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A novel BWM integrated MABAC decision-making approach to optimize the wear parameter of CrN/TiAlSiN coating

  • *Corresponding author: Saikat Ranjan Maity

    *Corresponding author: Saikat Ranjan Maity 
Abstract Full Text(HTML) Figure(6) / Table(22) Related Papers Cited by
  • Using a multi-criteria decision-making (MCDM) method combined with a Taguchi ($ L_{16} $) design of experiment, the wear parameter for CrN/TiAlSiN coated hardened DAC-10 tool steel is optimized. Temperature, sliding velocity, applied load, and sliding distance together forms the wear parameter. Wear rate, friction coefficient, surface roughness, wear depth, and worn surface hardness were all tested to see how it affected by the wear parameters. The criteria weight was derived using the best-worst method (BWM) and combined with the Multi-Attributive Border Approximation area Comparison (MABAC) approach to rank the alternatives. The obtained data were then subjected to sensitivity testing using three-phase techniques. The suggested MCDM technique was validated through all phases of sensitivity analysis, with alternative $ {WP}_6 $ (T = 100 $ ^{\circ} $C, Sv = 0.05 m/s, L = 5 N, and Sd = 2000 m) showing as the best alternative. Furthermore, the proposed method BWM-MABAC was tested on previously published outcomes, and the results showed an excellent correlation between present and past studies, with a rank correlation coefficient value of greater than 0.99.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:

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  • Figure 1.  (a) Cross-sectional FE-SEM micrograph and (b) corresponding line EDS of CrN/TiAlSiN coating

    Figure 2.  Representation of $ G_- $, G and $ G_+ $

    Figure 3.  Algorithm of the proposed methodology

    Figure 4.  Sensitivity analysis of BWM-MABAC method using criteria weight change

    Figure 5.  Effect of dynamic matrices on the ranking of MABAC method

    Figure 6.  Comparison between proposed MABAC and other developed MCDM methods

    Table 1.  Literature review

    Author
    (Year)
    Materials Optimization Technique Process parameter Wear responses
    Kaushik et al. (2018)[21] AA6063/SiCp composites Taguchi integrated GRA-PCA Applied Load, Sliding distance and Weight percentage of SiC Wear rate, Frictional force and specific wear rate
    Stalin et al. (2018) [65] AA6063-Si3N4 composite Taguchi Load, Weight percentage of reinforcement, Sliding velosity and distance Wear rate
    Singh et al. (2018) [63] Phyllanthus Emblica seeds oilbased lubricants Response surface methodology (RSM) Blend ratio, Load and Sliding velosity Specific wear rate and CoF
    Singh et al. (2018) [62] AA6082-T6/ TiB2 composites RSM Reinforcement, Sliding speed, Load and Sliding distance Wear
    Prakash et al. (2018) [51] (413/B4C) composites Integrated Taguchi with Gray relational analysis Reinforcement, Sliding speed, Load and Sliding distance Specific wear rate and CoF
    Aliyu et al. (2020) [2] UHMWPE composites Taguchi SiC loading, Consolidation pressure and Holding time Specific wear rate
    Suresha et al. (2019) [66] Polyaryletherketone composites Taguchi Noramal load, Filler content and Sliding velosity and distance Specific wear rate and CoF
    Stalin et al. (2019) [64] Aluminium composites ANN integrated teaching learningbased optimization algorithm Reinforcement, Sliding speed, Load and Sliding distance Wear rate
    Gajalakshmi et al. (2019) [14] Aluminium alloy (AA6026) hybrid GRA with a RSM Load, Speed of pin and Track diameter Wear, CoF and Frictional force
     | Show Table
    DownLoad: CSV

    Table 2.  Literature review (continue)

