# Predictive Modelling and Multi-Objective Optimization of Surface Integrity Parameters in Sustainable Machining Processes of Magnesium Alloy

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Work Material, Tool, and Experimental Setup

#### 2.2. Surface Roughness Measurement

#### 2.3. Micro-Hardness and Material Removal Rate Measurement

#### 2.4. Design of Experiment

## 3. Results and Discussion

#### 3.1. Statistical Analysis and Empirical Modelling

^{2}and f·d, respectively), as the p-values were found to be greater than 0.05. On the other hand, the R-squared value was found to be very close to 1 for each surface roughness model developed for dry turning, which shows the goodness of fit of data, as mentioned in Table 5. Also, the Adj. R-Squared value was in good agreement with the Pred. R-squared value.

^{2}and f·d had p-values of 0.76 and 0.19, respectively, which are both higher than 0.05, and are thus not significant for the model. For Rt, all the factors of the model except for Vc and d were significant. The R-squared value was approaching 1 and the Adj. R-Squared value was close to the Pred. R-squared value for all the surface roughness models (Table 6), which indicates the goodness of fit of the data.

^{2}, Vc·f and Vc·d) for dry conditions and four factors (d, f

^{2}, Vc·d and f·d) for cryogenic conditions were found to be insignificant for the micro-hardness model (Table 7). The R-squared value was 0.996 and 0.988 for the micro-hardness model developed for dry and cryogenic conditions, respectively. As desired, Adj. R-Squared and Pred. R-squared values were in close agreement with each other for both micro-hardness models.

#### 3.2. Influence of Process Parameters

#### 3.3. Optimization of Process Parameters

- Case 1: Minimize surface roughness parameters (Ra, Rz and Rt) with maximum micro-hardness (μH).
- Case 2: Minimize surface roughness parameters (Ra, Rz and Rt) with maximum micro-hardness (μH) and maximum material removal rate (MMR).

## 4. Conclusions

- The mathematical predictive models for surface roughness parameters (Ra, Rz, and Rt) and micro-hardness of the turned AZ31 magnesium alloy samples were successfully developed for both sustainable machining processes. The results predicted by the proposed models were in close agreement with the experimental ones (0.3–1.6%).
- The parametric analysis shows that micro-hardness and surface finish of the machined samples were most affected by the cutting parameters, namely cutting velocity and feed rate. For surface roughness, the most dominant factor was cutting velocity, irrespective of the turning environment. However, for the micro-hardness of the machined sample turned under cryogenic conditions, the most dominant factor was the feed rate.
- Better surface finish of the machined samples was obtained under cryogenic conditions compared to dry conditions. However, surface roughness showed a decreasing trend with the cutting velocity and an increasing trend with the feed rate for both dry and cryogenic cutting conditions.
- Higher micro-hardness was measured for all machined samples. Micro-structural and XRD analysis of the machined samples confirmed this finding. Grain refinement layers were found on the machined samples, due to strain hardening. Moreover, from XRD, it was found that the crystallite size was smaller on the machined samples, which is in good agreement with the micro-structural results. Furthermore, lattice strain was higher in the turned samples and was highest for cryogenic cutting conditions, which is in close agreement with the micro-hardness results.
- Two multi-objective optimization cases were conducted in the present study:
- ➢
- In the first case, the objective was to maximize the micro-hardness and minimize the surface roughness. The optimal turning parameters were found to be Vc = 150 m/min, f = 0.11 rev/min, and d = 0.2 mm, with results Ra = 0.292 μm, Rz = 1.707 μm, Rt = 3.065 μm, and micro-hardness = 90.79 HV.
- ➢
- For the second case, maximization of MMR was also included in the objective. The optimal result for this case was Vc = 150 m/min, f = 0.11 rev/min, and d = 0.6 mm, with results Ra = 0.332 μm, Rz = 2.153 μm, Rt = 3.793 μm, micro-hardness = 90.8 HV and MMR = 9.9 mm
^{3}/min.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**An overview of the surface roughness analysis approach and surface roughness parameters utilized in the study.

