Calculate welding heat input and peak temperature distribution using the Rosenthal analytical solution. Adjust welding current, voltage, travel speed, and material to evaluate HAZ width and cooling rates.
The core of the Rosenthal solution for a moving point heat source on a thick plate is the temperature distribution equation. It assumes a quasi-steady state, meaning the temperature pattern around the heat source is stable as it moves.
$$T - T_0 = \frac{Q}{2 \pi k R}\exp\left(-\frac{v (R + x)}{2 \alpha}\right)$$Where:
$T$ = Temperature at a point (K)
$T_0$ = Initial/ambient temperature (K)
$Q$ = Heat input power (W) = Arc efficiency × Voltage × Current
$k$ = Thermal conductivity (W/m·K)
$v$ = Welding speed (m/s)
$\alpha$ = Thermal diffusivity (m²/s)
$R$ = Distance from the heat source (m), $R = \sqrt{x^2 + y^2 + z^2}$
$x$ = Coordinate in the welding direction
A primary output of practical interest is the cooling rate. For many steels, the critical cooling rate is evaluated at 500°C. A simplified derivative of the Rosenthal solution gives this rate.
$$\frac{dT}{dt}\bigg|_{T=500}= - 2 \pi k \frac{(500 - T_0)^2}{Q/v}$$This equation reveals a key insight: the cooling rate is proportional to the square of the temperature difference and inversely proportional to the heat input per unit length ($Q/v$) . This is why, in the simulator, increasing the voltage or current (which increases $Q$) slows down the cooling, while increasing the welding speed $v$ makes cooling much faster.
Procedure Qualification & WPS Development: Before welding on a critical structure like a pressure vessel, engineers use this calculation to define a Welding Procedure Specification (WPS). They ensure the chosen voltage, current, and speed yield a cooling rate that avoids brittle microstructures, preventing catastrophic failure in service.
High-Strength Steel Welding: Advanced steels used in military vehicles or mining equipment are highly sensitive to heat. Engineers simulate different scenarios to find the narrow "window" of parameters that provides enough penetration without causing excessive hardening and cracking in the Heat-Affected Zone (HAZ).
Automotive Tailor-Welded Blanks: In car body manufacturing, different grades and thicknesses of steel are laser-welded together before stamping. Controlling heat input is vital to maintain the strength of each material. The model helps optimize laser power and travel speed for a consistent, strong seam.
Pipeline Girth Welding: During the construction of cross-country pipelines, welding must be done in various environmental temperatures. Engineers adjust pre-heat temperature (the $T_0$ parameter in the simulator) based on forecasts to ensure the cooling rate stays within safe limits, guaranteeing weld integrity over decades.
When starting to use this tool, there are several pitfalls that engineers, especially those learning CAE on the job, often fall into. First and foremost, understand that the Rosenthal solution is not a universal solution. It is a classical solution based on the bold assumption of a "moving point heat source." For instance, a real arc has a width rather than being a point, and material thermal properties change with temperature. Consider the tool's results as a "first approximation" for grasping trends, and make it a habit to always verify with actual measurements or higher-fidelity FEM simulations, especially for critical components.
Second, the setting for thermal efficiency η. The default value (e.g., 0.8 for MIG) is merely a representative value. In reality, it varies with factors like shield gas type, wire stick-out length, and beading. A difference of just 0.1 in this value can significantly change the calculated t8/5. In practice, the trick is to estimate an η suitable for your own process by back-calculating from t8/5 values measured under your company's standard welding conditions.
Third, the selection criteria for "thin plate" vs. "thick plate". Simple judgments like "Is 5mm a thin plate? Is 12mm a thick plate?" are risky. What's important is "whether heat spreads uniformly in the plate thickness direction." If forced cooling from the backside (e.g., using a water-cooled jig) is applied, the condition becomes closer to the thick plate model. Conversely, even with a 15mm plate, welding simultaneously from both sides might be better approximated by the thin plate model. Develop an intuition for selecting the appropriate model by comparing simulation results with measured thermal histories.
For a T-joint in ASTM A36 steel with 6mm thickness: voltage 24V, current 180A, travel speed 400 mm/min yields heat input Q = (24 × 180 × 60) / 400 = 648 J/mm = 0.648 kJ/mm. Using thermal diffusivity α = 0.12 cm²/s and assuming ambient 20°C, the Rosenthal solution predicts cooling rate t₈/₅ ≈ 12–18°C/s. Reducing travel speed to 300 mm/min increases cooling rate to ~22°C/s, requiring preheat (150°C minimum) to prevent cold cracking in HAZ.