Multi criteria decision making through TOPSIS and COPRAS on drilling parameters of magnesium AZ91

M.Varatharajulu,Muthukannan Duraiselvam,M.Bhuvanesh Kumar,G.Jayaprakash,N.Baskar

aDepartment of Production Engineering,National Institute of Technology,Tiruchirappalli 620015,Tamilnadu,India

b Department of Mechanical Engineering,A.V.C.College of Engineering,Mannampandal,609305,Tamilnadu,India

cDepartment of Mechanical Engineering,Saranathan College of Engineering,Tiruchirapalli 620012,Tamilnadu,India

d Department of Mechanical Engineering,Kongu Engineering College,Perundurai 638060,Tamilnadu,India

Abstract Magnesium(Mg)alloys are extensively used in the automotive and aircraft industries due to their prominent properties.The selection of appropriate process parameters is an important decision to be made because of the cost reduction and quality improvement.This decision entails the selection of suitable process parameters concerning various conflicting factors,so it has to be addressed with the Multiple Criteria Decision Making(MCDM)method.Therefore,this work addresses the MCDM problem through the TOPSIS(Technique for Order Preference by Similarity to Ideal Solution)and COPRAS(COmplex PRoportional ASsessment)methods.The assessment carried out in the material Mg AZ91 with the Solid Carbide(SC)drill bit.The dependent parameters like drilling time,burr height,burr thickness,and roughness are considered with the independent parameters like spindle speed and feed rate.Drilling alternatives are ranked using the above said two methods and the results are evaluated.The optimum combination was found on the basis of TOPSIS and COPRAS for simultaneous minimization of all the responses which is found with a spindle speed of 4540 rpm and a feed rate of 0.076 mm/rev.The identical sequencing order was observed in TOPSIS and COPRAS method.The empirical model was developed through Box-Behnken design for each response.Superior empirical model developed for drilling time which is 3.959 times accurate than the conventional equation.The trends of various dependents based on the heterogeneity of various independents are not identical,these complex mechanisms are identified and reported.The optimized results of the Desirability Function Approach are greater accordance with the TOPSIS and COPRAS top rank.The confirmation results are observed with lesser deviation suggesting the selection of the above independent parameters.

Keywords:Machining processes;Magnesium;TOPSIS;COPRAS;MCDM;Burr;Roughness.

1.Introduction

The applications of various advanced engineering materials have gained significant attention in the fields of automobile,aerospace,electronics,electrical and medical in recent years[1-3].This is due to the fact that they possess superior mechanical properties with less weight[4].Few specific materials and their alloys related to aluminum(Al),magnesium(Mg)are majorly used in structural applications because of high specific strength and low density.They are also difficult to machine due to their brittleness in nature[5-8].With these afore mentioned requirements,aviation industries demand other unique physical-mechanical properties such as rigidity and fatigue strength.The growing requirements necessitate the applications of composite materials[9-14].One of the major challenges while processing advanced materials is machining using conventional tools.The primary concern for researchers while machining advanced materials is the out-put characteristics in terms of Material Removal Rate(MRR),surface finish,tool wear,surface metallurgical characteristics and so on[15-18].Material deformation during machining plays a significant role in deciding the quality of the final component[19].Drilling is one of the fundamental machining operation carried out earlier to reaming,tapping and boring[20].The consistency and dimensional accuracy of a drilled hole is primarily affected by the cutting edge of a drill bit[21].This phenomenon depends on the cutting tool profile and material.The carbide twist drills[20]are performing comparatively better than any other tools in terms of life and surface damage[22,23].For assessing the machinability of Mg alloys using drilling,the tools are further coated and used[24].During drilling,some left out noticed along the tool periphery in the work piece due to the plastic deformation usually called as burr[25].It has many adverse feature-like minor wounds of assembly labors,inappropriate mating and functional problems[26].Hence,it requires deburring process,which additional increases approximately 20–30% of manufacturing cost[27].Controlling the burr height and thickness during machining itself is a necessary study which is highlighted in the present work.