**Figure 6.**Variation of different responses with cutting parameters and conditions: (

**a**) Ra; (

**b**) Rz; (

**c**) Rt; and (

**d**) micro-hardness (μH).

**Figure 7.**Micro-structures of the samples (

**a**) before turning, (

**b**) after dry turning and (

**c**) after cryogenic turning.

**Figure 9.**Crystallite size for each peak and the average crystallite size for the as-received sample, after dry turning and after cryogenic turning.

**Figure 10.**Lattice strain for each peak and the average crystallite size for the as-received sample, after dry turning and after cryogenic turning.

**Table 1.**Studies conducted on surface roughness and micro-hardness of magnesium alloys machined in a cryogenic environment.

Author/Year [Reference] | Material Removal Process | Work Material | Surface Roughness Parameters | Micro-Hardness | ||
---|---|---|---|---|---|---|

Ra | Rz | Rt | ||||

Pu et al. (2012) [29] | Burnishing | AZ31B- Mg | √ | - | - | - |

Kheireddine et al. (2013) [28] | Drilling | AZ31B-Mg | - | - | - | √ |

Dinesh et al. (2015) [30] | Turning | ZK60 Mg | √ | - | - | √ |

Dinesh et al. (2017) [31] | Orthogonal cutting | ZK60 Mg | √ | - | - | √ |

Danish et al. (2017) [19] | Turning | AZ31 Mg | √ | - | - | - |

Shen et al. (2017) [32] | Orthogonal cutting | AZ31B Mg | - | - | - | √ |

Danish et al. (2019) [33] | Turning | AZ31C Mg | √ | - | - | √ |

CURRENT STUDY | Turning | AZ31 Mg | √ | √ | √ | √ |

Element | Aluminum | Zinc | Manganese | Mg |
---|---|---|---|---|

Weight % | 3.42 | 0.97 | 0.14 | Balance |

Turning Parameter and Levels | Cooling Techniques | Responses | ||||
---|---|---|---|---|---|---|

Cutting velocity (Vc), m/min | Feed rate (f), mm/rev | Depth of cut (d), mm | 1. Dry 2. Cryogenic turning with LN _{2} jet | Surface roughness Ra (μm) Rz (μm) Rt (μm) | Micro-hardness μH, (Hv) | Material Removal rate MRR, (mm ^{3}/min) |

50 | 0.10 | 0.2 | ||||

100 | 0.12 | 0.4 | ||||

150 | 0.14 | 0.6 |

S. no. | Vc | f | d | Dry Turning | Cryogenic Turning | MRR. | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Ra | Rz | Rt | μH | Ra | Rz | Rt | μH | |||||

1 | 150.00 | 0.10 | 0.20 | 0.582 | 3.781 | 6.338 | 60.9 | 0.281 | 1.513 | 2.967 | 88.6 | 3 |

2 | 100.00 | 0.12 | 0.40 | 0.815 | 4.473 | 8.659 | 65.4 | 0.421 | 2.472 | 4.495 | 89.1 | 4.8 |

3 | 100.00 | 0.12 | 0.40 | 0.815 | 4.473 | 8.662 | 65.6 | 0.421 | 2.47 | 4.456 | 89.2 | 4.8 |

4 | 150.00 | 0.14 | 0.20 | 0.742 | 4.046 | 7.927 | 68.3 | 0.414 | 2.334 | 4.376 | 97.2 | 4.2 |

5 | 100.00 | 0.12 | 0.20 | 0.755 | 4.38 | 8.056 | 66.1 | 0.381 | 2.303 | 4.133 | 94.2 | 2.4 |

6 | 100.00 | 0.10 | 0.40 | 0.768 | 4.312 | 8.293 | 62.5 | 0.374 | 2.033 | 3.996 | 85.2 | 4 |

