SPECIFIC OPTIMAL AWJM PROCESS PARAMETERS FOR TI-6AL-4V ALLOY EMPLOYING THE MODIFIED TAGUCHI APPROACH

The high strength-to-weight ratio titanium alloys have good resistance to corrosion and temperature, which are extensively being used in turbine engines and aircraft structures. Machining of such alloys demands advanced processes like abrasive water jet machining (AWJM) to realize the repeatable desired shapes. This paper presents a set of optimal AWJM parameters (viz. traverse speed, abrasive flow rate and stand-off-distance) for maximizing the material removal rate (MRR) and minimizing the surface roughness (Ra) of the Ti-6Al-4V.Amulti-objective optimization technique is applied on the multiple response test data of the Taguchi’s 9 L orthogonal array. Analysis of variance (ANOVA) has been carried out to examine the statistical significance of AWJM parameters. The traverse speed is found to have significant effect on Ra and MRR.


INTRODUCTION
In any manufacturing process, performance indicators are quality and productivity [1].A few of the non-conventional processes adopted by industries are: (i) LBM (laser beam machining); (ii) WJM (water jet machining); (iii) AWJM (abrasive water jet machining); (iv) EDM (electric discharge machining); (v) WEDM (wire electric discharge machining); and (vi) ECM (electro chemical machining).AWJM offers high manoeuvrability, nullified HAZ in cutting process, and low machining force exertion [2][3][4][5].AWJM process parameters are categorized into [6]: (i) Hydraulic parameters (water pressure and water flow rate or water jet nozzle diameter); (ii) Abrasive parameters (type, size, shape, and flow rate of abrasive particles); (iii) Cutting parameters (traverse rate, stand-off distance, number of passé, angle of attack, and target material); (iv) Mixing parameters (mixing method (forced or suction), Abrasive condition (dry or slurry) and mixing chamber dimensions).The selection of process parameters depends on the operator's expertise or experience.Machining handbooks generally provide information on process parameters for frequently used materials in conservative nature.Optimal AWJM process parameters are thus required to exploit its capabilities and potentials through minimization of the testing, timeconsumption and expenditure.
Industries can expect better accuracy and surface finish without thermal distortion for hard and brittle materials through AWJM process [7][8][9][10].Several materials adopted this process.
Mhamunkar and Raut [36] have carried out an interesting experimental investigation as per Taguchi's L9 orthogonal array [37] for obtaining optimal AWJM parameters of Ti-6Al-4V by using the Taguchi based GRA (grey rational analysis).They have considered traverse speed, abrasive flow rate and stand-off-distance as AWJM process parameters, whereas material removal rate (MRR) and surface roughness (Ra) are performance indicators.Taguchi method can suggest the optimal process variables to a single response characteristic.GRA is adopted in multi-objective optimization problems having multiple responses with dissimilar quality characteristics [38][39][40][41][42][43].
This paper examines the adequacy of Taguchi approach in solving multi-objective optimization problems related to the specification of AWJM parameters for Ti-6Al-4V.The modified Taguchi method [44] is considered for estimating the range of performance indicators.A simple multiobjective optimization technique [45,46] is adopted and suggested a set of optimal AWJM parameters.Empirical relations are developed for MRR and Ra and validated with test data [36].

TEST DATA
Mhamunkar and Raut [36]  (where water jet is formed and mixed with abrasive particles-forming abrasive water jet).Water in pipes is carried to the jet or cutting head.The stand-off-distance between mixing tube and material is typically 0.5 to2.5 mm.Mitutoyo make Surface roughness tester is used to measure the surface roughness (Ra) and evaluated the material removal rate (MRR) considering traverse speed, abrasive flow rate and stand-off-distance as AWJM parameters.For simplicity, AWJM parameters, namely, traverse speed, abrasive flow rate and stand-off-distance are designated by A, B and C respectively.Table-1 gives the assigned 3 levels for the AWJM parameters and the measured performance indicators (MRR and Ra) for the set levels as per Taguchi's L9 orthogonal array.

MODIFIED TAGUCHI APPROACH
Depending on the number of process parameters ( ) p n and the assigned levels ( ) l n Taguchi method [37,[47][48][49][50] suggests a suitable orthogonal array to conduct few tests for tracing optimal process parameters.The number of experiments (NTaguchi) required as per Taguchi approach [397] NTaguchi ( )  From AVOVA Table-1, the optimal AWJM parameters to achieve minimum surface roughness (Ra) are identified as A1B3C1, wherein subscripts denote the levels of the parameters.The optimal AWJM parameters to achieve maximum material removal rate (MRR) are A3B3C3.It should be noted that the above two sets of AWJM parameters to achieve minimum Ra and maximum MRR are found to be different.Tests are not conducted for these two cases.Confirmation tests are mandatory.
Additive law [37] can provide estimates of performance indicators (viz., Ra and MRR) using the mean values from the ANOVA Table .The procedure for the estimates of Ra and MRR is explained below.The performance indicator is denoted by , whose estimate for the AWJM parameters ( for the AWJM process parameters The additive law suggests estimate of  for the specified AWJM parameters ( ) as: Here mean  is the grand mean of  for the 9 test runs.
Exclusion of the fictitious parameter ( D ), equation (2) reduces to  3) provides the range of estimates.The test data [36] in Table-2 falls within the estimated range.Tables 3 and 4 give the estimates of Ra and MRR for all possible 27 combinations of AWJM parameters.The minimum Ra for the identified optimal AWJM parameters (A1B3C1) is expected to be within 2.2499 -2.8740 m  (see S.No.7 of Table -3).The optimum value of Ra from the confirmation test is reported as 2.4658 m  [36].The maximum MRR for the identified optimal AWJM parameters (A3B3C3) is expected to be within  Estimates of Ra and MRR from the empirical relations (4) and ( 5) in Figures 2 and 3 are matching well with those obtained using the additive law (3) in Tables 3 and 4. Superimposing the minimum and maximum deviation values to equations ( 4) and ( 5), one can find the range of Ra and MRR estimates for the specified AWJM parameters.Figures (4 and 5) show the comparison of estimates of Ra and MRR with measured data [36] for all combinations of 27 sets of AWJM parameters in Tables 3 and 4. Measured data is found to be within or close to the bounds of estimates.Lower and upper bound estimates of MRR in Figure -5 show very close due to insignificance corrections to the empirical relation (5).Appropriate optimization technique is required for selecting optimal parameters to achieve the desired performance indicators [62][63][64].

