 0 (16)
where b0 is the free term of the regression equation, the coefficients b1, b2 … bk and b12, b13, bk -1 are the linear and interacting terms, respectively. Xi represents the input parameters; (χr, r, Vc, f, ap) for (Ra) and (Vc, f, ap) for (MRR); and Y represents the outputs (surface roughness, material removal rate). Correlative mathematical models of Ra and MRR are given below by Eq. ( 17) and Eq. ( 18), respectively, with respective coefficients of determination R 2 of 99.72% and 99.77%. These mathematical equations are useful for the estimation of outputs parameters in the range of intervals selected in this study. To verify the reliability of correlative mathematical models of Ra and MRR, the normal probability plot vs. residuals were traced in Fig. 8 (a,b) respectively. It can be seen from Fig. 8 (a,b) that the cloud of residuals is reasonably distributed around to the straight line and there are no unusual data points in the data set. This implies that errors are distributed normally. shows the residuals which are associated with the eighteen experimental runs of surface roughness and material removal rate, respectively. This residual is equal to the difference between the observed and predicted values of the output responses. The residuals of surface roughness belong to the interval of -0.015 to 0.020 µm versus the residuals of material removal rate, which belong at the interval of -600 to 400 mm 3 /min. The residuals do not represent any obvious pattern, this implies that the predictive equations are reliable for estimating the responses at any particular design points which belong at the range intervals selected in this study. Fig. 10 (a,b) also shows a comparison between the predicted values of Ra and MRR, respectively obtained from the linear regression equations and the observed ones. This comparison proves that the estimated output responses are very close to those measured (good agreement between predicted and observed values). These figures confirm that the linear regression models are suitable for estimating the responses without carrying out experimental runs with respect to the range intervals considered in this investigation.

Multi-objective optimization using GRA based Taguchi design

The identification of the optimal levels combination of machining parameters using multi-objective optimization (GRA) was carried out based on the S/N ratio of measured and calculates data of surface roughness (Ra) and material removal rate (MRR), respectively. They are obtained during the dry turning operations of AISI D3 steel with ceramic cutting insert (CC650) based on Taguchi design (L18 OA). The simultaneous improvement in term of maximization both surface quality and productivity are proposed as an objective function. The use of this technique optimization includes the following steps which is mentioned in the second part of this paper.

Step 1: The normalization of S/N ratios for Ra and MRR in the range between zero and one using Eq. 5 (The larger-the-better) were determined for grey relational generation. The normalized data are given in Table 6.

Step 2: Calculation of

) ( 0 k i 
for normalized values of S/N ratio (Ra, MRR) using Eq. ( 7) is necessary for the computation of grey relational coefficients (GRC). Grey relational coefficients (GRC) were computed using Eq. 6 for the determination of grey relational grade (GRG).

)

( 0 k i 
and GRC values are given in Table 6.

Step 3: Grey relational grade (GRG) was computed by Eq. ( 10). The calculated results of GRG are shown in Table 6. This implies that the multi-objective optimization is converted to a single equivalent objective optimization. Step 4: Main effect plot for (GRG) was traced in order to select the optimal levels combination (Fig. 11).

The mean of GRG ratio for each level of the machining parameters is presented in Table 7. In grey relational analysis the highest value of (GRG) corresponds to the best levels combination of machining parameters. Therefore, the optimal level of the machining parameters is the level with the greatest GRG value. So it can be concluded that the best level for each machining parameter was found as follow (Fig. 11): χr2 r3Vc3 f1 ap3, in other words, the optimal levels combination for Ra and MRR were obtained at a major cutting edge angle of 75°, insert radius of 1.6 mm, cutting speed of 440 m/min, feed of 0.08 mm/rev and depth of cut of 0.45 mm. The results of the use of this optimal levels combination are: Ra = 0.41µm and MRR = 15840 mm 3 /min. Step 5: In order to confirm the selected optimal levels combination of machining parameters through the use of GRA technique for the improvement of surface roughness and material removal rate, a comparison assessment was performed between the values of grey relational grade obtained from the optimal experiment with that predicted  ˆ by using the Eq. ( 11). Based on the results in Table 8, a notable agreement was remarked between the value found experimentally (0.69) calculated by the estimation formula (0.74). While the grey relational grade was improved from initial levels combination (χr2 r2 Vc2 f2 ap2) to the optimal levels combination of machining parameters (χr2 r3Vc3 f1 ap3) by 0.13. According to confirmation runs, the surface roughness and material removal rate are ameliorating approximately 1.21, 0.69 times, respectively.

Conclusions

This investigation has detailed the procedure of applying the grey relational analysis based on Taguchi design for a simultaneous optimization in turning process. Through the results obtained in this study, the following conclusions can be drawn:

1. The mixed orthogonal array of Taguchi L18 is adopted in this investigation to get a small number of experiment runs for identifying the optimal levels of machining parameters using grey relational analysis.

2. Based on the ANOVA analyse of S/N ratio for (Ra), it's found that the feed rate maintains a strong effective parameter affecting the surface roughness followed by nose radius and the interaction (f×ap) with contributions of 50.21%, 20.27%, and 12.69%, respectively.

3. The results given by ANOVA of S/N ratio for (MRR) shows that depth of cut is the most significant with the respective contribution 54.85%. The feed rate followed by cutting speed presents a statistical significance with contribution of 21.84% and 21.64%, respectively.

