# Effect of Temperature Distribution in Ultrasonically Welded Joints of Copper Wire and Sheet Used for Electrical Contacts

## Abstract

**:**

## 1. Introduction

## 2. Experimental Details

## 3. Finite Element Analysis

#### 3.1. CAD Model

#### 3.2. Material Properties

#### 3.3. Element Selection and Meshing of CAD Model

#### 3.4. Assumptions for Thermal Analysis

- Unsteady state is considered for thermal analysis.
- Full contact is established with no air gap between the specimens.
- Room temperature is 30 °C.
- The area in which the friction is effective is assumed to be the area of deformation
- Surfaces exposed to air are set under free convection.

#### 3.5. Measurement of Area of Deformation

_{DZ}) play a significant role in calculation of heat flux required for simulation and it is estimated as the rectangular area bordering the interface as shown in Figure 8. The area of deformation for each joint is measured for all the trials of experiments using Tool maker’s microscope (Mitutoya South Asia, NewDelhi, India) [20].

#### 3.6. Calculation of Heat Flux

^{2}, $\mathrm{P}$ is the power in W, ${\mathrm{A}}_{\mathrm{w}}$ is the weld area in m

^{2}, ${\mathrm{F}}_{\mathrm{w}}$. is the weld force in N, ${\mathrm{V}}_{\mathrm{avg}}$ is the average sonotrode velocity and equals $4\times {\mathsf{\epsilon}}_{0}\times {\mathrm{f}}_{\mathrm{w}}$, ${\mathsf{\epsilon}}_{0}$ is the amplitude of vibration of the sonotrode, and ${\mathrm{f}}_{\mathrm{w}}$ is the welding frequency. The weld force (F

_{w}) is given by Equation (2).

_{T}is the average temperature dependent yield strength in N/m

^{2}, F

_{N}is the clamping force in N, and A

_{DZ}is the area of deformation in m

^{2}. By substituting Equation (2) into Equation (1), the heat flux due to deformation is obtained as shown in Equation (3).

_{DZ}is the A

_{W}. Applying this condition, the heat flux due to deformation can be calculated, as shown in Equation (4).

^{6}N/m

^{2}.

^{−6}m

^{2}, thus obtained as discussed in Section 3.5, is given by

^{6}W/m

^{2}

_{W}+ Q

_{FR}= 158.92 × 10

^{6}W/m

^{2}+ 90.85 × 10

^{6}W/m

^{2}= 249.77 × 10

^{6}W/m

^{2}.

## 4. Simulation and Experimental Trials

## 5. Results and Discussions

^{6}W/m

^{2}. The temperature obtained from simulation is 79.26 °C. The average temperature obtained from experiments for the same combination of process parameter using thermocouple is 79.85 °C. The strength of the joint in tension obtained is 187.721 N. As all the process parameter values are set at the lower levels, the temperature developed at the interface and the strength of the joint obtained in this trial is minimum when compared with all the other trials. The results from simulation and experiments are shown in Figure 10.

^{6}W/m

^{2}. The temperature obtained from simulation is 117.8 °C. The average temperature obtained from experiments for the same combination of process parameter is 117.64 °C. The strength of the joint obtained is 213.342 N. The results from simulation and experiments are shown in Figure 11.

^{6}W/m

^{2}. The temperature obtained from simulation is 141.2 °C. The average temperature obtained from experiments for the same combination of process parameter is 141.50 °C. The strength of the joint obtained is 231.432 N. As all the process parameter values were at higher levels, the temperature developed at the interface and the strength of the joint obtained in this trial is maximum when compared with all the other trials. The results from simulation and experiments are shown in Figure 12.