MULTI-OBJECTIVE OPTIMIZATION
Two different sets of AWJM parameters are found to achieve minimum Ra and maximum MRR.Process designer expects a set of AWJM parameters for achieving minimum Ra and maximum MRR.This problem is solved utilizing the multi-objective optimization technique [60] by defining a single objective function as a function of the two output responses after normalizing Ra and MRR with their maximum values: Minimization of  provides the maximum of MRR and minimum of Ra for a set of SPECIFIC OPTIMAL AWJM PROCESS PARAMETERS AWJM machining parameters.Equal weighing are given (i.e., 1  = 2  =1/2) to achieve common optimum process conditions in Table-5.ANOVA is performed on values of the multi-objective optimization function,  in Table-5 to trace the optimum process parameters for the minimum  and selected the optimal process parameters as A3B3C3.Mhamunkar and Raut [36] have obtained the same result from the ANOVA and GRA.Table-6 gives the summary of the specific optimal AWJM parameters and the estimates of the performance indicators.
the mean value of  corresponding to the th i level of the parameter A . ( ) j B  is designated as the mean value of  corresponding to the th j level of the parameter B . ( ) k C  is designated as the mean value of  corresponding to the th k level of the parameter C .( ) l D  is designated as the mean value of  corresponding to the th l level of the parameter D .

3 .
297 SPECIFIC OPTIMAL AWJM PROCESS PARAMETERS From equations (2) and (3), one can find the difference in estimates of  with inclusion and exclusion of the fictitious parameter ( D ) from ( ) mean l D   − .For the three levels, one can find the following three deviations ( ) The three deviation values for the surface roughness (Ra) are 0.4087, -0.2154 and -0.1933 m  .The minimum and maximum deviation values for the Ra are -0.2154 and 0.4087 m  respectively.Similarly, the three deviation values for the material removal rate, MRR are 0.0293, -0.0077 and -0.0217 gms/min.The minimum and maximum deviation values for the MRR are -0.0217 and 0.0293gms/min respectively.Select the minimum and maximum deviation values and superimpose them to the estimate of  from equation (3) to get the range of estimates.Table-2 gives comparison on estimates of Ra and MRR with measured data [36].Exclusion of the fictitious parameter ( D ) makes the estimates from equation (3) within 12% deviation, whereas inclusion of the fictitious parameter ( D ) indicates excellent matching with test data.Superimposing the minimum and maximum deviation values to equation ( of Ra and maximum of MRR.As in[62] the positive weighing factors ( 1

Figure- 6
shows the variation of surface roughness (Ra) and material removal rate (MRR) with traverse speed (A) for the abrasive flow rate (B) of 300 gms/min and the three levels of stand-off-distance (C).ANOVA results in Table-1 indicate insignificant %contribution of C on MRR.This is the reason why the MRR values in Figure-6 are very close for different values of C.5.CONCLUDING REMARKSTi-6Al-4Valloy possesses high strength, corrosion resistance, low thermal conductivity and oxidation resistance.The alloy is extensively being used for marine and automobile applications.Abrasive water jet machining (AWJM) is well suited for this alloy.A set of optimal AWJM parameters (viz.Traverse speed, abrasive flow rate and stand-off-distance) is identified to achieve maximum material removal rate (MRR) and minimum surface roughness (Ra) adopting the modified Taguchi method and multi-objective optimization.The dissimilar quality characteristics of Ra and MRR are made dimensionless and represented functionally by a single response characteristic.This optimization approach is similar to the Taguchi based utility concept.ANOVA indicates that traverse speed has major % contribution on Ra and MRR.Empirical relations are developed for MRR and Ra in terms of the AWJM process parameters and demonstrated their adequacy through comparison of test results.
3.8431 -3.8941gms/min (see S.No.27 of Table-4).The optimum value of MRR from the confirmation test is reported as 3.9853gms/min [36].Empirical relations for Ra and MRR are developed in terms of the AWJM parameters from the mean values of ANOVA Table-1 in the form

Table - 2
: Comparison on the estimates of the performance indicators (viz., Ra and MRR) with test

Table - 3
: Estimates of Ra ( m  ) for all 27 possible sets of AWJM parameters.

Table - 4
: Estimates of MRR (gms/min) for all 27 possible sets of AWJM parameters.

Table - 5
: Single objective optimization function (  ) with weighing factors 1  and 2  for the test data of Ra and MRR in Table-1.