# ANN Laser Hardening Quality Modeling Using Geometrical and Punctual Characterizing Approaches

^{*}

## Abstract

**:**

_{L}), beam scanning speed (V

_{S}) and initial hardness in the core (H

_{C}). LHQ modeling was conducted by modeling attributes extracted from the hardness profile curve using two effective techniques based on the punctual and geometrical approaches. The process parameters with the most influence on the responses were laser power, beam scanning speed and initial hardness in the core. The obtained results demonstrate that the geometrical approach is more accurate and credible than the punctual approach according to performance assessment criteria.

## 1. Introduction

_{H}), which constitutes an interesting response and does not reflect the full picture of treatment quality. A typical hardness curve obtained by laser hardening is illustrated in Figure 2. This curve is characterized by the melted layer (1). It also includes a hardened region (2) that records a high hardness value and is a homogeneous microstructure with nearly constant hardness and compressive residual stress levels. The over-tempered region (3) represents the hardness loss caused by a microstructural changes, and reaches minimum value. This region includes the hardness rise until it reaches the initial hardness value and is composed of a mixture of hard and over-tempered martensite since the temperature was between Ac1 and Ac3. The fourth region (4) records a constant hardness value that represents the tempered martensite constituting the initial microstructure in the part’s core before laser treatment. The LHQ is a feature that cannot be confined to a limited response, but rather a coherent set of response results depending strongly on process parameters. In addition to the hardness values H

_{H}, laser hardening quality can be also estimated through the depth of the four regions described previously, the melted region (d

_{M}), hardened region (d

_{H}), over-tempered region (d

_{L}) and total transformed region (d

_{C}). The hardness profile is a direct result of temperature distribution during and after heating and could greatly affect part distortion, martensite microstructure and compressive residual stresses resulting at the surface [8].

_{M}, d

_{H}, d

_{C}and H

_{H}can be controlled by input process parameters, so modeling these responses is a successful means of attaining the desired quality process while avoiding time and cost limitations. The modeling approach was the focus of several laser hardening or welding studies that were generally based on the artificial neural network (ANN) technique and the multi-regression method. Lambiase developed an expert model using the ANN technique to evaluate the temperature profile and temperature history of a laser-treated part under different processing conditions [9]. As a result, the measured hardness values showed relatively good correspondence with the predicted temperature profile. Woo used both multi-regression and artificial neural network techniques to develop models for assessing the hardened layer dimensions of SM45C steel, mainly the effect of coating thickness parameters [10]. Bappa highlighted the laser welding process by predicting welding quality [11]. His work aimed to establish a correlation between laser transmission welding parameters and output variables through a non-linear model based on artificial neural networks. After studying the effect of the process parameters on the responses of interest or LHQ, this study aims to develop models capable of predicting the hardness profile and controlling the LHQ according to input process parameters. The modeling technique is based mainly on the choice of modeled attributes. Hardness profile attribute characterization is a necessary step for modeling, so these attributes must provide a global representation of hardness profile behavior. Two different approaches were used during this study to characterize the hardness profile according to process parameters such as laser power and scanning speed. The extracted attributes were modeled using the artificial neural network based on multilayer perceptron (MLP). The generated models were analyzed using special evaluation criteria to determine the appropriate characterization approach for modeling the LHQ.

## 2. Experimental Aspect

#### 2.1. Experimental Conditions

_{L}) and scanning speed (V

_{S}) have the greatest effect and make the most significant contributions to the required results. All other parameters that were investigated in the relevant studies can be considered to have made fewer contributions when comparing laser beam power and scanning speed. The experimental aspect of this study was applying the laser heat treatment process to AISI 4340 steel to assess the parameters’ impact on the quality of the hardened layer. In addition to laser power and laser beam velocity, with four levels of each, the input parameters of the first experiment were restricted to initial steel hardness (H

_{C}) and surface roughness (R

_{a}), with two levels of each. The power varied from 400 to 1300 W with a step of 300 W, while the speed varied from 10 to 40 mm/s with 10 mm/s incrementing. The initial hardness values were 40 and 50 HRC, and the surface roughness was tuned at 0.8 and 2.4 µm.

