# Diagnosing and Balancing Approaches of Bowed Rotating Systems: A Review
## 3 Results  
This paper aims to review almost all the literature in the field of bowed rotating system diagnosis and balancing approaches.  
It can be seen from the cited articles that certain symptoms have been identified more frequently than others in the field of research on the dynamic behaviors of bowed rotor systems, including the diagnosis of this damage. Increased vibration amplitude (commonly in comparison to an unbalanced system) is found to be the most common sign of a bowed rotor system in the time-domain analysis, while zero-vibration amplitude, sometimes referred to as self-balancing speed, is found to be the second most prevalent feature. The last one can happen in a particular circumstance when the magnitudes of the shaft bow and disc eccentricity are similar, and these two faults also have a 180\({}^{\circ}\) phase difference. It should be emphasized that in some works, more than a single feature was detected.  
On the other hand, in the frequency domain, the most prevalent indicator of a bowed rotor system is the presence of the 1X and 2X harmonic components in the frequency graph. Moreover, the existence of the higher component, i.e., 3X, was discovered as a sign of a bowed system too.  
The referenced articles in which the most common signs of bowed rotating systems were discovered both in the time and frequency domain are represented by Figure 4 and its companion table, Table 1. In the aforementioned table, works are arranged chronologically, and some references are mentioned more than one time since in them, two or more domains were investigated. It is important to remember that until now, no distinct signature was identified in the time-frequency domain, and only statistical features were extrapolated from the transformed signals to this domain.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Researcher(s)** & **Investigated Fault(s)** & **Type(s) of Research** & **Symptom** & **Domain** \\ \hline [PERSON], [PERSON], and [PERSON] [6] & Unbalancing and ‘shaft bow & Theoretical & & \\ [PERSON] and [PERSON] [4] & Unbalancing, shaft bow, and disc skew & Theoretical & & \\ [PERSON] and [PERSON] [32] & Unbalancing and shaft bow & Theoretical– & & \\ [PERSON] et al. [27] & Shaft bow (geared system) & Theoretical & Zero-vibration & \\  & Unbalancing and shaft bow & Theoretical & (self-balancing & \\ [PERSON] et al. [28] & (geared system with viscoelastic supports) & Theoretical & & \\ [PERSON], [PERSON], and [PERSON] [16] & Unbalancing, shaft bow, and & Theoretical– & & \\  & rubbing & experimental & & \\ [PERSON] et al. [52] & Unbalancing, shaft bow, and & Theoretical– & & \\  & mechanical/electrical runout & experimental & & \\ \hline [PERSON], [PERSON], and [PERSON] [19] & Unbalancing, shaft bow & Experimental & Phase difference in the responses \\ [PERSON] [50] & Shaft bow (based on the & Experimental & \\  & industrial cases) & Experimental & \\ [PERSON] and [PERSON] [54] & Unbalancing, shaft bow & Experimental & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Most common symptoms of bowed rotor systems.  
Figure 4: Most common symptoms of bowed rotor systems: (**a**) time domain, (**b**) frequency domain.