Direct Stator Contact
There are, however, a number of effects of what may loosely be termed rotor- stator interaction. The appropriate point at which to begin the discussion is with rubbing of a rotor against its casing during part of the cycle. This seemingly simple picture is actually very complex and covers a wide range of faults and resultant behavior. In the first instance, we consider a "light" rub in which the rotor rubs against its containing stator over a narrow angle of travel during each rotation. This is depicted in Figure 6.10, and we now consider the likely sequence of events. It is assumed that at rest, the rotor and stator are not in contact (apart, that is from in the bearings) but some whirl due to imbalance causing the rotor to rub against the stator over a limited portion of its orbit.
The possibilities are well summarized by Muszynska (1989, 2005), but in many instances, there will be insufficient information to fully explain all details and consequently it is important to be aware of the various possibilities.
As the rotor contacts the stator
- a) Rubbing will cause heat generation leading to a thermal bend
- b) The change in support will alter the natural frequencies and dynamic response
A Rotor-Stator Rub.
- c) The impact will generate harmonics (and subharmonics)
- d) Friction can give rise to torsional excitation
- e) There may be a change in damping
- f) Deterioration in plant performance
- g) Generation of acoustic emission
Since the whirl is synchronous, the same point on the rotor rubs on each revolution and consequently heat is generated which causes the rotor to bend.
As discussed in Section 4.3, a bend also gives rise to a synchronous vibration signal, and at constant speed, the effect of this thermal bending is to modify the effective imbalance and so the vibration will change, in general in both magnitude and phase. Without embarking on the mathematical details, it is fairly straightforward to see how a cyclic pattern of behavior develops: because the effective imbalance is changed by the thermally induced bend, the rub conditions, and consequently the heating changes. This gives rise to a range of possible scenarios which depend on the combination of physical parameters. Clearly, the vibration will change in magnitude and phase over time. This is the Newkirk effect and was first discussed by Newkirk (1926).
Under some conditions, the amplitude will remain within acceptable limits and the result will be a synchronous response whose amplitude varies slowly over time and an example of this is shown in Figure 6.11. Various theoretical treatments have been reported (Muszynska, 1989) but the difficulty is really the uncertainty of the precise conditions within the machine. Nevertheless, models have been successful in reproducing trends at timescales that correspond well with observations.
Although not shown on this figure, it is interesting to observe the way in which phase varies with time. Often this reveals a gradual change as the heat developed at the rub causes a thermal bend, which in turn changes the effective imbalance on the rotor. Note that in Chapter 4 it is (strongly) argued that bends and imbalances are not equivalent; nevertheless, taken at a single rotor speed they can be considered together. The result is therefore a gradually changing effective unbalance which may take the form of a change in amplitude, phase, or both. From Figure 6.11 it is observed that the timescale associated with this process is about 20 min
An Example of the Newkirk Effect.
and long periods like this are typical of large machines. This characteristic time will be determined by a variety of factors, including the dimensions of the machine, thermal conductivity of the rotor, and the rotor flexibility. Other factors such as the mass imbalance and the clearance will only influence the extent of the thermal cycling.
There are a range of possibilities covering the interaction of a rotor and its stator:
- a) The rotor may rub constantly all around the circumference (although this is a rare condition).
- b) The rotor may constantly rub against one part of the stator.
- c) The rotor may contact the stator at one portion of its orbit on each cycle: this is the scenario which gives rise to the Newkirk Effect as described above.
But this seemingly simple process can give rise to a wide variety of consequences, and the parameters of a specific situation will determine which of the terms dominate. For successful diagnosis, the aim is to use a blend of all these factors to yield maximum insight into the problem.
There have been many papers on the topic of thermal rubs in rotating machines and this is not surprising in view of its importance. Treatments range from the purely empirical to detailed mathematical analyses, which is all a little frustrating in view of the limited available knowledge. It is important to appreciate that there are two quite distinct cases: If there is a short impact between rotor and casing, there will be an exchange of momentum but little heat generation. With a long rub the situation will be reversed, with little momentum exchange but considerable heat generation. In a real incident, one may observe a combination of these two extremes. Here we present a description of the rather slow rub case but even this yields a complex combination of phenomena.
To develop the discussion, consider the steady-state motion of a rotor which has both imbalance and a bend. The motion is described by
The complication with a rub is that the bend is thermally induced and it is time dependent. In all realistic scenarios, however, the thermal timescale is much longer than that of the dynamics and so it is valid to separate the two problems. As the rotor contacts the stator, heat Q(OwiH be generated and, although there will be some radiated losses, the net result will give rise to a thermal field within the rotor which will cause a bend. This time- dependent heat generation will give rise to a temperature profile within both rotor and, usually to a lesser extent, the stator. Focusing attention on the rotor, this nonuniform temperature profile gives rise to distortion, tending to bend the rotor. For a given heat input and known losses, the temperature profile of the rotor can, in principle, be calculated using standard methods, either analytical or numerical; but, of course, it is rare to have any precise knowledge of the conditions and, consequently, it is far more important to formulate a more general understanding of the processes involved.
The distribution of temperature within the rotor is easily translated into stresses and strains, which in turn result in a combination of forces and moments acting on the rotor giving rise to the bend term of Equation 6.22. This represents a complicated chain of events which is represented by the chart shown in Figure 6.12.
This process does, however, avoid one important question: does the rotor stay in contact with the stator long enough to generate significant heat, or does it simply undergo an impact and rebound? In either event, there will be significant changes to the dynamic behavior, but the two scenarios are markedly different.
In reality, any contact will give rise to both types of interaction with one dominating the other depending on the local parameters. It is worth briefly considering the physics of the interaction: as the rotor makes contact with the stator two interaction forces arise, one perpendicular to the surface and the other, a friction force, along the surface. Both these forces will be nonlinear functions of the relative displacement. The two components will remain in contact for some time, say r, which will be determined by the local stiffness properties of both components together with the velocity of the rotor.