Multi-criteria decision-making(MCDM)methods are useful resources to offer solutions to decision-making problems,including contrasting and multipurpose goals,both in real life and in professional environments[28,29].These challenges involve a small range of solutions,evidently recognized at the outset of the decision-making process.Each alternative is shown by its success in a variety of parameters.The complexity of a choice-based problem results from the existence of more than one criterion for the determination of alternatives.The approach depends heavily on the desires of the decision-makers(DMs)[30,31].To decide the favorable and unfavorable ideal alternatives from the decision matrix,the Technique for Order Preference by Similarity to Ideal Solution(TOPSIS)method was used[32].The TOPSIS process is applied successfully for the selection of sequential parameters for the drilling process over hybrid polymer matrix composite[33].The combination of CCD-TOPSIS with the surface response method demonstrates its superiority in optimizing process parameters while enhancing the efficiency characteristics of the GFRP marine-grade drilling process[34].The Taguchi is combined with TOPSIS for multi-response optimization of rotary ultrasonic drilling of BK7 concerning taper,chipping width and MRR[35].The process parameters of micro EDM of AISI 304 steel analyzed by the combination of TOPSIS and ANOVA,establishes its efficiency[36].The geometrical characteristics and performance measures are optimized in cryogenically chilled micro EDM drilling process using TOPSIS[37].Solving a multi-response problem in the drilling process,the TOPSIS identified as an effective method and it was applied in cryogenic drilling on Ti-6Al-4V[38].The hole drilling of thermal barrier coated Nickel superalloy C263 using a laser was optimized by TOPSIS[39].The DOE based experimental study used in Fuzzy-TOPSIS methodology,successfully applied to determine the optimized parameters in the laser drilling process[40].

The multi-objective Taguchi and TOPSIS were applied to optimize the process parameters in Carbon Fiber Reinforced Polymer(CFRP)composite polymer and identified the quadratic model using Response Surface Analysis(RSA)[41].Identification of appropriate cutting fluids beneficial for machining operations and increases the productivity,life of the tool and quality of the components.In order to do so,the modified similarity-based method was applied effectively via TOPSIS[42].The different conventional and nonconventional manufacturing processes successfully applied the TOPSIS algorithm for optimizing their process parameter.In addition,this algorithm is very useful in chemical engineering,maintenance engineering and civil engineering[43].Petkovi′c,Madi′c and Radenkovi′c[44]carried out a comparative analysis of the use of Weighted Aggregated Sum Product ASsessment(WASPAS)and COmplex PRoportional ASsessment(COPRAS)in MCDM methods to assist in the identification of the most effective non-conventional machining processes for ceramic machining.Taguchi based COPRAS was presented to identify the optimal combination of parameters in turning operation over stainless steel 304.The COPRAS method is successfully applied to convert the multi-objective into a single objective to carry out the examination[45].Five different normalization procedures evaluated by Yazdani,Jahan and Zavadskas[46]and suggested the superior one.The COPRAS method is applied for finding the best alternative in the drilling process on Al alloy using a solid carbide drill bit with a high-pressure coolant[47].In order to address the shortcomings of the fuzzy AHP methodology,the integration of a stable fuzzy AHP and fuzzy COPRAS was proposed for the machine tool selection.The specification of the consistency ratio(CR)is prevented while the fuzzy linguistic choice relationship is used to incorporate into the AHP.The suggested method of machine tool selection is intended to be conveniently extended[48].The stochastic type of COPRAS is effectively applied for selecting the suitable service provider in the cargo industry[31].

Development of relation between independent and dependent parameters are essential in the case of machining with newer material like Mg AZ91[2].Minimal cutting forces observed in the case of AZ91 when it was assessed with AZ31 during turning operation,however the machining characteristics of AZ alloys during drilling was not described so far[5].Assessment by past researches reveals that,not much research has been done in the Mg alloy during the drilling process through TOPSIS and COPRAS while MCDM is a concern.It is worth looking at the machining behavior of Mg AZ91.This study focuses on the identification of significant aspects through TOPSIS and COPRAS and comparing the ranking with Desirability Function Approach(DFA).Though both the methods are adopted widely in the other machining parameters for optimization,ranking using TOPSIS is based on the relative closeness coefficient and COPRAS is based on utility degree[49].Hence there may be differences with their results that may not be a standard one.Different MCDM tools may result in a different sequence of results that may not be acceptable for generic concern.The novel aspect of this presentstudy is the comparative analysis of two MCDM tools namely TOPSIS and COPRAS for the selection of generic drilling parameters to machine Mg alloys.The complex behavior mechanism was analyzed with the appropriate technical reason.

Fig.1.Methodology.