4. The descending order of influencing machining parameters on performance characteristics which was found by ANOVA analysis were confirmed by Pareto analysis and main effects plots for S/N ratios of (Ra) and (MRR). Effect of the interaction (f×ap) was also confirmed by 3D plot and contour.

5. The analysis of 2D profile and 3D topographical maps of the turned surface captured by optical platform of metrology modular Altisurf 500 has presented a great importance in the examination the effect of feed rate and nose radius of cutting tool.

6. The correlative mathematical models of Ra and MRR are very efficient because of their higher coefficients of determination (R 2 ) values of 99.72% and 99.77%, respectively. They have an important industrial interest, since they help to make estimations of responses without carrying out experimental runs with respect to the range intervals considered in this investigation.

7. The effectiveness of these models was verified by the normal probability plot vs. residuals and the Plot of residuals vs. run numbers. It is found that the residuals are reasonably distributed around to the straight line and do not represent any obvious pattern. The plot of estimated vs. observed values of responses are also found very close to each other.

8. The grey relational analysis was used to resolve the optimization complex problem by converting the multi-objective optimization into a single equivalent objective optimization.

9. The single equivalent objective optimization in this analysis called grey relational grade (GRG).

The highest value of this latter corresponds to the optimal levels combination of machining parameters. Therefore, the optimal levels combination for a simultaneous improvement of Ra and MRR was obtained at; (χr2 r3Vc3 f1 ap3); major cutting edge angle of 75°, insert radius of 1.6 mm, cutting speed of 440 m/min, feed of 0.08 mm/rev and depth of cut of 0.45 mm. The optimized responses found by the use of optimal levels selected by grey relational analysis were (Ra= 0.41µm and MRR= 15840 mm 3 /min).

10. It is notable that there was a good agreement between the value found experimentally (0.69) and the one calculated by the estimation formula (0.74). While the grey relational grade was improved from initial levels combination (χr2 r2 Vc2 f2 ap2) to the optimal levels combination (χr2 r3Vc3 f1 ap3) by 0.13. According to confirmation runs, the surface roughness and material removal rate were improved approximately 1.21, 0.69 times, respectively.

Fig. 1 .

 1 Fig. 1. Loop of multi-objective optimization of grey relational analysis (GRA) based on Taguchi experimental design.

Fig. 2 .

 2 Fig. 2. Schematic diagram of the experimental set-up.

Fig. 3 .

 3 Fig. 3. Contribution of significant terms on: (a) Surface roughness (Ra), (b) Material removal rate (MRR)

Fig. 4 .

 4 Fig. 4. Pareto analysis chart, for effect of machining parameters on: (a) surface roughness and (b) material removal rate.

Fig. 5 .

 5 Fig. 5. Main effect's plots of S/N for: (a) surface roughness, (b) material removal rate

Fig. 6 .

 6 Fig.6. 3D plot and contour for the response surface for: Effect of (f×ap) on the S/N (Ra)4.4 2D profile and 3D topography of turned surfaceFig.7shows a representative example of 2D profile and 3D image of turned surface envisioned by means of optical platform of metrology modular Altisurf 500 with isometric view. The aim of this investigation is to examine the effect of both feed rate and nose radius on surface roughness through a comparison between 2D profile and 3D topography of turned surfaces obtained as a result of various levels combinations of machining parameters. Turning operations were conducted by the same levels of machining parameters except the feed rate and tool nose radius; for the turned surface (a): χr = 75°, r = 0.8 mm, Vc = 220 m/min, f = 0.08 mm/rev, ap = 0.15 mm, for the turned surface (b): χr = 75°, r = 0.8 mm, Vc = 220 m/min, f = 0.16 mm/rev, ap = 0.15 mm; for the turned surface (c): χr = 75°, r = 1.6 mm, Vc = 220 m/min, f = 0.16 mm/rev, ap = 0.15 mm. It clearly appears by a comparison in Fig.7 (a, b) that the use of large feed rate yields a bad surface roughness. Because the distance between roughness asperities increases with the increase of feed rate. Whereas, by a comparison of turned surfaces (b and c) in Fig.7it is notable that that the use of large nose radius improves the surface roughness by the crushing of the asperities. When the nose radius of cutting tool increases, the contact languor between the beak of the tool and the machined surface is increased and this leads to crushing of the asperities and traces of advance of the tool as shown in Fig.7 (c).

  Ra = -0.751523 -0.0390656 χr + 2.11283 r + 0.00839753 Vc + 20.5609 f -9.98742 ap -0.00225299 χr×r + 5.98103e-005 χr×Vc + 0.116648 χr×f + 0.00051299 χr×ap -0.00318008 r×Vc -23.6922 r×f + 6.56501 r×ap -0.0255462 Vc×f -0.0163664 Vc×ap + 53.2321 f×ap (17) MRR = 12835.2 -40.4339 Vc -105222 f -41353.3 ap + 324.193 Vc×f + 126.452 Vc×ap + 332351 f×ap (18) χr = 75°, r = 0.8 mm, Vc = 220 m/min, f = 0.08 mm/rev, ap = 0.15 mm χr = 75°, r = 0.8 mm, Vc = 220 m/min, f = 0.16 mm/rev, ap = 0.15mm (a) (b) χr = 75°, r = 1.6 mm, Vc = 220 m/min, f = 0.16 mm/rev, ap = 0.15 mm (c) Fig. 7. Example of 2D profile and 3D topography of turned surface

Fig. 8 .