    Author
    (Year)
    Materials Optimization Technique Process parameter Wear responses
    Ming-Der et al. (2020) [37] Zr doped DLC coating The GAANFIS method Bias, Pulse frequency, CH4, Sputtering distance and C/Ze current Wear rate
    Sahoo (2009) [57] Ni-P coating Taguchi Bath temperature, Concentration of reducuing agent, Concentration of rource of nickel and Annealing temperature Wear depth
    Baradeswaran et al. (2013) [4] Al-Al2O3 composites Taguchi integrated with RSM Applied load and Sliding distnace Wear mass loss and CoF
    Rana et al. (2014) [53] AA5083/10 Wt. Sicp composite Taguchi Load, Sliding speed and distance Wear rate
    Baradeswaran et al. (2014) [5] Aluminium and B4C composites RSM Load, Sliding speed and distance Wear mass loss
    Chang et al. (2015) [11] UHMWPE composites RSM Filler loading, Applied load and Sliding speed Wear rate and CoF
    Saravanan et al. (2015) [60] TiN coating RSM Load, Sliding velosity and distance Wear mass loss and CoF
    Saravanan et al. (2016) [59] TiN coating RSM Load, Sliding velosity and distance Wear mass loss, CoF, Ra, Wear depth and Hardness
     | Show Table
    DownLoad: CSV

    Table 3.  Literature review (continue)

    Author
    (Year)
    Materials Optimization Technique Process parameter Wear responses
    Saravanan et al. (2016) [58] ${\gamma}$-irradiated Ti alloy against TiN coating RSM Load, Sliding velosity and distance Wear mass loss of TiN coating and counterbody
    Girish et al. (2016) [15] Hybrid metal matrix composite (Magnesium alloyAZ91) Taguchi Composition, Sliding velosity and distance Wear rate
    Achuthamenon Sylajakumari et al. (2018) [1] AA6063/ SiC composites Taguchi Load, Sliding speed and distance CoF and Wear rate
    Natrayan et al. (2020) [38] AA6061/ Al2O3/ SiC composite Taguchi Load, Sliding speed and distance Wear rate and CoF
    Sathish et al. (2019) [61] Mg-(5.6Ti +3Al)2.5B4C composites Taguchi Load, Sliding velosity and distance Wear rate
    Bramaramba et al. (2020) [8] Ferritic ductile cast iron Taguchi Load, Time, Grade and Heat treatment Wear mass loss and Hardness
    Premnath (2020) [50] Al-SiC nanocomposites Desirability approach Number of passes, Rotationa a nd Transverse speed Tensile strength, Microhardness and Wear loss
    Rajmohan et al. (2020) [52] Magnesiumsilicon composites Grey-Fuzzy algorithm integrated with Taguchi Load, Speed, Distance and Weight of SiC Wear rate and CoF
     | Show Table
    DownLoad: CSV

    Table 4.  Literature review (continue)

    Author
    (Year)
    Materials Optimization Technique Process parameter Wear responses
    Khatkar et al. (2021) [22] AZ91D-SiC -Gr composites Taguchi SiC and Graphite percentage, ]Applied load, Sliding speed and distance Wear rate
    Rao et al. (2021) [55] Al6061/WC composites A hybrid Gray relational analysis integrated with teaching learningbased optimization Volumetric percentage of WC, Load, Sliding velosity and distance Wear rate and CoF
    Kumar et al. (2021) [30] Cr-(CrN/ TiN) coating Taguchi Load, Sliding velosity and distance and Coolant type Ra, CoF and Wear mass loss
    Patnaik et al. (2021) [40] AlCrN coating RSM Load, Sliding velosity and distance Ra, CoF, Disc mass loss, Wear depth and Hardness
    Patnaik et al. (2021) [41] Silver alloyed a-C coating RSM Load, Sliding velosity and distance Ra, CoF, Disc mass loss, and Hardness
    Kumar et al. (2021) [31] TiAlN coating RSM Cutting speed, Feed rate and Depth of cut Ra and Tool wear rate
     | Show Table
    DownLoad: CSV

    Table 5.  Wear parameters and its levels

    Wear parameter Symbol Level Value
    Temperature (in $ ^{\circ} $C) T 4 25,100,200,300
    Sliding velocity (in m/s) $ S_v $ 4 0.01, 0.05, 0.1, 0.15
    Applied load (in N) L 4 5, 10, 15, 20
    Sliding distance (in m) $ S_d $ 4 500, 1000, 1500, 2000
     | Show Table
    DownLoad: CSV

    Table 6.  Experimental results (initial decision matrix)

