Abstract: Spiral vibration is a typical form of unstable vibration observed in large turbogenerators, compressors, turbines, and other rotating machinery. It originates from a local hot spot produced by soft rubbing between the rotor and stationary components. The resulting localized heat input causes thermal bowing of the rotor and, consequently, a slow rotation of the unbalance and vibration vectors. This paper investigates the forward spiral vibration observed during factory running tests of a 450 MVA, 3000 r/min hydrogen-cooled turbogenerator by combining field tests, hot-spot localization, rotordynamic analysis, and heat-input modeling. Brush-on/brush-off comparative tests confirm that the dominant hot spot is generated by frictional contact between the carbon brushes and collector rings. Based on the Kellenberger thermal model, three types of heat-input models—displacement-, velocity-, and acceleration-dependent models—are established, and their applicability is evaluated through eigenvalue-based stability analysis. The results show that carbon-brush contact pressure and friction direction are more strongly correlated with shaft vibration velocity; accordingly, the velocity-dependent heat-input model best reproduces the measured characteristics, including forward precession, a spiral period of approximately 60–75 min, and divergence during constant-speed operation at the rated speed of 3000 r/min. Engineering measures are therefore proposed to suppress spiral vibration by increasing the horizontal critical speed, optimizing bearing-support stiffness, and applying tilting-pad bearings. Field verification demonstrates a marked improvement in vibration stability at rated speed after the modification. The results provide a technical reference for the diagnosis, heat-input modeling, and structural mitigation of spiral vibration in large turbogenerators.