**3.1.2 Misalignment**

320 Mechanical Engineering

Basically this subsection deals with absolute vibration spectral components of frequencies determined by *f* = *nf*0, where *f*0 results from rotational speed, and to some extent also with relative vibration vectors or orbits. In practical applications, components corresponding to *n* > 4 are seldom accounted for; this means that we are dealing with first four harmonic and sub-harmonic (*n* < 1) components. As each of these is typically influenced by a number of condition parameters, it is convenient to speak in terms of possible malfunctions and faults

Unbalance is common to all rotating elements. Primary symptom of this malfunction is the 1 *f*0 component of absolute vibration in a direction perpendicular to the turbine shaft line. They are, however, many other possible malfunctions (some of them quite common) that produce similar vibration patterns; additional procedures are therefore usually needed for a

In general, a 'pure' unbalance, be it static, quasi-static or dynamic, produces a 1 *f*0 component that remains almost constant in amplitude and phase during steady-state operation and disappears at low rotational speed. As rotor systems are non-linear, this component is typically accompanied by higher harmonics (*n* > 1), with amplitudes decreasing as *n* increases. Shaft orbits usually are quite regular and nearly circular or slightly elliptical. If such vibration pattern is present, the probability of unbalance being the root cause is high. Proper

Rotor systems will always respond to balancing. Step changes of the 1 *f*0 component not related to any maintenance activities (but occurring mainly after turbine shutdown and subsequent startup) may be indicative of a loose rotor disk. Similarly, sudden and dramatic change may result from a broken rotor blade; such step changes are often big enough to enforce turbine tripping. Much slower, but continuous increase is often indicative of a permanent rotor bow (see also sub-section 3.1.3). An example is shown in Fig.3; it is easily

Fig. 3. Time history of the 1 *f*0 component with permanent rotor bow present: 230 MW unit, rear intermediate-pressure turbine bearing, vertical direction. Arrows indicate balancing sessions.

rotor balancing will usually reduce the residual unbalance to an acceptable level.

**3.1 Harmonic (low) frequency range** 

rather than frequencies.

**3.1.1 Unbalance** 

correct diagnosis.

Ideally the entire turbine-generator unit shaft line (with overall length approaching 70 m in large units in nuclear power plants) should be a continuous and smooth curve; a departure from such condition is referred to as misalignment. The shape of this line is determined by shaft supports (journal bearings). As they displace during the transition from 'cold' to 'hot' condition, due to changing temperature field (this process may take even a few days to complete), at the assembly stage care has to be taken to ensure that the proper shape is maintained during normal operation. Relative vertical displacements may be even of the order of millimeters (Gałka, 2009a).

Misalignment modifies distribution of load between individual shaft bearings and therefore affects shaft orbits. With increasing misalignment magnitude they typically evolve from elongated elliptical shape through bent ('banana') and finally to highly flattened one (Bently and Hatch, 2002). High misalignment may lead to oil film instability, but in large steam turbines (especially modern ones, with only one bearing per coupling) this is a very rare occurrence. As for absolute vibration, 2 *f*0 component in directions perpendicular to the turbine axis is generally recognized as the basic misalignment symptom. Care, however, has to be taken when dealing with the turbine-generator coupling, as this component may be dominated by the influence of the generator (asymmetric position of rotor with respect to the stator electromagnetic field); in the latter case, dependence on the excitation current is usually conclusive. Marked misalignment is often accompanied with relatively high amplitudes of harmonic components in axial direction, but this symptom can by no means be considered specific.
