# Study on the Depth and Evolution of Keyholes in Plasma-MIG Hybrid Welding

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Welding Test System

#### 2.2. Test Material

#### 2.3. Test Design and Inclined Plate Welding Test

_{P}), MIG current (I

_{M}), magnetic flux density (B), and welding speed (v), and then the response surface method is used to carry out central composite design. A four-factor and five-level test is designed, as shown in Table 3.

_{c}was set as 6. Therefore, the experimental group was 30 groups. After welding, the thickness of the initial collapse under the molten pool was measured (because the inclined plate was used in this test, so the thickness of the inclined plate at the time of penetration could be approximately taken as the depth of the keyhole) as the response value of the response surface method.

## 3. Keyhole Depth Research Based on Response Surface Method

#### 3.1. Prediction Model Reliability Analysis

^{2}; the remaining factors are not significant.

#### 3.2. Analysis of Influence of Welding Factors on Keyhole Depth

#### 3.2.1. Effect of Single Factor on Keyhole Depth

#### 3.2.2. The Influence of Multiple Factors Interaction on Keyhole Depth

_{1},a

_{2}), it can be concluded that when the plasma current changes from 180 to 220 A, the MIG current changes from 290 A to 310 A, the magnetic flux density is 1.65 mT, and the welding speed is 7.5 mm/s, the keyhole depth varied from 4.20 to 4.90 mm. The peak value of keyhole depth occurs when both current values are at their maximum. This is consistent with the influence of single factor on keyhole depth. In general, keyhole depth increases as plasma current or MIG current increases.

_{1},b

_{2}), it can be concluded that when the plasma current varies from 180 to 220 A, the magnetic flux density varies from 0.825 to 2.475 mT, the MIG current is 300 A, and the welding speed is 7.5 mm/s, the keyhole depth varied from 4.25 to 4.75 mm. The peak value of keyhole depth occurs when the plasma current reaches the maximum value and the magnetic field intensity reaches the minimum value in the selected range. Similarly, this is consistent with the effect of single factor on the keyhole depth. In the selected range of parameters, the decrease in magnetic field intensity or the increase in plasma current is conducive to the increase in keyhole depth. This is because the polarity of the plasma welding gun and the MIG welding gun are opposite in the welding process. Under the action of transverse magnetic fields, the plasma arc and the MIG arc are coupled. In addition, the plasma arc deflects under the action of a strong magnetic field and cannot be absolutely perpendicular to the base metal, which affects the straightness of plasma arc. Because the plasma arc presents a certain angle with the workpiece, the keyhole formation ability is weakened, so the penetration depth decreases.

_{1},c

_{2}), it can be concluded that when the plasma current varies from 180 to 220 A, the welding speed varies from 6.5 to 8.5 mm/s, the MIG current is 300 A, and the magnetic flux density is 1.65 mT, the keyhole depth varied from 4.30 to 4.95 mm. The peak value of keyhole depth occurs at the plasma current maximum value and the welding speed minimum value within the selected range. In other words, within the selected parameters, the decrease in welding speed or the increase in plasma current is conducive to the increase in keyhole depth, because both changes are conducive to the increase in welding heat input. According to the contour diagram, the influence of welding velocity (0.5 mm/s) on keyhole depth is much greater than that of plasma current (10 A). There was no obvious interaction between factor A and factor D.

_{1},a

_{2}) that when the MIG current varies from 290 to 310 A, the magnetic field intensity varies from 0.825 to 2.475 mT, the plasma current is 200 A, and the welding speed is 7.5 mm/s, the variation range of keyhole depth is 4.35~4.7 mm. Compared with the above combinations, the variation range of keyhole depth of this combination is the smallest.