2.Materials and methods

The methodology employed in the current study is shown in Fig.1.The proposed method begins with an experimental work based on the coded and actual factors as shown in Table 1.The X6323 model ALTO make three axes vertical machining center was used to perform the experimental work.Addison make micro grain solid carbide straight shank twistdrill bit of 6 mm diameter(Jobber series)(IS5101–1991/DIN 338)is used for the drilling process.[Flute length 57 mm,Overall length 93 mm,helix angle 300,point angle 1180].The work material used is Mg AZ91 alloy and the elemental contents are presented in Table 2.To confirm the designation of the selected material,energy dispersive spectroscopy has beenanalyzed as shown in Fig.2.Further,the material properties are confirmed by the basic microstructure,in which the second phase precipitate across the grain boundary can be noted,as shown in Fig.3.The dimensions of the prepared work specimen are 150 mm(L)×70 mm(W)×10 mm(T).The range of machining parameters is decided based on the tool manufacturer’s recommendation and the competency of the machine tool.The different set of independent combinations(17 run)derived based on Box-Behnken Design(BBD)and experimented(Table 3).For each experimental run,drilling time is measured using a stop watch.Before experimentation,the drilling time is calculated based on the basic formula.The ratio of length of workpiece(in mm)with cross product of spindle speed(in rpm)and feed rate(mm/rev.)providing drilling time.However,these values are noticed with larger disparities and the average deviation found larger with 16.687%(with experimental drilling time),which inquisitive to find a superior model.

Table 1Levels and ranges of input parameters.

Table 2Chemical composition of Mg AZ91.

Table 3Number of run versus coded and actual factors(Box-Behnken Design).

Fig.2.Energy Dispersive Spectroscopy report.

Fig.3.SEM images of work piece with(a)200X Magnification(b)500X Magnification.

After the drilling process,the burr height at the entry and exit of the hole is measured using a coordinated measuring machine named HELMEL 80–19(Model 216–142).The measurement of burr height is determined based on the average taken from four values measured over different places of both entry and exit portions respectively.The measurement of burr thickness is done using a digital vernier caliper(Mitutoyo CD 6 CS3).The thickness of the burr is considered as the difference between the external and internal diameter of the projected burr.The roughness of the resulting surface inside the hole is measured in different places using a surface roughness testing machine Mitutoyo SJ 210 and the average is taken for analysis.The responses measured during and after the experiments are presented in Table 4.The complete experimental setup and process flow are illustrated in Fig.4.The determination of entry and exit burr height using CMM,gauging surface roughness using surface roughness tester and the burr development in the workpiece material were illustrated in Fig.5.

Table 4Experimental data.

The objective of this study is to minimize multiple responses as stated above by identifying appropriate spindle speed and feed rate,which is more likely to be a multiresponse optimization problem.Hence to make a decision on this multi-response problem,TOPSIS and COPRAS techniques are incorporated.

3.Result and discussion

3.1.TOPSIS methodology

TOPSIS is an efficient and advanced MCDM methodology,which was first introduced by Hwang and Yoon[50]to obtain the finest choice based on the compromise solution principle.The acceptable solution can be seen as preferring the answer with the shortest route from the favorable ultimate limit and the longest route from the unfavorable ultimate limit[51].

The subsequent procedures are used for choosing the right alternatives using the TOPSIS algorithm[52,53].

Step 1:The identification of essential attributes(dependent and independent parameters)has to be done primary.Generally,the dependent parameters desire maximization considered as most preferable and the dependent parameters wishes minimization reckoned as least preferable.

Surmising the present study,all the parameters are considered are least preferable attribute(for minimization)while none of the parameter considered as a most preferable attribute.Because the diminishing the responses leads to an increase in the productivity and quality of the component.

Step 2:A matrix more often termed as decision matrix used to represent all the information,which has i row(m-alternatives)and j column(n-criteria).

The decision matrix[D17×6]is given in Eq.(1).

Step 3:The following formula[Eq.(2)]is used to determine the elements in the normalized matrixNij[53].

The calculation of normalized data[Eq.(3)]for first and last element is as follows

The calculated normalized decision matrix[N17×6]is presented in Eq.(4).

Step 4:The cross multiplication of individual weight with the respective column of normalized decision matrix will provide weighted normalized decision matrix.

whereWjis the weight criteria andNijis the normalized matrix.The weight(Wj)of each criterion is decided based on the expertise,which is 0.3 for drilling time,surface roughness and for rest it was 0.1.The weighted normalized value W17×6is calculated using Eq.(5)is given as Eq.(6).

