# Multi-Response Optimization of Surface Grinding Process Parameters of AISI 4140 Alloy Steel Using Response Surface Methodology and Desirability Function under Dry and Wet Conditions

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## Abstract

**:**

## 1. Introduction

- Experimentally investigation the influence of the input machining parameters (cross-feed, workpiece velocity, wheel velocity, and the depth of cut) on three responses (contact temperature, material removal rate (MRR), and machining cost) during surface grinding of AISI 4140 steel.
- Establishment of an empirical equation of each output responses in terms of input parameters based on the experimental data. Further this mathematical model is used to predict the output responses.
- Optimization of the output responses (minimum contact temperature, maximum MRR, and minimum machining cost) based on the DFA methodology. Further, optimal set of input parameters are investigated for these optimal responses.

## 2. Methodology and Experimental Procedures

#### 2.1. Materials and Instruments

^{3}. Single nozzle open metal-tube type was used to apply coolant at a flow rate 5 L/min. Flow rate was measured with Z-5615 Panel Flowmeter (Emerson Electric Limited, Rayong, Thailand).

#### 2.2.1. Experimental Set Up

^{4}× 5 = 80) was applied to run 80 experiments for this research work. Figure 2b shows the multilevel full factorial design of the design of experiments (DOE) applied to conduct experiments. Detailed calculations of the DOE are presented in the Supplementary Materials.

#### 2.2.2. Material Removal Rate (MRR) Calculation

- MRR is the material removal rate (mm
^{3}/min) - v
_{w}is the workpiece velocity or longitudinal table travel velocity (m/min) - a
_{p}is the depth of cut (mm) - b is the width of the cut (mm).

#### 2.2.3. Response Surface Methodology

_{0}, b

_{i}, b

_{ii}, and b

_{ij}) were calculated, based on the least-squares method [44].

#### 2.2.4. Desirability Function Approach

- X
_{i}—input variables value for i in the experiment, I = 1, 2,…, m.

## 3. Results and Discussions

## 4. Conclusions

- The wet condition dominates the overall desirability when the temperature is given the highest (≥20%) weightage. As our optimization goal was minimum temperature, the obtained result is as expected. Since the wet conditions keep the temperature down, the obtained result is achieved so. Again, in current scenario, cross-feed, wheel velocity, and depth of cut were at the lowest levels as a higher value of these parameter increases the amount of material removal per pass leading to increased temperature.
- Dry condition achieves the highest overall desirability if the cost is given the highest priority instead. As the optimization goal was minimum cost, the obtained result is as expected. The underlying reason of the obtained result is no use of cutting fluid in the dry condition, hence cost is reduced. However, in the wet condition, cost is added due to cost of cutting fluid and extra power consumption. Again, in the current scenario, except depth of cut and wheel velocity, all other input parameters are at their upper limit. This provides a higher material removal leading to short machining time and reduced cost. However, depth of cut and wheel velocity at its upper limit provides larger power consumption which in turn increases cost. Thus, depth of cut and wheel velocity was kept at the lowest level.
- If MRR is given priority (20:40:40), i.e., quick material removal, then all the input parameters are set at their highest level along with the wet machining condition. Larger MRR require higher cross-feed, depth of cut, wheel velocity, and higher workpiece velocity. Due to higher MRR, quick removal of chips is required which is very effective with wet machining condition. The obtained result exists at two levels of wheel velocity (15 and 25 m/s). At higher wheel velocity, grinding zone temperature is higher, which is expected. However, it may lead to poor surface quality. Hence, lower wheel velocity is found to be more suitable for grinding.
- For equal weights of responses, the optimal values are found to be 6 mm/pass of cross-feed, 12 m/min of workpiece velocity, 15 m/s of the wheel or cutting velocity, 0.095 mm of the depth of cut in wet condition, with a maximum overall desirability value of 0.863. Optimum value for other weights of responses can be found in Table 8.
- For dry cutting condition, keeping other parameters constant, desirability value increases with higher values of depth of cut until 0.095 mm, from where it decreases. This is because, up to a certain increase in depth of cut, high temperature is produced which drives the overall desirability down. If depth of cut is kept constant instead, then a positive relationship between the overall desirability values, and cross-feed and workpiece velocity is observed.
- For the wet conditions, it is observed that workpiece velocity and cross-feed are positively related to the higher overall desirability values whereas the depth of cut and wheel velocity have negligible effects.
- For a specific weight assignment, it is evident that the depth of cut positively affects the overall desirability values in the dry cutting condition, but it has a negligible effect in the wet condition.
- It must be kept in mind that these conjectures are not invariable; rather it depends on how the weights are assigned. Wheel velocity has no apparent effect on desirability when all weights are equal in our case. However, this scenario will most likely change if different weights are assigned.
- The confirmatory experiments corroborate that the predicted responses are in good agreement with the experimental results.