 8 Fig. 8. Normal probability plot of residuals for: (a) surface roughness, (b) material removal rate Fig. 9 (a, b)shows the residuals which are associated with the eighteen experimental runs of surface roughness and material removal rate, respectively. This residual is equal to the difference between the observed and predicted values of the output responses. The residuals of surface roughness belong to the interval of -0.015 to 0.020 µm versus the residuals of material removal rate, which belong at the interval of -600 to 400 mm 3 /min. The residuals do not represent any obvious pattern, this implies that the predictive equations are reliable for estimating the responses at any particular design points which belong at the range intervals selected in this study.

  Plot of residuals vs. run numbers for: (a) surface roughness, (b) removal material rate (a) (b) Fig. 10. Measured vs. predicted values of performance characteristics: (a) surface roughness, (b) material removal rate.

Fig. 11 .

 11 Fig. 11. Main effect's plots for GRG

Table 1

 1 Process parameters and their levels.

	Factor	symbol	Unit	Level 1	Level 2	Level 3
	Cutting speed	Vc	m/min	220	307	440
	Feed rate	f	mm/tr	0.08	0.12	0.16
	Depth of cut	ap	mm	0.15	0.3	0.45
	Nose radius	r	mm	0.8	1.2	1.6
	major cutting edge angle	χr	Degree(°)	45	75	-

Table 2

 2 Experimental results for surface roughness and material removal rate with their computed S/N ratios

	Trail no.	Machining parameters χr (°) r (mm)	Vc (m/min)	f (mm/rev)	ap (mm)	Response parameters Ra (µm) S/N (dB)	MRR (mm 3 /min)	S/N (dB)
	1	45	0.8	220	0.08	0.15	0.47	6.56	2640	68.43
	2	45	0.8	307	0.12	0.3	0.59	4.63	11052	80.87
	3	45	0.8	440	0.16	0.45	0.63	3.97	31680	90.02
	4	45	1.2	220	0.08	0.3	0.43	7.26	5280	74.45
	5	45	1.2	307	0.12	0.45	0.55	5.14	16578	84.39
	6	45	1.2	440	0.16	0.15	0.78	2.20	10560	80.47
	7	45	1.6	220	0.12	0.15	0.39	8.10	3960	71.95
	8	45	1.6	307	0.16	0.3	0.57	4.83	14736	83.37
	9	45	1.6	440	0.08	0.45	0.40	8.03	15840	84.00
	10	75	0.8	220	0.16	0.45	1.01	-0.09	15840	84.00
	11	75	0.8	307	0.08	0.15	0.43	7.40	3684	71.33
	12	75	0.8	440	0.12	0.3	0.65	3.70	15840	84.00
	13	75	1.2	220	0.12	0.45	0.39	8.18	11880	81.50
	14	75	1.2	307	0.16	0.15	0.54	5.35	7368	77.35
	15	75	1.2	440	0.08	0.3	0.33	9.72	10560	80.47
	16	75	1.6	220	0.16	0.3	0.51	5.79	10560	80.47
	17	75	1.6	307	0.08	0.45	0.41	7.74	11052	80.87
	18	75	1.6	440	0.12	0.15	0.43	7.33	7920	77.97

Table 3

 3 Analysis of Variance for S/N (Ra)

	Source	SS	DF	MS	F-value	Cont. %	Remarks
	χr	1.0755	1	1.0755	116.9	1.07	Significant
	r	20.4583	1	20.4583	2223.73	20.27	Significant
	Vc	0.0569	1	0.0569	6.18	0.06	Insignificant
	f	50.6817	1	50.6817	5508.88	50.21	Significant
	ap	1.3091	1	1.3091	142.29	1.3	Significant
	χr×r	1.3651	1	1.3651	148.38	1.34	Significant
	χr×Vc	0.0179	1	0.0179	1.95	0.02	Insignificant
	χr×f	1.1715	1	1.1715	127.34	1.16	Significant
	χr×ap	3.8569	1	3.8569	419.23	3.82	Significant
	r×Vc	2.7503	1	2.7503	298.95	2.72	Significant
	r×f	0.1536	1	0.1536	16.7	0.15	Insignificant
	r×ap	2.9522	1	2.9522	320.89	2.92	Significant
	Vc×f	0.3393	1	0.3393	36.88	0.34	Significant
	Vc×ap	1.9258	1	1.9258	209.33	1.91	Significant
	f×ap	12.8056	1	12.8056	1391.91	12.69	Significant
	Error	0.0183	2	0.0092		0.02
	Total	100.938	17			100

Table 4

 4 Analysis of Variance for S/N (MRR)

	Source	SS	DF	MS	F-value	Cont. %	Remarks
	Vc	107.757	1	7.253	10	21.64	Significant
	f	108.743	1	8.151	11.24	21.84	Significant
	ap	273.174	1	11.392	15.71	54.85	Significant
	Vc×f	0.306	1	0.264	0.36	0.06	Insignificant
	Vc×ap	0.034	1	0.027	0.04	0.01	Insignificant
	f×ap	0.012	1	0.012	0.02	0	Insignificant
	Error	7.978	11	0.725		1.60
	Total	498.004	17			100

Table 5

 5

	S/N response table for: (a) surface roughness (Smaller is better), (b) material removal rate (Larger is better)

