HISTORIA DE LA FILOSOFÍA OCCIDENTAL

Looseness related dynamic phenomena can be relatively easy to identify and eventually corrected, as they cause very characteristic modifications of rotor normal operational responses. The features of loose stationary parts, rotating parts and oversize, poorly lubricated bearings are presented in the following.

11.4.5.1 Loose stationary parts

A common type of vibrations is produced in loose non-rotating machine parts. Typical examples of these may be a bearing shell with excessive clearance with respect to the bearing housing. Other examples may be a loose bearing housing, loose pedestal support, loose grout or a frame set on the earth without tie downs.

Symptoms of looseness of the casing on its supports can be observed listening to the machine with a listening rod and feeling with the fingertips for differential vibration at mating surfaces. It is always a good idea to check all bolts in the support structure for tightness, including casing hold down bolts and soleplate bolting. A thorough checkout should be made for any gaps between feet and other mounting surfaces, using a feeler gage, giving special attention to clearances under casing feet, cracks in the foundation, and clearances in guide keys.

Based on experience, this type of problem produces a spectrum with a high amplitude peak at running frequency, followed by a string of vibration components at multiples and submultiples of running frequency (Fig. 11.19).

Fig. 11.19 (from [11.18])

The unbalance force carried by the rotor may occasionally exceed the gravity force and/or other lateral forces applied to the rotor and pedestal. This

causes a periodic lifting of the pedestal, resulting in system stiffness softening, its cyclic variability and impacting. As a result, the rotor may exhibit changes in the synchronous response, and an appearance of fractional subsynchronous vibrations ((1/2)X, (1/3)X,…) in some speed ranges. Most common is the occurrence of the (1/2)X vibration component, often measured on rotating equipment.

11.4.5.2 Excessive rotor/bearing clearance

Specific dynamic phenomena are caused by increased looseness in bearings (often referred to as “dead band”), usually due to poor lubrication.

Excessive clearances between journals and plain bearing bushes, as well as between rolling element bearings and housing, produce periodic variations of the stiffness of rotor/bearing system (Fig. 11.20), thus providing conditions for parametric unbalance-related excitation which can lead to rotor instability.

Fig. 11.20 (from [11.24])

These phenomena are similar to those occurring during the rotor-to-stator rubbing, namely variable stiffness, impacting and friction. The similarity is, however, of the “mirror image” type. The rubbing system is described as “normal-tight”, while the system with increased clearances is described as “normal-loose”

[11.25]. As shown in section 11.4.4, a rubbing rotor becomes periodically stiffer, which leads to an increase of the average stiffness. In the rotor/bearing system with excessive clearances, the average stiffness decreases. This tends to lower the rotor critical speed. If the normal rotor resonance is greater than 1/2 the normal operating speed and the system is lightly damped, the resonance of the rotor will be lowered by the effective decreased stiffness to coincide with the nearest lower fraction of running speed. The rotor will lock into this exact submultiple [11.25].

The diagnosis of excessive clearance, and distinguishing it from the rubbing, should be based on the rotor centerline position and 1X data, frequency spectrum and orbit analysis. While exhibiting similar spectra, the journal/bearing contact is usually maintained during a longer fraction of the vibration period than the rotor/stator rubbing contact, thus the orbits are substantially different from the rub case. While maintaining the contact, the journal slides on the bearing surface, and a part of the orbit follows the bearing clearance circle. The journal remains close to the bearing surface even when the contact is broken. This is different from rubbing when more impacting and unsteady transient motion occurs.

Fig. 11.21 (after [11.21])

Figure 11.21 shows the half spectrum cascade recorded during start-up of a journal rotating in a bearing with relatively large radial clearance in a brass bushing. Subsynchronous vibrations of (1/2)X and (1/3)X, as well as self-excited vibrations are present.

11.4.5.3 Loose rotating parts

Looseness may occur at discs or thrust collars mounted on rotating shafts or at bearings untightened in bearing pedestals. A loose disc will still rotate, but at a different speed than that of the rotating shaft. A loose bearing may start rotating, dragged into rotation by the shaft. Their response is a function of clearances, the friction conditions between the shaft and the loose part, as well as the tangential external force applied to the loose part.

Depending on a particular machine, the drag force can drive the loose part at a higher frequency than the rotational frequency (e.g.: a loose turbine disc) or

slow down the loose part. At steady-state conditions, the friction and fluid drag may balance each other, and the loose part rotational frequency, ω_l, becomes constant. If it does not differ very much from the rotational speed, Ω, the resulting vibrations exhibit the characteristic of beat (Fig. 11.22).

Most often, however, the looseness of a rotating part leads to transient conditions. The loose part related vibrations have most often a subsynchronous frequency tending to the natural frequency of the rotor. These vibrations look somewhat similar to fluid whirl/whip vibrations, and may sometimes be confused with the latter.

Fig. 11.22 (from [11.21])

The time signal from a bearing that is loose on a shaft will also be truncated (clipped). The extent and shape of the truncation depend on the physical characteristics (stiffness, mass and damping) of the transmission path between the rotor and stator. Spectral analysis of a truncated waveform yields a number of discrete sum and difference frequencies.