## 5. Strength and Limitations of the Study

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Nomenclature

a_{p} | depth of cut (mm) |

b | width of the cut (mm) |

b_{0}, b_{i}, b_{ii}, b_{ij} | coefficient of intercept, linear, quadratic and interaction of input variables respectively |

b_{jo}, b_{jk}, b_{jkk}, b_{jkl} | are the regression coefficients |

Cost_{dry} | total cost at dry machining condition (BDT) |

Cost_{wet} | total cost at wet machining condition (BDT) |

D_{i} | overall desirability of all responses |

a_{pi} | the depth of cut at experiment i |

${d}_{ij}\left({\widehat{Y}}_{ij}\right)$ = 0 | denotes the lowest desirability value of output response (Yij) |

${d}_{ij}\left({\widehat{Y}}_{ij}\right)$ = 1 | denotes the highest desirability value of output response (Yij) |

f_{b} | cross-feed (mm/pass) |

f_{bi} | cross-feed at experiment i |

G_{ij} | target value of the jth response (Yij) $0\le {d}_{ij}\left({\widehat{Y}}_{ij}\right)\le 1$ |

${G}_{ij}^{max}$ | maximum goal of output j at experiment i |

${G}_{ij}^{min}$ | minimum goal of output j at experiment i |

m | no. of experimental runs |

M_{ij} | lower level of output j at experiment i |

MRR | material removal rate (mm^{3}/s) |

n | no. of output responses variables |

N_{ij} | higher level of output j at experiment i |

p | no. of input independent parameters |

Temp_{dry} | Temperature at dry machining condition (°C) |

Temp_{wet} | Temperature at wet machining condition (°C) |

v_{s} | wheel velocity (m/s) |

v_{si} | the wheel velocity at experiment i |

v_{w} | workpiece velocity or longitudinal table travel velocity (m/min) |

v_{wi} | workpiece velocity at experiment i |

Y_{ij} | output responses value at ith experiment of jth response, j = 1, 2,…, n |

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**Figure 2.**A schematic diagram depicting the design of experiment (DOE) conducted for this research work. (

**a**) shows high low level of the parameters and (

**b**) shows the multilevel full factorial design (2

^{4}× 5 = 80) applied to run 80 experiments.

**Figure 3.**(

**a**) Schematic diagram of the experimental setup where inset A and B shows photograph images workpiece before slot cutting and after slot cutting using wire EDM, and (

**b**) pictorial view of the experimental setup. A—Workpiece before machining. B—Wire cut on the workpiece. 1—Thermocouple setup on the workpiece. 2—Dry machining setup. 3—Wet machining setup. 4—Workpiece after machining.