#### 2.2. Experimental Design

_{16}orthogonal arrays were an adequate test strategy for this study, while L

_{8}remained an appropriate choice for validation tests.

#### 2.3. Experimental Set-Up

_{a}) of approximately 2.4 µm and CAMI-Grit-200 sandpaper with an average particle diameter of 68 µm to obtain a surface roughness (R

_{a}) of approximately 0.8 µm. The laser beam was provided by a Nd:YAG robotic cell, and the value range levels of machine parameters such as beam power and scanning speed were taken to ensure the complete austenitization of the steel layer during the heat treatment (Table 1). Once the treatment was performed, the hardness profile was characterized by using a Clemex microhardness measurement machine using 500 g load, which provided the hardness profile shape of each test. The hardness is evaluated first in HV and converted to HRC scale.

#### 2.4. Experimental Results Analysis

_{H}) was established according to the analytic methods depicted above. ANOVA analysis was performed with a stepwise mode, which automatically eliminate the insignificant terms. Table 2 presents the detailed statistical analysis confirming that f-value is important for almost all factors except the roughness surface and a p-value of less than 0.09. In this case, the laser power (P

_{L}), scanning speed (V

_{S}) and initial hardness (H

_{C}) were all significant model terms. Based on the ANOVA results, the parameters predominantly affecting the LHQ were laser beam power (52.76%) and beam scanning speed (32.92%). The contribution of initial hardness was less than 5%, and the factor related to surface roughness had no effect on the case depth in that situation. However, the contribution of the total error was about 8.73%. This result means that the process responses were somehow not controlled by the all-important input parameters. The coefficient of determination (R

^{2}) is mainly used to measure the relationship between experimental data and measured data. In this case, R

^{2}was equal to 91.26%, proving a high correlation between experimental results and predicted results. The predicted R

^{2}of 54.34% was in representative agreement with the adjusted R

^{2}of 81.27%. Adequate precision measures the signal to noise ratio. The standard deviation related to the case depth prediction model was evaluated at 0.3201.

_{a}) was replaced by surface nature (S

_{N}). In this case, the first level correspond to the surface as initially treated and the second level is that obtained after machine tool finishing. Some similarities were noted regarding f-value and p-value concerning the analysis considering R

_{a}. In fact, f-value was very important, exceeding 10 for the least significant factor (S

_{N}), and the p-value was less than 0.015 for S

_{N}again. It was also clear that P

_{L}has the largest effect on the response value, V

_{S}has less of an effect and H

_{C}has a little more effect. The three interaction terms affected the case depth less but were not ignored. This study allows for determination of the various effects and the ranking of each effect on the case depth (d

_{H}). Based on the data in Table 3, the variation in the three characteristics represents each parameter’s degree of influence on the response. It was confirmed by analyzing their contributions that P

_{L}affects d

_{H}by more than 58.66% and that V

_{S}contributes to the overall variation by more than 16%. The initial hardness influences the case depth by about 19% with an error of less than 2.5%. Most of the parameters were therefore taken into account during this study. It is important to note the non-presence of interactions between the four factors used in this study. The coefficient of determination (R

^{2}) was about 96.03%, proving a high correlation between experimental results and predicted results. The predicted R

^{2}of 79.26% was in reasonable agreement with the adjusted R

^{2}of 91.49%. Adequate precision measures the signal to noise ratio. The standard deviation related to the case depth prediction model was evaluated at 0.3240.

_{H}increased with power and initial hardness and decreased with speed and surface roughness. d

_{H}also increased with power and initial hardness and decreased with speed and surface nature. The drawn points match up to the averages of the observations for each factor level. These results confirm the relative importance of the contribution of different factors in the variation of d

_{H}. The effects of the four factors in both cases (R

_{a}and S

_{N}) do not follow the same tendencies. Overall, the case depth recorded maximum values at 1.3 kW, 10 mm/s, 50 HRC and R

_{a}of approximately 0.8 µm. However, the minimum value was recorded at 0.4 kW, 40 mm/s and 40 HRC when the surface roughness was adjusted to 0.8 µm. The case depth recorded maximum values at 1.3 kW, 10 mm/s and 50 HRC when the surface was treated. However, the minimum value was recorded at 0.4 kW, 40 mm/s and 40 HRC when the surface was polished.

