| Abstract Scope |
This presentation introduces a new theoretical framework for heat transfer in high-frequency electric resistance welding (HFW). Specifically, it focuses on the practical application of a proposed engineering expression to predict the location of critical isotherms, such as the onset of melting along the weld interface. HFW relies on intense volumetric heating from an AC source that decays exponentially with depth, interacting dynamically with a continuously moving substrate. To capture this complex thermal behavior, a novel dimensionless framework was developed. Two new governing dimensionless groups are introduced: the Scott number, capturing the ratio of thermal penetration depth to the depth of AC-Joule heating, and the Haga number, representing the balance between heat generation and thermal conduction. Together, these numbers delineate two asymptotic regimes of the process: one dominated by AC-Joule heating, and the other by thermal conduction. By mathematically blending these regimes, a unified, non-empirical expression was derived to predict isotherm locations across all operating conditions. The practical use of this expression was validated using V-samples extracted from interrupted mill-stop welds. Current state-of-the-art process design relies heavily on costly empirical mill trials or computationally stiff numerical simulations. The newfound ability to rapidly predict thermal boundaries using a single, physics-based closed-form expression provides a robust, low-cost tool for optimizing input power, mill speed, and AC frequency for any mill geometry. |