Forcing Frequencies

The value of vibration analysis of machinery is based on the fact that specific elements in the rotating parts of any machine will produce forces in the machine that will cause vibration at specific frequencies. One of the most important of the forcing frequencies is the RPM of the shaft, and it arises from the fact that any rotor will always have a certain amount of residual imbalance. This imparts a radial centripetal force on the bearings, causing the structure to vibrate at the 1X, or fundamental, frequency. The so-called bearing tones, which are characteristic of each bearing geometry, are forces generated by defects in the races and rolling elements of the bearing itself. Gear tooth-mesh frequencies come from the individual impacts of gear teeth against each other, and the tooth-mesh frequency is equal to the number of teeth on the gear times the gear RPM. Vane pass or blade pass frequencies are similar to tooth mesh and are equal to the number of vanes in an impeller or number of blades in a fan times the RPM. Each forcing frequency will create a peak in the vibration spectrum, the amplitude of the peak being dependent on the severity of the condition that causes it. Thus the frequency indicates the type of problem and the amplitude indicates its severity.

As an example of a simple forcing frequency, the ceiling fan illustrated below would produce vibration component each time a blade struck the fly swatter, giving rise to a peak in the spectrum at 5 times the turning speed.

The figure below, showing a centrifugal air compressor, illustrates some of the forcing frequencies in the spectrum.

Following is an example of forcing frequency calculation for a gear-driven machine:

Let us assume that the motor/gear/fan components have the following element counts:

In this case of a multiple shaft machine, we must consider that the fundamental frequencies of the motor and fan shafts are different. Let us assume that the motor is again running at 1780 RPM. To calculate the fan shaft RPM, we must first find the reduction ratio of the gearbox. To find this we would look at the number of gear teeth on each of the gears. Divide the drive pinion tooth count by the driven gear tooth count:

or

Next, multiply this ratio by the motor shaft RPM to find the fan shaft RPM;

We would now say that the fundamental frequency of the motor is 1780 CPM and the fundamental frequency of the fan is 640.8 CPM.

We multiply the number of elements on each component by the fundamental frequency of the shaft from which it rotates. The components that are on the motor shaft will be multiplied by 1780 CPM and the components on the fan shaft will be multiplied by 640.8 CPM. To make this easier, let us separate the components with their corresponding shafts:

The Frequency Axis

When plotting vibration spectra from rotating machines, you have several choices of units for the frequency axis. Probably the most natural unit is the cycle per second, or hertz (Hz). Another unit in common use is Revolutions Per Minute (RPM), or Cycles per Minute (CPM). Hz is converted to CPM by multiplying by 60. Many people feel that CPM is a convenient scale to use because the machines are described in terms of RPM. This practice results in quite large numbers for the frequency axis, however, and many other people prefer to use Hz because the smaller numbers are more convenient.

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