Vibration characteristics of shaft crack

Shaft cracks are critical faults in rotating machinery that can lead to catastrophic failure if undetected. Vibration analysis provides a powerful tool for early crack detection during machine operation. Characteristic vibration responses include changes in 1X and 2X amplitude and phase, reduction in critical speed, and internal loop orbit shape [1–3]. In some cases, strong 3X components are also observed as discussed in [4–6]. This article reviews the vibration mechanisms associated with shaft cracks, outlines practical detection methods, and highlights monitoring strategies using steady-state and transient vibration data.

Introduction

Rotating machinery shafts are subjected to cyclic stresses, thermal loads, and dynamic forces throughout their service life. Over time, these factors can initiate cracks that compromise shaft integrity. Although shaft cracks are relatively rare compared to other faults such as unbalance or misalignment, their consequences are severe ranging from unexpected shutdowns to complete rotor failure.

Traditional inspection methods often fail to detect cracks during early stages because they require disassembly or visual access. In contrast, vibration monitoring offers a non-invasive and continuous diagnostic approach. By analyzing harmonic components, orbit behavior, and critical speed shifts, engineers can identify crack signatures before they progress to catastrophic levels.

This article focuses on the vibration characteristics of shaft cracks, explaining how bowing and asymmetric stiffness alter machine dynamics. It also discusses practical detection workflows and monitoring strategies that can be implemented using modern condition monitoring systems.

Shaft crack detection

Vibration data is a powerful diagnostic tool for detecting shaft cracks during machine operation. Two primary vibration symptoms are observed:

1. Shaft Crack as Rotor Bow

• Mechanism: A transverse crack causes the rotor to bow, altering the 1X vibration response at both normal operating speeds and slow-roll conditions.

• Effects:

  • Increased residual unbalance due to increased mass eccentric of bow condition.

  • Higher vibration amplitudes as unbalance forces grow with reducing shaft stiffness over time.

  • Shift in critical speed because natural frequency decreases with reduced stiffness (proportional to square root of (k/m) ).

• Diagnostic Clues:

  • Slow-roll vectors at 1X and 2X are inconsistent between runs under similar thermal conditions (cold startup or hot shutdown). The same thermal condition should be compared.

  • Unlike temporary rotor sag from gravity, crack-induced bowing is irreversible and progressively worsens.

2. Shaft Crack as Asymmetric Stiffness

• Mechanism: A crack introduces directional stiffness asymmetry, producing strong 2X vibration responses. The rotor produced twice deflection/vibration per revolution, example vibration plots of this behaviors is shown in Fig. 1 below.

• Effects:

  • Rotor stiffness is lower in the crack direction, similar to a ruler bending more easily along one axis.

  • With preload from gravity or fluid forces, the rotor vibrates twice per revolution, explaining the strong 2X component.

  • 2X amplitude and phase continue to evolve as the crack grows.

• Transient Behavior:

  • 2X vibration can excite the first balance critical speed at half the critical speed, producing internal loop orbit shapes.

  • Some studies report strong 3X responses, exciting critical speed at one-third of the rotor speed, though the mechanism remains unclear and is based mainly on case data.

Fig.1: Example of vibration behaviors due to asymmetric stiffness rotor. Note this is not actual vibration data from cracked shaft but it revealed similar symptoms.

Summary of Vibration Characteristics

• Changes in 1X amplitude and phase at steady-state and slow-roll speeds.

• Changes in 2X amplitude and phase under similar conditions.

• Reduction in first balance critical speed due to decreased stiffness.

• Early excitation of critical speed by 2X vibration at half-speed, with internal loop orbit shapes.

• Occasional evidence of leading phase during transients, attributed to non-linear crack breathing.

Additional characteristics such as thermal sensitive, spilt resonance, etc. can be found in a comprehensive review [7] with more case study of power plant machines in [8].

Monitoring shaft crack

Effective monitoring relies on tracking both steady-state and transient vibration data:

• 1X and 2X Vectors: Trend plots and polar plots (amplitude–phase–time) can reveal deviations from baseline conditions (refer to Fig. 2). Acceptable regions [1] should be defined from known healthy states, as example in Fig. 3 below.

• Critical Speed Tracking: Compare startup and shutdown data against reference baselines to detect shifts in critical speed.

• Slow-Roll Data: Non-repeatable vectors at 1X and 2X provide strong evidence of crack progression (Fig. 4).

• Condition Monitoring Systems: Modern software offers overlays, reference management, and transient data comparison, making crack detection more practical and reliable.

Fig. 2: Trend plots of 1X and 2X vibration amplitude with corresponding polar plots of the same data but phase angle is also available.

Fig. 3: Example of acceptance region concept, source [2]

Fig. 4: Example of slow roll data collection from transient data plots such as Bode plots in this case.

Conclusions

Shaft cracks represent one of the most severe faults in rotating machinery, capable of leading to catastrophic failure. Although rare, their detection is vital for ensuring machine reliability and safety. Vibration monitoring particularly analysis of 1X and 2X responses, orbit distortion, and critical speed shifts provides an effective, non-invasive method for early crack identification. By leveraging modern condition monitoring tools and consistent baseline comparisons, engineers can prevent unexpected failures and extend the operational life of critical machinery.

References

1. Bently, D.E., Muszynska, A.: DETECTION OF ROTOR CRACKS. In: The Proceeding of the Fifteen Turbomachinery Symposium. Texas A&M University Turbomachinery Laboratory (1986).

2. Bently Nevada Corporation: Early Shaft Crack Detection on Rotating Machinery Using Vibration Monitoring and Diagnostics. , Reno (1988).

3. Bently, D.E., Hatch Charles T.: Fundamentals of Rotating Machinery Diagnostics. Bently Pressurized Bearing Press (2002).

4. Krämer, E.: Dynamics of Rotors and Foundations. Springer Berlin Heidelberg (1993). https://doi.org/10.1007/978-3-662-02798-1.

5. Bachschmid, N., Pennacchi, P., Tanzi, E.: Cracked rotors: A survey on static and dynamic behaviour including modelling and diagnosis. Springer Berlin Heidelberg (2010). https://doi.org/10.1007/978-3-642-01485-7.

6. Lees, A.W.: Vibration Problems in Machines: Diagnosis and Resolution. CRC Press (2020).

7. Popaleny, P., Blackwell, J., Péton, N.: Compressor Rotor Crack Case. In: Asia Turbomachinery & Pump Symposium 2022. Turbomachinery Laboratory, Texas A&M Engineering Experiment Station (2022).

8. Herz, F., Nordmann, R.: Vibrations of Power Plant Machines: A Guide for Recognition of Problems and Troubleshooting. Springer Nature Switzerland AG (2020). https://doi.org/10.1007/978-3-030-37344-3.