The weighted normalized matrix[W17×6]is presented in Eq.(7).

Step 5:Estimation of the positive ultimate solution(A??)and the negative ultimate solution(A?).These are analyzed using following formula,Eq.(8)and Eq.(9):

J=1,2,3,…,n-whereJis related with the benefit criteriaJ’=1,2,3,…,n-whereJ’is related with the cost criteria.The positive ideal solution(A??)is considered based on minimization whereas the unfavorable ideal solution(A?)is reckoned based on maximization.Deeming the present study all the six responses have to be minimized for increasing the productivity and quality of the component.The respective favorable and unfavorable ideal solution are given below[Eq.(10)]

Step 6:The separation measure is obtained using Eq.(11).The same for each preference from the favorable ultimate one is specified by Eq.(12).

Similarly,the unfavorable ultimate one is calculated using Eq.(13)and it is specified by Eq.(14).

Step 7:The relative closeness is examined using Eq.(15)for each alternative and it is described in Eq.(16).

The best alternative is chosen based onCi?value and closeness to ultimate solution.The separation measure of favorable,unfavorable ultimate solution and relative closeness value are presented in Table 5.

Table 5Separation measure of positive,negative ideal solutions and relative closeness value.

Table 6Relative weight,utility degree and its rank.

Fig.4.Experimental setup and process flow.

Step 8:Ranking based on relative closeness value.

According to the calculated results,the complete ranking of the alternative is obtained as 17–16–15–12–13–14–5–7–2–10–6–4–3–8–1–9–11.The optimal experimental design is sequenced as follows 15＞9＞13＞12＞7＞11＞8＞14＞16＞10＞17＞4＞5＞6＞3＞2＞1.It means that the best-combined input is in run 15,and the worst is in run 1.Run 15 has 91.33% relative closeness and run 1 has 33.7% relative closeness.The superior combination to minimize the responses identified in run 15 succeeding to run 9 and 13.The optimal combination was identified with a spindle speed of 4540 rpm and a feed rate of 0.076 mm/rev.Therefore,it is suggested to select the above sequence in order to diminish the manufacturing cost and to enhance the quality of the component.

3.2.COPRAS methodology

Zavadskas,Kaklauskas and Sarka[54]conceived the COPRAS which entails direct and proportional reliance on the importance and usefulness of the alternatives available in the presence of mutually contrasting parameters.COPRAS en-compasses the success of variants in terms of various parameters and related weights by using the step-by-step ranking and determining the system of choice of variants in terms of their relevance and their degree of usefulness.Variety of dynamic decision-making problems COPRAS proposes to take advantage of this approach in the application of engineering[55].The primary benefit of this technique is its ease of use and friendliness.However,when dealing with qualitative metrics and characteristics,it has its drawbacks[56].

Fig.5.Response measurement(a)burr height measurement using CMM(b)surface roughness measurement using SR tester(c)burr development at the tool exit portion(d)sample roughness measurement for run number 9.

The subsequent steps are used for choosing the right alternatives using the COPRAS algorithm[57].

Step 1:Identification of the objective and the significant attributes(same as that of TOPSIS).

Step 2:Representation of decision matrix[Eq.(1)].

Step 3:The following formula[Eq.(17)]is used to calculate the elements in the normalized matrixNij[57].In order to bring the unit free responses,the normalization is essential for comparing them[58].

The calculation of normalized data for first and last element is as follows[Eq.(18)].

Eq.(19)shows the normalized decision matrix[N17×6].The calculated decision matrix correctness can be crosschecked on the following basis.The summation of an individual attribute should be equal to the ratio of unity to the number of runs.Referring Eq.(19),the average of each attribute is 0.0588 is equal to the ratio of unit to number of run(1/17=0.0588).

Step 4:The procedure followed in TOPSIS is same in determining the weighted normalized decision matrix[Eq.(20)],even the same weight is considered in order to keep them constant.

The perceived weighted normalized matrix[W17×6]is given in Eq.(21).

Step 5:Calculation ofPi,which is identified by the summation of attributes those need to be maximized.That is,the summation over the beneficial criteria[59].

In the above Eq.(22),k is the number of responses which necessitate to be maximized.Concerning the current study,none of the attribute has to be maximized;therefore,all thePivalue is equal to zero.

Step 6:Calculation ofRi,which is calculated by the summation of attributes those need to be minimized.That is,the summation over the non-beneficial criteria[59].