_{1},b

_{2}), when the MIG current varies from 290 to 310 A, the welding velocity varies from 6.5 to 8.5 mm/s, the plasma current is 200 A, and the magnetic field intensity is 1.65 mT, the keyhole depth varies from 4.35 to 4.90 mm. The peak value of keyhole depth occurs at the maximum value of the MIG current and the minimum value of the welding speed within the selected parameters; that is, the reduction of welding speed or the increase in MIG current is conducive to the increase in keyhole depth. Similar to the plasma current, the increase in the MIG current is also conducive to the increase in the heat input in the welding process.

_{2}), when the welding speed is constant, the change in the MIG current has little influence on the keyhole depth; otherwise, when the MIG current is constant, the change in the welding speed can bring significant influence on the keyhole depth. By observing the response surface and contour map, there is no obvious mutual influence between factor B and factor D.

_{1},c

_{2}) that when the magnetic field intensity varies from 0.825 to 2.475 mT, the welding speed varies from 6.5 to 8.5 mm/s, the plasma current is 200 A, and the MIG current is 300 A, the depth of keyhole varies from 4.30 mm to 4.80 mm. The peak of keyhole depth occurs when the magnetic flux density and welding speed are both at the minimum in the selected range. By observing the contour diagram in Figure 7(c

_{2}), it can be found that the welding speed has a greater effect on the keyhole depth. According to the response surface and contour map, there is no obvious mutual influence between factor C and factor D.

## 4. Numerical Simulation of Keyhole Behavior in Plasma-MIG Welding

#### 4.1. Establishment of Analytical Model

#### 4.1.1. Basic Assumption

- (1)
- The molten metal generated in the welding process cannot be compressed and is idealized as a laminar Newtonian body and the plasma arc as Newtonian fluid;
- (2)
- The metal melts under the heating of the arc, and the volume change of the solid phase transformation is negligible, and no metal is lost due to evaporation;
- (3)
- The welding process follows the three conservation laws, that is, the law of conservation of mass, energy, and momentum;
- (4)
- In the molten pool, only liquid surface tension, arc pressure, gravity, electromagnetic force, and buoyancy are considered.