7 | 100.00 | 0.14 | 0.40 | 0.921 | 4.783 | 9.724 | 70.1 | 0.51 | 2.72 | 5.543 | 93.3 | 5.6 |

8 | 150.00 | 0.12 | 0.40 | 0.722 | 3.987 | 7.656 | 62.4 | 0.353 | 2.215 | 3.768 | 89.6 | 7.2 |

9 | 100.00 | 0.12 | 0.60 | 0.851 | 4.587 | 9.016 | 64 | 0.453 | 2.623 | 5.156 | 93 | 7.2 |

10 | 100.00 | 0.12 | 0.40 | 0.816 | 4.477 | 8.662 | 65.4 | 0.419 | 2.471 | 4.461 | 89.2 | 4.8 |

11 | 100.00 | 0.12 | 0.40 | 0.814 | 4.469 | 8.659 | 65.6 | 0.42 | 2.471 | 4.451 | 89.2 | 4.8 |

12 | 50.00 | 0.10 | 0.60 | 0.862 | 4.976 | 9.118 | 66.1 | 0.506 | 2.898 | 5.067 | 82 | 3 |

13 | 150.00 | 0.10 | 0.60 | 0.731 | 3.944 | 7.829 | 58 | 0.318 | 1.946 | 3.543 | 88 | 9 |

14 | 100.00 | 0.12 | 0.40 | 0.812 | 4.478 | 8.662 | 65.6 | 0.42 | 2.47 | 4.531 | 89.2 | 4.8 |

15 | 50.00 | 0.12 | 0.40 | 0.891 | 5.134 | 9.414 | 72 | 0.512 | 3.201 | 5.125 | 86.3 | 2.4 |

16 | 50.00 | 0.14 | 0.20 | 0.948 | 5.422 | 9.973 | 76.1 | 0.541 | 3.331 | 5.434 | 95.4 | 1.4 |

17 | 100.00 | 0.12 | 0.40 | 0.815 | 4.465 | 8.706 | 65.6 | 0.421 | 2.471 | 4.452 | 89.3 | 4.8 |

18 | 150.00 | 0.14 | 0.60 | 0.911 | 4.432 | 9.527 | 65.4 | 0.465 | 2.762 | 5.541 | 96.7 | 12.6 |

19 | 50.00 | 0.14 | 0.60 | 0.998 | 5.687 | 10.38 | 75.4 | 0.643 | 3.46 | 6.674 | 95 | 4.2 |

20 | 50.00 | 0.10 | 0.20 | 0.833 | 4.855 | 8.699 | 69.7 | 0.422 | 2.738 | 4.256 | 83 | 1 |

^{3}/min).

Dry Turning | Source | SOS | DOF | Mean Square | F-Value | p-Value |
---|---|---|---|---|---|---|

