Advanced Diagnostics of Centrifugal Compressor Shaft Vibration: A Technical Review

Turbomachinery is indispensable across critical industrial sectors, including power generation, oil and gas, and aviation. However, the intricate dynamic behavior of rotating components can result in excessive shaft vibration. Unmitigated vibration can lead to performance degradation, component damage, unplanned shutdowns, and even catastrophic equipment failure. Mastering diagnostic and mitigation strategies for turbomachinery vibration is essential for ensuring safe and reliable operation.

This article provides an in-depth review of shaft vibration diagnostics, with a focus on industrial centrifugal compressors, detailing common causes, advanced signal analysis techniques, and the integration of vibration and operational data. This article draws on recent field diagnostics and test campaigns performed on industrial centrifugal compressors operating under API 617 conditions, reflecting both traditional rotordynamic theory and modern condition monitoring practice.

Centrifugal Compressor Typologies

Centrifugal compressors are categorized based on their mechanical structure, particularly the arrangement of their impellers and shafts.

An overhung compressor features one- or two-stage impellers mounted at the end of the shaft, extending beyond the casing. This design is prevalent in applications demanding moderate compression, such as HVAC, refrigeration, and pipeline systems. The compression process involves gas acceleration from the impeller, followed by diffusion in a volute-shaped casing to convert kinetic energy into pressure. This configuration can impose significant axial and radial loads on the shaft and bearings, necessitating rigorous attention to design details to ensure operational reliability and mitigate wear.

A barrel compressor derives its name from the cylindrical shape of its casing and impeller section. Gas is drawn into the axial rotating impeller and accelerated radially outward. The casing’s design promotes a spiral flow pattern, which efficiently increases gas pressure. The gas then passes through a stationary diffuser, converting its kinetic energy into pressure energy before exiting the discharge nozzle. These compressors are widely employed in high-volume, high-pressure applications like oil and gas production and chemical processing, and are valued for their high efficiency and reliability.

Integrally geared compressors utilize impellers overhung on multiple pinion ends. The impellers are arranged in series, with each pinion operating at a distinct speed. This unique and mechanically complex arrangement permits higher pressure ratios compared to single-stage designs, while simultaneously reducing the overall physical footprint of the compressor. These compressors are utilized in applications requiring high pressure ratios, such as natural gas processing and power generation.

A single-shaft turbo compressor integrates a compressor (typically a centrifugal impeller) and a turbine (or expander) on a single, common shaft. The compressor section draws in and pressurizes the gas. This compressed gas subsequently flows to the turbine, where its kinetic energy is converted into the mechanical energy required to drive the compressor. This consolidated single-shaft design results in a compact and highly efficient system, offering reduced maintenance needs and simplified control logic compared to multi-shaft alternatives. They are common in refrigeration, air separation plants, and natural gas compression.

Rotordynamics and Vibration Characterization

The complex dynamic behavior of rotating components in compressors is characterized by vibrations occurring in three principal planes relative to the shaft: lateral, torsional, and axial (Figure 1). Lateral vibration occurs perpendicular to the shaft’s longitudinal axis. Lateral vibration is frequently a result of imbalance, external forces, or resonance, which can lead to machinery shutdown/trips. Torsional vibration is a twisting oscillation about the longitudinal axis. Torsional vibration is caused by changes in rotational speed, external forces, or resonance, and can result in fatigue fractures. Axial vibration manifests along the shaft’s longitudinal axis. Imbalanced forces or flow-induced phenomena, particularly in compressors and turbines, can trigger this vibration, potentially causing component rubbing and/or shaft damage.

Vibration analysis techniques such as modal analysis, frequency response analysis, and finite element analysis (FEA) are employed during design to preemptively identify and mitigate these issues.

Vibration phenomena are quantified using several metrics: frequency, motion/displacement, velocity, and acceleration. Frequency is measured in Hertz (Hz), while amplitude can be specified as displacement (mils or micrometers), velocity (in/s or m/s), or acceleration (m/s² or in terms of g-forces [g]). For shaft vibration, displacement is the preferred unit, while casing vibration is best characterized by acceleration, as it more accurately reflects the forces involved.

A critical speed of a rotor is the rotational speed at which the system's natural frequency coincides with the excitation frequency from an applied load or disturbance. Operating at critical speed can lead to a significant increase in vibration amplitude. The undamped natural frequency (ω_n) is fundamentally represented by ω_n=√(k/m), where k is stiffness and m is mass. With the addition of damping (C), the system's response is governed by the damped natural frequency ω_d=ω_n √(1-ζ² ) where ζ is the damping ratio: ζ=C/2√mk.