_{N}) of the treated plate had a greater impact on d

_{H}and on the other output response than surface roughness (R

_{a}). The error contribution of the second experiment, in which the surface nature was considered as a fourth input parameter, was relatively small compared to the first experiment. This proves that the second experiment considered the important parameters and that laser hardening quality is strongly controlled by these parameters compared to the first experiment. Since the error contribution was less when R

_{a}was replaced by S

_{N}in the ANOVA analysis, the selection of P

_{L}, V

_{S}, H

_{C}and S

_{N}as input parameters is promising and constitutes an effective choice for LHQ element models. Consequently, elaboration process using the best selection of parameters based on its effect and contribution helps the modeling and the validation steps.

## 3. LHQ Assessment Model

_{M}, d

_{H}, d

_{C}and H

_{H}depending on the input variables using systematic and rigorous approaches. It is well known that the modeling process is based on two important pillars; the type and number of variables to include in the model and the technique used to develop the robust model. According to ANOVA results and as mentioned earlier, the error of modeling and validation due to process input variables is expected to be minimal in the present study, which guarantees the success of the first modeling pillar to some extent. Regarding development of the model approaches, which are generally divided into two categories, theoretical modeling is an undesirable modeling option because of the complexity of the phenomena and the lack of understanding of fundamental laser hardening process behavior. In this case, empirical modeling is an appropriate means of reaching the study’s objective. The advantage of using the empirical approach is its ability to develop robust models with easily available information on the variables to include in the model [14].

_{L}, V

_{S}, H

_{C}and S

_{N}). This combination of variables was proposed by Taguchi’s OAs (L

_{16}), which were included in the models. Once the tests were done, response result data collection for modeling began; the data collection was done using specific techniques that will be explained later in the paper. A statistical analysis procedure to determine the impact, contribution and relationship between the process input variables and the data collected was carried out while taking into account all the conditions that could influence the modeling. The crucial step in the modeling sequences was the choice of technique for modeling and performance criteria. Once this step has been completed, it will take time to train the generated models, followed by the performance evaluation [16]. Based on certain performance evaluation criteria such as mean square error (MSE), a comparative study was carried out to compare the model’s credibility and the accuracy of the modeled LHQ to that measured in this study.

#### Modeling Techniques

_{M}, d

_{M}), (H

_{H}, d

_{H}), (H

_{L}, d

_{L}) and (H

_{C}, d

_{C}). The coordinate values depend on the process input variables, and the variations in these points in relation to the process variables define hardened profile sensitivity. Modeling the hardness profile curve with this technique means that LHQ will also be modeled.

_{1}, m

_{2}and m

_{3}, which represent the slopes, by means of which certain quality elements such as d

_{H}and d

_{C}can be calculated (Figure 6). m

_{1}is the result of dividing the difference between H

_{H}and H

_{M}and the difference between d

_{H}and d

_{M}(Equation (1)). m

_{2}is the result of dividing the difference between H

_{L}and H

_{H}and the difference between d

_{H}and d

_{M}(Equation (2)). m

_{3}is the result of dividing the difference between H

_{C}and H

_{L}and the difference between d

_{C}and d

_{L}(Equation (3)). Note that the slopes m

_{1}and m

_{3}are positive and m

_{2}is negative. Using these approaches to model the hardness profile is an effective way to model the LHQ. Otherwise, in this study, the LHQ modeling process is defined by d

_{M}, d

_{H}, d

_{C}and H

_{H}modeling.

