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

Sunil Kumar; Saikat Ranjan Maity; Lokeswar Patnaik

doi:10.3934/jimo.2022061

Article Contents

2023, Volume 19, Issue 4: 2676-2703. Doi: 10.3934/jimo.2022061

This issue Previous Article Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in Hilbert spaces Next Article Asset prices with investor protection and past information

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

1.
Department of Mechanical Engineering, National Institute of Technology Silchar, Assam- 788 010, Inida
2.
School of Mechanical Engineering, Sathyabama Institute of Science and Technology (Deemed to be University), Chennai - 600119, Tamil Nadu, India

^*Corresponding author: Saikat Ranjan Maity
^*Corresponding author: Saikat Ranjan Maity

Received: November 2021

Revised: March 2022

Early access: April 2022

Published: April 2023

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Abstract

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.

Keywords:

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

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

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Figure 3. Algorithm of the proposed methodology

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

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

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

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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

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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

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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

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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

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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

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Table 6. Experimental results (initial decision matrix)

Experimental run (Alternative, WP)	Wear parameters				Wear responses (Criteria, WR)
Experimental run (Alternative, WP)	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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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

Alternative	Wear parameters			Wear responses (Criteria)
Alternative	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

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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

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

Alternative	Wear parameters			Wear responses (Criteria)
Alternative	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

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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

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

Alternative	Wear parameters			Wear responses (Criteria)
Alternative	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

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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

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References

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