**Figure 6.**Contour plot of the temperature for each combination of input parameters. (

**a**) Surface grinding under dry condition and (

**b**) surface grinding under wet condition.

**Figure 7.**Contour plot of the total cost for each combination of input parameters. (

**a**) Surface grinding under dry condition and (

**b**) surface grinding under wet condition.

**Figure 8.**Surface plot of individual desirability (

**a**) for temperature in wet condition, and (

**b**) for MRR in wet condition.

**Figure 9.**Surface plot and corresponding contour plot for overall desirability in dry condition. (

**a**) show the combined effect of cross-feed and depth of cut, (

**b**) table velocity and depth of cut and (

**c**) wheel velocity and depth of cut on overall desirability.

**Figure 10.**Surface plot and corresponding contour plot for overall desirability in wet condition (equal weightage). (

**a**) show the combined effect of cross-feed and depth of cut, (

**b**) table velocity and depth of cut and (

**c**) wheel velocity and depth of cut on overall desirability.

**Table 1.**Grinding process parameters optimization using different analysis techniques in the literature.

Type of Grinding | Material Used | Parameter Optimized | Optimized Output | Analysis Technique | Ref. |
---|---|---|---|---|---|

Dry grinding | Mild steel | Wheel speed, workpiece speed, depth of dressing and lead of dressing | Minimum production cost, maximum production rate and the finest possible surface grinding finish | Genetic Algorithm (GA) | [24] |

Mild Steel | Wheel speed, workpiece speed, depth of dressing and lead of dressing | Production cost, production rate and surface finish | Particle swarm optimization (PSO) algorithm | [25] | |

Mild Steel | Wheel speed, workpiece speed, depth of dressing and lead of dressing | Production cost, production rate and surface finish | Quantum Based Optimization Method (QBOM) | [26] | |

Mild Steel | Wheel speed, workpiece speed, depth of dressing and lead of dressing | Production cost, production rate and surface roughness | Hybrid Particle Swarm Optimization (HPSO) algorithm | [27] | |

1.2080 Steel | Wheel speed, workpiece speed and depth of cut | Surface finish, total grinding time and production cost | Non-dominated sorting genetic algorithm (NSGA II) | [28] | |

1.2080 Steel | Wheel speed, workpiece speed and depth of cut | Surface quality, total grinding time and production cost | Dragonfly algorithm | [29] | |

EN24 steel | Wheel speed, table speed and depth of cut | Surface roughness and metal removal rate | RSM optimization | [17] | |

Soda-lime glass | Wheel speed, depth of cut and feed rate | Surface roughness | RSM and Monte Carlo Simulation | [30] | |

Steel | Speed of wheel, speed of workpiece, depth of dressing and lead of dressing | Production cost, production rate and surface finish | Particle swarm optimization, Gravitational search algorithm and Sine Cosine algorithm | [31] | |

Stainless steel material AISI 304 | Feed rate, speed of table and depth of cut | MRR and surface roughness | ANOVA, Taguchi method | [32] | |

EN 24 steel | Wheel speed, depth of cut and feed rate timing | Surface roughness | RSM | [33] | |

Conventional grinding | Silicon nitride ceramic | Feed rate, depth of cut, type of diamond wheel and lubrication type | Grinding forces, workpiece surfaceroughness, surface damages and wheel wear | Adaptiveneuro-fuzzy inference system (ANFIS) and Taguchi method | [34] |

Tungsten carbide insert | Feed rate and cutting speed | Production costs, grinding burn, surface roughness and temperature at the grinding surface | Constrained Bayesian optimization combined with Gaussian process Models | [35] | |

Ti-6Al-4V | Coolant types, cooling techniques and grinding depths | Surface hardness and surface morphology | Taguchi method and ANOVA | [36] | |

9CrSi annealing tool steel | Coolant concentration, coolant flow, cross-feed, table speed and depth of cut | Surface roughness | Taguchi method | [37] | |

Ti-6Al-4V-ELI | Types of coolant and graphene percentage in the coolant | Surface roughness, grinding force, specific grinding energy and coefficient-of-friction | Experimental (conventional) | [38] | |

MQL grinding | EN8 flat plate | Depth of cut, type of lubricant, feed rate, grinding wheel speed, coolant flow rate and nanoparticlesize | G ratio and surface finish | Taguchi based Grey relational analysis, ANOVA | [39] |

Two soft steels (CK45 and S305) and two hard steels (HSS and 100Cr6) | Depth of cut, cutting speed and feed rate | Grinding forces, friction coefficient, surface roughness, surface morphology and form of the chips | RSM, ANOVA, GA | [40] | |