Ra | Model | 0.161832566 | 9 | 0.017981396 | 7125.834759 | <0.0001 |

Vc | 0.0712336 | 1 | 0.0712336 | 28229.11285 | <0.0001 | |

f | 0.0553536 | 1 | 0.0553536 | 21936.03891 | <0.0001 | |

d | 0.0243049 | 1 | 0.0243049 | 9631.771593 | <0.0001 | |

Vc^{2} | 0.000162278 | 1 | 0.000162278 | 64.30919571 | <0.0001 | |

f^{2} | 0.002527778 | 1 | 0.002527778 | 1001.731514 | <0.0001 | |

d^{2} | 0.000343841 | 1 | 0.000343841 | 136.2604701 | <0.0001 | |

Vc·f | 0.000990125 | 1 | 0.000990125 | 392.3759344 | <0.0001 | |

Vc·d | 0.007140125 | 1 | 0.007140125 | 2829.555075 | <0.0001 | |

f·d | 0.000210125 | 1 | 0.000210125 | 83.27028731 | <0.0001 | |

Residual | 13.552 | 10 | 1.355 | - | - | |

R-Squared = 0.9998, Adj R-Squared = 0.9997 and Pred R-Squared = 0.9992 | ||||||

Rz | Model | 4.385992 | 9 | 0.487332 | 2131.035 | <0.0001 |

Vc | 3.462146 | 1 | 3.462146 | 15139.47 | <0.0001 | |

f | 0.626 | 1 | 0.626 | 2737.411 | <0.0001 | |

d | 0.130416 | 1 | 0.130416 | 570.2924 | <0.0001 | |

Vc^{2} | 0.020663 | 1 | 0.020663 | 90.35539 | <0.0001 | |

f^{2} | 0.01493 | 1 | 0.01493 | 65.2858 | <0.0001 | |

d^{2} | 0.000258 | 1 | 0.000258 | 1.127228 | 0.3133 | |

Vc·f | 0.034453 | 1 | 0.034453 | 150.6586 | <0.0001 | |

Vc·d | 0.003321 | 1 | 0.003321 | 14.52281 | 0.0034 | |

f·d | 0.016836 | 1 | 0.016836 | 73.62198 | <0.0001 | |

Residual | 0.002287 | 10 | 0.000229 | - | - | |

R-Squared = 0.9995, Adj R-Squared = 0.9990 and Pred R-Squared = 0.9934 | ||||||

Rt | Model | 15.56307 | 9 | 1.72923 | 1742.162 | <0.0001 |

Vc | 6.900625 | 1 | 6.900625 | 6952.231 | <0.0001 | |

f | 5.262052 | 1 | 5.262052 | 5301.404 | <0.0001 | |

d | 2.378513 | 1 | 2.378513 | 2396.301 | <0.0001 | |

Vc^{2} | 0.054075 | 1 | 0.054075 | 54.47954 | <0.0001 | |

f^{2} | 0.305444 | 1 | 0.305444 | 307.7287 | <0.0001 | |

d^{2} | 0.053307 | 1 | 0.053307 | 53.70529 | <0.0001 | |

Vc·f | 0.0705 | 1 | 0.0705 | 71.02736 | <0.0001 | |

Vc·d | 0.641278 | 1 | 0.641278 | 646.0739 | <0.0001 | |

f·d | 0.001176 | 1 | 0.001176 | 1.184921 | 0.3019 | |

Residual | 0.009926 | 10 | 0.000993 | - | - | |

R-Squared = 0.9993, Adj R-Squared = 0.9987 and Pred R-Squared = 0.9940 |

Cryogenic Turning | Source | Sum of Squares | Degree of Freedom | Mean Square | F-Value | p-Value |
---|---|---|---|---|---|---|

