Page 134 - Intro Predictive Maintenance

Vibration Monitoring and Analysis 125

motion forces; however, the intervals or frequencies generated by these machines are
not always associated with one complete revolution of a shaft. In a two-cycle recip-
rocating engine, the pistons complete one cycle each time the crankshaft completes
one 360-degree revolution. In a four-cycle engine, the crank must complete two com-
plete revolutions, or 720 degrees, in order to complete a cycle of all pistons.

Because of the unique motion of reciprocating and linear-motion machines, the level
of unbalanced forces generated by these machines is substantially higher than those
generated by rotating machines. For example, a reciprocating compressor drives each
of its pistons from bottom-center to top-center and returns to bottom-center in each
complete operation of the cylinder. The mechanical forces generated by the reversal
of direction at both top-center and bottom-center result in a sharp increase in the vibra-
tion energy of the machine. An instantaneous spike in the vibration profile repeats
each time the piston reverses direction.

Linear-motion machines generate vibration profiles similar to those of reciprocating
machines. The major difference is the impact that occurs at the change of direction
with reciprocating machines. Typically, linear-motion-only machines do not reverse
direction during each cycle of operation and, as a result, do not generate the spike of
energy associated with direction reversal.

7.4 VIBRATION THEORY
Mathematical techniques allow us to quantify total displacement caused by all vibra-
tions, to convert the displacement measurements to velocity or acceleration, to sepa-
rate this data into its components using FFT analysis, and to determine the amplitudes
and phases of these functions. Such quantification is necessary if we are to isolate and
correct abnormal vibrations in machinery.

7.4.1 Periodic Motion
Vibration is a periodic motion, or one that repeats itself after a certain interval of time
called the period, T. Figure 7–6 illustrates the periodic-motion time-domain curve of
a steam turbine bearing pedestal. Displacement is plotted on the vertical, or Y-axis,
and time on the horizontal, or X-axis. The curve shown in Figure 7–6 is the sum of
all vibration components generated by the rotating element and bearing-support struc-
ture of the turbine.

Harmonic Motion
The simplest kind of periodic motion or vibration, shown in Figure 7–7, is referred to
as harmonic. Harmonic motions repeat each time the rotating element or machine
component completes one complete cycle.

The relation between displacement and time for harmonic motion may be expressed
by: