# The Peak, Peak to Peak and RMS values in vibration analysis

In vibration analysis, correctly interpreting the signals from an asset and being able to act on them is crucial to the success of predictive maintenance.

In general, interpretation involves analyzing vibration signals in the time domain, that is, plotted on a t-axis. In this way, it is possible to analyze changes or patterns of vibration by means of different parameters.

In this text we will comment on some of the metrics that can help in the correct interpretation of this type of signal, they are: peak, peak to peak and RMS.

## Peak Value

This is the value of the largest amplitude present in the signal, also called “True peak value” in many platforms. Its increase may indicate the appearance of impacts in the signal.

The peak value represents a point value and does not take into account the total signal energy, that is, any fluctuation or transient vibration of higher value can influence this metric.

In the example below, the bearing housing of a discharge pulley of a conveyor belt presents vibration amplitudes close to 1g, with the axial axis presenting higher values.

When we look closely, we can see that the peak of this signal of duration 4s corresponds to 1.1194g at time 2.52s. Note that in this case no other parts of the signal matter, since the peak value is only the highest amplitude value.

## Peak to Peak Value

Another complementary metric is the Peak to Peak value. This value is the measurement from the minimum peak to the maximum peak of the signal. Like the peak value, its increase can indicate the emergence of impacts.

Similarly, the Peak to Peak amplitude does not provide any information about the amount of energy within the vibration signal, it only provides information about the highest and lowest values.

Following in the previous example, it is possible to observe that the largest value is 1.1194g, while the smallest value corresponds to -0.6306g, occurring at time 2.87s of the signal. By calculating the distance from one point to the other we obtain a Peak to Peak value of 1.75g for the axial axis.

Once again, see that the rest of the signal does not matter. A clearer example of this is the following signal where we can see even more significant impacts. Notice how these impacts break away from the rest of the signal and provide a final Peak to Peak value of:

1,4099 g + 0,9965 = 2,4064 g

Joel Nunes, expert in vibration analysis at Dynamox, comments that the peak to peak metric is essential for monitoring low rotation equipment. Assets of this type generally have low vibration amplitudes / low energy values, which hinders the use of metrics such as RMS (we’ll discuss more about it below) and favors the use of metrics such as peak or peak to peak.

We have seen so far two examples of metrics that punctually act with maximum values and are a good representation of impacts. However, it is necessary to enrich any analysis by also looking at a metric that better represents the total energy, that is, the total signal content. An excellent metric for this is the RMS value.

## RMS

RMS (Root Mean Square): Effective value of the signal. It is calculated based on the entire sample using the following formula:

More practically, it is a measure of the vibratory energy of the equipment.

Unlike the Peak and Peak to Peak values, the RMS value is not a point value, but rather a representation of the total signal energy.

As a fault progression occurs in a monitored asset, the RMS value tends to evolve. This happens because the number of peaks increases, thus impacting the total signal energy.

In general, the RMS value shows little change in the early stages of mechanical failures, because there is little change in the total signal energy. However, as the failures worsen, the RMS value tends to increase more significantly.

The good news regarding the RMS value calculation is that most vibration analysis software already brings the calculated value for user interpretation.

Let’s look at an example of a ball mill gearbox. This gearbox has an error in the transmission of power and movement of the external gear, crown and pinion.

Notice in the upper left corner that both the Peak to Peak (PP) and the RMS value are shown by the software. The difference between them is significant precisely because the RMS takes into account the entire signal.

As the failure gets worse, this value will tend to increase, indicating a higher level of vibration at the monitored point, with more impacts and higher amplitudes.

Look at the case of this same gearbox a few months later (the same scale was used for both graphs plotted in the velocity domain):

A signal trend graph with well-adjusted limits can be useful in tracking the evolution and worsening of this and other types of failure.

Below is a graph with RMS values in velocity for the horizontal axis of the equipment. The point highlighted in green corresponds to the first waveform shown above, with a still controlled RMS value. The red point corresponds to the last waveform, with higher RMS values, according to the evolution of the reported defect.

See that for this second case, alarm levels A2 (most critical level) had already been reached a few months ago, pointing to this evolution.

According to Joel Nunes, one of the benefits of using the RMS value is precisely how “biased” and “behaved” this metric generally is. Because it is not as affected by outliers (as in the case of Peak to Peak metrics), the RMS value generally follows a more standardized and easy-to-follow trend.

In addition, it is common for vibration standards to present limits indicated in RMS, which also favors their use. Are you interested in this content? Keep following our blog and check in the next weeks the **sequence of this text where we will bring other useful metrics in vibration analysis**: crest factor, kurtosis and skewness.