# Assessing Electrode Characteristics in Continuous Resistance Spot Welding of BH 340 Steel Based on Dynamic Resistance

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Procedure

#### Experimental Materials and Welding Conditions

## 3. Experimental Results and Discussion

#### 3.1. Diameter of the Electrode Tip

#### 3.2. Dynamic Resistance Signal Characteristics

#### 3.3. Establishing Models for the Extracted Features

_{i}represents each independent variable, and $f({x}_{1},{x}_{2},\cdots {x}_{n})$ indicates the dependent variable. The regression coefficient a

_{i}can be estimated from the obtained experimental data using the least squares regression method.

_{3}has the largest correlation coefficient with the electrode diameter of 0.882, while the feature r

_{e}of the dynamic resistance has the smallest correlation coefficient value. Features with correlation coefficients less than 0.5 were discarded, and the remaining nine features (${r}_{0}$, ${t}_{\alpha}$, ${r}_{\alpha}$, ${t}_{\beta}$, ${r}_{\beta}$, $P$, ${k}_{1}$, ${k}_{2}$, and ${k}_{3}$) were used as inputs to the upcoming regression model to predict the electrode tip diameter (D). The regression model was obtained using the stepwise regression analysis method and MATLAB software (MATLAB R2017b.). The basic idea of the stepwise regression analysis method is to automatically select the most important variables from a large number of available variables and build a prediction model for regression analysis. The basic idea is to introduce the independent variables one by one, and the condition for introducing them is that the sum of squares of the partial regression is significant after testing. At the same time, each time a new independent variable is introduced, the old independent variables should be tested one by one, and the independent variables with insignificant partial regression sums of squares should be eliminated. In this way, variables are introduced and eliminated until no new variables are introduced and no old variables are eliminated. The 43 groups of data obtained from the welding experiment and the carbon printing experiment on carbon paper are divided into two groups: training samples and test samples. To obtain the regression model, 33 groups of all data were randomly selected as training samples, and another 10 groups of the test samples were used to verify the simulation accuracy and performance of the model. All regression and ANOVA results were performed on the average values of the two sets of data.

^{2}, the adjusted R

^{2}and the sum of squared prediction errors, the fit of the regression model can be evaluated. A good regression model should have a coefficient of determination close to 1 and a small sum of squared prediction errors. The R

^{2}coefficient of this model is 0.9000, which implies that 90% of the experimental data agrees with the predicted data. The model only fails to predict the remaining 10% of the data. The adjusted R

^{2}is 0.8897, which is very adjacent to 0.9000 and also close to 1. Among the p-values of all the nine features, only ${r}_{0},$ $P$, and ${k}_{3}$ have p-values lower than 0.05, so the conclusion that can be drawn that they are highly significant [29] and should be retained in this linear regression model.

^{2}and adjusted R

^{2}are very similar and close to 1, and their values are higher than those of the first linear model. In such a case, the linear regression model with interaction terms is more accurate in predicting the electrode diameter. Figure 12 is a good illustration of this statement. The graph reflects that the residual error of the second model is smaller.

_{0}, P and k

_{3}are the features extracted from the dynamic resistance.

## 4. Conclusions

^{2}values are approximately 0.89 and 0.95, respectively.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 11.**Dynamic resistance variations with number of welds (Symbols used in this diagram correspond to those in Figure 10).

**Figure 14.**Prediction of electrode tip diameter versus measured value based on the linear regression model with interaction term when welding with a pair of new electrodes.

**Figure 15.**Relative errors based on the linear regression model with interaction term when welding with a pair of new electrodes.

Chemical Compositions | Mechanical Properties | Zn Coating | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

C | Si | Mn | P | S | Al | Cu | R_{el} (MPa) | R_{m} (MPa) | A80 (%) | Elongation/A80 (%) | Thickness/t (µm) | Mass/m (g/m^{2}) |

0.025 | 0.03 | 0.44 | 0.009 | 0.015 | 0.044 | ≤0.2 | 360 | 425 | 28 | 41 | 15 | 200 |

_{el}yield strength, R

_{m}ultimate tensile strength, A80 elongation.

Chemical Compositions | Physical Properties | ||||
---|---|---|---|---|---|

Cu | Cr | Zr | Hardness (HV0.1) | Thermal Conductivity (W/mK) | Electrical Conductivity (%IACS) |

Balance | 1.00 | 0.10 | 150 | 75 | 325 |

Welding Current | Welding Time | Hold Time | Electrode Force |
---|---|---|---|

4 kA | 60 ms | 10 ms | 360 N |

Characteristics | Equation | Unit | Definition |
---|---|---|---|

${r}_{0}$ | - | mΩ | The resistance of the initial point. |

${t}_{\alpha}$ | - | ms | The position of the α point. |

${r}_{\alpha}$ | - | mΩ | The resistance of the α point. |

${t}_{\beta}$ | - | ms | The position of the β point. |

${r}_{\beta}$ | - | mΩ | The resistance of the β point. |

${r}_{e}$ | - | mΩ | The resistance of the end point. |

P | $p={\displaystyle \int r(t)dt}$ | mΩ·ms | The integration of dynamic resistance. |

${k}_{1}$ | ${k}_{1}=\frac{{r}_{0}-{r}_{\alpha}}{{t}_{\alpha}}$ | Ω/s | The decreasing speed between the initial point and the α point. |

