# Identification of Close Modes on Frequency in Rotating Systems
## 3 Conclusions  
The balancing process consists of determining the mass to be placed on the rotor to allow reducing high vibration levels. Commonly used strategies are the modal balancing and influence coefficient methods. These balancing processes are commonly applied offline, mounting the rotor on instrumented balancing benches, where, by significantly reducing horizontal stiffness, the natural frequencies of the rotor in that lateral direction drop, requiring lower rotational speeds (compared to the nominal working speed) for the balancing process and ensuring that the vibration modes are separated. However, the vibration levels obtained on the balancing bench are not necessarily preserved when the rotor is mounted on its bearings and structure due to differences in stiffness. In cases where the vibration level is not in the desired range, the on-site balancing process can continue. It is in these particular situations that it would be possible to present close modes in frequency in the vibration mode pair from the different natural rotor frequencies, where the (polar or Bode) response diagrams used to calculate the modal parameters apparently show only one mode. The effect of close modes on frequency during the modal balancing or influence coefficient process has been little studied in turbomachinery. In the area of structure, it is a niche that continues to develop because it is a common problem during the dynamic  
Figure 10: Identification of close modes in bearing 2 in field turbogenerator for (**a**) natural frequency, (**b**) damping ratio, (**c**) phase angle and (**d**) vibration amplitude at resonance. analysis of buildings or bridges, as it is essential to know the modal parameters of natural frequency, damping, and vibration amplitude for each mode. However, during the modal balancing of rotating systems, it is critical to also know the phase angle of the vibration modes, which will allow finding the location of the correction weights. However, because the phase angle of a vibration mode generated by an imbalance force can be in any position from 0 to 360\({}^{\circ}\), identification of close modes is no trivial matter. Therefore, it is important to first develop strategies that allow identifying the presence of close modes in a rotor's response diagram to later develop tools that allow extracting the modal parameters present. A proposed solution for identifying close modes in rotating systems was proposed in the present research work, where numerical signals (equivalent to the angular movement of a sensor) are generated in different angular positions from two vibration signals placed in a bearing, which presents a variation of the phase angle with respect to sensor movement when obtaining the modal parameters of each signal in the presence of close modes in frequency. The proposed methodology was applied to ideal signals considering two close vibration modes separated by \(\Delta\omega\ =\ 0\) % and \(\Delta\omega\ =\ 1.38\) %. Likewise, it was applied to a field turbogenerator's vibration signals, which showed additional acquisition problems, high runout, and a vibration level within the range permitted by the ISO 1940 standard, identifying the presence of close modes in one of the modes. Conceptualization R.A.F.-D.; methodology R.A.F.-D. and P.C.-A. ; validation A.d.J.B.-G.; formal analysis R.A.F.-D.; resources P.C.-A. ; data curation A.d.J.B.-G.; writing-original draft and preparation R.A.F.-D. and A.d.J.B.-G.; writing-review and editing P.C.-A. and R.A.F.-D.; visualization A.d.J.B.-G.; supervision A.d.J.B.-G.; funding acquisition R.A.F.-D. All authors have read and agreed to the published version of the manuscript. This work was supported by the Tecnological Institute in Sonora by the project PROFAPI 2021 and by the Engineering and Technology Deparment. The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by the Institutional Review Board (or Ethics Committee) of TECNOLOGICAL INSTITUTE IN SONORA. This study not involving humans or animals.