vibration and envelope modulation

In this article, which is the first in a series, This is the subject of vibration modulation and envelope with a fundamental role in diagnosis by vibration analysis in machines. Here is the introduction to a series of articles on this topic.

1 Introduction to vibration and envelope modulation

Mechanical vibration is one of the most evident physical manifestations of the operation of a rotating machine.. Whenever a machine operates, the dynamic interaction between its components — veins, bearings, gears, engagements, rotors and structural elements — generates time-varying forces that propagate in the form of vibrations. These vibrations carry information about the mechanical state of the machine and can be analyzed to identify changes in its behavior., allowing defects to be detected before they develop into serious failures.

The first vibration analysis methods were essentially based on measuring the global level of vibration, expressed in acceleration, speed or displacement. Although these parameters continue to be important for assessing the severity of vibrations, It was quickly found that its overall value contains limited information about the origin of the problem. Machines with different defects may present similar overall levels, while defects in the initial phase may not cause any significant change in these values.

The introduction of Fast Fourier Transform (FFT – Fast Fourier Transform) represented a decisive advance in diagnostic engineering.

This approach, appointed by spectral analysis, continues to be one of the fundamental tools of vibration engineering. Yet, Industrial experience has demonstrated that many defects do not initially manifest themselves through the appearance of new, well-defined frequencies. Instead, cause small changes in the way an existing vibration evolves over time.

These changes can translate into periodic variations in the amplitude, the frequency or phase of a vibration already present in the machine. This phenomenon is known for modulation.

Modulation is particularly important because it constitutes a mechanism that makes information associated with incipient defects more easily detectable., by moving it to a frequency band — around the carrier frequency — with a better signal-to-noise ratio. A small damage located on a carriageway, for example, can generate reduced energy impacts, practically invisible in the conventional spectrum. However, These impacts excite high natural frequencies of the structure and modulate their amplitude periodically. The information about the defect is then no longer concentrated at the impact frequency and begins to manifest itself in the form of side bands around the carrier frequency or, after demodulation, across a clearly identifiable spectrum of surroundings.

This principle is common to several mechanical components:

in the bearings, the passage of rolling elements over a defect produces periodic impacts that modulate structural resonances;
in the gears, the wear, eccentricity or a broken tooth cause cyclical variations in the gearing force, giving rise to sidebands around the gear frequency;
in electric motors, electromagnetic defects or rotor eccentricities generate modulations related to the frequency of the electrical network, the slip frequency or rotation speed;
in pumps and fans, hydraulic or aerodynamic phenomena can modulate mechanical components associated with the rotor.

That way, modulation should not be seen as a secondary phenomenon or a simple mathematical curiosity. On the contrary, constitutes a direct consequence of the dynamic interaction between the different elements of the machine and provides extremely sensitive information about the evolution of its mechanical state.

Figure 1.1 – Conceptual comparison between conventional FFT analysis and modulation analysis, showing how an incipient defect can be practically invisible in traditional FFT, but clearly identifiable after envelope demodulation.

Demodulation distributes the effect energy into sidebands around the carrier frequency. The demodulation (envelope) retrieves the low-frequency information associated with the defect.

From a signal processing point of view, modulation establishes a connection between a low-frequency mechanical phenomenon — such as shaft rotation or the passage of a rolling element — and a higher-frequency vibration, often associated with a structural resonance. This interaction causes relevant information to be “transported” by high frequency vibration, making it possible to detect defects whose energy would be insufficient to be observed directly in the conventional spectrum.

Figure 1.2 – Flowchart of the diagnosis chain, from mechanical defect to diagnosis (defect → dynamic force → vibration → sensor → acquisition → FFT/demodulation → diagnosis).

It is precisely this ability to reveal hidden information that has made modulation analysis one of the most important tools in modern machine diagnostic engineering.. Techniques such as envelope analysis (usually implemented through the Hilbert Transform), cepstral analysis, Spectral kurtosis and cyclostationary analysis exploit this principle to identify defects at very early stages, often weeks or months before a significant increase in the overall vibration level occurs.

In current industrial systems, This capacity assumes strategic importance. Critical equipment, like turbines, centrifugal compressors, speed reducers, electrical generators, process pumps and wind turbines, they often operate continuously and any unexpected failure can translate into high economic costs, safety risks and production losses. The early detection provided by modulation techniques allows planning interventions during scheduled shutdowns, reduce the risk of catastrophic failures and extend component life.

This document constitutes an introduction to vibration and envelope modulation.