Table 5a Table 5b

 5a5b

										80% of problems
			20% of causes
	Level	χr	r	Vc	f	ap	Level	Vc	f	ap
	1 2	5.636 6.125	4.361 6.308	5.968 5.85	7.786 6.181	6.157 5.989	1 2	76.8 79.69	76.59 80.11	74.58 80.61
	3	-	6.973	5.823	3.675	5.496	3	82.82	82.61	84.13
	Delta	0.489	2.611	0.145	4.11	0.661	Delta	6.02	6.02	9.54
	Rank	4	2	5	1	3	Rank	3	2	1

Table 6

 6 Results of grey relational generation, calculation of Δ0i (k), grey relational coefficient and grey relational grade

		Grey relational generation	Calculation of Δ0i (k)	Grey relational coefficient	Grey relational grade
	Trail no.	S/N	S/N (MRR)	S/N	S/N (MRR)	S/N	S/N	GRG
		Larger-the-better
	Ideal sequence	1	1	1	1	1	1
	1	0,708	0,000	0,292	1,00	0,632	0,333	0,483
	2	0,531	0,576	0,469	0,42	0,516	0,541	0,529
	3	0,470	1,000	0,530	0,00	0,485	1,000	0,743
	4	0,774	0,279	0,226	0,72	0,689	0,409	0,549
	5	0,578	0,739	0,422	0,26	0,543	0,657	0,600
	6	0,306	0,558	0,694	0,44	0,419	0,531	0,475
	7	0,851	0,163	0,149	0,84	0,771	0,374	0,572
	8	0,550	0,692	0,450	0,31	0,526	0,619	0,573
	9	0,845	0,721	0,155	0,28	0,763	0,642	0,703
	10	0,000	0,721	1,000	0,28	0,333	0,642	0,488
	11	0,786	0,134	0,214	0,87	0,700	0,366	0,533
	12	0,445	0,721	0,555	0,28	0,474	0,642	0,558
	13	0,858	0,605	0,142	0,39	0,779	0,559	0,669
	14	0,598	0,413	0,402	0,59	0,554	0,460	0,507
	15	1,000	0,558	0,000	0,44	1,000	0,531	0,765
	16	0,638	0,558	0,362	0,44	0,580	0,531	0,555
	17	0,818	0,576	0,182	0,42	0,733	0,541	0,637
	18	0,780	0,442	0,220	0,56	0,695	0,473	0,584

Table 7

 7 Mean of GRG ratio for each level of the machining parameters

	Level	χr	r	Vc	f	ap
	1 2	0.580 0.589	0.555 0.594	0.552 0.563	0.611 0.585	0.525 0.588
	3	-	0.604	0.637	0.556	0.639
	Delta	0.009	0.049	0.085	0.055	0.114
	Rank	5	4	2	3	1

Table 8

 8 Results of the confirmation experiment Initial machining parameters

	Optimal machining parameters
	Prediction	Experiment

Acknowledgments

This work was executed in the Mechanics and Structures Research Laboratory (LMS), May 8th 1945 University of Guelma, Algeria in partnership with LaMCoS (INSA-Lyon, France). Authors would like to thank the Algerian Ministry of Higher Education and Scientific Research (MESRS) and the Delegated Ministry for Scientific Research (MDRS) for granting financial support through CNEPRU Research Project, Code: J0301520140021.


Irène Jarskyâ

Irène Jarsky

« Présentation d?Inharmonique : interview avec

Cette interview avec Irène Jarsky, la soprano qui a créé et participé à la genèse d?Inharmonique, nous fait découvrir une facette de l??uvre parfois inconnue du public. Parmi les points les plus remarquables, signalons : le processus de composition dans les années 1970, l?interaction entre le compositeur et l?interprète, et surtout, les nuances interprétatives qui dépassent la notation musicale traditionnelle. Plus de quarante ans après la création de l??uvre, cette interview montre que plusieurs questions restent encore d?actualité, notamment celle ayant trait à la recherche-création. Cela atteste de son caractère novateur et de sa place d?honneur dans le répertoire musical contemporain de la fin du XXe siècle.

Introduction

La soprano Irène Jarsky a créé Inharmonique en 1977. Interprète reconnue du répertoire contemporain, son éventail artistique s?étend du chant français à la Seconde École de Vienne. Sa rencontre avec Risset eut lieu au moment où elle-même s?intéressait à la recherche musicale et aux nouvelles manières de faire du son. Ce n?est donc pas un hasard si la collaboration de ces deux artistes a donné naissance à un lien profond qui a perduré au-delà de la création d?Inharmonique.

Les informations recueillies lors de cette interview sont bien plus qu?une présentation de l??uvre ou une succession d?anecdotes. Au contraire, Irène Jarsky donne des pistes importantes pour l?interprétation et l?avenir de la pièce. Cette interview est une source historique majeure du processus créatif d?I nharmonique, mais aussi du répertoire faisant appel à l?informatique musicale. L?interview a été menée par le musicologue Vincent Tiffon, Professeur à Aix-Marseille Université, dont la thèse doctorale a été co-dirigée par Risset lui-même et qui est aujourd?hui le responsable de la numérisation et de la mise en ligne des archives du compositeur au Fonds Risset au laboratoire PRISM à Marseille. Dans un premier temps, Irène Jarsky raconte sa rencontre avec Risset alors qu?elle menait des recherches sur l?émission vocale. Ensuite, il s?établit une riche discussion sur Inharmonique et son interprétation. L?interview s'achève avec des réflexions sur les principaux critères interprétatifs de l??uvre.

