Kurtosis in Vibration Analysis for Fault Detection

Definition: What is Kurtosis?

Kurtosis is a statistical parameter that describes the shape of a probability distribution. In vibration analysis, it is applied to the time waveform signal to measure its “peakedness” or “impulsiveness.” A signal with high kurtosis is characterized by sharp, distinct peaks or impacts, while a signal with low kurtosis is flatter or more rounded. It provides a single numerical value that can indicate a change in the underlying character of the vibration signal, even if the overall energy (RMS value) has not changed significantly.

The Diagnostic Value of Kurtosis

The primary value of kurtosis in condition monitoring is its high sensitivity to early-stage, impulsive faults. Many mechanical defects begin as microscopic cracks or spalls. As these developing faults make contact, they generate short-duration, high-frequency impacts. These impacts cause sharp peaks in the vibration time waveform, which dramatically increase the kurtosis value long before the fault has grown large enough to affect the machine’s overall RMS vibration level.

Kurtosis is therefore an excellent tool for:

• Early Bearing Fault Detection: It is one of the most effective methods for detecting the very first signs of a spall on a bearing race or rolling element.
• Gear Tooth Fault Detection: A cracked or broken gear tooth will produce a distinct impact once per revolution, which is easily detected by a rising kurtosis value.
• Detecting Intermittent Rubs or Impacts: Any non-uniform, impacting event within a machine can be highlighted by this measurement.

Interpreting Kurtosis Values

Kurtosis is a normalized value. For a perfect Gaussian (normal) distribution, which is typical of the random background vibration in a healthy machine, the kurtosis value is **3.0**. Deviations from this value are diagnostically significant:

• Kurtosis ≈ 3.0: Indicates that the vibration is random and Gaussian, suggesting normal, healthy operation.
• Kurtosis > 3.0: Indicates that the signal is becoming more “peaky” or impulsive than normal. A rising kurtosis value is a clear warning sign of developing impacts. Values of 5, 10, or even higher are common when significant bearing or gear defects are present.
• Kurtosis < 3.0: Indicates that the signal is flatter than a normal distribution. This can sometimes occur with certain types of rubbing or when the signal is dominated by a very clean, sinusoidal vibration.

The Kurtosis Lifecycle of a Bearing Fault

When tracking a bearing fault from inception to failure, the kurtosis value often follows a predictable pattern:

1. Healthy Stage: Kurtosis is stable and close to 3.0.
2. Early Fault Stage: A microscopic defect forms. Sharp, distinct impacts are generated, causing the kurtosis to rise significantly (e.g., to 5.0 or higher). The overall RMS vibration may still be low. This is the ideal time to detect the fault.
3. Developed Fault Stage: As the defect grows larger and spreads, the impacting becomes more frequent and less distinct. The signal starts to resemble random noise again, although at a much higher energy level. Consequently, the kurtosis value may *decrease* and return towards 3.0, while the RMS vibration level now starts to rise dramatically.
4. Late/Failure Stage: The bearing is heavily damaged, and the vibration is high and often random. Kurtosis remains near 3.0, but the RMS value is now in alarm.

This lifecycle highlights why kurtosis is so valuable. The “sweet spot” for detection is in the early stages when kurtosis rises. Relying on RMS alone would mean the fault is not detected until it has already become significant.

Limitations

While powerful, kurtosis should be used alongside other techniques like spectrum and waveform analysis. It can be sensitive to random, non-machine-related shocks, so it is best used as a trending parameter. A consistent rise in kurtosis over time is a much more reliable indicator than a single high reading.

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