Frequency identifies how often a movement occurs. The significance of this is that machines tend to mechanically generate vibration at multiples (harmonics) of their running speeds. For instance, unbalance causes movement (vibration) at a rate of precisely once per revolution, referred to 1x RPM). A pump with 5 vanes on the impeller can generate hydraulic pulses, measured as mechanical vibration at precisely 5x RPM and so forth.

Frequency is closely tied to the amplitude units of displacement, velocity and acceleration. In fact, the four variables are related in such a way that if you know any two of them, you can calculate the other two mathematically.

For instance, you can walk back 5 meters one way and then 5 meters back (10 meters round trip, or peak to peak) in 6 seconds. In vibration terms:

- Your pk-pk displacement is 10 meters
- Your period is 6 seconds (time required for 1 cycle)

Frequency is represented as the number of cycles during a given period. You could do ten such trips in one minute. Since the total distance travelled is 100 meters, your average speed is 100 meters/min or (dividing by 60) 3.33 meters/sec. Of course, that is the average speed. Since you are constantly speeding up or slowing down, your peak speed would be somewhat higher - perhaps twice the average (400 mpm or 6.67 mps).

Looking more closely at the relationship between these variables.

- You must walk back and forth repeatedly 5 meters each way (the 'displacement')
- You find you can comfortably accomplish this trip 5 times per minute (the 'frequency)
- Those two variables will establish a third - the speed at which you must walk (the 'velocity')

- You may keep the length of the trip the same (10 meters total - the displacement)
- You must now make the trip 10 times per minute instead of 5

To meet those requirements, you must walk twice as fast; doubling the frequency while leaving the displacement the same results in doubling the velocity.

- You must now walk back and forth 10 meters each way (20 meters total - the displacement)
- You must make 5 trips per minute (the same as in Example #1)

To meet those requirements, you must walk twice as fast; doubling the frequency while leaving the displacement the same results in doubling the velocity.

These animations are equivalent to example #2 on the previous page - we are leaving the displacement the same while increasing the frequency of the vibration. In this case, the frequency is 7x greater in the animation on the right.

These animations are equivalent to example #2 on the previous page - we are leaving the displacement the same while increasing the frequency of the vibration. In this case, the frequency is 7x greater in the animation on the right.

The first thing you should notice is the relative speed of the two bearings. The bearing on the right is obviously achieving a much greater speed (velocity) than the one on the left. The speed is, as you have probably guessed, 7x greater.

What we are interested in is the effect of the vibration on the bearing's life and the machine's health. It doesn't take a vibration 'expert' to recognize that it will be the bearing on the right. But since the displacement (stress) is constant, the determining factor must be something else - either the fatiguing effect, which velocity is sensitive to, or the forces being applied which acceleration is sensitive to.

The reason has to do with each amplitude unit's sensitivity to different modes of machinery failures. There are three types of failures occurring:

- Stress (bending a component excessively causes it to fail)
- Fatigue (something simply wears out over time)
- Force (a 'pushing' or 'striking' action causes failure)

The graph below shows the sensitivity of each unit to the likelihood of failure over a wide range of frequencies.

Notice that at low frequencies (primarily below 300 cpm or 5 Hz), displacement is the most sensitive. That is due to the fact that a stress failure, where something is bent back and forth until it breaks, is the most likely failure mode at those low frequencies.

Once you get above 300 cpm, the most likely failure mode increasingly becomes the 'fatigue' mode, to which velocity is the most sensitive unit. Fatigue failures usually occur when a component simply wears out - it tires of the repeated back and forth movement over an extended period of time and many cycles. This usually applies between about 300 cpm and 120,000 cpm (5 - 2000 Hz).

Above 120,000 cpm (2000 Hz), the most likely failure mode is 'force'-related. When you reach these very, very high frequencies, for example where an entire rotor structure back and forth 2000 times per second or more, massive amounts of force are required to move that structure back and forth even a tiny distance at such a tremendously high frequency. It is that tremendous pushing or striking action that causes the failure.

The chart shows the number of failures vs. the number of running hours. Notice that a relatively high number of failures occur during the first hours of runtime. These failures are known as 'infant mortality' because they occur shortly after start-up - in other words, a machine that is new or rebuilt is started up and has severe problems. Within a few hours, days or possibly weeks, a catastrophic failure occurs. If the failure is mechanical in nature (it could also be electrical or lubrication related), it will be a stress failure - components being bent back and forth so much that something simply breaks.

Once a machine runs for a certain number of hours (rotations) however, it becomes stress relieved and the likelihood of failure changes to favour fatigue - a component wearing out. If the movement (vibration) is high but not quite high enough to cause an 'infant mortality' stress failure, the fatigue failure will still occur in a relatively short period of time, which is one reason why the number of failures on the curve doesn't ever quite get to zero.

Acceleration amplitude is a more complex concept. Because of the nature of sinusoidal motion, the velocity is constantly changing and to change the velocity of something, acceleration must be applied; to speed your car up, you apply the accelerator and to slow your car down, you apply the brake.