Genèse d?Inharmonique

> RFIM Numéros > n° 9 -Inharmonique (1977) de Jean-Claude Risset : création, ré-création et avenir Vincent Tiffon : Pouvez-vous introduire la pièce Inharmonique, et notamment parler de votre participation à ce projet de Jean-Claude Risset ?

Irène Jarsky : Quand j?ai rencontré Jean-Claude, je cherchais une façon d?échapper à l?enseignement que j?avais eu au Conservatoire, à savoir surtout les grands « moments vocaux », belcantistes et autres. Il me semblait que les possibilités de la voix humaine étaient emprisonnées dans un carcan de normes figées. Je cherchais donc autre chose. Quand nous nous sommes rencontrés, il m?a proposé de participer à la musique qui accompagnait la pièce Little Boy, du nom de la bombe qui est tombée sur Hiroshima. À ce moment-là, Jean-Claude développait les sons paradoxaux ; c?est-à-dire des progressions sans fin de sons vers le grave et qui parviennent aux registres aigus, ou bien qui accélèrent et arrivent à un ralentissement, tout ce qui comporte une « tromperie » de la perception auditive habituelle.

À tout ce que j?avais appris jusque-là (timbre, espace acoustique, transmission des émotions), s?ajoutait un nouvel espace beaucoup plus vaste et aux multiples définitions. C?était entre 1965 et 1975, l?époque où l?on commençait à élargir le domaine sonore et à l?utiliser d?une façon beaucoup plus complexe pour la musique. Nous avons commencé à travailler là-dessus. Au départ, tout cela était très nouveau pour moi, mais c?était très passionnant. En même temps, c?était l?époque aussi où les ethnomusicologues nous ont ramené et offert un accès plus large aux témoignages des musiques extra-européennes, des civilisations qui utilisaient le son autrement, en faisant appel à des techniques ancestrales très lointaines et très passionnantes. Nous avons exploré tout ce qu?étaient les « champs harmoniques », c?est?à-dire à partir du son fondamental tout le spectre qu?on pouvait rendre évident à la voix. Jean-Claude s?est beaucoup passionné pour cela. Nous sommes allés dans ce sens-là.

V.T. Si je comprends bien, vous l?avez rencontré au moment de Little Boy, autour de 1965. I.J. Oui. V.T. À ce moment-là, le projet d?Inharmonique était-il déjà présent ? I.J. Non, ça s?est fait petit à petit. C?est-à-dire que Jean-Claude, de son côté, cherchait tous les rapports qui pouvaient exister entre l?électronique et l?émission vocale. En rapport aux enregistrements que nous avions réalisés, il m?a donc demandé de participer petit à petit à des séances de recherches Ces séances ont donné Inharmonique et plusieurs ?uvres postérieures. L?idée de départ, c?était de reconstituer la même structure que celles des sons instrumentaux. C?est là qu?il y a eu plein d?expériences. Nous nous sommes finalement aperçus que le spectre utilisé pour les sons acoustiques était beaucoup plus complexe et beaucoup plus vaste que ce que l?on imaginait. Il a fallu affiner, affiner les filtres, affiner l?association, affiner les recherches elles-mêmes. Je ne les ai pas faites moi-même, mais j?ai été témoin au fur et à mesure des choix qui se faisaient. I.J. C?était l?époque aussi où je faisais des recherches pour savoir comment on pouvait produire des sons extrêmement aigus avec la voix, que je qualifierais d?« harmoniques », et que les chanteurs appelaient des ?sons-sifflets?. Toutes les émissions sonores que l?on pouvait produire avec la voix m?intéressaient. C?est là qu?avec Jean-Claude, nous avons commencé à travailler en studio. Nous nous demandions par exemple comment une voix pouvait sortir d?un son électronique avec des variantes, c?est-à-dire avec des choix de structures qui étaient différents. C?est aussi le moment où la musique concrète s?est développée.

Recherche-création : relation interprète compositeur

V.T. Pour cette pièce Inharmonique en particulier, comment avez-vous participé au processus de composition ? Jean-Claude est bien évidemment le compositeur de la pièce, mais il a travaillé de manière étroite avec vous. Comment avez-vous échangé avec Jean-Claude ? Dans quelle mesure interveniez-vous ? Êtes-vous intervenue directement dans le travail compositionnel ? Quelle était votre place, votre rôle dans ce processus ? création, ré-création et avenir I.J. Mon rôle était de lui faire entendre tout ce que je pouvais émettre avec la voix : à partir de là, il travaillait. Il cheminait avec ces exemples, et ensuite, nous choisissions parmi les résultats de ces avancées réciproques. Par exemple, ce que j?ai proposé, en rapport avec mes recherches en laboratoire à l?hôpital de la Timone [à Marseille], c?est une série d?enregistrements avec des chanteurs en utilisant l?appareil de « Xéroradiographie ». C?était une sorte de radiographie des personnages en état de mouvement, qui permettait de ?voir? non seulement l?ossature, mais aussi tous les tendons, les muscles. On avait une espèce de corps transparent. Cela permettait de voir quels étaient les mouvements pour produire des sons extrêmes, des sons très très aigus ou très très graves, ou complexes, et de voir comment physiologiquement le corps s?adaptait à la position nécessaire pour produire ces sons-là. La machine n?est plus utilisée je crois? À ce moment-là, ce qui m?a intéressée aussi dans l?émission de sons, c?était la possibilité d?émettre un son en continu en utilisant l?expiration et l?inspiration : c?est-à-dire, essayer d?arriver à peu près à faire les mêmes sons, pas sur toutes les échelles, mais dans des endroits précis du registre. Au début d?Inharmonique, les sons qui durent très longtemps sont faits une fois en expiration et une fois en inspiration (Figure 1). V.T. Ces recherches étaient-elles en collaboration avec Jean-Claude ? I.J. Ah non ! Tout cela était indépendamment de Jean-Claude. Mais, nous nous en sommes servi tous les deux lorsque nous avons construit Inharmonique.

