A Deterministic Limit for Tribological Seizure: Deriving the Critical Asperity Radius via Contact Thermal Dissipation

The prediction of catastrophic galling and seizure in high-speed sliding contacts relies heavily on empirical Pressure-Velocity (PV) limits and Blok's foundational flash temperature theory. While these thermodynamic frameworks effectively estimate bulk lubrication failure based on aggregate operating conditions, they fail to deterministically define the exact spatial boundary where a localized asperity clash triggers a cascading transition into irreversible cold-welding and mechanical lock-up. This paper introduces a strict continuum framework for micro-mechanical tribology. By modeling the contact interface as a dynamic thermodynamic balance between the spatial capacity for advective heat removal (thermal dissipation) and the localized rate of plastic asperity friction, we derive a universal critical galling radius (Rgall). We demonstrate that engine seizure is not a probabilistic outcome of bulk fluid failure, but an exact deterministic limit where localized flash-heating strictly overpowers the thermal-distribution capacity of the surrounding base metal and elastohydrodynamic film. We propose a blueprint for Active Tribological Telemetry (ATT) using ultrasonic reflectometry to provide real-time thermal prediction prior to catastrophic seizure.