Stability is the shaft's inherent ability to resist excessive vibration from self-excitation. Exceeding certain speed thresholds can increase risk of instability, leading to excessive noise, vibration, and damage.

The forced response is the vibration amplitude resulting from mass asymmetry, which generates a centrifugal force. Amplification factors (AFs) quantify the degree of vibration amplification at specific peaks. To mitigate imbalance, corrective measures like shaft balancing are implemented. These concepts, along with separation margins, are thoroughly addressed in industry standards. In the turbomachinery industry, the primary types of standards utilized are American Petroleum Institute (API) and International Organization for Standardization (ISO). API and ISO standards serve complementary but distinct roles in turbomachinery vibration guidance.

API standards are prescriptive and machine-specific, defining minimum design, stability, and acceptance requirements for critical equipment such as centrifugal compressors, and are typically applied during design, procurement, factory testing, and commissioning. In contrast, ISO standards are measurement-focused and broadly applicable, providing standardized methods for assessing vibration severity, primarily casing vibration, during operation and condition monitoring. While ISO standards help identify and track vibration symptoms in service, they do not ensure rotor stability or adequate design margins. Effective vibration management therefore relies on using API standards to establish inherent machine robustness and ISO standards to monitor and maintain that condition throughout the equipment’s operating life.

While numerous standards exist in the industry, the following are some of the primary standards covering design, vibration, and balancing:

1. Compressor Design, Performance, and Acceptance Criteria

• API 617 (ninth edition) - Axial and Centrifugal Compressors and Expander-Compressors: Primary reference for industrial centrifugal compressors, defining vibration limits, separation margins, stability criteria, and rotordynamic analysis requirements.
• API 672 - Packaged, Integrally Geared Centrifugal Air Compressors: Applicable to integrally geared machines, including requirements for vibration acceptance and gear-related dynamic behavior.

2. Field Vibration Measurement and Severity Evaluation

• ISO 20816 - Mechanical Vibration - Evaluation of machine vibration by measurements on non-rotating parts. The current ISO framework for assessing casing vibration severity in the field.
• ISO 10816 (legacy reference) - Superseded by ISO 20816 but still encountered in legacy specifications and the literature.

3. Rotor Balancing Standards

• ISO 21940-11 - Procedures and tolerances define balance quality grades and allowable residual unbalance.
• ISO 21940-14 - Evaluation of balance quality and provides guidance on assessing balancing results and acceptance criteria.

Advanced Vibration Diagnostics Techniques

Effective diagnosis transforms raw vibration data into actionable engineering insight.

Time domain analysis examines the time waveform, which is the vibration signal plotted as a function of time. The primary purpose is to identify anomalies and irregularities. Essential metrics utilized include peak-to-peak amplitude, RMS amplitude, crest factor, and kurtosis, which collectively assess the overall vibration severity and highlight transient or periodic components. Techniques include visual waveform analysis for pattern recognition and time synchronous averaging to separate periodic from non-periodic signal components. This analysis aids in pinpointing root causes like misalignment or imbalance by characterizing the amplitude, frequency, and duration of the vibration components.

The frequency spectrum is arguably the most critical data for determining the source of high vibration. Frequency domain analysis converts the time-domain signal into its constituent frequency components, typically using the Fourier transforms. Specific frequency components are directly traceable to a particular component or subsystem of the compressor. The amplitude and phase of these components are analyzed to determine the magnitude and time delay of the vibration. The Fast Fourier Transform (FFT) is a computationally efficient algorithm for the Discrete Fourier Transform (DFT), making spectral analysis feasible for real-time vibration diagnostics. Other valuable methods include spectral analysis and power spectral density (PSD).

A Bode plot, as seen in Figure 2, graphically represents vibration amplitude (gain) and phase angle as a function of rotor speed. Bode plots are instrumental in identifying critical speeds during both ramp-up and coast-down operations. The plot typically displays the direct (total) vibration and the synchronous (1X) vibration corresponding to the rotor’s running speed. The phase angle indicates the angle relative to the Keyphasor where the maximum 1X vibration is recorded. Coast-down plots are generally preferred for diagnostic purposes as they are free of driver-induced forcing functions.

Bode plots are also crucial for runout compensation. At low speeds, the 1X measurement largely reflects shaft runout (the non-vibration component caused by mechanical and electrical imperfections) rather than true vibration. By subtracting this low-speed runout from the entire 1X measurement, a “compensated” curve is obtained, which provides a more accurate depiction of the synchronous shaft vibration. Failure to compensate for large runout can lead to significantly erroneous vibration readings.