#### 4.1.2. Governing Equation

- (1)
- Mass conservation equation$$\frac{\partial \rho}{\partial \mathrm{t}}+\frac{\partial}{\partial {\mathrm{X}}_{\mathrm{i}}}\left(\rho {\mathrm{u}}_{\mathrm{i}}\right)={\mathrm{S}}_{\mathrm{m}}$$
^{3}); S_{m}is mass added by the sparse phase to the continuous phase (kg). - (2)
- Energy conservation equation$$\rho {c}_{p}\left(\frac{\partial T}{\partial t}+u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial y}+w\frac{\partial T}{\partial z}\right)=\frac{\partial}{\partial x}\left(\lambda \frac{\partial T}{\partial x}\right)+\frac{\partial}{\partial y}\left(\lambda \frac{\partial T}{\partial y}\right)+\frac{\partial}{\partial z}\left(\lambda \frac{\partial T}{\partial z}\right)+S$$
^{3}); λ is thermal conductivity; S is the energy equation source term; c_{p}is the specific heat capacity (J/kg·°C). - (3)
- Momentum conservation equation$$\begin{array}{c}{\rho}_{1}[\frac{\partial {\mathrm{u}}_{1}}{\partial \mathrm{t}}+({\mathrm{u}}_{1}-{\mathrm{v}}_{0})\frac{\partial {\mathrm{u}}_{1}}{\partial \mathrm{x}}+{\mathrm{v}}_{1}\frac{\partial {\mathrm{u}}_{1}}{\partial \mathrm{y}}+{\mathrm{w}}_{1}\frac{\partial {\mathrm{u}}_{1}}{\partial \mathrm{z}}]=-\frac{\partial {\mathrm{p}}_{1}}{\partial \mathrm{x}}+{\mu}_{1}(\frac{{\partial}^{2}{\mathrm{u}}_{1}}{\partial {\mathrm{x}}^{2}}+\frac{{\partial}^{2}{\mathrm{u}}_{1}}{\partial {\mathrm{y}}^{2}}+\frac{{\partial}^{2}{\mathrm{u}}_{1}}{\partial {\mathrm{z}}^{2}})+{\mathrm{S}}_{\mathrm{x}}\hfill \\ {\rho}_{1}\left[\frac{\partial {\mathrm{v}}_{1}}{\partial \mathrm{t}}+\left({\mathrm{u}}_{1}-{\mathrm{v}}_{0}\right)\frac{\partial {\mathrm{v}}_{1}}{\partial \mathrm{x}}+\mathrm{v}\frac{\partial {\mathrm{v}}_{1}}{\partial \mathrm{y}}+\mathrm{w}\frac{\partial {\mathrm{v}}_{1}}{\partial \mathrm{z}}\right]=-\frac{\partial {\mathrm{p}}_{1}}{\partial \mathrm{x}}+{\mu}_{1}\left(\frac{{\partial}^{2}{\mathrm{v}}_{1}}{\partial {\mathrm{x}}^{2}}+\frac{{\partial}^{2}{\mathrm{v}}_{1}}{\partial {\mathrm{y}}^{2}}+\frac{{\partial}^{2}{\mathrm{v}}_{1}}{\partial {\mathrm{z}}^{2}}\right)+{\mathrm{S}}_{\mathrm{y}}\hfill \\ {\rho}_{1}\left[\frac{\partial {\mathrm{w}}_{1}}{\partial \mathrm{t}}+\left({\mathrm{u}}_{1}-{\mathrm{v}}_{0}\right)\frac{\partial {\mathrm{w}}_{1}}{\partial \mathrm{x}}+\mathrm{v}\frac{\partial {\mathrm{w}}_{1}}{\partial \mathrm{y}}+\mathrm{w}\frac{\partial {\mathrm{w}}_{1}}{\partial \mathrm{z}}\right]=-\frac{\partial {\mathrm{p}}_{1}}{\partial \mathrm{x}}+{\mu}_{1}\left(\frac{{\partial}^{2}{\mathrm{w}}_{1}}{\partial {\mathrm{x}}^{2}}+\frac{{\partial}^{2}{\mathrm{w}}_{1}}{\partial {\mathrm{y}}^{2}}+\frac{{\partial}^{2}{\mathrm{w}}_{1}}{\partial {\mathrm{z}}^{2}}\right)+{\mathrm{S}}_{\mathrm{z}}\hfill \end{array}$$
_{0}is the welding speed (mm/s); u, v, and w are components of welding velocity; μ is the coefficient of metal viscosity; p is the pressure in the fluid.

#### 4.1.3. Heat Source Model

- (1)
- Conical heat source model

_{e}is the upper surface radius of the conical heat source (m); r

_{i}is the radius of lower surface of conical heat source (m); Q is the plasma arc effective heat input. $\chi $ is the ratio coefficient of peak heat flow on the upper and lower surfaces of the heat source.

- (2)
- Double ellipsoidal heat source model [30]

