# How is Vibration Described?

By watching, feeling, and listening to machine vibration, we can sometimes roughly determine the severity of the vibration. We may observe that certain kinds of machine vibration appear 'rough', others 'noticeable', and yet others 'negligible'. We can also touch a vibrating bearing and feel that it is 'hot', or hear that it is 'noisy', and so conclude that something is wrong.

Describing machine vibration with these general terms is, however, imprecise and depends on the person making the assessment. What appears 'rough' to one person may appear acceptable to another.

Verbal description is usually unreliable.

To accurately analyze a vibration problem it is necessary to describe the vibration in a consistent and reliable manner. Vibration analysts rely primarily on numerical descriptions, rather than on verbal descriptions, to analyze vibration accurately, and to communicate effectively.

The two most important numerical descriptors of machine vibration are amplitude and frequency.

Amplitude describes the severity of vibration, and frequency describes the oscillation rate of vibration (how frequently an object vibrates). Together, amplitude and frequency of vibration provide a basis for identifying the root cause of vibration.

## What is Amplitude?

The amplitude of vibration is the magnitude of vibration.

A machine with large vibration amplitude is one that experiences large, fast, or forceful vibratory movements. The larger the amplitude, the more movement or stress is experienced by the machine, and the more prone the machine is to damage.

Vibration amplitude is thus an indication of the severity of vibration.

In general, the severity or amplitude of vibration relates to:

(a) the size of the vibratory movement

(b) the speed of the movement

(c) the force associated with the movement

In most situations it is the speed or velocity amplitude of a machine that gives the most useful information about the condition of the machine.

What is velocity? Velocity is simply speed measured in a particular direction, as shown below.

Velocity amplitude can be expressed in terms of its peak value, or what is known as its root-mean-square value.

The peak velocity amplitude of a vibrating machine is simply the maximum (peak) vibration speed attained by the machine in a given time period, as shown below.

In contrast to the peak velocity amplitude, the root-mean-square velocity amplitude of a vibrating machine tells us the vibration energy in the machine. The higher the vibration energy, the higher the root-mean-square velocity amplitude.

The term 'root-mean-square' is often shortened to 'rms'. It is useful to remember that the rms amplitude is always lower than the peak amplitude.

How do we decide whether the peak amplitude or the rms amplitude is to be used? It is really a matter of personal choice. However, it is essential to always use the same amplitude type when making comparisons.

Velocity amplitude, whether peak or rms, is always expressed with a unit. Listed below are two commonly used velocity amplitude units. (Some vibration analysts prefer the logarithmic amplitude unit adB. However, discussion on logarithmic scales and units is beyond the scope of this article.)

## What is Frequency?

A vibrating machine component oscillates, that is, it goes through repeated cycles of movement. Depending on the force causing the vibration, a machine component may oscillate rapidly or slowly.

The rate at which a machine component oscillates is called its oscillation or vibration frequency. The higher the vibration frequency, the faster the oscillation.

You can determine the frequency of a vibrating component by counting the number of oscillation cycles that are completed every second. For example, a component going through 5 vibration cycles every second is said to be vibrating at a frequency of 5 cycles per second. As shown below, one cycle of a signal is simply one complete sequence of the shortest pattern that characterizes the signal.

Just as a person's pulse rate or frequency indicates the person's state of excitement or general health condition, the vibration rate or frequency of a machine component is often a useful indicator of the condition of the machine.

Frequency, as with amplitude, is always expressed with a unit.

Commonly used frequency units are cps (cycles per second), Hz (Hertz), and cpm (cycles per minute). Hertz is a unit equivalent to 'cycles per second'. One Hz is equal to one cps (one cycle per second), or 60 cpm (60 cycles per minute).

## What is A Waveform?

The graphical display of electrical signals from a person's heart (electrocardiogram or ECG) is useful for analyzing the medical condition of the person's heart. In a similar way, graphical displays of vibratory motion are useful tools for analyzing the nature of vibration.

We can often find clues to the cause and severity of vibration in the graphical display of vibratory motion.

One display commonly used by vibration analysts is the waveform. A waveform is a graphical representation of how the vibration level changes with time. Shown below is an example of a velocity waveform. A velocity waveform is simply a chart that shows how the velocity of a vibrating component changes with time.

The amount of information a waveform contains depends on the duration and resolution of the waveform. The duration of a waveform is the total time period over which information may be obtained from the waveform. In most cases, a few seconds are sufficient. The resolution of a waveform is a measure of the level of detail in the waveform and is determined by the number of data points or samples characterizing the shape of the waveform. The more samples there are, the more detailed the waveform is.

## What is A Spectrum?

Another kind of display commonly used by vibration analysts is the spectrum. A spectrum is a graphical display of the frequencies at which a machine component is vibrating, together with the amplitudes of the component at these frequencies. Shown below is an example of a velocity spectrum.

But how can a single machine component be simultaneously vibrating at more than one frequency?

The answer lies in the fact that machine vibration, as opposed to the simple oscillatory motion of a pendulum, does not usually consist of just one simple vibratory motion. Usually, it consists of many vibratory motions taking place simultaneously.

For example, the velocity spectrum of a vibrating bearing usually shows that the bearing is vibrating at not just one frequency but at various frequencies. Vibration at some frequencies may be due to the movement of bearing elements, at other frequencies due to the interaction of gear teeth, and at yet other frequencies due to the rotation of motor windings.

Because a spectrum shows the frequencies at which vibration occurs, it is a very useful analytical tool. By studying the individual frequencies at which a machine component vibrates, as well as the amplitudes corresponding to those frequencies, we can infer a great deal about the cause of the vibration and the condition of the machine.

In contrast, a waveform does not clearly display the individual frequencies at which vibration occurs. A waveform instead displays only the overall effect. It is thus not as easy to diagnose machine problems using waveforms. With the exception of a few specialized cases, spectra (and not waveforms) are usually the primary tool for analyzing machine vibration. Spectra is the plural of spectrum.

The information a spectrum contains depends on the Fmax and resolution of the spectrum. The Fmax of a spectrum is the frequency range over which information may be obtained from the spectrum.

How high Fmax needs to be is dependent on the operating speed of the machine. The higher the operating speed, the higher Fmax needs to be. The resolution of a spectrum is a measure of the level of detail in the spectrum, and is determined by the number of spectral lines characterizing the shape of the spectrum. The more spectral lines, the more detailed the spectrum.

### Summary

In this section we described machine vibration using methods that are useful for analysis purposes.

We defined the terms 'amplitude' and 'frequency', and described the physical significance of these terms. Amplitude is a measure of vibration severity while frequency is a measure of oscillation rate.

Together, the amplitude and frequency of a vibrating machine component provide us with an understanding of the condition of the machine as well as the cause of the vibration.

We noted that machine vibration is much easier to analyze when it is graphically displayed, and we presented the two most common displays: waveforms and spectra. Usually, spectra are more useful for analysis purposes.

To find out how to set up your own machine vibration monitoring program, contact Commtest Instruments Ltd or one of our representatives for a demonstration of a vbSeries vibration monitoring system. For the address of your nearest representative please visit our website at http://www.commtest.com