An orbit plot visualizes the shaft’s motion within a measurement plane. By utilizing two orthogonal proximity probes, the shaft’s displacement and phase measurements are plotted in a polar coordinate system, tracing its path, which is typically elliptical or circular. Orbit plots can show the direct orbit (all frequencies) or be filtered to display motion at specific harmonics (e.g., 1X, 2X, 0.5X), providing insight for common fault diagnosis.

Meanwhile, waterfall plots (Figure 3) display the frequency spectrum as a function of time, creating a stacked, 3D-like graph. The x-axis represents frequency, the y-axis represents time, and the intensity or color indicates the vibration magnitude. This visualization is invaluable for identifying the frequencies contributing to overall vibration and trends over the machine’s operational lifespan, making it a cornerstone of predictive maintenance and complex troubleshooting.

Rotordynamic Testing and Analysis

Modal testing is an experimental technique to determine the natural frequencies and corresponding mode shapes of a structure, such as a compressor shaft. The process involves preparing the shaft with sensors, exciting it with a controlled input (like a shaker or hammer), measuring the response (displacement, velocity, or acceleration), and analyzing the data with specialized software to extract modal parameters. The results are then validated against predicted natural frequencies and mode shapes derived from the FEA model to check for discrepancies. This offers critical insight into the shaft’s dynamic behavior. An example can be seen in Figure 4.

Operating Deflection Shapes (ODS) record and illustrate a structure’s deflection during actual, on-site operation. The resulting shape reveals areas of maximum and minimum deflection. Unlike modal testing, the excitation source is not necessarily known. ODS provides a quantitative understanding of how the structure is vibrating under operational conditions, which is particularly helpful in identifying issues like mechanical looseness at structural connections (Silva and Kuecker, 2015). ODS can also be paired with modal testing by comparing deflection shapes to the structure’s predicted mode shapes at identified natural frequencies.

Traditional Experimental Modal Analysis (EMA) for stability measurements requires external excitation devices, such as shakers. This can be costly and impractical for many turbomachinery setups, especially drivethrough machines. Operational Modal Analysis (OMA) addresses this by determining system stability using only the existing output vibrations from installed proximity probes. OMA fundamentally assumes that the natural excitations inherent to the machine’s operation are sufficient to excite the natural frequencies of interest and identify the corresponding logarithmic decrements. This makes OMA a powerful, non-invasive tool for monitoring machine stability during its normal operational cycle.

A root cause analysis (RCA) is a systematic process for identifying the underlying cause(s) of a problem, such as compressor shaft vibration. The process is structured to move from symptom to cause and corrective action. The following steps are taken during this process: information gathering, problem definition, cause identification, data analysis, root cause determination, and corrective actions. From here, the compressor’s subsequent performance is monitored to ensure proper operation.

A structured method often used in RCA is the Fishbone Diagram (sometimes called an Ishikawa diagram), which can be found in Figure 5. The diagram organizes potential causes into major categories, typically based on the 5Ms and E (Manpower, Method, Materials, Machines, Measurement, Environment), with sub-causes branching off to systematically identify contributors to the problem.

Another system known as Fault Tree Analysis (FTA), Figure 6, is a systematic technique that uses a diagram to identify all potential causes that could lead to a specific top event, in this case, compressor shaft vibration. Contributing factors (intermediate events) are connected to the top event using logic gates. Analyzing the fault tree identifies the “cut set,” the minimum combination of events most likely to cause the top event, allowing for targeted corrective action development.

Sources of Shaft Vibration and Their Signatures

Vibration sources are best characterized by their unique frequency signatures, which offer important diagnostic clues.

Imbalance is a primary vibration source, occurring when the rotor’s mass distribution is asymmetrical, causing the center of mass to be offset from the rotational axis. Imbalance is identified by a large 1X (synchronous) vibration. The same imbalance can yield vastly different vibration responses depending on the structural support and proximity to a critical speed.

Imbalance can be classified as:

• Static imbalance: The principal inertial axis is merely offset from the rotational axis. It is corrected by placing an equal mass opposite the heavy spot.
• Dynamic imbalance: The principal inertial axis is tilted and offset to the rotational axis, due to a combination of static imbalances in multiple planes along the length of the rotor. It is corrected by placing or removing mass at multiple planes along the length of the rotor.