Electrochemical grinding | 100Cr6 hardened steel (bearing steel) | Specific material removal rate | Maximum temperature, grinding forces and friction coefficient | Experimental (conventional) | [41] |

Composite carbide inserts | Voltage and cutting speed | Current density, material removal rate (MRR) and surface finish | Response surface methodology (RSM), Desirability function | [42] |

Properties | Specification | |||||||
---|---|---|---|---|---|---|---|---|

Work material | AISI 4140 alloy steel | |||||||

Dimension | 72 mm × 37 mm × 27.3 mm | |||||||

Type | Solid | |||||||

Chemical composition | Carbon | Chromium | Iron | Manganese | Molybdenum | Phosphorous | Silicon | Sulfur |

0.380–0.430 | 0.8–1.10 | Balance | 0.75–1.0 | 0.15–0.25 | 0.035 | 0.15–0.30 | 0.040 | |

Hardness | 40 HRC | |||||||

Tensile strength | 655 MPa | |||||||

Yield strength | 415 MPa | |||||||

Hardness, Brinell | 197 | |||||||

Density | 7.85 g/cm^{3} | |||||||

Melting point | 1416 °C |

Grinding Conditions with Specification | Grinding mode | Single pass surface grinding, down cut |

Grinding machine | Okamoto hydraulic surface grinder | |

Nozzle angle | 15° | |

Flow rate | 5 L/min | |

Flow measuring device | Z-5615 Panel Flowmeter | |

Machining condition | Dry, Wet (Flood) | |

Labor cost | 0.06 BDT/s | |

Power consumption cost | 8 BDT/unit | |

Cutting fluid cost | 0.5 BDT/s | |

Dressing Cut Parameter | Dresser | Single point diamond, HS050 |

Total depth of dressing | 300 μm | |

Dressing speed | 400 mm/min | |

Grinding wheel wear per dress, radially | 3.75 μm |

SI. No. | Grinding Input Parameters | Level 1 | Level 2 | Level 3 | Level 4 | Level 5 |
---|---|---|---|---|---|---|

1 | Workpiece velocity, v_{w} (m/min) | 5 | 12 | - | - | - |

2 | Wheel velocity, v_{s} (m/s) | 15 | 25 | - | - | - |

3 | Depth of cut, a_{p} (mm) | 0.07 | 0.08 | 0.09 | 0.095 | 0.10 |

4 | Cross-feed, f_{b} (mm/pass) | 3 | 6 | - | - | - |

5 | Cutting condition | Dry | Wet | - | - | - |

Objectives | Parameters/ Condition | Workpiece Velocity, v_{w} (m/min) | Wheel Velocity, v _{s} (m/s) | Depth of Cut, a_{p} mm | Cross-Feed, f_{b} (mm/Pass) |
---|---|---|---|---|---|

The optimum level for temp | Dry | 12–20 | 2–10 | 0.065–0.085 | 0.1–2.5 |

The optimum level for the cost | 12–15 | - | 0.03–0.13 | 6.5–8 | |

The optimum level for temp | Wet | 15–20 | 1–12 | 0.062–0.080 | - |

The optimum level for the cost | 15–20 | - | - | 7–10 |

Variable Type | Variables | Target | Lower Bound | Upper Bound |
---|---|---|---|---|

Independent (input parameters) | Cutting condition | Dry or Wet | N/A | N/A |

Cross-feed (mm/pass) | In range | 3 | 6 | |

Workpiece velocity (m/min) | In range | 5 | 12 | |

Wheel velocity (m/s) | In range | 15 | 25 | |

Depth of cut (mm) | In range | 0.07 | 0.10 | |

Dependent (response) | Temperature (°C) | Minimize | 109.78 | 313.67 |

MRR (mm^{3}/min) | Maximize | 1050 | 7200 | |

Total cost (BDT) | Minimize | 0.91 | 29.48 |

Individual Desirability | Overall Desirability (Equal Weightage 33:33:33) | Overall Desirability (20:40:40) | Overall Desirability (15:25:60) | ||
---|---|---|---|---|---|