In the above formula Eq.(23),(m-k)is the number of responses which required to be lessened.Conceiving the current study,all of the attributes have to be minimized,due to their adverse features.The sample calulation is presented in Eq.(24).

Step 7:Perceiving the diminutive value ofRi[Eq.(25)].

Step 8:Determination of the relative weight of each responsesQi.The relative noteworthy value of a response shows the measure of contentment achieves by that response.The larger is the priority of the alternative is based on the higher value ofQi.The superior selection among the alternatives is based on the largest relative valueQmax[59].

Applying the values calculated through the Eq.(26),Eq.(28)and Eq.(29)in Eq.(27),the relative weight can be calculated,which is presented in Eq.(30).

Rather,Eq.(25)some researcher will follow the following Eq.(31),however both the equation will return the same results.

Step 9:Computation of the optimality criterionQmax

Step 10:Computation of the precedence of the work.The major weight(relative weight of response)Qi,the longer is the primacy(rank)of the work.SurmisingQmax,the agreement degree is the largest.

Step 11:Estimation of the utility degree of each response.The degree of utility of the responses,which assist to a complete ranking of responses,is calculated by evaluating the preferences of all responses with the most effective[Eq.(34)]and can be defined as follows[59]:

From the application of Eq.(31)and Eq.(32),the above one is examined[Eq.(35)].These utility degree values of each alternative vary from 0% to 100%.

Based on the evidence presented on the requirements for the response of the drilling process,reasonable strategies can be sought to increase efficiency and minimize costs.According to the calculated results,the complete ranking of the alternative is obtained as 17–16–15–12–13–14–6–7–2–11–5–3–4–8–1–9–10.The optimal experimental design is sequenced as follows 15＞9＞12＞13＞11＞7＞8＞14＞16＞17＞10＞4＞5＞6＞3＞2＞1.It means that the bestcombined input is in run 15,and the worst is in run 1.Run 15 is the best alternative with 100% utility degree and run 1 is the worst alternative with 44% utility degree(Table 6).The superior combination to minimize the responses identified in run 15 succeeding to run 9 and 12.The optimal combination was identified with a spindle speed of 4540 rpm and a feed rate of 0.076 mm/rev.Therefore,it is suggested to select the above sequence in order to diminish the manufacturing cost and to augment the quality of the component.

Table 7Confirmation test result.

The ranking performance of TOPSIS has greater concurrence with the COPRAS methods.There are 64.71% of ranking coincide with the COPRAS,deeming the higher and lower order it was identical.The 1st,2nd,7th,8th,9th,12th to 17th rankings are the same(Fig.6).Distinguishing ranking was observed for 35.29% of data;however,the sequence is coherent.The significant similarities between the two ranking methods are observed.The computational techniques of the two approaches are simple and easy in terms of recognizing and implementing these methods for comparing the alternatives and choosing the drilling parameters.

Fig.6.Comparison of TOPSIS and COPRAS ranking.

3.3.Modeling through Response Surface Methodology(RSM)

The empirical models have been developed for the present study using BBD[2,3].The coefficient of determination(R2)value obtained for various responses are 99.68,97.64,89.2,94.77,99.57 and 94.13 respectively,seem better the prediction ability of the developed model.The developed individual responses are presented in Eqs.(36)to(41).In the following equation,dtdenotes drilling time,bhenrepresents entry burr height,bhexspecifies exit burr height,btenindicates entry burr thickness,btexdesignates exit burr thickness,srspecifies surface roughness,Ndenotes spindle speed andFrepresents feed rate.

The accordance between the experimental and RSM data is evident from Fig.7.The 17 number of runs are converted into 9 by taking the average in the middle value of the feed rate.Reckoning the BBD,the run 2 and 3 are similar,run 5 and 6 are the same,from 7 to 11 are identical,run 12 and 13 are equal,run 15 and 16 are indistinguishable.Therefore,Fig.7 has a 9 number of runs in the abscissa.Based on the accordance,these empirical models can be applied for the identification of suitable inputs by process planning engineer.Once the superior model is developed,the BBD is further extended to optimization through DFA.The procedure for DFA followed from the past literature[3,60].The result of DFA is greater concurrence with the top rank of TOPSIS and COPRAS.Conceiving Eq.(36),the RSM drilling time is determined,subsequently the average percentage of deviation is calculated with 4.215% which is 3.959 times superior than drilling time(Fig.7a)which is calculated based on basic formula.