Sources of imbalance include poor component balance, rotor bowing, debris accumulation, and material erosion/loss. Hydraulic imbalance, caused by flow path asymmetry in high-density gas compressors, also generates a 1X forcing function dependent on speed and fluid density. For flexible rotors operating above the first bending mode, high speed balancing is often necessary, using the influence coefficient method with trial weights to minimize vibration at operating speeds.

The Morton Effect is a thermal synchronous rotor instability caused by asymmetric heating at the fluid film bearings, leading to thermal bending (bowing) of the shaft. An initial imbalance causes the shaft to whirl, leading to uneven heating and an additional thermal imbalance, creating a feedback loop. A signature of the Morton Effect is a climbing 1X vibration amplitude on a Bode plot with no other system changes, followed by a resulting hysteresis loop when the speed is reduced.

Misalignment is a condition where two intended coaxial components, like shafts, are not perfectly aligned. It is categorized into parallel misalignment, where shafts remain parallel but are offset by a distance, or angular misalignment, where shafts are offset by an angle (Figure 7).

Misalignment introduces reaction forces at the coupling that affect the rotor’s vibration response. While a strong 2X harmonic is frequently cited as the definitive signature, this generalization is not always appropriate. Misalignment forces can simply change the amplitude of the 1X vibration, or in some cases, result in a “banana-shaped” orbit with two peaks per revolution, demonstrating the 2X harmonic (Palazzolo, et al, 1992). Since other faults can also generate strong 2X components, a comprehensive diagnostic approach is required.

Instability is a self-excited vibration that grows in amplitude due to insufficient damping. Rotordynamic stability is quantified by the logarithmic decrement (log dec); a positive log dec indicates a stable system with sufficient damping, while a negative value signifies instability, leading to increasing vibration until limited by nonlinear effects.

Instability often manifests as sub-synchronous vibrations at the rotor’s natural frequency when operating above it. This is caused by cross-coupling forces (aerodynamic effects, seal dynamics, internal friction, or bearing characteristics) that create a tangential force, inducing shaft whirl (forward or backward precession).

Key sources of whirl instability include:

• Hysteretic Whirl: Caused by internal rotor damping, where internal friction generates a tangential force inducing forward whirl (Ehrich, 1992).
• Fixed Geometry Fluid Film Journal Bearings: Can produce destabilizing cross-coupled stiffness terms due to asymmetric fluid pressure profiles. Tilting-pad journal bearings eliminate these destabilizing forces.
• Labyrinth Seals: Produce substantial destabilizing forces due to circumferential fluid flow, which increase with tangential velocity. Mitigation involves swirl brakes or shunt injection to reduce the tangential flow (Childs, 1997).
• Aerodynamic Cross-Coupling (Alford Forces): Shaft eccentricity alters blade tip clearances, creating an imbalance of tangential forces that can destabilize the rotor (Alford, 1965).

Limit cycle vibration, a non-linear self-excited vibration, resulting from an instability that has a non-linear limiting factor where the amplitude remains constant and non-zero, often appears as a low-amplitude, sub-synchronous component on a Cascade plot.

Fractures, Looseness, and Rubs

Fractures in impellers, blades, or the shaft immediately result in a significant increase in vibration. More subtle rotor cracks may be indicated by an unexpected shift in 1X vibration levels over time or difficulty in field balancing (Bently and Williams, 1986). A crack typically also includes a significant super-synchronous (2X or 3X) component. Modal testing can reveal rotor anisotropy, which is a key sign of a crack.

Mechanical looseness can be structural or related to rotating components. Structural looseness typically manifests as an increase in 1X vibration and may result in significant differences between the vibration measured in the horizontal compared to vertical planes, with an erratic phase angle. Rotating looseness (e.g. excessive radial bearing clearance) presents with high 1X vibration, rich super-harmonics (2X, 3X, 4X), and sub-harmonics (1/2X, 1/3X), along with erratic phase angles.

Rubs often arise secondary to primary issues (e.g., high imbalance or misalignment) or poor design clearances. Rubs cause localized heating due to friction, leading to rotor thermal bow and an ensuing change in 1X vibration amplitude and phase. Rubs introduce non-linear support characteristics, which complicate the vibration signature. Key symptoms include: changes in 1X vibration over time (Bachsmid, et al., 2004), an abnormal or chaotic orbit shape, a rich spectrum of sub-synchronous and super-synchronous (2X, 3X) harmonics, and the presence of reverse precession components.

Gear and Fluid-Related Vibration

In integrally geared systems, gear mesh frequency (GMF) is a prominent vibration source arising from tooth engagement. Gear issues can lead to transverse, axial, and torsional vibration. Causes include gear tooth wear/damage, misalignment (often indicated by a 2X GMF), insufficient backlash, and resonance.