V.T. Avez-vous d?autres exemples de transferts de recherches réalisées avec cette équipe à la Timone vers les processus compositionnels, ou des idées compositionnelles dans Inharmonique ? I.J. Disons qu?Inharmonique est inspirée d?une pratique tibétaine visant à produire des sons graves dont on déploie le spectre harmonique. Ce sont des moines qui pratiquent cela depuis très longtemps. Nous étions plusieurs à cette époque à chercher comment on pouvait le reproduire. En fait, l?idée de faire apparaître les harmoniques à partir d?un son de base, c?était d?essayer de comprendre comment le son était construit : pourquoi les différences de timbre, de puissance, où cela se passait, pourquoi et comment. Donc, l?autre partie que nous avons partagée avec Jean-Claude, c?est justement celle qui est basée sur l?apparition des harmoniques durant un son tenu (Figure 1). À ce moment-là, l?électronique produit une sorte de halo avec une voix, et cette voix glisse d?un harmonique sur l?autre. Ce qui m?a intéressée, c?est comment on pouvait détailler la composition harmonique d?un son aigu.

V.T. Auriez-vous d?autres collaborations à rappeler avec cette équipe de la Timone ? Vous avez parlé des sons qui se rapprochent des techniques des moines Tibétains. Est-ce que vous avez d?autres exemples ? I.J. Après Inharmonique, nous avons fait plusieurs pièces avec Jean-Claude. Dans la dernière que nous > RFIM Numéros > n° 9 -Inharmonique (1977) de Jean-Claude Risset : création, ré-création et avenir avons faite, Invisible (elle s?appelait initialement Invisible Irène), l?idée fondamentale de Jean-Claude, il me semble, était de faire un ch?ur uniquement avec des transformations de ma propre voix : mais il n?a pas pu mener à bien ce projet parce qu?il était basé sur ce fameux texte d?Irène? suite à ma découverte de l?auteur italien qui a écrit Le città invisibili? V.T. Italo Calvino. I.J. Voilà, exactement? Cela a tourné court, parce que nous n?avons pas eu le droit d?utiliser tous ces textes (plusieurs villes portant des prénoms de femmes). Donc, il n?y en a qu?une qui est restée, celle qui avait le prénom d?Irène, et c?est avec celle-ci qu?il a construit le dernier travail auquel nous avons participé tous les deux.

Construire Inharmonique

V.T. Revenons au traitement de la voix par l?électronique dans Inharmonique. Est-ce que Risset avait une idée précise de ce qu?il voulait ? I.J. Pas toujours, c?était en fonction de ce qu?il entendait et de ce que je lui proposais. C?est à partir de là que son imagination entrait en jeu. Nous avons enregistré énormément de choses et on ne se voyait pas pendant dix-quinze jours, et il revenait avec tout un tas de propositions dans lesquelles je m?insérais complètement. C?est vraiment lui qui composait, ce n?était pas moi... V.T. Vous dites que vous ne le voyez pas pendant, par exemple, quinze jours. Cela veut dire que vous aviez une période de rendez-vous très proches ? I.J. Oui, à partir du moment où il avait décidé de finir sa pièce, il fallait vraiment que l?on travaille? V.T. Lorsque vous vous voyiez tous les dix ou quinze jours, cette période a duré combien de temps ? I.J. Je ne sais plus, c?était par séquence. À un certain moment, il fallait qu?il ait le studio. Il n?avait pas toujours le temps, Jean-Claude. Il devait séparer le temps par rapport à ses autres activités. Donc, d?un coup, il était là et on travaillait de tel jour à tel jour.

V.T. Les séances de travail avaient-elles lieu à l?Ircam ou à Marseille ? I.J. Inharmonique a été faite surtout à Marseille, mais par exemple le passage à 13?18?? a été enregistré à l?Ircam (Figure 2). Alors, c?était sa façon à lui de ramasser des pierres, de ramasser des séquences qu?il utilisait après, et de les travailler comme il avait envie. Entre l?Ircam et Marseille, il n?y a que lui, je crois, qui pourrait dire le nombre d?heures qu?il a passé dans un endroit ou l?autre. I.J. Ce qu?il m?a proposé n?était pas improvisé. C?était déjà une espèce de décor, un nid de sons dans lequel j?étais censée me promener tranquillement, en toute liberté. Donc, à la fois c?est bien, et en même temps, je ne suis pas compositeur. Chez un interprète, ce qui est intéressant à ces instants-là, c?est le plaisir de la « promenade ». C?est-à-dire, le fait de pouvoir s?insérer dans un son qui est irréel, plutôt « inhumain » -disons dans le sens littéral du terme -et d?amener petit à petit à une couleur qui est plus complexe, parce qu?elle est « humaine ». Il y a donc tout un spectre qui se confronte au spectre qui est proposé par le compositeur et qui permet d?avoir un développement temporel à ce moment-là.