- (3)
- Droplet heat source model

#### 4.1.4. Model Building and Meshing

#### 4.1.5. Initial Conditions and Boundary Conditions

- (1)
- Initial conditions

- (2)
- Energy boundary conditions

- (3)
- Momentum boundary conditions

#### 4.2. Material Thermal and Physical Parameters and Welding Parameters

#### 4.3. Keyhole Evolution and Molten Pool Flow Behavior

## 5. Conclusions

- (1)
- Taking plasma current, MIG current, magnetic field intensity and welding current as input values and keyhole depth as a response value, a prediction model is established. After variance analysis and model reliability analysis, the prediction of this model meets the expected effect. The results show that the influences of the above four factors on keyhole depth are as follows: welding speed > magnetic field intensity > plasma current > MIG current, and the welding speed and magnetic field intensity have significant effects on keyhole depth. Only plasma current and MIG current have significant interaction with each other. No significant interaction was found between the other groups.
- (2)
- The numerical analysis model is established, and the simulation results show that the internal characteristic morphology of the keyhole is like a parabola in the stable welding state. After a certain time of welding, the boundary between the plasma internal weld pool and the MIG internal weld pool disappears, forming a common weld pool. After the MIG arc starts and the droplet transition is completed, there will be an obvious molten pool crest region and depression region between the two arcs. The crest region will oscillate under the action of arc force and plasma flow force. The flow mode and movement mechanism of metal in keyhole are described. New molten metal is produced under the plasma arc. The molten metal in the front end of the keyhole passes through the bottom of the keyhole to the rear end of the keyhole. This will move the keyhole forward.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Zhang, B.; Shi, Y.; Cui, Y.; Wang, Z.; Hong, X. Prediction of Keyhole TIG Weld Penetration Based on High-Dynamic Range Imaging. J. Manuf. Process.
**2021**, 63, 179–190. [Google Scholar] [CrossRef] - Li, Y.; Tian, S.; Wu, C.S.; Tanaka, M. Experimental Sensing of Molten Flow Velocity, Weld Pool and Keyhole Geometries in Ultrasonic-Assisted Plasma Arc Welding. J. Manuf. Process.
**2021**, 64, 1412–1419. [Google Scholar] [CrossRef] - Liu, X.F.; Jia, C.B.; Wu, C.S.; Zhang, G.K.; Gao, J.Q. Measurement of the Keyhole Entrance and Topside Weld Pool Geometries in Keyhole Plasma Arc Welding with Dual CCD Cameras. J. Mater. Process. Technol.
**2017**, 248, 39–48. [Google Scholar] [CrossRef] - Fabbro, R.; Slimani, S.; Coste, F.; Briand, F. Study of Keyhole Behaviour for Full Penetration Nd-Yag CW Laser Welding. J. Phys. D Appl. Phys.
**2005**, 38, 1881–1887. [Google Scholar] [CrossRef] - Jia, C.B.; Wu, C.S.; Zhang, Y.M. Sensing Controlled Pulse Key-Holing Condition in Plasma Arc Welding. Trans. Nonferrous Met. Soc. China English Ed.
**2009**, 19, 341–346. [Google Scholar] [CrossRef] - Zhang, Y.M.; Zhang, S.B.; Liu, Y.C. A Plasma Cloud Charge Sensor for Pulse Keyhole Process Control. Meas. Sci. Technol.
**2001**, 12, 1365–1370. [Google Scholar] [CrossRef][Green Version] - Bakkiyaraj, M.; Palanisamy, P.; Balasubramanian, V. Evaluating the Tensile Strength of Friction Welded (AA6061 & AA7075-T6) Dissimilar Joints by Using Response Surface Methodology. Mater. Res. Express
**2019**, 6, 086527. [Google Scholar] [CrossRef] - Subramanian, R.; Natarajan, B.; Kaliyaperumal, B.; Chinnasamy, R. Effect of MIG Welding Process Parameters on Microstructure and Tensile Behavior of Hastelloy C276 Using Response Surface Methodology. Mater. Res. Express
**2019**, 6, 066540. [Google Scholar] [CrossRef] - Shahi, A.S.; Pandey, S. Modelling of the Effects of Welding Conditions on Dilution of Stainless Steel Claddings Produced by Gas Metal Arc Welding Procedures. J. Mater. Process. Technol.
**2008**, 196, 339–344. [Google Scholar] [CrossRef] - Jahanzaib, M.; Hussain, S.; Wasim, A.; Aziz, H.; Mirza, A.; Ullah, S. Modeling of Weld Bead Geometry on HSLA Steel Using Response Surface Methodology. Int. J. Adv. Manuf. Technol.
