The occurrence of spiral vibrations in rotating machines is a well-known but not very common phenomenon. However, this kind of shaft vibration, usually caused by light rubs between rotating and stationary parts, may give rise to a slow considerable increase of the amplitude of the synchronous (1X) vibration. Owing to the rubs, the normal contact forces cause a friction-induced thermal bow, which in turn determines rather slow changes in amplitude and phase of the 1X vibration vector. The curve described in a polar plot by the tip of the vibration vector is a spiral. The occurrence of expansive vibrations may cause serious damage. Many studies about this malfunction are focused on the stability analysis of spiral vibrations. Simplified or r...