> RFIM Numéros > n° 9 -Inharmonique (1977) de Jean-Claude Risset : création, ré-création et avenir V.T. Dans la partition, pour les improvisations ou les semi-improvisations, la notation est prescriptive. Êtes-vous intervenue dans cette notation ? I.J. Non, il n?y a rien de noté pour moi. Il y avait la partition électronique, je l?avais sous les yeux et je l?avais dans les oreilles, mais le son vocal n?était pas noté.

V.T. Oui, ce n?est pas noté. Mais, il y a des instructions qui guident l?interprète dans ces moments de liberté. Vous êtes l?interprète privilégiée d?Inharmonique, mais la pièce peut être chantée par d?autres chanteuses. Est-ce que vous intervenez dans les choix de notation ? I.J. J?essaie de me souvenir de nos séances de travail? Les échanges étaient vraiment à la fois sur l?instant et en même temps avec la notion de l?épaisseur de l??uvre, et toujours de la couleur que je pouvais amener. Je n?étais pas là comme une chanteuse traditionnelle, mais comme un producteur de son, et des sons à inventer. Je pense que Jean-Claude aurait été content de refaire cette pièce avec quelqu?un d?autre, qui amènerait d?autres spectres sonores? En tout cas, c?était tout sauf de la voix chantée accompagnée. L?idée était vraiment d?entrer à l?intérieur d?un spectre sonore, d?y faire entrer sa propre émission vocale à l?intérieur, et de le laisser vivre en fonction de la proposition électronique que donnait Jean-Claude. V.T. À propos de cette proposition électronique, Jean-Claude dit que son idée est de « composer le son lui-même » avec les moyens électroniques. Est-ce que lorsque vous travailliez avec lui, il vous demandait la même chose ? C?est-à-dire, vous a-t-il demandé d?être « productrice » de nouvelles formes sonores avec la voix, un peu comme lorsqu?on fait de la synthèse par ordinateur. I.J. Mais oui, c?était convenu dès le départ. Il attendait de moi que je lui fasse des propositions aussi.

Synchronie voix et électronique

V.T. Comment concevez-vous la synchronie entre la voix et l?électronique ? Est-ce qu?au moment du concert, le chronomètre est toujours nécessaire ? I.J. Non, non, non. Et à la limite, je pense qu?une différence d?une prestation à l?autre ne l?aurait pas du tout gêné. Je crois que ce qui est important, c?est cette appartenance à un processus qui se déploie dans le temps, mais qui n?est pas absolu. C?est-à-dire que si un autre producteur de son, chanteur, féminin ou masculin, venait à ajouter, dans ces passages plus improvisés, des choses plus personnelles, Jean-Claude en aurait été très content. C?est vraiment comme une prairie qui se déployait devant nous et dans laquelle je mettais ce que j?étais capable de faire à l?époque. Et lui choisissait parmi mes propositions.

V.T. La question était plus sur la synchronisation qui est souvent considérée comme un problème dans la musique mixte avec le temps différé, avec les bandes magnétiques. D?expérience, j?ai remarqué que les interprètes ne se sont pas gênés par ce problème car ils mémorisent la partie électronique, et finalement ils s?affranchissent de la question du chronomètre. Est-ce que c?était également votre cas ? I.J. Tout à fait.

V.T. Donc vous saviez exactement comment vous insérer dans les sons électroniques avec une certaine souplesse interprétative ? I.J. Tout à fait, et je dois dire qu?heureusement que je les connaissais, parce que c?était mon « chemin » à moi. Sachant ce que j?allais entendre, je pouvais me glisser dedans. Mais, n?importe qui d?autre qui aurait songé à travailler comme ça aurait pu amener quelque chose de plus personnel. Au niveau du temps, je crois qu?il est complètement dicté par la qualité du son, c?est-à-dire, qu?il ne peut pas être associé à n?importe quoi.

V.T. Vous confirmez donc, comme beaucoup d?interprètes de ces musiques mixtes (avec sons > RFIM Numéros > n° 9 -Inharmonique (1977) de Jean-Claude Risset : création, ré-création et avenir électroniques fixés), que la synchronie n?est pas un problème ? I.J. Ce n?est pas un problème, mais en revanche, ce qui est très important, c?est d?être complètement imbibé du support électronique, sinon, on peut faire n?importe quoi, l?on peut ajouter n?importe quoi sur cette partition dont la base électronique est fixe après avoir été longuement travaillée.

Rapport scénique

V.T. Vous parlez de double (chant et électronique) : c?est une des grandes thématiques de Jean-Claude dans les musiques mixtes. Dans cette pièce Inharmonique, comme dans d?autres, cela renvoie, à mon sens, à la question scénique de la musique mixte : c?est une musique de concert, indubitablement. Cela ne s?écoute pas bien au disque. Quand vous avez créé la pièce, avez-vous travaillé et joué la partie scénique ? Avez-vous travaillé avec lui sur des stratégies ? I.J. Non, nous n?avons pas eu de stratégies, les choses se sont faites assez vite, et l?idée c?était vraiment qu?un monde sonore existe dans l?obscurité, et petit à petit, une voix émerge, les sons électroniques prennent chair et deviennent un être humain. L?idée de la lumière était complètement concomitante : le noir au début, la lumière monte? Il y a un goût de mystère.

