Displacement, Velocity and Acceleration

What are the units of vibration? It is sometimes referred to in mm/s (millimeter’s per second) and other times in microns.

When a body moves back and forth, the movement can be defined in several ways - one is by simply measuring how much it is moving from one end to the other- this is peak-to-peak displacement however it doesn't give us any hint of the energy in this movement.

Why would energy be important?

Consider if a leaf were to sway gently in a breeze several centimeters, it would not hurt anyone but if a turbine were to vibrate 100 microns, it would probably create havoc. Therefore, it is important not only to know how much movement there is but also some measure that tells us how fast is that moment.

Those of you who remember their school physics will remember the definition of velocity - it is the rate of change of displacement and this is exactly how it is in vibration also. It takes into account not only the displacement amplitude but also the frequency.

From our basic trigonometric relationships, we know that the harmonic movement can be represented in mathematics as follows:

If you were to write the first differential of the above function (displacement) with time, this would give us the rate of change of this function -Velocity . It is again a sine wave that is displaced by 90 degrees in phase .

Velocity is a valuable measure of vibration, much more than displacement. In the mid-1950s, most standards of vibration worldwide described acceptable levels in displacement and later specified different acceptable levels depending upon the speed.

However, in the 1960s, the standard shifted in favour of velocity. A large number of companies in India still measure displacement in microns or mills and have not moved into measuring velocity.

Almost all contemporary standards of vibration are based on velocity.

There are three good reasons for measuring velocity.

1. It provides a uniform measurement that is typically independent of the rotor speed. Thus from 600 RPM to 60000 RPM, we can specify velocity and it would have Universal meaning.

2. Velocity squared is related to energy directly. Double the velocity would have four times the energy.

3. Velocity is also a great parameter that gives even weightage to the various causes of vibration whether these are low-frequency causes like worn belts or high-frequency causes like faulty bearings.

If the rate of change of velocity is computed then we get acceleration. Acceleration is the double differential of displacement and increases as a square of the frequency.

Acceleration is sometimes used in cases where we need to emphasize high-frequency vibrations as in bearing monitoring or if you need to de-emphasize the low frequencies, for instance on a ship to remove the effect of roll on the measurement of on-board equipment.


Baseline Technologies was established in 1990 and offers Portable Instruments for measurement of Sound and Vibration, including analysis, monitoring, field-balancing, and custom measurement solutions in the above areas. More information can found on our website : https://www.baselinetechno.com/