    Experimental run
    (Alternative, WP)
    Wear parameters Wear responses (Criteria, WR)
    T $S_v$ L $S_d$ ${WR}_1$ (WR, × ${10}^{-8}$ ${mm}^3Nm^{-1}$) ${WR}_2$ (CoF) ${WR}_3$ (Ra, μm) ${WR}_4$ (WD, μm) ${WR}_5$ (Hv)
    ${WP}_1$ 25 0.01 5 500 8.45 0.58 7.8 2.71 1746
    ${WP}_2$ 25 0.05 10 1000 8.31 0.56 7.1 2.87 1698
    ${WP}_3$ 25 0.1 15 1500 9.71 0.55 6.7 2.98 1648
    ${WP}_4$ 25 0.15 20 2000 10.89 0.53 5.9 3.68 845
    ${WP}_5$ 100 0.01 10 1500 6.71 0.49 5.1 0.73 2576
    ${WP}_6$ 100 0.05 5 2000 5.67 0.51 5.4 0.67 2781
    ${WP}_7$ 100 0.1 20 500 6.77 0.56 7.3 1.63 2409
    ${WP}_8$ 100 0.15 15 1000 7.2 0.52 6.4 0.84 2384
    ${WP}_9$ 200 0.01 15 2000 8.54 0.46 3.9 1.47 2127
    ${WP}_{10}$ 200 0.05 20 1500 8.24 0.57 7.5 2.14 1898
    ${WP}_{11}$ 200 0.1 5 1000 6.72 0.59 8.1 0.89 2317
    ${WP}_{12}$ 200 0.15 10 500 7.83 0.61 8.7 0.98 2235
    ${WP}_{13}$ 300 0.01 20 1000 9.37 0.64 8.9 3.37 1107
    ${WP}_{14}$ 300 0.05 15 500 8.71 0.68 9.1 2.93 1283
    ${WP}_{15}$ 300 0.1 10 2000 9.12 0.67 8.7 3.29 997
    ${WP}_{16}$ 300 0.15 5 1500 8.5 0.65 8.4 2.79 1321
     | Show Table
    DownLoad: CSV

    Table 7.  Pairwise comparison vector for best to other criteria

    Best to Others $ {WR}_1 $ $ {WR}_2 $ $ {WR}_3 $ $ {WR}_4 $ $ {WR}_5 $
    Best criteria: Wear rate ($ {WR}_1 $) 1 2 7 5 3
     | Show Table
    DownLoad: CSV

    Table 8.  Pairwise comparison vector for other to worst criteria

    Others to the worst criteria Worst criteria: Surface roughness (Ra)
    ${WR}_1$ 8
    ${WR}_2$ 4
    ${WR}_3$ 1
    ${WR}_4$ 3
    ${WR}_5$ 5
     | Show Table
    DownLoad: CSV

    Table 9.  Weight of criteria and inconsistency rate

    Criteria $ {WR}_1 $ $ {WR}_2 $ $ {WR}_3 $ $ {WR}_4 $ $ {WR}_5 $
    Weights 0.427 0.253 0.050 0.101 0.169
    Ksi* 0.07
     | Show Table
    DownLoad: CSV

    Table 10.  Normalized decision matrix

    Alternative $ {WR}_1 $ $ {WR}_2 $ $ {WR}_3 $ $ {WR}_4 $ $ {WR}_5 $
    $ {WP}_1 $ 0.467 0.455 0.250 0.322 0.465
    $ {WP}_2 $ 0.494 0.545 0.385 0.269 0.441
    $ {WP}_3 $ 0.226 0.591 0.462 0.233 0.415
    $ {WP}_4 $ 0.000 0.682 0.615 0.000 0.000
    $ {WP}_5 $ 0.801 0.864 0.769 0.980 0.894
    $ {WP}_6 $ 1.000 0.773 0.712 1.000 1.000
    $ {WP}_7 $ 0.789 0.545 0.346 0.681 0.808
    $ {WP}_8 $ 0.707 0.727 0.519 0.944 0.795
    $ {WP}_9 $ 0.450 1.000 1.000 0.734 0.662
    $ {WP}_10 $ 0.508 0.500 0.308 0.512 0.544
    $ {WP}_11 $ 0.799 0.409 0.192 0.927 0.760
    $ {WP}_12 $ 0.586 0.318 0.077 0.897 0.718
    $ {WP}_13 $ 0.291 0.182 0.038 0.103 0.135
    $ {WP}_14 $ 0.418 0.000 0.000 0.249 0.226
    $ {WP}_15 $ 0.339 0.045 0.077 0.130 0.079
    $ {WP}_16 $ 0.458 0.136 0.135 0.296 0.246
     | Show Table
    DownLoad: CSV