**2017**, 89, 2087–2098. [Google Scholar] [CrossRef] - Song, C.; Dong, S.; He, P.; Yan, S.; Zhao, X. Correlation of Process Parameters and Porosity in Laser Welding of 7A52 Aluminum Alloy Using Response Surface Methodology. Procedia Manuf.
**2019**, 37, 294–298. [Google Scholar] [CrossRef] - Rosli, N.A.; Alkahari, M.R.; Ramli, F.R.; Fadzli bin Abdollah, M.; Kudus, S.I.A.; Herawan, S.G. Parametric Optimisation of Micro Plasma Welding for Wire Arc Additive Manufacturing by Response Surface Methodology. Manuf. Technol.
**2022**, 22, 59–70. [Google Scholar] [CrossRef] - Apelgren, P.; Amoroso, M.; Säljö, K.; Montelius, M.; Lindahl, A.; Stridh Orrhult, L.; Gatenholm, P.; Kölby, L.; Arulkumar, S.; Parthiban, S.; et al. Ac Ce Pte d M Us Pt. Mater. Today Proc.
**2019**, 27. 0-31. [Google Scholar] - Kumar, V.; Mandal, A.; Das, A.K.; Kumar, S. Parametric Study and Characterization of Wire Arc Additive Manufactured Steel Structures. Int. J. Adv. Manuf. Technol.
**2021**, 115, 1723–1733. [Google Scholar] [CrossRef] - Li, T.Q.; Wu, C.S. Numerical Simulation of Plasma Arc Welding with Keyhole-Dependent Heat Source and Arc Pressure Distribution. Int. J. Adv. Manuf. Technol.
**2015**, 78, 593–602. [Google Scholar] [CrossRef] - Jian, X.; Wu, C.S.; Zhang, G.; Chen, J. A Unified 3D Model for an Interaction Mechanism of the Plasma Arc, Weld Pool and Keyhole in Plasma Arc Welding. J. Phys. D Appl. Phys.
**2015**, 48, 465504. [Google Scholar] [CrossRef] - Qiao, J.; Wu, C.; Li, Y. Numerical Analysis of Keyhole and Weld Pool Behaviors in Ultrasonic-Assisted Plasma Arc Welding Process. Materials
**2021**, 14, 703. [Google Scholar] [CrossRef] [PubMed] - Kuang, J.H.; Hung, T.P.; Chen, C.K. A Keyhole Volumetric Model for Weld Pool Analysis in Nd:YAG Pulsed Laser Welding. Opt. Laser Technol.
**2012**, 44, 1521–1528. [Google Scholar] [CrossRef] - Wu, C.S.; Huo, Y.S. Numerical Analysis of Keyhole Geometry and Temperature Profiles in Plasma Arc Welding. J. Manuf. Process.
**2013**, 15, 593–599. [Google Scholar] [CrossRef] - Jian, X.; Wu, C.S. Numerical Analysis of the Coupled Arc-Weld Pool-Keyhole Behaviors in Stationary Plasma Arc Welding. Int. J. Heat Mass Transf.
**2015**, 84, 839–847. [Google Scholar] [CrossRef] - Li, T.Q.; Chen, L.; Zhang, Y.; Yang, X.M.; Lei, Y.C. Metal Flow of Weld Pool and Keyhole Evolution in Gas Focusing Plasma Arc Welding. Int. J. Heat Mass Transf.
**2020**, 150, 119296. [Google Scholar] [CrossRef] - Hertel, M.; Füssel, U.; Schnick, M. Numerical Simulation of the Plasma-MIG Process-Interactions of the Arcs, Droplet Detachment and Weld Pool Formation. Weld. World
**2014**, 58, 85–92. [Google Scholar] [CrossRef] - Zhang, C.; Hu, Q.; Pu, J.; Wu, H. Study on the Molten Pool Fluid Behavior of PAW-Cable-Type Seven-Wire GMAW Hybrid Welding. Crystals
**2022**, 12, 306. [Google Scholar] [CrossRef] - Gao, Z.; Jiang, P.; Mi, G.; Cao, L.; Liu, W. Investigation on the Weld Bead Profile Transformation with the Keyhole and Molten Pool Dynamic Behavior Simulation in High Power Laser Welding. Int. J. Heat Mass Transf.
**2018**, 116, 1304–1313. [Google Scholar] [CrossRef] - Wu, C.S.; Zhang, T.; Feng, Y.H. Numerical Analysis of the Heat and Fluid Flow in a Weld Pool with a Dynamic Keyhole. Int. J. Heat Fluid Flow
**2013**, 40, 186–197. [Google Scholar] [CrossRef] - Wu, D.; Tashiro, S.; Hua, X.; Tanaka, M. Analysis of the Energy Propagation in the Keyhole Plasma Arc Welding Using a Novel Fully Coupled Plasma Arc-Keyhole-Weld Pool Model. Int. J. Heat Mass Transf.
**2019**, 141, 604–614. [Google Scholar] [CrossRef] - Miao, X.; Zhang, H.; Ge, F.; He, Z.; Gao, J.; Su, Z. Research on Arc Morphology and Keyhole Behavior of Molten Pool in Magnetically Controlled Plasma-GMAW Welding. Int. J. Metals.
**2023**, 13, 148. [Google Scholar] [CrossRef] - Xu, G.X.; Wu, C.S.; Qin, G.L.; Wang, X.Y.; Lin, S.Y. Adaptive Volumetric Heat Source Models for Laser Beam and Laser + Pulsed GMAW Hybrid Welding Processes. Int. J. Adv. Manuf. Technol.
**2011**, 57, 245–255. [Google Scholar] [CrossRef] - Miao, J.Y. Study on Weldpool Fluid Behavior of Plasma arc Welding + Cable-Wire Pulsed GMAW Hybrid Welding. Master’s Thesis, Jiangsu University of Science and Technology, Zhenjiang, China, 2012. (In Chinese). [Google Scholar]
- Goldak, J.; Chakravarti, A.; Bibby, M. A New Finite Element Model for Welding Heat Sources. Metall. Trans. B
**1984**, 15, 299–305. [Google Scholar] [CrossRef]

