A hydrodynamic seal (10) for use with a rotating shaft (24) is disclosed. The seal includes a face seal (20) and a mating ring (22) fixed or connected to rotate with the shaft. A clamping nut (30) is adjacent to the mating ring and includes threads to secure a portion of the clamping nut to the shaft via a threaded interface (32). Embodiments of the seal and related assembly include at least one of: a spring component (140) with or on the clamping nut; a clamping surface (150) on an interface between the mating ring and the clamping nut, the clamping surface being substantially parallel to a thread pitch on the threaded interface; and a pilot surface (250) on the clamping nut.