# Vibration condition monitoring fundamentals – Vibration Metrics

# Vibration Metrics

In condition monitoring, vibration analysis is crucial for checking the health of machinery. Typically, a single vibration measurement is converted into a frequency spectrum using the Fast Fourier Transform (FFT) for detailed analysis. However, plotting or trending multiple measurements creates a complex 3D surface, making it hard to observe and set monitoring thresholds.

To simplify this, experts have developed ways to convert a full vibration measurement into a single value. This makes it easier to visualize trends and set thresholds. Examples of these vibration metrics include Root Mean Square (*RMS*), peak-to-peak values, and kurtosis. Each metric captures different aspects of the vibration data, helping to provide a clear picture of the machinery’s condition.

In this article, we review some of the most important vibration metrics.

## Different metrics

Let us assume the following is a single vibration measurement. Several important functions such as

min, max, and mean, and *RMS* are visualized on the measurement.

**Figure 1: **Time signal with Mean, Max, Min, and *RMS *marked out

### Peak-to-peak

Peak-to-peak measurement in vibration analysis refers to the difference between a vibration signal’s maximum positive and maximum negative amplitudes. This measure indicates the total range of vibration displacement, helping to identify the extremes of machine movement and potential impacts that could indicate issues such as imbalance or misalignment.

### Peak

Peak (0 to peak) measurement in vibration analysis refers to the maximum absolute value of the vibration signal from its baseline (zero). It captures the highest single amplitude of the vibration, indicating the most significant deviation from the normal state. People use peak measurement because it can quickly highlight the most extreme vibration level, which is crucial for detecting sudden or severe changes in machinery conditions that might not be evident in the peak-to-peak measurement. Peak measurement is simpler and provides immediate insight into potential issues like impacts or sudden loads.

### RMS (root mean square)

*RMS* is a statistical measure of the magnitude of a varying quantity. In vibration analysis, it reflects the overall level of vibration energy, providing an average value that helps assess the intensity of the vibrations. This makes *RMS* useful for detecting changes in machine health and performance.

*RMS* is calculated by:

There are also two dimensionless measures of how peaky the signal is, *crest factor* and *kurtosis*.

### Kurtosis

*Kurtosis* is a statistical measure that indicates the “tailedness” or sharpness of the peak of a vibration signal’s amplitude distribution. In vibration analysis, high *kurtosis* values suggest the presence of infrequent but extreme deviations, often indicative of impulsive events such as impacts, shocks, or faults. People use *kurtosis* because it is sensitive to these extreme events and can detect anomalies or irregularities in machinery that other metrics like *RMS *or peak values might miss. This makes *kurtosis* valuable for identifying early signs of mechanical defects.

*Kurtosis* is calculated by:

where is the mean and is the standard deviation of the data.

### Crest Factor

The *crest factor* is the ratio of the peak value of a vibration signal to its *RMS* value. Vibration analysis helps identify the presence of spikes or transient events in the vibration signal. A high *crest factor* indicates that the vibration signal has sharp peaks or impacts relative to its overall energy level. People use the *crest factor* because it can highlight intermittent faults or abnormalities in machinery, such as gear tooth defects or bearing issues, that might not be apparent from *RMS* or peak measurements alone.

Let us look at two examples of how *Kurtosis* and *Crest Factor* capture the “spikyness” of the signal.

In Figure 2, we have a sum of a few sinusoidal waves lacking spikyness. Therefore it gives a relatively low *kurtosis* and *crest factor*. The *kurtosis *for a pure sinusoid wave is 1.5 and the *kurtosis* for a pure noise is 3. The *crest factor* for the pure sinusoid is 1.4 but the *crest factor* does not have a value for pure noise.

**Figure 2: **Harmonic time signal with the *kurtosis *and *crest factor *values.

Here we have the same signal with a burst of energy in the middle. We see that the values for both *crest factor* and *kurtosis *increase indicating the signal is less harmonic and has an uneven behavior.

The *crest factor* is calculated by peak-to-peak/*RMS*.