    Table 11.  Weighted normalized decision matrix

    Alternative $ {WR}_1 $ $ {WR}_2 $ $ {WR}_3 $ $ {WR}_4 $ $ {WR}_5 $
    $ {WP}_1 $ 0.627 0.368 0.062 0.134 0.247
    $ {WP}_2 $ 0.638 0.391 0.069 0.129 0.243
    $ {WP}_3 $ 0.524 0.403 0.073 0.125 0.239
    $ {WP}_4 $ 0.427 0.426 0.080 0.101 0.169
    $ {WP}_5 $ 0.769 0.472 0.088 0.201 0.320
    $ {WP}_6 $ 0.854 0.449 0.085 0.203 0.338
    $ {WP}_7 $ 0.764 0.391 0.067 0.170 0.305
    $ {WP}_8 $ 0.729 0.437 0.075 0.197 0.303
    $ {WP}_9 $ 0.619 0.506 0.099 0.176 0.281
    $ {WP}_10 $ 0.644 0.380 0.065 0.153 0.261
    $ {WP}_11 $ 0.768 0.357 0.059 0.195 0.297
    $ {WP}_12 $ 0.677 0.334 0.053 0.192 0.290
    $ {WP}_13 $ 0.551 0.299 0.052 0.112 0.192
    $ {WP}_14 $ 0.605 0.253 0.050 0.127 0.207
    $ {WP}_15 $ 0.572 0.265 0.053 0.114 0.182
    $ {WP}_16 $ 0.623 0.288 0.056 0.131 0.210
     | Show Table
    DownLoad: CSV

    Table 12.  Border approximation area matrix (BAA)

    Criteria $ {WR}_1 $ $ {WR}_2 $ $ {WR}_3 $ $ {WR}_4 $ $ {WR}_5 $
    G 0.641 0.369 0.067 0.150 0.250
     | Show Table
    DownLoad: CSV

    Table 13.  Distance of alternative from BAA

    Alternative $ {WR}_1 $ $ {WR}_2 $ $ {WR}_3 $ $ {WR}_4 $ $ {WR}_5 $
    $ {WP}_1 $ -0.014 -0.001 -0.004 -0.016 -0.003
    $ {WP}_2 $ -0.003 0.022 0.002 -0.021 -0.007
    $ {WP}_3 $ -0.117 0.034 0.006 -0.025 -0.011
    $ {WP}_4 $ -0.214 0.057 0.014 -0.048 -0.081
    $ {WP}_5 $ 0.128 0.103 0.021 0.051 0.070
    $ {WP}_6 $ 0.213 0.080 0.018 0.053 0.088
    $ {WP}_7 $ 0.123 0.022 0.000 0.021 0.055
    $ {WP}_8 $ 0.088 0.068 0.009 0.047 0.053
    $ {WP}_9 $ -0.021 0.137 0.033 0.026 0.031
    $ {WP}_10 $ 0.003 0.011 -0.002 0.003 0.011
    $ {WP}_11 $ 0.127 -0.012 -0.007 0.045 0.047
    $ {WP}_12 $ 0.037 -0.035 -0.013 0.042 0.040
    $ {WP}_13 $ -0.089 -0.070 -0.015 -0.038 -0.058
    $ {WP}_14 $ -0.035 -0.116 -0.017 -0.023 -0.043
    $ {WP}_15 $ -0.069 -0.104 -0.013 -0.035 -0.068
    $ {WP}_16 $ -0.018 -0.081 -0.010 -0.018 -0.040
     | Show Table
    DownLoad: CSV

