Analytical Model of Quasi-Steady Temperature Field in Hot Wire TIG Welding

Literature Overview

The paper by Zhao Fuhai, Hua Xueming, Ye Xin, and Wu Yixiong, published in the Journal of Shanghai Jiao Tong University (2012, Vol. 46, No. 7, pp. 1063-1068), presents a mathematical analytical model for the quasi-steady temperature distribution of the hot wire in Hot Wire Tungsten Inert Gas (HW-TIG) welding. The work originates from the Welding Engineering Research Institute of Shanghai Jiao Tong University and addresses a critical gap in the quantitative understanding of hot wire preheating behavior. The model is built upon the principle of superposition, combining the effects of resistive heating and molten pool heat transfer on the wire temperature distribution. This is significant because HW-TIG welding is increasingly used for thick-section pipe welding where controlling the weld root geometry and reducing cracking susceptibility are paramount.

Core Technical Framework

The authors establish the model based on two fundamental physical principles: energy conservation and Fourier's law of heat conduction. The resistive heating component is modeled as a distributed heat source along the wire, while the molten pool heat transfer is treated as a boundary condition at the wire tip. The superposition principle allows the total temperature field to be decomposed into two independent sub-problems that are solved separately and then added together.

The governing equation for the wire temperature field can be expressed as:

Resistive heating contribution: proportional to the square of the wire current density and the electrical resistivity of the wire material
Molten pool heat transfer contribution: dependent on the heat flux from the arc and the weld pool to the wire tip region

The quasi-steady assumption is valid because the wire feed speed is relatively constant during normal welding operation, and the thermal time constant of the wire is much shorter than the welding time scale. This simplification is justified for practical industrial conditions where wire feed speeds range from 3 to 10 m/min.

Key Process Parameters and Their Effects

Parameter	Effect on Wire Temperature	Direction of Influence	Engineering Implication
Wire current density	Increases temperature at all positions	Positive correlation	Higher current density provides stronger preheating but may cause wire deformation
Wire feed speed	Decreases temperature at all points	Negative correlation	Faster feeding reduces preheat time, requiring higher current compensation
Stick-out length (dry extension)	Increases tip preheat temperature	Positive correlation	Longer stick-out allows more resistive heating but reduces arc stability

The study reveals a numerical matching relationship among these three parameters under specific conditions. This is practically valuable because in industrial HW-TIG welding of thick-walled pipes (such as API 5L X70 line pipes with wall thickness exceeding 20 mm), the operator must balance these three variables simultaneously to achieve the desired root weld geometry.

Technical Analysis and Critical Evaluation

The model's accuracy is validated against experimental measurements, and the authors report high precision. However, several assumptions deserve scrutiny from an engineering practice perspective:

The uniform wire material property assumption neglects the temperature-dependent resistivity of the wire. In reality, as the wire heats from ambient to the melting point (approximately 1500°C for low-carbon steel wire), the electrical resistivity increases by approximately 50-60%, which would alter the resistive heating distribution.
The quasi-steady assumption breaks down during start and end of weld beads, where the thermal boundary conditions change rapidly. For multi-pass welding of large-diameter pipes, these transient periods can account for significant portions of the total welding cycle.
The model does not incorporate the effect of arc force on wire deflection, which is particularly relevant when welding in positions other than flat (GTAW-F), such as vertical-up or overhead positions commonly encountered in field pipe welding.

Integration with Engineering Practice

In the context of heavy-wall pipe welding for oil and gas pipelines, HW-TIG welding is employed for the root pass of pipes with wall thicknesses ranging from 15 mm to over 60 mm. The analytical model presented in this paper provides a theoretical basis for selecting optimal hot wire parameters. For example, when welding API 5L X65 pipes with 30 mm wall thickness in the 6G position, a typical hot wire current of 200-400 A through a 1.6 mm ER70S-6 wire is used. The model helps predict whether the wire tip temperature is sufficient to achieve full penetration without excessive burn-through.

The numerical matching relationship identified by the authors can be used to develop look-up tables for field welders, reducing the reliance on trial-and-error parameter selection. This is particularly important for field construction where welding conditions vary with ambient temperature, wind, and pipe geometry.

Study Insights and Implications

This work demonstrates that rigorous mathematical modeling of welding thermal phenomena remains essential for process optimization, even in an era of increasingly sophisticated numerical simulation tools. The analytical approach offers computational efficiency and physical transparency that numerical methods sometimes lack. For the welding engineering community working on thick-section pipe fabrication, this model provides a valuable tool for rapid parameter screening before committing to full-scale experimental trials. The superposition approach could potentially be extended to include additional heat sources, such as external preheating or friction stir welding auxiliary heating, creating a more comprehensive thermal analysis framework for complex multi-process welding scenarios.