Temp. | MRR | Total Cost | |||

0.533 | 0 | 0.890 | 0 | 0 | 0 |

0.527 | 0.025 | 0.891 | 0.228 | 0.193 | 0.338 |

0.377 | 0.049 | 0.891 | 0.255 | 0.236 | 0.380 |

0.249 | 0.061 | 0.891 | 0.239 | 0.237 | 0.377 |

0.086 | 0.074 | 0.891 | 0.179 | 0.207 | 0.337 |

0.458 | 0 | 0.888 | 0 | 0 | 0 |

0.456 | 0.025 | 0.890 | 0.217 | 0.187 | 0.330 |

0.312 | 0.049 | 0.890 | 0.240 | 0.227 | 0.369 |

0.186 | 0.061 | 0.890 | 0.217 | 0.223 | 0.361 |

0.024 | 0.074 | 0.890 | 0.117 | 0.160 | 0.278 |

0.615 | 0.240 | 0.969 | 0.524 | 0.507 | 0.639 |

0.601 | 0.298 | 0.970 | 0.559 | 0.550 | 0.673 |

0.444 | 0.357 | 0.970 | 0.537 | 0.557 | 0.672 |

0.311 | 0.386 | 0.970 | 0.489 | 0.535 | 0.650 |

0.144 | 0.415 | 0.970 | 0.388 | 0.472 | 0.590 |

0.542 | 0.240 | 0.968 | 0.502 | 0.494 | 0.627 |

0.532 | 0.298 | 0.969 | 0.536 | 0.537 | 0.660 |

0.379 | 0.357 | 0.969 | 0.509 | 0.539 | 0.656 |

0.249 | 0.386 | 0.969 | 0.454 | 0.511 | 0.628 |

0.084 | 0.415 | 0.969 | 0.324 | 0.424 | 0.544 |

0.487 | 0.171 | 0.954 | 0.431 | 0.420 | 0.562 |

0.484 | 0.220 | 0.953 | 0.467 | 0.463 | 0.597 |

0.339 | 0.269 | 0.953 | 0.444 | 0.468 | 0.595 |

0.213 | 0.293 | 0.951 | 0.391 | 0.441 | 0.567 |

0.052 | 0.318 | 0.951 | 0.251 | 0.344 | 0.468 |

0.423 | 0.171 | 0.953 | 0.411 | 0.408 | 0.550 |

0.425 | 0.220 | 0.952 | 0.447 | 0.451 | 0.585 |

0.284 | 0.269 | 0.951 | 0.418 | 0.451 | 0.579 |

0.160 | 0.293 | 0.950 | 0.355 | 0.416 | 0.542 |

0.001 | 0.318 | 0.950 | 0.068 | 0.156 | 0.259 |

0.591 | 0.649 | 0.995 | 0.726 | 0.756 | 0.827 |

0.580 | 0.766 | 0.994 | 0.762 | 0.805 | 0.860 |

0.427 | 0.883 | 0.992 | 0.721 | 0.800 | 0.850 |

0.297 | 0.942 | 0.992 | 0.653 | 0.764 | 0.818 |

0.132 | 1.000 | 0.991 | 0.508 | 0.665 | 0.735 |

0.528 | 0.649 | 0.993 | 0.699 | 0.739 | 0.813 |

0.522 | 0.766 | 0.992 | 0.735 | 0.787 | 0.845 |

0.373 | 0.883 | 0.991 | 0.689 | 0.779 | 0.832 |

0.246 | 0.942 | 0.990 | 0.613 | 0.735 | 0.794 |

0.082 | 1.000 | 0.989 | 0.434 | 0.604 | 0.683 |

0.951 | 0 | 0.052 | 0 | 0 | 0 |

0.942 | 0.025 | 0.031 | 0.091 | 0.057 | 0.050 |

0.882 | 0.049 | 0.022 | 0.099 | 0.064 | 0.047 |