    Table 14.  Criteria function and ranking of alternative

    Alternative Criteria function ($ S_i $) Rank
    $ {WP}_1 $ -0.038 10
    $ {WP}_2 $ -0.006 9
    $ {WP}_3 $ -0.113 11
    $ {WP}_4 $ -0.273 15
    $ {WP}_5 $ 0.373 2
    $ {WP}_6 $ 0.452 1
    $ {WP}_7 $ 0.222 4
    $ {WP}_8 $ 0.266 3
    $ {WP}_9 $ 0.205 5
    $ {WP}_10 $ 0.026 8
    $ {WP}_11 $ 0.201 6
    $ {WP}_12 $ 0.071 7
    $ {WP}_13 $ -0.270 14
    $ {WP}_14 $ -0.234 13
    $ {WP}_15 $ -0.289 16
    $ {WP}_16 $ -0.168 12
     | Show Table
    DownLoad: CSV

    Table 15.  Different Scenario of criteria weight for sensitivity analysis

    Scenarios Criteria weight
    $ {WR}_1 $ $ {WR}_2 $ $ {WR}_3 $ $ {WR}_4 $ $ {WR}_5 $
    S1 0.500 0.125 0.125 0.125 0.125
    S2 0.125 0.500 0.125 0.125 0.125
    S3 0.125 0.125 0.500 0.125 0.125
    S4 0.125 0.125 0.125 0.500 0.125
    S5 0.125 0.125 0.125 0.125 0.500
    S6 0.200 0.200 0.200 0.200 0.200
     | Show Table
    DownLoad: CSV

    Table 16.  Value of Spearman's rank correlation coefficient between MCDM methods

    MCDM methods MABAC TOPSIS MOORA VIKOR TODIM WASPAS
    MABAC 1.000 0.974 0.973 0.974 1.000 0.977
    TOPSIS 0.974 1.000 1.000 1.000 1.000 0.997
    MOORA 0.973 1.000 1.000 1.000 1.000 0.997
    VIKOR 0.974 1.000 1.000 1.000 1.000 0.997
    TODIM 1.000 1.000 1.000 1.000 1.000 0.997
    WASPAS 0.977 0.997 0.997 0.997 0.997 1.000
     | Show Table
    DownLoad: CSV

    Table 17.  Initial decision matrix for selection of optimal wear parameters for AlCrN coated stainless steel [49]

    Alternative Wear parameters Wear responses (Criteria)
    Load Sliding velocity Sliding distance Ra, in $\mu$m CoF Disc mass loss (Ml, in mg) WD (Wd-, in $\mu$m) Microhardness (Hv)
    ${WP}_1$ 10 10 2000 1.5 0.27 52.8 5 1441
    ${WP}_2$ 15 20 1000 3.6 0.58 39.7 4.6 421
    ${WP}_3$ 10 30 1000 6.6 0.76 22.5 1.2 902
    ${WP}_4$ 10 10 1000 2.2 0.4 21.8 2.8 1201
    ${WP}_5$ 15 30 1500 5.8 0.63 48 4.9 274
    ${WP}_6$ 15 20 2000 3.1 0.44 67.8 8.6 335
    ${WP}_7$ 10 20 1500 2.7 0.52 20.4 2.9 1007
    ${WP}_8$ 10 30 2000 5.7 0.64 27 3.3 821
    ${WP}_9$ 15 10 1000 1.3 0.26 64.1 8.4 651
    ${WP}_10$ 5 30 1000 6.9 0.73 9.7 1.5 1435
    ${WP}_11$ 5 20 2000 4.2 0.6 17.6 2.2 1777
    ${WP}_12$ 10 20 1500 2.7 0.52 21.3 3.1 994
    ${WP}_13$ 5 10 1500 2.6 0.38 19.4 1.8 2021
    ${WP}_14$ 5 20 1000 5 0.65 6.9 1.1 1549
    ${WP}_15$ 10 20 1500 2.8 0.49 21.3 3.1 1001
     | Show Table
    DownLoad: CSV