## 4. Results and Discussion

_{M}and H

_{H}models using the geometrical approach were less than the maximum relative errors of the punctual model, while the opposite is the case for H

_{M}and H

_{L}. Considerable values of XRE in m

_{1}and m

_{3}, which represent the passage from (d

_{M}, H

_{M}) to (d

_{H}, H

_{H}) and from (d

_{L}, H

_{L}) to (d

_{C}, H

_{C}) respectively, can be explained by the H

_{M}and H

_{L}error effect while training models using ANN. Concerning m

_{2}, the XRE value was infinitely small due to the small size of the transition region compared to the corresponding hardness variation. The mean square error MSE and total square error TSE criteria provide the same information on model performances but with different values.

_{H}, d

_{M}, d

_{H}and d

_{C}. The mean absolute percentage error (MRE) is considered in order to evaluate the accuracy of the LHQ models and to compare the modeled attributes according to the characterization approach used to extract them. Using the geometrical approach, d

_{H}and d

_{C}were not included in the list of extracted attributes. d

_{H}and d

_{C}models were not generated directly, but were rather the result of modeling other attributes. Based on the MRE value, the results presented in Table 6 demonstrate that the laser hardening quality variable models present better accuracy when the geometrical approach was implemented; the difference is small.

## 5. Conclusions

- Laser hardening processing was performed on 4340 steel during which the parameters of laser power, beam scanning speed, initial hardness and surface roughness were considered and for which the testing strategy was designed according to the Taguchi method (OA). The analysis of variance indicated that the machine parameters (laser power and beam scanning speed, in order of importance) have the greatest impact on process quality, followed by initial hardness.
- The impact of surface roughness was quite low compared to the rest of the variables. By repeating the same experimental process and exchanging the surface roughness variable for surface nature, it was determined that for a certain defined interval, surface nature has more of an impact than surface roughness; the experiment’s total error contribution decreased when surface nature was used. The results of the experiment’s second process were considered for the modeling process in this study.
- Structured approaches were adopted to model the LHQ variables according to the second experiment parameters using a multilayer perceptron ANN calculation model. The generated models were evaluated through performance evaluation criteria, and the results allowed us to conclude the following. Modeling the extracted attributes from the hardness profile curve using both approaches is an ingenious way to model LHQ elements with excellent accuracy.
- According to the accuracy of the generated models, the geometrical attributes are the most appropriate variables for LHQ modeling, rather than the punctual attributes. However, both approaches proposed are effective techniques that provide promising LHQ models.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Metallographic cross-section of the hardened region (

**a**) and representation of a typical cross-section of a laser-hardened plate (

**b**).

Parameters | Levels |
---|---|

Power (kW) | 0.4, 0.7, 1.0 and 1.3 |

Speed (mm/s) | 10, 20, 30 and 40 |

Initial hardness (HRC) | 40, 50 |

Surface roughness (µm) | 0.8, 2.4 |

Source | DF | Sum of Squares | Mean Square | f-Value | p-Value | Contributions (%) |
---|---|---|---|---|---|---|

P_{L} (kW) | 3 | 0.81125 | 0.27042 | 14.09 | 0.002 | 52.76 |

V_{S} (mm/s) | 3 | 0.50625 | 0.16875 | 8.79 | 0.009 | 32.92 |

H_{C} (HRC) | 1 | 0.07562 | 0.07562 | 3.94 | 0.088 | 4.91 |

R_{a} (µm) | 1 | 0.01000 | 0.01000 | 0.52 | 0.494 | 0.65 |

Error | 7 | 0.13437 | 0.01920 | – | – | 8.73 |

Total | 15 | 1.53750 | – | – | – | 100 |

Characteristic | DoF | Sum of Squares | Mean Square | f-Value | p-Value | Contributions (%) |
---|---|---|---|---|---|---|

