Case study
Seal-Induced Rotor Instability Case Study
Mechanical engineering case study on diagnosing seal-induced rotor instability in a centrifugal compressor using subsynchronous vibration, cross-coupled stiffness, orbit evidence and release criteria.
This case study follows a centrifugal compressor that develops a growing subsynchronous vibration after seal replacement. The key question is whether the vibration is a balance problem, an oil-whirl problem or a seal-induced rotor stability problem driven by cross-coupled fluid forces.
The example is simplified, but the workflow is realistic for high-speed compressors, pumps, turbines and test rigs where annular seals, balance-piston seals or labyrinth seals can add destabilizing rotor-dynamic coefficients.
Case Context
| Item | Field value |
|---|---|
| Machine | centrifugal compressor |
| Seal type | annular balance-piston seal |
| Speed sweep | 6000\ \text{rpm} to 9000\ \text{rpm} |
| First forward rotor mode | 63\ \text{Hz} |
| Maximum seal pressure differential | 6.5\ \text{bar} |
| Hold criterion | subsynchronous shaft motion above 45\ \mu\text{m}_{pp} |
| Trip criterion | subsynchronous shaft motion above 70\ \mu\text{m}_{pp} |
| Primary instruments | proximity probes and once-per-revolution reference |
| Main evidence | waterfall spectrum, order tracking, orbit plot and shaft centerline trend |
The compressor had acceptable 1x vibration before the seal change. After the maintenance outage, the 1x component remains modest, but a forward subsynchronous orbit appears as the seal pressure differential rises.
The timing matters. If the same subsynchronous vibration had existed before the outage, the first suspects would include bearing condition, process excitation, rotor rub, long-term alignment drift or a measurement change. Because the symptom appears after seal work and grows with pressure differential, the seal becomes a primary suspect.
Speed Sweep Evidence
The commissioning sweep records the following data:
| Speed | Running frequency | Subsynchronous peak | Peak order | Shaft-relative amplitude | Seal pressure differential |
|---|---|---|---|---|---|
| 6000\ \text{rpm} | 100\ \text{Hz} | 44.0\ \text{Hz} | 0.44x | 18\ \mu\text{m}_{pp} | 4.1\ \text{bar} |
| 7500\ \text{rpm} | 125\ \text{Hz} | 55.0\ \text{Hz} | 0.44x | 34\ \mu\text{m}_{pp} | 5.2\ \text{bar} |
| 8400\ \text{rpm} | 140\ \text{Hz} | 61.5\ \text{Hz} | 0.44x | 48\ \mu\text{m}_{pp} | 6.0\ \text{bar} |
| 9000\ \text{rpm} | 150\ \text{Hz} | 62.0\ \text{Hz} | 0.41x | 66\ \mu\text{m}_{pp} | 6.5\ \text{bar} |
At 8400\ \text{rpm}, the running frequency is:
The subsynchronous order is:
At 9000\ \text{rpm}, a pure 0.44x component would be expected near:
Instead, the observed peak remains near:
That is close to the measured first forward rotor mode:
The evidence suggests a subsynchronous instability that is approaching modal lock-in, not ordinary 1x unbalance response.
The pressure trend reinforces the diagnosis. The amplitude grows as the seal pressure differential increases from 4.1\ \text{bar} to 6.5\ \text{bar}, while the synchronous 1x component remains within the previous baseline range. That pattern does not prove the seal mechanism alone, but it is consistent with a fluid-force source whose coefficients change with pressure, swirl and clearance.
Cross-Coupled Stiffness Screen
The rotor-dynamic model estimates the destabilizing seal cross-coupled stiffness as:
The effective direct damping for the participating forward mode is estimated as:
Using the observed whirl frequency near 62\ \text{Hz}:
The damping stiffness scale is:
A simple cross-coupling screen is:
The screen is above 1, so the seal coefficient is large enough to plausibly overcome the stabilizing damping in this simplified review. The screen does not replace a full rotor-dynamic stability analysis, but it explains why the measured forward subsynchronous orbit grows with speed and pressure differential.
The screen also explains why a small change in seal geometry can matter. The design review does not need the seal force to be the largest force in the machine. It only needs the destabilizing part of that force to be large enough relative to modal damping. When the margin is close to unity, modest uncertainty in clearance, gas density, swirl or damping estimate can change the release decision.
Hold Decision
The hold criterion is crossed at 8400\ \text{rpm}:
The trip criterion is not crossed at 9000\ \text{rpm}:
That does not justify continuing to rated operation. The subsynchronous component is growing, the orbit is forward, the peak is close to the forward mode and the seal pressure differential is high. The correct action is to hold the release and investigate the seal condition before an endurance run.
The radial running clearance at the probe plane is:
The approximate orbit radius at 9000\ \text{rpm} is:
The clearance fraction is:
The rotor is not close to full clearance contact, but stability criteria are already more important than clearance fraction alone.
The release decision can be summarized as:
| Evidence | Meaning | Decision impact |
|---|---|---|
| 1x component remains modest | simple imbalance is not the dominant symptom | do not balance first |
| sub-1x component grows with pressure differential | fluid-force mechanism is plausible | review seal and process state |
| forward orbit near first forward mode | destabilizing whirl is plausible | hold endurance release |
| S_{cc}=1.11 | cross-coupled stiffness can overcome damping in the screen | require corrective action |
| orbit radius below clearance | no immediate clearance contact proof | does not override stability concern |
Corrective Action
Inspection finds that the replacement seal has tighter-than-planned effective clearance and no effective swirl control at the inlet. The engineering team chooses a controlled correction rather than adding balance weights:
- verify probe calibration, slow-roll runout and tachometer timing;
- inspect seal clearance and installation concentricity;
- add or restore anti-swirl features at the seal inlet;
- correct seal clearance to the approved range;
- repeat the speed sweep with the same measurement setup;
- keep the hold criterion active until the repeat sweep is stable.
After correction, the estimated seal cross-coupled stiffness is reduced to:
The effective direct damping estimate is revised to:
The new cross-coupling screen is:
The repeat sweep shows the subsynchronous component below 26\ \mu\text{m}_{pp} through 9000\ \text{rpm}, no lock-in near 63\ \text{Hz} and stable bearing temperature. The machine is released for a limited endurance run with trend monitoring.
The release is deliberately limited. It permits operation only inside the tested pressure and speed envelope, with trend alarms active and a repeat inspection interval defined. If the compressor later operates at higher pressure ratio, different gas density, different recycle condition or a changed seal temperature, the stability evidence must be revisited.
Distinction from Similar Faults
Seal-induced instability can look similar to oil whirl because both can create forward subsynchronous vibration. The difference in this case is the strong connection to seal pressure differential, seal replacement history and modelled seal cross-coupled stiffness.
It is also different from unbalance response. The 1x vector is not the dominant issue, and the subsynchronous component does not respond like a controlled trial-weight vector. Adding a balance weight may reduce a small 1x component while leaving the self-excited seal problem in place.
It is not automatically a critical-speed problem either. A critical speed describes a speed-frequency crossing or strong modal response. Here the critical-speed information matters because the subsynchronous component approaches the first forward mode, but the forcing mechanism is the seal-generated cross-coupled force. The final diagnosis connects both: seal force supplies energy, and the rotor mode provides the dynamic shape that responds.
Validation Limits
The simplified stability screen depends on linearized coefficients and a chosen operating point. Seal forces can change with pressure ratio, gas density, swirl, clearance, wear, temperature, rotor eccentricity and surface condition. A field decision should therefore combine model evidence with measured waterfall spectra, filtered and unfiltered orbits, shaft centerline trend, bearing temperature, pressure differential and repeatability.
Common mistakes include continuing the sweep because the trip level has not yet been crossed, treating every subsynchronous component as oil whirl, assuming the new seal is correct because it matches the part number, and accepting a reduced amplitude without confirming that lock-in and pressure sensitivity disappeared.
The minimum validation package should include raw time waveforms, speed reference quality, probe calibration, slow-roll runout, seal installation measurements, pressure differential trend, gas condition, orbit direction convention, filtering settings and pre-outage baseline comparison. Without those details, the same plot can be argued several ways, and the release decision becomes a label instead of an engineering conclusion.