${k}_{2}$ | ${k}_{2}=\frac{{r}_{\beta}-{r}_{\alpha}}{{t}_{\beta}-{t}_{\alpha}}$ | Ω/s | The increasing speed between the α point and the β point. |

${k}_{3}$ | ${k}_{3}=\frac{{r}_{\beta}-{r}_{e}}{60-{t}_{\beta}}$ | Ω/s | The decreasing speed between the β point and the end point. |

Extracted Features | ${\mathit{r}}_{0}$ | ${\mathit{t}}_{\mathit{\alpha}}$ | ${\mathit{r}}_{\mathit{\alpha}}$ | ${\mathit{t}}_{\mathit{\beta}}$ | ${\mathit{r}}_{\mathit{\beta}}$ | ${\mathit{r}}_{\mathit{e}}$ | P | ${\mathit{k}}_{1}$ | ${\mathit{k}}_{2}$ | ${\mathit{k}}_{3}$ | D |
---|---|---|---|---|---|---|---|---|---|---|---|

Correlation coefficients | −0.573 | 0.513 | −0.597 | 0.597 | −0.730 | 0.023 | −0.639 | −0.625 | −0.585 | −0.882 | 1 |

Source | Sum of Squares | df | Mean Square | F Value | p Value |
---|---|---|---|---|---|

Model | 2.1767 | 3 | 0.7256 | 87.0441 | <0.0001 |

Residual | 0.2417 | 29 | 0.0083 | ||

Cor total | 2.4185 | 32 | |||

Standard deviation | 0.0913 | Mean | 3.6073 | ||

R-Squared | 0.9000 | Adjusted R-Squared | 0.8897 |

Term | Estimated Value | Standard Error | T-Value | p-Value | p Value |
---|---|---|---|---|---|

Constant | 4.0292 | 0.1450 | 27.7970 | <0.0001 | <0.0001 |

r_{0} | −0.0123 | 0.0056 | −2.1981 | 0.0361 | |

P | 0.0065 | 0.0014 | 4.8235 | <0.0001 | |

k_{3} | −46.4429 | 3.8793 | −11.9720 | <0.0001 |

Source | Sum of Squares | df | Mean Square | F Value | p Value |
---|---|---|---|---|---|

Model | 2.3145 | 4 | 0.5786 | 155.8613 | <0.0001 |

Residual | 0.1039 | 28 | 0.0037 | ||

Cor total | 2.4185 | 32 | |||

Standard deviation | 0.0609 | Mean | 3.6073 | ||

R-Squared | 0.9570 | Adjusted R-Squared | 0.9509 |

Term | Estimated Value | Standard Error | T-Value | p-Value | p Value |
---|---|---|---|---|---|

Constant | 2.7135 | 0.2366 | 11.4662 | <0.0001 | <0.0001 |

r_{0} | 0.0016 | 0.0044 | 0.3715 | 0.7130 | |

P | 0.0128 | 0.014 | 9.3516 | <0.0001 | |

k_{3} | 32.4732 | 13.2098 | 2.4583 | 0.0204 | |

Pk_{3} | −0.4262 | 0.07 | −6.0922 | <0.0001 |

Item | Symbol | Unit | Linear Regression Model | Regression Model with Interaction Terms |
---|---|---|---|---|

Minimum | ${D}_{\mathrm{min}}$ | mm | 0.018 | 0.0013 |

Maximum | ${D}_{\mathrm{max}}$ | mm | 0.50 | 0.30 |

Mean | ${D}_{\mathrm{mean}}$ | mm | 0.11 | 0.072 |

Medium | ${D}_{\mathrm{med}}$ | mm | 0.058 | 0.042 |

Standard deviation | $\sigma $ | mm | 0.14 | 0.089 |

Range | $\Delta $ | mm | 0.48 | 0.30 |

**Table 11.**The statistical values of the residuals based on the linear regression model with interaction terms when welding with a pair of new electrodes.

Item | Minimum | Maximum | Mean | Medium | Standard Deviation | Range |
---|---|---|---|---|---|---|

Unit | mm | mm | mm | mm | mm | mm |

Value | 0.02 | 0.72 | 0.32 | 0.26 | 0.21 | 0.7 |

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## Share and Cite

**MDPI and ACS Style**

Zhao, D.; Vdonin, N.; Slobodyan, M.; Butsykin, S.; Kiselev, A.; Gordynets, A.
Assessing Electrode Characteristics in Continuous Resistance Spot Welding of BH 340 Steel Based on Dynamic Resistance. *J. Manuf. Mater. Process.* **2023**, *7*, 218.
https://doi.org/10.3390/jmmp7060218

**AMA Style**

Zhao D, Vdonin N, Slobodyan M, Butsykin S, Kiselev A, Gordynets A.
Assessing Electrode Characteristics in Continuous Resistance Spot Welding of BH 340 Steel Based on Dynamic Resistance. *Journal of Manufacturing and Materials Processing*. 2023; 7(6):218.
https://doi.org/10.3390/jmmp7060218

**Chicago/Turabian Style**

Zhao, Dawei, Nikita Vdonin, Mikhail Slobodyan, Sergei Butsykin, Alexey Kiselev, and Anton Gordynets.
2023. "Assessing Electrode Characteristics in Continuous Resistance Spot Welding of BH 340 Steel Based on Dynamic Resistance" *Journal of Manufacturing and Materials Processing* 7, no. 6: 218.
https://doi.org/10.3390/jmmp7060218