P_{L} (kW) | 3 | 0.94092 | 0.31364 | 55.94 | 0 | 58.66 |

V_{S} (mm/s) | 3 | 0.25717 | 0.08572 | 15.29 | 0.002 | 16.03 |

H_{C} (HRC) | 1 | 0.30526 | 0.30525 | 54.45 | 0 | 19.03 |

S_{N} | 1 | 0.06126 | 0.06125 | 10.93 | 0.013 | 3.81 |

Error | 7 | 0.03924 | 0.00560 | – | – | 2.47 |

Total | 15 | 1.60384 | – | – | – | 100 |

Variables | MAE | XRE | MSE | TSE | ||||
---|---|---|---|---|---|---|---|---|

T | V | T | V | T | V | T | V | |

H_{H} | 0.219 | 0.0640 | 1.149 | 0.497 | 0.0801 | 0.022154 | 1.2816 | 0.022154 |

H_{M} | 0.2656 | 0.1234 | 1.1 | 0.7709 | 0.099818 | 0.046141 | 1.5971 | 0.415267 |

H_{L} | 0.2219 | 0.0816 | 0.893 | 0.5932 | 0.0689 | 0.035358 | 1.1026 | 0.318228 |

d_{M} | 0.0131 | 0.0098 | 0.075 | 0.0493 | 0.000315 | 0.000187 | 0.00505 | 0.001688 |

d_{H} | 0.0295 | 0.012 | 0.141 | 0.0626 | 0.00138 | 0.000374 | 0.02208 | 0.003367 |

d_{L} | 0.0386 | 0.0117 | 0.173 | 0.0605 | 0.002342 | 0.000264 | 0.03747 | 0.002384 |

d_{C} | 0.0303 | 0.0065 | 0.137 | 0.0258 | 0.001444 | 0.000006 | 0.02311 | 0.000539 |

Variables | MAE | XRE | MSE | TSE | ||||
---|---|---|---|---|---|---|---|---|

T | V | T | V | T | V | T | V | |

H_{H} | 0.1529 | 0.05290 | 0.81 | 0.3248 | 0.040455 | 0.008447 | 0.647286 | 0.076024 |

H_{M} | 0.2465 | 0.09083 | 1.56 | 0.3969 | 0.148896 | 0.013468 | 2.382342 | 0.121213 |

H_{L} | 0.2068 | 0.24019 | 1.14 | 1.4457 | 0.081355 | 0.154602 | 1.301689 | 1.391424 |

d_{M} | 0.0094 | 0.00844 | 0.06 | 0.0463 | 0.000191 | 0.000179 | 0.003058 | 0.001618 |

m_{1} | 0.5264 | 0.41324 | 2.35 | 1.7062 | 0.411062 | 0.321390 | 6.577006 | 2.892513 |

m_{2} | 0.00034 | 0.00031 | 0 | 0.0020 | 1.95 × 10^{−7} | 2.57 × 10^{−7} | 3.12 × 10^{−6} | 2.83 × 10^{−7} |

m_{3} | 0.49373 | 0.25813 | 2.31 | 1.0456 | 0.359161 | 0.106389 | 5.746584 | 0.957505 |

Q-Element | Geometrical Approach | Punctual Approach | |
---|---|---|---|

T | H_{H} | 0.2537 | 0.3626 |

d_{M} | 3.7599 | 5.1309 | |

d_{H} | 0.9377 | 4.7073 | |

d_{C} | 0.9425 | 3.0091 | |

V | H_{H} | 0.08836 | 0.1080 |

d_{M} | 2.77873 | 3.1369 | |

d_{H} | 0.73379 | 1.9079 | |

d_{C} | 1.29508 | 0.6520 |

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**MDPI and ACS Style**

Maamri, I.; Barka, N.; El Ouafi, A.
ANN Laser Hardening Quality Modeling Using Geometrical and Punctual Characterizing Approaches. *Coatings* **2018**, *8*, 226.
https://doi.org/10.3390/coatings8060226

**AMA Style**

Maamri I, Barka N, El Ouafi A.
ANN Laser Hardening Quality Modeling Using Geometrical and Punctual Characterizing Approaches. *Coatings*. 2018; 8(6):226.
https://doi.org/10.3390/coatings8060226

**Chicago/Turabian Style**

Maamri, Ilyes, Noureddine Barka, and Abderrazak El Ouafi.
2018. "ANN Laser Hardening Quality Modeling Using Geometrical and Punctual Characterizing Approaches" *Coatings* 8, no. 6: 226.
https://doi.org/10.3390/coatings8060226