Ra | Model | 0.124974 | 9 | 0.013886 | 10042.47 | <0.0001 |

Vc | 0.062885 | 1 | 0.062885 | 45478.89 | <0.0001 | |

f | 0.045158 | 1 | 0.045158 | 32658.93 | <0.0001 | |

d | 0.011972 | 1 | 0.011972 | 8657.962 | <0.0001 | |

Vc^{2} | 0.000358 | 1 | 0.000358 | 258.8798 | <0.0001 | |

f^{2} | 0.001202 | 1 | 0.001202 | 869.4938 | <0.0001 | |

d^{2} | 4.6 × 10^{−5} | 1 | 4.6 × 10^{−5} | 33.28402 | 0.0002 | |

Vc·f | 7.2 × 10^{−5} | 1 | 7.2 × 10^{−5} | 52.07101 | <0.0001 | |

Vc·d | 0.001201 | 1 | 0.001201 | 868.2117 | <0.0001 | |

f·d | 0.000128 | 1 | 0.000128 | 92.57068 | <0.0001 | |

Residual | 1.38 × 10^{−5} | 10 | 1.38 × 10^{−6} | - | - | |

R-Squared = 0.9998, Adj R-Squared = 0.9998 and Pred R-Squared = 0.9991 | ||||||

Rz | Model | 4.061161 | 9 | 0.45124 | 5552.296 | <0.0001 |

Vc | 2.360016 | 1 | 2.360016 | 29038.88 | <0.0001 | |

f | 1.210344 | 1 | 1.210344 | 14892.71 | <0.0001 | |

d | 0.21609 | 1 | 0.21609 | 2658.885 | <0.0001 | |

Vc^{2} | 0.16281 | 1 | 0.16281 | 2003.303 | <0.0001 | |

f^{2} | 0.021384 | 1 | 0.021384 | 263.1211 | <0.0001 | |

d^{2} | 7.78 × 10^{−6} | 1 | 7.78 × 10^{−6} | 0.09571 | 0.7634 | |

Vc·f | 0.029041 | 1 | 0.029041 | 357.3296 | <0.0001 | |

Vc·d | 0.040898 | 1 | 0.040898 | 503.2305 | <0.0001 | |

f·d | 0.000162 | 1 | 0.000162 | 1.993333 | 0.1883 | |

Residual | 0.000813 | 10 | 8.13 × 10^{−5} | - | - | |

R-Squared = 0.9998, Adj R-Squared = 0.9996 and Pred R-Squared = 0.9982 | ||||||

Rt | Model | 12.86389 | 9 | 1.429322 | 489.277 | <0.0001 |

Vc | 4.046232 | 1 | 4.046232 | 1385.082 | <0.0001 | |

f | 5.989212 | 1 | 5.989212 | 2050.192 | <0.0001 | |

d | 2.318423 | 1 | 2.318423 | 793.6287 | <0.0001 | |

Vc^{2} | 0.023855 | 1 | 0.023855 | 8.165749 | 0.0170 | |

f^{2} | 0.145303 | 1 | 0.145303 | 49.73911 | <0.0001 | |

d^{2} | 0.03024 | 1 | 0.03024 | 10.3516 | 0.0092 | |

Vc·f | 0.04836 | 1 | 0.04836 | 16.55448 | 0.0023 | |

Vc·d | 0.012012 | 1 | 0.012012 | 4.112048 | 0.0701 | |

f·d | 0.129541 | 1 | 0.129541 | 44.34354 | <0.0001 | |

Residual | 0.029213 | 10 | 0.002921 | - | - | |

R-Squared = 0.9977, Adj R-Squared = 0.9957 and Pred R-Squared = 0.9851 |

Micro-Hardness | Source | Sum of Squares | Degree of Freedom | Mean Square | F-Value | p-Value |
---|---|---|---|---|---|---|

