It is important to understand that
with sinusoidal vibration, the relationship between acceleration, velocity
and displacement is fixed and frequency dependent. It is not possible to
vary any one of these three parameters without affecting another, and for
this reason, one must consider all of them simultaneously when specifying
or observing sine vibration.
The three parameters of acceleration,
velocity and displacement are all linear scalar quantities and in that respect,
at any given frequency, each has a constant, proportional relationship with
the other. In other words, if the frequency is held constant, increasing
or decreasing the amplitude of any one of the three parameters results in
a corresponding proportional increase or decrease in both of the other two
parameters. However, the constant of proportionality between the three parameters
is frequency dependent and therefore not the same at different frequencies.
In general, sinusoidal vibration
testing uses the following conventions for measurement of vibration levels.
Acceleration is normally specified and measured in its peak sinusoidal value and is normally
expressed in standardized and normalized dimensionless units of g's
peak. In fact, a g is numerically equal
to the acceleration of gravity under standard conditions, however, most
vibration engineering calculations utilize the dimensionless unit of g's and convert
to normal dimensioned units only when required.
Velocity is specified in peak amplitude as well. Although not often used in vibration
testing applications, velocity is of primary concern to those interested
in machinery condition monitoring. The normal units of velocity are inches
per second in the English system or meters or millimeters per second in the metric
system of units.
Displacement is usually expressed in normal linear dimensions, however, it is measured
over the total vibration excursion or peak to peak amplitude. The normal
units of displacement are inches for English or millimeters for the metric
system of units.
As mentioned previously, these
quantities are not independent and are related to each other by the frequency
of the vibration. Knowing any one of these three parameter levels, along with
the frequency of operation, is enough to completely predict the other two
levels. The sinusoidal equations of motion stated in normal vibration testing
units are as follows. |