Piezo Accelerometer Tutorial
What is Vibration?
Relation between Acceleration, Velocity and Displacement
So far we have set all amplitudes to "one unit" i.e. we have chosen the scale to plot the curves in a way that they appeared uniform with the same amplitude. This made it easier to show the basic characteristics of sinusoidal vibration and particularly the phase shift between a, v and d.
However the amplitudes of acceleration, velocity and displacement are always in a determined relation to each other. This relation is given by the frequency.
In the following we want to explore this law in more details.
In a harmonic vibration we can choose one amplitude (for example the acceleration) and the frequency. With this set the other amplitudes (velocity and displacement) will be in a fixed relation.
With constant acceleration and increasing frequency
the velocity decreases proportionally with the inverse frequency:
The displacement decreases with the
inverse frequency squared:
For low frequencies the values for v and d become very large and for high frequencies very small.
For this reason we normally use logarithmic scales for the frequency and the amplitude.
A logarithmic scale is non-linear. The values increase always a distinct factor from division to division. For example a factor 10 like on the sample on the right.
This allows showing the values over several decades.
The velocity amplitude V decreases -1 decade per decade of the frequency
and the displacement amplitude D decreases -2 decades per decade of the frequency.
Dimensions of Acceleration, Velocity and Displacement
In the chapter about linear acceleration we have seen the dimensions of the vibration parameters
displacement : meters (m) or milli-meters (mm)
velocity : meters per second (m/s) or milli-meters per second (mm/s)
acceleration : meters per second per second (m/s²)
These are also the correct dimensions to use for the vibration terms in the SI-system
However in wide parts of the industry particularly in aeronautics we use also an English system with the following units:
displacement : inch (in) or mils (in/1000)
velocity : inch/second (ips)
acceleration : g ( = acceleration of gravity)
1g = 9.81 m/s²
An additional particularity is that
the displacement is normally measured in "peak to peak" (pk-pk) values
while the velocity and acceleration are mostly given in "peak" (pk).