Fluid-related vibration is caused by flow path dynamics:

• Flow irregularities: Turbulence created by upstream pipe bends can interact with compressor blades, causing vibration.
• Rotating stall: Airflow disruption causes air separation from the blade surface, forming a recirculating flow that moves at a sub-synchronous velocity, leading to instability and vibration.
• Surge: A drop in flow below the surge line causes gas flow reversal, creating a "shock" pressure wave.

Integration with Operational Data

Effective diagnosis often hinges on integrating vibration data with operational and maintenance information. A thorough review of the maintenance history (lubricant replacement, repair, inspection) is essential to determine if component wear, neglect, or previous inadequate repairs are contributing to the vibration.

Temperatures and pressures of the process fluid are critical operational parameters. Unintended operating conditions can increase stress on components, leading to premature wear and vibration. Fluctuations in flow, temperature and pressure can result in unsteady flow and force variations on rotating components. Furthermore, temperature changes cause the casing to expand or contract, potentially affecting rotor-stator alignment. Tracking these temperatures and pressures in time and fusing the vibration data and operating data can produce insightful outcomes in observing condition-based issues with turbomachinery operating in the field. Often, if continuous machine performance data is not recorded a priori, diagnosing gradual condition-based symptoms becomes challenging, if not impossible. This highlights the importance of obtaining data while the machine is healthy prior to an issue occurring. Other items to track for historical perspective include gas compressor fluid chemistry, mole weight, ambient temperature, power, etc.

The oil system is crucial for maintaining oil flow and pressures; monitoring oil temperature, pressure, and conducting regular oil analysis is vital. Oil temperature deviations can affect oil viscosity. Viscosity that is too low can lead to metal-to-metal contact, while viscosity that is too high can result in inadequate lubrication, both causing high vibrations. In terms of oil pressure, both low and high pressure can lead to high vibrations; low pressure causes inadequate lubrication and wear, while high pressures can cause seal failure and leakage. Oil analysis is key for detecting contaminants and wear particles. It provides an early warning of potential issues that could lead to severe damage. Maintaining optimal oil conditions is essential for preventing high vibration and extending equipment lifespan.

Conclusion

The effective diagnosis and mitigation of shaft vibration are critical for the sustained and reliable operation of industrial centrifugal compressors. This technical review underscores the necessity of a comprehensive diagnostic framework that employs advanced signal processing techniques, including time domain, frequency domain, orbit analysis, modal testing, and operational analysis, to accurately identify and characterize the root causes of vibration. The successful integration of these detailed vibration analyses with critical operational data, such as oil system health and process flow conditions, allows for a proactive approach to turbomachinery health monitoring. This ensures the operational integrity and safety of these essential systems across all industrial applications.

References

1. Alford, J. S., 1965, “Protecting Turbomachinery from Self-Excited Rotor Whirl,” ASME Journal of Engineering for Power, 87 (4), pp. 333–344.

2. Bachschmid, N., Pennacchi, P. and Vania, A., 2004. Diagnostic significance of orbit shape analysis and its application to improve machine fault detection. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 26, pp.200-208.

3. Bently, D.E. and Williams, E.B., 1986. Detection of rotor cracks. In Proceedings of the 15th turbomachinery symposium. Texas A&M University. Turbomachinery Laboratories.

4. Childs, D.W. and Vance, J.M., 1997. Annular Gas Seals And Rotordynamics Of Compressors And Turbines. In Proceedings of the 26th Turbomachinery Symposium. Texas A&M University. Turbomachinery Laboratories.

5. Ehrich, F.F., 1992. Handbook of Rotordynamics. McGraw-Hill, New York.

6. Palazzolo, et al., 1992. Gear Coupling Misalignment Induced Forces and their Effects on Machinery Vibration. In Proceedings of the 21st Turbomachinery Symposium. Texas A&M University.

7. Silva, R.A. and Kuecker, K.J., 2015. Tips for Troubleshooting with the Operating Deflection Shape (ODS) Technique. In Proceedings of the 44th Turbomachinery Symposium. Turbomachinery Laboratories, Texas A&M Engineering Experiment Station.

About the Authors

Karl Wygant is the Senior Manager of Advanced Technology Programs at Ebara Elliott Energy.

Brian Hantz is an Advanced Technology Programs Engineer at Ebara Elliott Energy.

Jason Wilkes is a Senior Research Engineer at the Southwest Research Institute.