“Turbo generator sets are centrifugal machines commonly used in industry to generate electricity. They usually operate continuously for long periods of time and, in some cases, forced stoppage can be very costly. Because the rotating parts generally consist of long shafts, torsional resonances (usually the first three or four modes) must be avoided to increase service life and reduce the risk of catastrophic breakdown. One of the main excitation frequencies in these machines is 2xFsupply (120 Hz in North America), which is caused by current reversals and induces vibration of electromagnetic origin. Moreover, the rotating magnetic fields inside the generator create tangential forces that tend to excite torsional resonances (Figure 1). It is therefore necessary to ensure that no torsional mode is present at or close to 120 Hz. Part I of this article describes a non intrusive method that can identify the frequency and angular displacement of the torsional modes under constant speed conditions, without any significant load applied to the machine. Two applications are presented in Part II: a turbo generator set turning at 60 Hz and a roll-drive in the dryer section of a paper machine.

Angular Vibration and Torsional Modes The driven equipment in drive mechanisms tends to lag the driving equipment due to its moment of inertia and load and torsional stiffness. 

The lag creates a longitudinal deformation along the line axis of the shaft (torsion), Torsion can be considered static if there are no significant load fluctuations. In addition, dynamic forces can generate torsional deformations that depend on the torsional response of the system relative to the forcing excitation. These additional deformations add to the static component and can cause high shear stresses within the shaft. The, result is a reduction of service life and possibly early breakage of the shaft. Dangerous situations occur when a torsional natural frequency (torsional mode) is excited by one of the main excitation forces; i.e., 2xFsupply (120 Hz in North America).

Angular vibration consists of a dynamic angular motion that can be interpreted as a local speed fluctuation, or an angular oscillation around a fixed point on the shaft. If the angular vibration varies in amplitude and/or phase at two different locations on the shaft, there is undoubtedly torsion in a dynamic sense. Each torsional mode has its own frequency, damping, and mode shape, containing node(s) and anti-nodes (Figure 2).”