For Dry turning | Model | 376.3987 | 9 | 41.82207 | 275.2646 | <0.0001 |

Vc | 196.249 | 1 | 196.249 | 1291.672 | <0.0001 | |

f | 145.161 | 1 | 145.161 | 955.4209 | <0.0001 | |

d | 14.884 | 1 | 14.884 | 97.96353 | <0.0001 | |

Vc^{2} | 7.652784 | 1 | 7.652784 | 50.3691 | <0.0001 | |

f^{2} | 1.622784 | 1 | 1.622784 | 10.68084 | 0.0085 | |

d^{2} | 0.638409 | 1 | 0.638409 | 4.201882 | 0.0675 | |

Vc·f | 0.10125 | 1 | 0.10125 | 0.666407 | 0.4333 | |

Vc·d | 0.28125 | 1 | 0.28125 | 1.851132 | 0.2035 | |

f·d | 1.05125 | 1 | 1.05125 | 6.919119 | 0.0251 | |

Residual | 1.519341 | 10 | 0.151934 | - | - | |

R-Squared = 0.9960, Adj R-Squared = 0.9924 and Pred R-Squared = 0.9263 | ||||||

For Cryogenic turning | Model | 343.6334 | 9 | 38.18149 | 92.40286 | <0.0001 |

Vc | 33.856 | 1 | 33.856 | 81.93476 | <0.0001 | |

f | 258.064 | 1 | 258.064 | 624.5395 | <0.0001 | |

d | 1.369 | 1 | 1.369 | 3.313111 | 0.0987 | |

Vc^{2} | 9.458182 | 1 | 9.458182 | 22.8897 | 0.0007 | |

f^{2} | 0.845682 | 1 | 0.845682 | 2.046631 | 0.1830 | |

d^{2} | 39.61506 | 1 | 39.61506 | 95.87222 | <0.0001 | |

Vc·f | 8.20125 | 1 | 8.20125 | 19.84781 | 0.0012 | |

Vc·d | 0.01125 | 1 | 0.01125 | 0.027226 | 0.8722 | |

f·d | 0.06125 | 1 | 0.06125 | 0.148231 | 0.7083 | |

Residual | 4.132068 | 10 | 0.413207 | - | - | |

R-Squared = 0.9881, Adj R-Squared = 0.9774 and Pred R-Squared = 0.9192 |

**Table 8.**Maximum percentage error between predicted and experimental values for the models developed for the surface roughness and micro-hardness of the AZ31C magnesium alloy.

Models | Maximum Percentage Error | |
---|---|---|

Dry Turning | Cryogenic Turning | |

For Ra | 0.298% | 0.409% |

For Rz | 0.316% | 0.724% |

For Rt | 0.557% | 1.591% |

For μH | 0.756% | 1.634% |

Name | Goal | Lower Limit | Upper Limit | Lower Weight | Upper Weight | Importance |
---|---|---|---|---|---|---|

Cutting velocity | is in range | 50 | 150 | 1 | 1 | 3 |

Feed rate | is in range | 0.1 | 0.14 | 1 | 1 | 3 |

Depth of cut | is in range | 0.2 | 0.6 | 1 | 1 | 3 |

Ra, Cry | minimize | 0.281 | 0.643 | 1 | 1 | 3 |

Rz, Cry | minimize | 1.513 | 3.46 | 1 | 1 | 3 |

Rt, Cry | minimize | 2.967 | 6.674 | 1 | 1 | 3 |

μH, Cry | maximize | 82 | 97.2 | 1 | 1 | 3 |

MMR, Cry | maximize | 1 | 12.6 | 1 | 1 | 3 |

Process Parameters/Responses | Optimal Solution | |
---|---|---|

Case 1 | Case 2 | |

Vc (m/min) | 150 | 150 |

f (mm/rev) | 0.11 | 0.11 |

d (mm) | 0.2 | 0.6 |

Ra (μm) | 0.292 | 0.332 |

Rz (μm) | 1.707 | 2.153 |

Rt (μm) | 3.065 | 3.793 |

μH (HV) | 90.79 | 90.8 |

MMR (mm^{3}/min) | 3.3 | 9.9 |

Desirability | 0.837 | 0.71 |

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**MDPI and ACS Style**

Danish, M.; Rubaiee, S.; Ijaz, H.
Predictive Modelling and Multi-Objective Optimization of Surface Integrity Parameters in Sustainable Machining Processes of Magnesium Alloy. *Materials* **2021**, *14*, 3547.
https://doi.org/10.3390/ma14133547

**AMA Style**

Danish M, Rubaiee S, Ijaz H.
Predictive Modelling and Multi-Objective Optimization of Surface Integrity Parameters in Sustainable Machining Processes of Magnesium Alloy. *Materials*. 2021; 14(13):3547.
https://doi.org/10.3390/ma14133547

**Chicago/Turabian Style**

Danish, Mohd, Saeed Rubaiee, and Hassan Ijaz.
2021. "Predictive Modelling and Multi-Objective Optimization of Surface Integrity Parameters in Sustainable Machining Processes of Magnesium Alloy" *Materials* 14, no. 13: 3547.
https://doi.org/10.3390/ma14133547