3.4.Characterization

The behavior study of the spindle speed and feed rate over all the responses are performed through RSM 3D graph and individual value plot(Fig.8).Considering drilling time(Fig.8a,b),an increase in spindle speed decreases the drilling time at all levels of feed rate.This is because of increasedshearing rate over the material during machining[25,61].The recent study found that,enhancing spindle speed propagating incisaling action.Incisaling action is introduced by the recent work which includes material removal along the shearing action[62].During the lower range of feed rate sudden drop-in drilling time was observed and for a medium and larger range of feed rate,reduction in drilling time is gradual.Increasing feed rate declines drilling time till intermittent range thereafter increases while the spindle speed is in minimal and intermittent range.Till intermittent range of feed rate the augmented dribbling action propagating material removal causes drop-off in drilling time,beyond intermittent range due to the same phenomena the material removal found larger which leads to poor extrusion of chips causes ascent in drilling time.While the spindle speed is high,the amplifying feed rate lessens drilling time that too with plodding way.The combination of minor spindle speed and minor feed rate produces larger drilling time and on the other hand shorter drilling time identified at the combination of major spindle speed and major feed rate.

Fig.7.Validation of experimental results for various responses(a)drilling time(b)entry burr height(c)exit burr height(d)entry burr thickness(e)exit burr thickness(f)surface roughness.

Fig.8.Spindle speed versus feed rate on various responses(a)Drilling time:3D graph(b)Drilling time:Individual value plot(c)Entry burr height:3D graph(d)Entry burr height:Individual value plot(e)Exit burr height:3D graph(f)Exit burr height:Individual value plot(g)Entry burr thickness:3D graph(h)Entry burr thickness:Individual value plot(i)Exit burr thickness:3D graph(j)Exit burr thickness:Individual value plot(k)Surface roughness:3D graph(l)Surface roughness:Individual value plot.

Fig.8.Continued

In view of entry burr height(Fig.8c & d),entry burr thickness(Fig.8g & h),exit burr thickness(Fig.8i & j)and surface roughness(Fig.8k & l),the spindle speed has a sinusoidal relation and larger is the spindle speed shorter is the entry burr height till 1960 rpm thereafter matures till 3680 rpm;beyond this point,the response condenses.This occurrence is found in all ranges of feed rate.Increase in spindle speed till 1960 rpm increases incisaling rate causes minimal responses,thereafter further increase in incisaling rate increases more material removal results in lack of room for movement of chips and consequences larger responses.Once,it reaches 3680 rpm,due to higher centrifugal material ejection the chips are thrown away from the base material causes lesser responses.Type of chip generated during perforation process has a significant role in the response behavior pattern[16,61].Types of chips reported in the past study[63]are ribbon type,tubular type,cork screw type,helical type,spiral type,arc type,elemental type and needle type.All these types are in three different form and they are short,long and snarled.Concerning the present study,chips are identified with elemental type,short and snarled helical type.Feed rate has erratic relation over the responses[other than drilling time and exit burr height].For the lower and middle range of spindle speed;the longer is the feed rate,the shorter is the responses.This could be because of high temperature generation due to faster tool penetration which leads to thermal softening resulting minimal response[64].For the higher range of spindle speed;lengthening the feed rate shrinkages the response till the middle range thereafter extends.When both the independent are high,due to the increased tool vibration and wobbling the chips are left around the periphery even it has larger material ejection and higher thermal softening.It has greater concurrence with the past study[65],due to high heat distribution on surface causes shorter chips which left around the periphery.Least responses are observed during the lower spindle speed(1960 rpm)at different feed rate and greater responses are noticed at higher spindle speed(3680 rpm)at any ranges of feed rate.The minimal entry burr height(Fig.8d)observed in the combination of higher speed and medium feed,larger entry burr height attained in the lower speed and feed.The arrangement of diminutive independents are producing least entry burr thickness(Fig.8h)and it was largest when those independents are maximal.The mixture of intermittent speed and higher feed produced minimal exit burr thickness(Fig.8j).The minimal surface roughness(Fig.8l)observed in the amalgamation of higher speed and lower feed.These two responses(exit burr thickness and surface roughness)are found larger with lower speed and intermittent feed.