    Table 18.  Criteria function and ranking of alternative

    Alternative Criteria function ($ S_i $) Rank
    $ {WP}_1 $ 0.0594 9
    $ {WP}_2 $ -0.1347 12
    $ {WP}_3 $ -0.0636 11
    $ {WP}_4 $ 0.1960 4
    $ {WP}_5 $ -0.2922 14
    $ {WP}_6 $ -0.3116 15
    $ {WP}_7 $ 0.1324 5
    $ {WP}_8 $ -0.0609 10
    $ {WP}_9 $ -0.1414 13
    $ {WP}_10 $ 0.0971 8
    $ {WP}_11 $ 0.2010 3
    $ {WP}_12 $ 0.1233 7
    $ {WP}_13 $ 0.3284 1
    $ {WP}_14 $ 0.2114 2
    $ {WP}_15 $ 0.1288 6
     | Show Table
    DownLoad: CSV

    Table 19.  Initial decision matrix for selection of optimal wear parameters for DLC coated tungsten carbide [78]

    Alternative Wear parameters Wear responses (Criteria)
    Depth of cut (DoC, in mm) Cutting speed (Vc, in m/min) Feed rate (f, in mm /rev) Temperature in cutting zone (Tc, in $^{\circ}$C) Ra, in $\mu$m Flank wear (Wf, in $\mu$m)
    ${WP}_1$ 0.375 480 0.125 72.8 0.565 96.25
    ${WP}_2$ 0.375 600 0.25 80 0.491 100.67
    ${WP}_3$ 0.375 720 0.375 79.6 0.64 113.33
    ${WP}_4$ 0.635 480 0.25 79.3 0.389 85.33
    ${WP}_5$ 0.635 600 0.375 133.6 0.558 86.25
    ${WP}_6$ 0.635 720 0.125 112.2 0.319 94.25
    ${WP}_7$ 0.895 480 0.375 160.4 0.482 96.25
    ${WP}_8$ 0.895 600 0.125 167.7 0.46 103.75
    ${WP}_9$ 0.895 720 0.25 202 0.467 115.42
     | Show Table
    DownLoad: CSV

    Table 20.  Criteria function and ranking of alternative

    Alternative Criteria function ($S_i$) BWM-MABAC Ranking TOPSIS Ranking [78]
    ${WP}_1$ 0.040 3 4
    ${WP}_2$ 0.032 4 3
    ${WP}_3$ -0.143 8 5
    ${WP}_4$ 0.408 1 1
    ${WP}_5$ 0.007 5 6
    ${WP}_6$ 0.379 2 2
    ${WP}_7$ -0.064 7 7
    ${WP}_8$ 0.006 6 8
    ${WP}_9$ -0.381 9 9
     | Show Table
    DownLoad: CSV

    Table 21.  Initial decision matrix for selection of optimal wear parameters for AA6063/SiCp composite [31]

    Alternative Wear parameters Wear responses (Criteria)
    Load (L, in N) Sliding distance ($S_d$, in m) Wt ($\%$) of SiC Wear rate (WR, in $10^{-3}$ ${mm}^3/m$) Frictional force (FF, in N) Specific wear rate (SWR, in $10^{-3}$ ${mm}^3/m$)
    ${WP}_1$ 20 523 3.5 11.03 12.01 0.5515
    ${WP}_2$ 20 1046 7 4.486 3.56 0.2243
    ${WP}_3$ 20 1570 10.5 2.83 2.15 0.1415
    ${WP}_4$ 30 523 7 9.311 4.15 0.3103
    ${WP}_5$ 30 1046 10.5 5.194 8.17 0.1731
    ${WP}_6$ 30 1570 3.5 5.34 13.22 0.178
    ${WP}_7$ 40 523 10.5 10.016 17.56 0.2504
    ${WP}_8$ 40 1046 3.5 7.58 19.05 0.1895
    ${WP}_9$ 40 1570 7 5.427 6.61 0.1356
     | Show Table
    DownLoad: CSV

    Table 22.  Criteria function and ranking of alternative

    Alternative Criteria function ($S_i$) BWM-MABAC Ranking GRA-PCA Ranking [31]
    ${WP}_1$ 0.168 9 9
    ${WP}_2$ 0.941 2 3
    ${WP}_3$ 1.133 1 1
    ${WP}_4$ 0.521 7 7
    ${WP}_5$ 0.912 4 4
    ${WP}_6$ 0.876 5 5
    ${WP}_7$ 0.463 8 8
    ${WP}_8$ 0.681 6 6
    ${WP}_9$ 0.933 3 2
     | Show Table
    DownLoad: CSV
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