0.832 | 0.061 | 0.022 | 0.104 | 0.069 | 0.049 |

0.770 | 0.074 | 0.024 | 0.112 | 0.076 | 0.054 |

0.943 | 0 | 0.030 | 0 | 0 | 0 |

0.923 | 0.025 | 0.018 | 0.075 | 0.046 | 0.036 |

0.850 | 0.049 | 0.016 | 0.088 | 0.056 | 0.039 |

0.795 | 0.061 | 0.020 | 0.100 | 0.066 | 0.046 |

0.727 | 0.074 | 0.026 | 0.113 | 0.077 | 0.056 |

0.991 | 0.240 | 0.603 | 0.524 | 0.461 | 0.517 |

0.985 | 0.298 | 0.583 | 0.556 | 0.496 | 0.534 |

0.927 | 0.357 | 0.573 | 0.575 | 0.523 | 0.548 |

0.879 | 0.386 | 0.572 | 0.580 | 0.533 | 0.553 |

0.818 | 0.415 | 0.575 | 0.581 | 0.542 | 0.559 |

0.988 | 0.240 | 0.610 | 0.526 | 0.463 | 0.520 |

0.970 | 0.298 | 0.597 | 0.558 | 0.499 | 0.540 |

0.900 | 0.357 | 0.595 | 0.577 | 0.527 | 0.558 |

0.847 | 0.386 | 0.598 | 0.581 | 0.539 | 0.565 |

0.780 | 0.415 | 0.605 | 0.582 | 0.548 | 0.572 |

0.951 | 0.171 | 0.500 | 0.434 | 0.371 | 0.422 |

0.942 | 0.220 | 0.485 | 0.466 | 0.404 | 0.440 |

0.882 | 0.269 | 0.481 | 0.486 | 0.431 | 0.456 |

0.832 | 0.293 | 0.484 | 0.491 | 0.442 | 0.464 |

0.770 | 0.318 | 0.489 | 0.494 | 0.451 | 0.471 |

0.943 | 0.171 | 0.467 | 0.423 | 0.360 | 0.404 |

0.923 | 0.220 | 0.460 | 0.455 | 0.394 | 0.425 |

0.850 | 0.269 | 0.465 | 0.475 | 0.422 | 0.444 |

0.795 | 0.293 | 0.471 | 0.480 | 0.433 | 0.453 |

0.727 | 0.318 | 0.480 | 0.481 | 0.443 | 0.461 |

0.991 | 0.649 | 0.792 | 0.799 | 0.765 | 0.780 |

0.985 | 0.766 | 0.776 | 0.837 | 0.810 | 0.802 |

0.927 | 0.883 | 0.772 | 0.859 | 0.845 | 0.821 |

0.879 | 0.942 | 0.774 | 0.863 | 0.859 | 0.829 |

0.818 | 1.000 | 0.779 | 0.861 | 0.870 | 0.836 |

0.988 | 0.649 | 0.787 | 0.797 | 0.763 | 0.776 |

0.970 | 0.766 | 0.779 | 0.834 | 0.809 | 0.802 |

0.900 | 0.883 | 0.783 | 0.854 | 0.845 | 0.824 |

0.847 | 0.942 | 0.789 | 0.858 | 0.860 | 0.834 |

0.780 | 1.000 | 0.798 | 0.854 | 0.870 | 0.842 |

Weights (%) | Cutting Condition | Cross-Feed (mm/pass) | Workpiece Velocity (m/min) | Wheel Velocity (m/s) | Depth of Cut (mm) | Temp. (°C) | MRR (mm^{3}/min) | Total Cost (BDT) | Overall Desirability |
---|---|---|---|---|---|---|---|---|---|

33.33:33.33:33.33 (Equal) | Wet | 6 | 12 | 15 | 0.095 | 140.854 | 6840 | 8.36 | 0.863 |