## 6. Conclusions

- The results from simulation and experiments conducted based on Taguchi’s L9 orthogonal array reveal that the maximum temperature developed during welding is less than the melting point of the work material, validating that the USMW is a solid state welding process.
- It is observed from the analysis that the influence of heat generated due to deformation and friction is significant in the process of formation of joint. The results of temperature from simulation are found to be in good agreement with results of temperature from experiments measured using thermocouple. Thus, the developed finite element model is validated.
- The results of temperature developed at the interface are compared with results of strength of the joint under tensile loading. It is inferred that the strength of the joint correlate well with the temperature developed at the interface indicating that the temperature at the interface has significant effect on strength of the joint. It is observed that the strength of the joint depends on the variations of heat generated during welding under different process parametric conditions.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 10.**Trial 1, comparison of temperatures (°C): (

**a**) results from experiments (Trial 1); and (

**b**) result from simulation (Trial 1): Minimum temperature 30.04 °C, Maximum temperature 79.26 °C.

**Figure 11.**Trial 5, comparison of temperatures (°C): (

**a**) results from experiments (Trial 5); and (

**b**) result from simulation (Trial 5): Minimum temperature 30.06 °C, Maximum temperature 117.8 °C.

**Figure 12.**Trial 9, comparison of temperatures (°C): (

**a**) results from experiments (Trial 9); and (

**b**) result from simulation (Trial 9): Minimum temperature 30.09 °C, Maximum temperature 141.12 °C.

Factors | Units | Designation | Level 1 | Level 2 | Level 3 |
---|---|---|---|---|---|

Clamping force | N | A | 795 | 995 | 1195 |

Amplitude of vibration of sonotrode | µm | B | 30 | 42.5 | 57 |

Weld time | second | C | 2 | 2.5 | 3 |

Properties | Value |
---|---|

Young’s Modulus (GPa) | 115 |

Poisson ratio | 0.3 |

Density (kg/m^{3}) | 8940 |

Thermal conductivity (W/m °C) | 391 |

Specific heat (J/Kg °C) | 385 |

Thermal expansion co-efficient(°C^{−1}) | 1.66 × 10^{−5} |

Trial No. | Clamping Force (N) | Amplitude of Vibration of Sonotrode (μm) | Weld Time (s) | Temperature from Simulation (°C) | Temperature from Experiments (°C) | Strength of the Joint in Tension * (N) | ||
---|---|---|---|---|---|---|---|---|

Trial 1 | Trial 2 | Average | ||||||

1 | 795 | 30 | 2 | 79.26 | 79.97 | 79.73 | 79.85 | 187.721 |

2 | 995 | 30 | 2.5 | 110.9 | 110.06 | 110.25 | 110.16 | 210.107 |

3 | 1195 | 30 | 3 | 137.2 | 137.38 | 137.01 | 137.20 | 224.946 |

4 | 795 | 42.5 | 2 | 83.27 | 83.25 | 83.39 | 83.32 | 193.548 |

5 | 995 | 42.5 | 2.5 | 117.8 | 117.55 | 117.73 | 117.64 | 213.342 |

6 | 1195 | 42.5 | 3 | 139.9 | 139.01 | 139.38 | 139.20 | 227.621 |

7 | 795 | 57 | 2 | 99.16 | 99.74 | 99.37 | 99.56 | 202.369 |

8 | 995 | 57 | 2.5 | 119.5 | 119.60 | 119.00 | 119.30 | 217.638 |

9 | 1195 | 57 | 3 | 141.2 | 141.13 | 141.87 | 141.50 | 231.432 |

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**MDPI and ACS Style**

Pradeep Kumar, J.
Effect of Temperature Distribution in Ultrasonically Welded Joints of Copper Wire and Sheet Used for Electrical Contacts. *Materials* **2018**, *11*, 1010.
https://doi.org/10.3390/ma11061010

**AMA Style**

Pradeep Kumar J.
Effect of Temperature Distribution in Ultrasonically Welded Joints of Copper Wire and Sheet Used for Electrical Contacts. *Materials*. 2018; 11(6):1010.
https://doi.org/10.3390/ma11061010

**Chicago/Turabian Style**

Pradeep Kumar, Jeyaraj.
2018. "Effect of Temperature Distribution in Ultrasonically Welded Joints of Copper Wire and Sheet Used for Electrical Contacts" *Materials* 11, no. 6: 1010.
https://doi.org/10.3390/ma11061010