Acceleration measures the rate of change of velocity. Velocity is changed when either a pushing or striking action is applied.

- The rate of change in velocity (acceleration) is more affected by frequency - how often something is changing direction - than displacement - how far it is moving
- Components moving at high frequencies will never fail due to stress (displacement) because the displacement amplitude is very small
- Although there are frequencies where velocity and acceleration overlap in their sensitivity to failures, the higher the frequency involved (especially above about 120,000 cpm), the less likely a fatigue failure is
- Acceleration is sensitive to the likelihood of a force-related failure. In other words, a failure due to the pushing and/or striking action the component is being subjected to

Consider a high speed centrifugal compressor. This machine, through its normal operation, generates some incredibly high vibration frequencies - well over 1,000,000 cpm (16.67kHz) in certain cases depending on the specifics of the machine. These vibrations are generated by the gear teeth meshing together and referred to as gear mesh frequency.

As an example, consider a machine that generates a gear mesh frequency of 1,080,000 cpm (18kHz). Let's assume that there is some vibration (movement) occurring at the gear meshing frequency due to the interaction of the gear teeth. Assuming further that the amount of physical movement - the distance back and forth, so to speak - is 3 millionths of an inch (0.003 mils, or 0.076 um). To cause the structure (rotor) to move back and forth even such an incredibly tiny amount 18,000 times per second requires a force equal to 50x the force of gravity and failure will occur due to the incredibly high forces being generated.

Every machine has certain operational characteristics which must be considered when creating the database. Similar machines have similar characteristics and similar (many times identical) database point set-ups. The critical question that must be asked for every machine for which you are creating a database is simply what problems may develop on this machine and what vibration frequencies will be generated by each of these problems.

You may need multiple measurements on a particular location to get the level of protection you would like; in other words, you must create each database point with a specific purpose in mind.

Consider a motor driving some component connected with a coupling. What problems may occur on the motor and what vibration frequencies will each generate?

- Mechanical influences (unbalance, misalignment, etc.) at 1x, 2x, and 3x rpm (also be referred to as orders)
- Pumps can generate hydraulically-related vibration at the number of vanes x rpm - vane pass frequency
- Compressors do likewise at lobe pass and vane pass frequencies (to name only 2 types)
- Fans can generate at blade pass frequency
- With rolling element bearings, vibration at 30kcpm - 50 x rpm (up to 150kcpm) is typically generated during stages leading up to failure

Consider the following example for which we will discuss the frequencies encountered: a direct driven screw compressor with an input speed of 3580 rpm. The motor directly drives a bull gear with 48 teeth which drives a pinion gear with 36 teeth. The rotor being driven by the pinion gear has 4 lobes while the driven rotor has 6 lobes. To determine what frequencies the potential problems may create, we need to specifically lay out the frequencies that will be generated on this machine and consider what problems can develop from the machine components. The machine schematic is shown here:

Let’s calculate exactly what frequencies need to be monitored on the compressor end only:

Compressor Schematic Motor Speed = 3580 rpm.

We need to monitor the compressor bearings over a range of frequencies spanning 3182 cpm (1x 6-lobe rotor) to 515,520 cpm (3x gear mesh frequency). Although this can technically be done with a single reading, using only one amplitude unit would be a problem since velocity is no good at 515,520 cpm and acceleration is no good at 3182 cpm.

As stated earlier, there are formulas that relating each of the amplitude units to one another through the vibration frequency. The following just lists a few of the possible variations. You should note that the software carries out the formulas - the following pages attempt to illustrate the concept only.

Slow Speed:

Typically generates lower amplitudes. For shafts < 300 rpm, Time Domain plots should be used.

Typically tolerates much lower amplitude levels. Guidelines (vibration alarms) for each machine must be established. Since this equipment usually involves keeping the finish quality within certain tolerances or specifications, establishing a vibration level just below which those machines go "out-of-tolerance" can be a very effective method. Bearings should be monitored regardless of the overall machine condition.

Typically generates higher amplitude levels: Refers to machines that have large forces normally or a lot of vibration sources. High pressure, lobe-type blowers (Roots, for instance) often involve motor frequencies, belt frequencies, lobe pass frequencies, 2-rotor speeds, gear frequencies and aerodynamic forces as well as loaded and unloaded conditions. The resulting vibration patterns can be high relative to the General Machine amplitude references and yet normal for your machine. Be careful in over-reacting. At least one manufacturer's vibration guidelines are as follows:

Program Needs: Programs must be set up based on the needs of the individual pieces of equipment. Unless your program has loads of similar or identical pieces of equipment, a broad brush cannot necessarily be used. The actual frequencies being generated on the machines must be determined or at least estimated reasonably well. That information should then be used to specify the plots and data collected based on that. The successful analyst will also get to "know" the machines and their typical vibration patterns. That knowledge is possibly the analyst's strongest line of defence against unexpected failures.

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