For all ranges of spindle speed;increase in feed rate,decreases exit burr height till medium range,later increases(Fig.8e & f).This could be due to high temperature generation due to faster tool penetration which leads to thermal softening resulting minimal exit burr height till intermittent feed range,subsequently due to the amplified frictional force among workpiece material and drill bit causing deficient strain,due to which breaking of chips decreased and resulted in retentive burrs at exit of holes[64].The poorer exit burr height is produced during all ranges of the spindle speed at medium feed rate and greater exit burr height is produced by all ranges of the spindle speed and lower range of feed rate.Burr generation found minimal at entry side when it was evaluated with exit side.Initially shearing noticed due to plastic deformation,when drill bit penetrates in the material with chisel edge followed by cutting lip and peripheral cutting edge[66].Till cutting tool engages with workpiece,it produces elemental chips and fan chips which ousted at the top surface causes minimal burr height and thickness.Once,it engages with the workpiece surface,sheared material starts to move through flute and some chips are left with the periphery causing noticeable burr height and thickness in the entry side.The thin lamina of material is bent and exiled when drill bit near the bottom due to tearing[67].Due to negligible shearing and ousting,the chips are left around the periphery causing higher burr height and thickness in the exit side.

3.5.Confirmation test

To verify the enhancement of the output characteristics,validation test has been carried out of the drilling process with an optimum combination of parameters.Based on TOPSIS,COPRAS and DFA,the optimal drilling independents is found at experiment number 15 with the spindle speed of 4540 rpm and a feed rate of 0.076 mm/rev.With these suggested independents,the confirmation test carried out with three trails and the average value taken for evaluation.The results of the confirmation test are presented in Table 7.Theconfirmation test results are concurrent with the initial values having an error percent of 4.622,confirms the validation of suggested inputs.

4.Conclusion

In the current study TOPSIS and COPRAS algorithms are applied for multi-objective optimization to determine the superior amalgamation of drilling parameters such as spindle speed and feed rate for simultaneous minimization of all the responses while drilling Mg AZ91 with carbide tools.

·The TOPSIS method is worn to choose the greatest arrangement of drilling parameters.Based on the value of relative closeness,the responses are sorted as follows:17–16–15–12–13–14–5–7–2–10–6–4–3–8–1–9–11.The optimal experimental design is sequenced as follows 15＞9＞13＞12＞7＞11＞8＞14＞16＞10＞17＞4＞5＞6＞3＞2＞1.

·The same arrangement based on COPRAS is as follows:17–16–15–12–13–14–6–7–2–11–5–3–4–8–1–9–10.The optimal experimental design is sequenced as follows 15＞9＞12＞13＞11＞7＞8＞14＞16＞17＞10＞4＞5＞6＞3＞2＞1.

·From both the algorithm,the best-combined input is observed in run 15,and the worst is observed in run 1.The sequencing performances of TOPSIS and COPRAS methods are identical.

·The optimal arrangement identified based on TOPSIS and COPRAS of drilling independent for simultaneous minimization of all the responses are identified with a spindle speed of 4540 rpm and feed rate of 0.076 mm/rev.The same process parameter identified as optimum input through DFA.

·The result of the confirmation test validates the proposed independent parameter with minimal error percentage.

·The empirical model is developed with a higher reliability measure through BBD[Eqs.(36)to(41)],which can be applied for finding the independents without experimentation.

·For drilling time,a superior mathematical model was established that is 3.959 times more accurate than the standard model drilling time.

·The rate of incisaling found larger with an addition of spindle speed causes larger material removal rate,resulting drilling in a faster rate.Poor extrusion of chips making the process time consuming.Centrifugal material ejection found with larger speed is the reason for minimal responses in general.

·Dribbling action found with feed rate influencing on material removal,extending the study with lack of room for movement of chips affecting response.Faster tool penetration found with larger feed rate resulting minimal responses.

·The experiment can be done at a faster rate with a higher combination of both the response.The lower combination of both the responses produces minimal entry burr thickness.The combination of lower spindle speed with a higher feed rate produces entry burr height in a minimal way.

·The higher surface quality components achieved through the mixture of higher spindle speed with a lower feed rate.The intermittent spindle speed associated with a higher feed rate minimizes the exit burr height and exit burr thickness.

The effect of process parameters of drilling parameters using coated tools is not considered in the present work,might be worth some investigation.Two different process input parameters alone considered in the present investigation.Inclusion of other parameters like material thickness,drill diameter,drill bit point angle,drill type,cutting fluid may enhance the rate of prediction.The responses considered are also limited.Consideration of thrust force,torque,material removal rate,tool wear and study of chip formation would be a good extension.