20:40:40 | Wet | 6 | 12 | 15 | 0.100 | 143.945 | 7200 | 7.77 | 0.870 (tied) |

6 | 12 | 25 | 0.100 | 150.119 | 7200 | 6.32 | |||

15:25:60 | Dry | 6 | 12 | 15 | 0.080 | 204.565 | 5760 | 1.01 | 0.860 |

100:0:0 (temperature only) | Wet | 3 | 12 | 15 | 0.070 | 109.785 | 2520 | 12.24 | 0.991 |

0:0:100 (total cost only) | Dry | 6 | 12 | 15 | 0.070 | 191.799 | 5040 | 1.08 | 0.995 |

Schemes | Cutting Condition | Optimum Cutting Parameters | Optimum Process Parameters | Absolute Error (%) | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Experimental Values | Predicted Values | ||||||||||

Weights (%) | Temp. (°C) | Total Cost (BDT) | Overall Desirability | Temp. (°C) | Total Cost (BDT) | Overall Desirability | Temp. (°C) | Total Cost (BDT) | Overall Desirability | ||

33.33:33.33: 33.33 (Equal) | Wet | (f_{b}, v_{w}, v_{s}, a_{p})= (6, 12, 15, 0.095) | 140.854 | 8.36 | 0.863 | 134.555 | 7.366 | 0.844 | 4.47 | 7.37 | 2.2 |

20:40:40 | Wet | (f_{b}, v_{w}, v_{s}, a_{p})= (6, 12, 15, 0.1) | 143.945 | 7.77 | 0.870 (tied) | 146.954 | 7.226 | 0.864 | 2.08 | 7.23 | 0.69 |

(f_{b}, v_{w}, v_{s}, a_{p})= (6, 12, 25, 0.1) | 150.119 | 6.32 | 154.771 | 6.69 | 0.867 | 3.099 | 5.85 | 0.35 | |||

15:25:60 | Dry | (f_{b}, v_{w}, v_{s}, a_{p})= (6, 12, 15, 0.08) | 204.565 | 1.01 | 0.860 | 195.43 | 1.09 | 0.852 | 4.46 | 7.9 | 0.93 |

100:0:0 (temperature only) | Wet | (f_{b}, v_{w}, v_{s}, a_{p})= (3, 12, 15, 0.07) | 109.785 | 12.24 | 0.991 | 111.69 | 12.25 | 0.989 | 1.73 | 0.16 | 0.20 |

0:0:100 (total cost only) | Dry | (f_{b}, v_{w}, v_{s}, a_{p})= (6, 12, 15, 0.07) | 191.799 | 1.08 | 0.995 | 193.33 | 1.08 | 0.994 | 0.80 | 0 | 0.10 |

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## Share and Cite

**MDPI and ACS Style**

Roy, R.; Ghosh, S.K.; Kaisar, T.I.; Ahmed, T.; Hossain, S.; Aslam, M.; Kaseem, M.; Rahman, M.M.
Multi-Response Optimization of Surface Grinding Process Parameters of AISI 4140 Alloy Steel Using Response Surface Methodology and Desirability Function under Dry and Wet Conditions. *Coatings* **2022**, *12*, 104.
https://doi.org/10.3390/coatings12010104

**AMA Style**

Roy R, Ghosh SK, Kaisar TI, Ahmed T, Hossain S, Aslam M, Kaseem M, Rahman MM.
Multi-Response Optimization of Surface Grinding Process Parameters of AISI 4140 Alloy Steel Using Response Surface Methodology and Desirability Function under Dry and Wet Conditions. *Coatings*. 2022; 12(1):104.
https://doi.org/10.3390/coatings12010104

**Chicago/Turabian Style**

Roy, Rakesh, Sourav Kumar Ghosh, Tanvir Ibna Kaisar, Tazim Ahmed, Shakhawat Hossain, Muhammad Aslam, Mosab Kaseem, and Md Mahfuzur Rahman.
2022. "Multi-Response Optimization of Surface Grinding Process Parameters of AISI 4140 Alloy Steel Using Response Surface Methodology and Desirability Function under Dry and Wet Conditions" *Coatings* 12, no. 1: 104.
https://doi.org/10.3390/coatings12010104