**Figure 1.**Welding system overall distribution physical diagram: 1—Plasma-MIG hybrid torch; 2—MIG power supply; 3—PAW power supply; 4—welding process control system; 5—walking mechanism; 6—welding robot.

**Figure 2.**Plasma-MIG hybrid welding schematic diagram: 1—base metal, 2—tungsten electrode, 3—plasma nozzle, 4—molten metal, 5—welding wire, 6—plasma arc, 7—MIG arc, 8—weld, 9—the welding height (distance of plasma nozzle from workpiece), 10—magnetic field.

**Figure 4.**Model prediction analysis diagram. (

**a**) Residuals and prediction diagrams; (

**b**) graph of residual and number of experiments; (

**c**) relationship between predicted and actual values.

**Figure 5.**Influence of single factor on keyhole depth: (

**a**) plasma current; (

**b**) MIG current; (

**c**) magnetic flux density; (

**d**) welding speed.

**Figure 6.**Interactive response surface and contour map of different factors: (

**a**,

_{1}**a**) are the interactive response surfaces and contour maps of A: plasma current and B: MIG current, respectively; (

_{2}**b**,

_{1}**b**) are the interactive response surfaces and contour maps of factors A: plasma current and C: magnetic field intensity, respectively; (

_{2}**c**,

_{1}**c**) are the interactive response surfaces and contour maps of factors A: plasma current and D: welding velocity, respectively.

_{2}**Figure 7.**Interactive response surface and contour map of different factors: (

**a**,

_{1}**a**) are the interactive response surfaces and contour maps of B: MIG current and C: magnetic flux density, respectively; (

_{2}**b**,

_{1}**b**) are the interactive response surfaces and contour maps of factors B: MIG current and D: welding speed, respectively; (

_{2}**c**,

_{1}**c**) are the interactive response surfaces and contour maps of factors C: magnetic flux density and D: welding speed, respectively.