V.T. Est-ce que vous avez participé à l?élaboration de la mise en scène ? Jusqu?à quel point avez-vous participé à cette élaboration ? I.J. Nous avons décidé cela ensemble, mais c?était uniquement basé sur l?apparition de la lumière.

V.T. En partant d?une situation acousmatique pour rendre visible ce qui n?est pas visible dans le son ? I.J. Voilà.

Jouer Inharmonique

V.T. Dans Inharmonique, il y a plusieurs passages (notamment à 5?18??) où la voix sort de la résonance d?une cloche, comme si c?était une augmentation de sons électroniques (Figure 4). Comment concevez-vous l?interprétation de ces passages-là ? > RFIM Numéros > n° 9 -Inharmonique (1977) de Jean-Claude Risset : création, ré-création et avenir I.J. Exactement comment je l?ai dit. Il faut essayer d?identifier le son électronique et voir à quel point nous pouvions trouver une émission qui donne quasiment le même effet acoustique. Et au-delà, peut-être donner une forme de vie, ou bien une différence. Mais cela part effectivement de la partition. S?il n?y avait pas de notation musicale traditionnelle, l?oreille serait le conducteur. Si l?on n?entend pas le spectre électronique au moment où il est émis et où il appelle à une collaboration humaine, on ne peut pas fusionner. Il faut être complètement pénétré du son électronique pour voir où l?on peut s?immiscer petit à petit, donner une apparence humaine ou pas, en fonction de la décision élaborée entre le compositeur et l?interprète.

V.T. Pensez-vous qu?un interprète autre que vous doive absolument avoir une connaissance aiguisée de la physique acoustique pour comprendre le spectre des sons électroniques ? Est-ce nécessaire pour qu?il développe sa propre capacité à produire des sons inhabituels et à répondre au mieux à ces jeux de dialogue ? I.J. Je pense même que c?est la base. Il n?y a pas de formation de l?oreille aux sons électroniques. On sera toujours à l?extérieur, comme se définit un chanteur accompagné. Tout notre travail avec Jean-Claude était de trouver des correspondances, une osmose. Pourquoi tel son émis par la voix humaine est difficilement reconnaissable, et inversement tels sons électroniques qui suggèrent à la voix humaine d?arriver à l?imiter en double. C?est le jeu. Si l?on n?a pas de formation à ce niveau-là, je pense qu?on doit faire autre chose.

L?avenir d?Inharmonique

V.T. : Pouvez-vous préciser ou ajouter des recommandations pour d?autres interprètes ? J?imagine que Jean-Claude ou vous-même n?avez pas tout écrit sur la partition ? I.J. Il faut déjà être complètement pénétré par le support électronique, l?avoir entendu, réentendu et réentendu et l?avoir complètement intégré. C?est à partir de là qu?on peut essayer des émissions vocales qui soient liées à ces constructions sonores qui étaient la passion de Jean-Claude, et pas seulement des émissions vocales « normales », V.T. Sur la question scénique, est-ce que vous avez des recommandations fortes à porter pour respecter au mieux cette pièce ? I.J. Tout dépend de l?apparence de la personne qui va jouer, qui va entrer dans ce monde. L?idée est de ne pas montrer d?autres outils que la nécessité acoustique, qu?elle soit de la production de son, de la tenue physique, de l?intensité de la bande, enfin, toutes ces choses qui ne devraient faire qu?un seul bloc. La partition demande un travail énorme. Je pense que la jouer par c?ur est trop complexe. Mais il faut essayer de la rendre la plus discrète possible et, soi-même, essayer d?avoir le moins de description physique de ce qui se passe du point de vue sonore. Il faut travailler et retravailler pour pouvoir intégrer complètement ce processus et cette chronologie du déroulement de l??uvre.

Il faut que les ?uvres existent, il faut qu?Inharmonique vive, même différente d?hier. C?est bien qu?elle existe.

V.T. Dans cette dialectique entre, d?une part, une ?uvre fixée sur bande et partition et, d?autre part, une ?uvre qui a sa propre vie et qui est reprise par d?autres interprètes en jouant leurs propres variations, il faut tenir compte de l?idée initiale de Jean-Claude (ou de n?importe quel compositeur). Je comprends bien qu?il ne faut pas fixer une interprétation idéale, mais il y a quand même une idée initiale. C?est une ?uvre basée sur le son, comme beaucoup d?autres pièces de Risset, et il faut que l?interprète incarne ce son. Le corps n?a pas une place prépondérante comme dans d?autres situations vocales occidentales.

Figure 1 .

 1 Figure 1. Passage vers 4?40?? d?Inharmonique.

Figure 2 .

 2 Figure 2. Passage vers 13?35?? d?Inharmonique.

Figure 4 .

 4 Figure 4. Passage vers 5?18?? d?Inharmonique.

  I.J. Je suis tout à fait d?accord. > RFIM Numéros > n° 9 -Inharmonique (1977) de Jean-Claude Risset : création, ré-création et avenir Pour citer ce document: Irène Jarsky, « Présentation d?Inharmonique : interview avec Irène Jarsky », RFIM [En ligne], Numéros, n° 9 -Inharmonique (1977) de Jean-Claude Risset : création, ré-création et avenir, Mis à jour le 11/09/2023 URL: http://revues.mshparisnord.org/rfim/index.php?id=704 Cet article est mis à disposition sous contrat Creative Commons