Page 53 - Rotating Machinery Pratical Solutions to Unbalance and Misalignment

Resonance and Beat Frequencies

Step 1. If at time zero, both machines were in phase, that is they
were both at the maximum amplitude, the resulting beat would be
at its maximum. After 1/10 th of a second, the first machine would
have completed 127.5 cycles and be at a minimum, while the sec-
ond machine would have completed 128 cycles and be at a maxi-
mum. If the two amplitudes were equal, the vibrations would be
180 degrees out of phase and thus cancel each other. At 1/5 th of
a second, the first machine would have completed 255 cycles and
the second machine 256 cycles. Both machines would now be at a
maximum and the amplitudes would add together.
th
th
It can be seen that at time 1/10 , 3/10 , 5/10 th … will pro-
th
th
th
duce minimums while 2/10 , 4/10 , 6/10 … will produce mini-
mums. Thus the beat frequency is produced at 5 Hz. Note that this
is the difference in the two original frequencies.
A component that is vibrating close to its natural frequency
or one of its harmonics can exhibit beat frequencies as well. The
beat frequency is the result of the two amplitudes coming in and
out of phase with one another. When they are in phase, their
amplitudes are added together; when they are out of phase, they
subtract from one another.
The result is a beat frequency with an amplitude greater than
either contributing source, and a frequency that is comprised of
the multiple vibration amplitudes adding and subtracting from
one another. The frequency of the wave form depends on ampli-
tudes, frequency and phase angle of the contributing sources.
A simple beat frequency is shown in Figure 3-8, where two
vibrating sources of different frequencies, amplitudes, and phase
angles are contributing to the beat wave. Beat frequencies come
into and out of phase as the contributing waves add and subtract
from one another. Note that the composite wave is not a perfect
sine wave as are the contributing sources.
The actual frequency of a beat is the sum of two or more
vibrating sources adding and subtracting from one another as il-
lustrated in Figure 3-8. They can be eliminated by either removing
one or more of the sources of vibration, or changing the frequency
of one or more of the sources.