_{2}**Figure 9.**Temperature field distribution of the weld section and three-dimensional fluid flow diagram of the molten pool at different time: (

**a**,

**c**,

**e**,

**g**) are the temperature field of the weld section at 100 steps, 1000 steps, 1500 steps, and 2000 steps, respectively; (

**b**,

**d**,

**f**,

**h**) are the three-dimensional fluid flow diagrams of the molten pool at 100 steps, 1000 steps, 1500 steps, and 2000 steps, respectively.

**Figure 10.**Temperature field distribution of the weld section and three-dimensional fluid flow diagram of the molten pool at different times: (

**a**,

**c**,

**e**,

**g**) are the temperature field of the weld section at 2700 steps, 3400 steps, 4000 steps, and 4880 steps, respectively; (

**b**,

**d**,

**f**,

**h**) are the three-dimensional fluid flow diagrams of the molten pool at 2700 steps, 3400 steps, 4000 steps, and 4880 steps, respectively.

C | Ni | S | Mn | Cr | P | Si | Fe |
---|---|---|---|---|---|---|---|

0.07 | 8–10.5 | 0.03 | 1.00–2.50 | 17.5–19.5 | 0.45 | 0.75 | balance |

C | Ni | S | Mn | Cr | P | Si | Fe |
---|---|---|---|---|---|---|---|

≤0.080 | 8.00–10.0 | ≤0.030 | 1.40–1.85 | 17.0–19.0 | 0.30–0.65 | ≤0.030 | balance |

Level | A: I_{P}/A | B: I_{M} /A | C: B/mT | D: v/mm•s^{−1} |
---|---|---|---|---|

2 | 240 | 320 | 3.3 | 9.5 |

1 | 220 | 310 | 2.475 | 8.5 |

0 | 200 | 300 | 1.65 | 7.5 |

−1 | 180 | 290 | 0.825 | 6.5 |

−2 | 160 | 280 | 0 | 5.5 |

Serial Number | A (A) | B (A) | C (mT) | D (mm/s) | Keyhole Depth (mm) |
---|---|---|---|---|---|

1 | 180 | 290 | 0.825 | 6.5 | 5.36 |

2 | 220 | 290 | 0.825 | 6.5 | 4.83 |

3 | 180 | 310 | 0.825 | 6.5 | 4.74 |

4 | 220 | 310 | 0.825 | 6.5 | 5.02 |

5 | 180 | 290 | 2.475 | 6.5 | 4.69 |

6 | 220 | 290 | 2.475 | 6.5 | 4.67 |

7 | 180 | 310 | 2.475 | 6.5 | 4.44 |

8 | 220 | 310 | 2.475 | 6.5 | 5.25 |

9 | 180 | 290 | 0.825 | 8.5 | 4.95 |

10 | 220 | 290 | 0.825 | 8.5 | 4.47 |

11 | 180 | 310 | 0.825 | 8.5 | 4.16 |

12 | 220 | 310 | 0.825 | 8.5 | 4.91 |

13 | 180 | 290 | 2.475 | 8.5 | 4.51 |

14 | 220 | 290 | 2.475 | 8.5 | 4.42 |

15 | 180 | 310 | 2.475 | 8.5 | 4.04 |

16 | 220 | 310 | 2.475 | 8.5 | 4.36 |

17 | 160 | 300 | 1.65 | 7.5 | 4.28 |

18 | 240 | 300 | 1.65 | 7.5 | 5.07 |

19 | 200 | 280 | 1.65 | 7.5 | 4.16 |

20 | 200 | 320 | 1.65 | 7.5 | 5.05 |

21 | 200 | 300 | 0 | 7.5 | 4.98 |

22 | 200 | 300 | 3.3 | 7.5 | 4.48 |

23 | 200 | 300 | 1.65 | 5.5 | 5.4 |

24 | 200 | 300 | 1.65 | 9.5 | 4.49 |

25 | 200 | 300 | 1.65 | 7.5 | 4.78 |

26 | 200 | 300 | 1.65 | 7.5 | 4.5 |

27 | 200 | 300 | 1.65 | 7.5 | 4.38 |

28 | 200 | 300 | 1.65 | 7.5 | 4.63 |

29 | 200 | 300 | 1.65 | 7.5 | 4.2 |

30 | 200 | 300 | 1.65 | 7.5 | 4.35 |

Source | Quadratic Sum | Degree of Freedom | p-Value | F-Value | Mean Square Error |
---|---|---|---|---|---|

Model | 2.91 | 14 | 0.0165 | 3.19 | 0.208 |

A | 0.286 | 1 | 0.0537 | 4.38 | 0.286 |

B | 0.0267 | 1 | 0.5322 | 0.4088 | 0.0267 |

C | 0.3902 | 1 | 0.0273 | 5.98 | 0.3902 |

D | 1.04 | 1 | 0.0012 | 15.97 | 1.04 |

AB | 0.6724 | 1 | 0.0058 | 10.31 | 0.6724 |

AC | 0.0625 | 1 | 0.3432 | 0.9581 | 0.0625 |

AD | 0.0001 | 1 | 0.9693 | 0.0015 | 0.0001 |

BC | 0.021 | 1 | 0.5786 | 0.3223 | 0.021 |

BD | 0.038 | 1 | 0.457 | 0.5829 | 0.038 |

CD | 0.0042 | 1 | 0.8026 | 0.0648 | 0.0042 |

A^{2} | 0.0439 | 1 | 0.4249 | 0.6727 | 0.0439 |

B^{2} | 0.0139 | 1 | 0.6512 | 0.2129 | 0.0139 |

C^{2} | 0.0792 | 1 | 0.2878 | 1.21 | 0.0792 |

D^{2} | 0.317 | 1 | 0.0435 | 4.86 | 0.317 |

Residual error | 0.9785 | 15 | 0.0652 | ||

Lack of fit | 0.7606 | 10 | 0.28 | 1.74 | 0.0761 |

Error | 0.2179 | 5 | 0.0436 | ||

Total | 3.89 | 29 |

**Table 6.**Thermophysical parameters of 304 stainless steel materials [29].

Designation | Symbol | Numerical Value | Unit |
---|---|---|---|

solidus temperature | T_{s} | 1723 | K |

liquidus temperature | T_{l} | 1790 | K |

latent heat of fusion | H_{m} | 2.738 × 10^{5} | J/kg |

density | ρ | 7930 | Kg/m^{3} |

coefficient of thermal expansion | β_{0} | 1.2 × 10^{−5} | K^{−1} |

convective heat transfer coefficient | α_{c} | 80 | W/m^{2}K |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Miao, X.; Zhang, H.; Cao, W.; He, Z.; Wang, B.; Ge, F.; Gao, J.
Study on the Depth and Evolution of Keyholes in Plasma-MIG Hybrid Welding. *Crystals* **2023**, *13*, 412.
https://doi.org/10.3390/cryst13030412

**AMA Style**

Miao X, Zhang H, Cao W, He Z, Wang B, Ge F, Gao J.
Study on the Depth and Evolution of Keyholes in Plasma-MIG Hybrid Welding. *Crystals*. 2023; 13(3):412.
https://doi.org/10.3390/cryst13030412

**Chicago/Turabian Style**

Miao, Xinglin, Hongtao Zhang, Wenhuan Cao, Zhenyu He, Bo Wang, Fuchen Ge, and Jianguo Gao.
2023. "Study on the Depth and Evolution of Keyholes in Plasma-MIG Hybrid Welding" *Crystals* 13, no. 3: 412.
https://doi.org/10.3390/cryst13030412