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## Section 1, Slow Speed Machinery Such as Cooling Tower Fans, Other Low Speed Fans and Blowers, Mixers, Papermachine Rolls, etc.

During the earlier days of vibration analysis and correction, displacement amplitude was the unit most often used. Almost no one used velocity or acceleration unless they were in much more sophisticated work such as noise control. Displacement was more easily visualized, and it was appropriate when the typical vibration job was to balance a fan or blower. As vibration understanding progressed, velocity became more and more popular. As velocity mathematically combined frequency with displacement, it supposedly didn't make any difference if the vibration intensity was measured on a medium speed machine or a high speed machine. This made monitoring much easier.

For example, if the velocity measured on an 1800 rpm motor was 0.2 in/sec and the reading measured on a 3600 rpm motor also was 0.2 in/sec, then both machines would be considered to have the same vibration intensity. Theoretically, both machines were receiving the same amount of punishment as shown by their vibration amplitudes. When speeds were lower, such as 1200 rpm, or higher such as 10,000 rpm, the same evaluations were made based on the velocity amplitudes. However, as the machine speeds get lower and lower, a problem does occur which, if not properly dealt with, can produce seriously defective judgements regarding a machine's condition as shown by vibration readings.

It will help to first review some of the differences between the uses for displacement and velocity units. The fine points of explaining displacement as compared to velocity will not be discussed in this section. Instead, discussion will include only what is needed to understand the problems that can occur with low speed or low frequency vibration measurements.

As a reminder, displacement is the distance a point on a machine travels from the top to the bottom of its vibration cycle. If a dial indicator is used as the vibration measuring instrument and has its indicator tip placed against the vibrating part, the indicator needle will oscillate back and forth. The displacement amplitude will be the distance measured from the lowest dial reading to the highest.

This is called displacement "peak-to-peak" and is most commonly used in North America. In other parts of the world, displacement rms (root, mean, square) may be used, which is a number that is less than the peak-to-peak reading (0.707 times pk-pk). However for visualization purposes, the type of displacement units used makes no difference.

Velocity is defined as "the rate of change of displacement." Assuming a constant displacement, the resulting velocity amplitude depends on the vibration frequency. For example, if a peak-to-peak displacement remains at 1 mil, the resulting velocity at 1800 rpm will be 0.094 or almost 0.1 in/sec. At 3600 rpm, the same 1 mil displacement will produce 0.188 or almost 0.2 in/sec. The changes in velocity vary directly with the changes in frequency. So far there is no problem, but now let's look at the problem created with lower and lower speeds.

Acceleration is defined as the rate of change of velocity. It is a measure of force and is the direct output from most vibration sensors used in portable instruments today. The instruments convert acceleration to velocity and displacement units by performing single or double integration on the signal.

Assume that the vibration "alert" velocity amplitude is the typical 0.3 in/sec (slightly under 8 mm/sec). At 3600 rpm, 1.6 mils will give you 0.3 in/sec. At 1800 rpm it will take 3.2 mils, at 1200 rpm it will take 4.8 mils, and at 1000 rpm it will take 5.7 mils.

Considering 1000 rpm and above as "normal" speeds, if the 1000 rpm rotor is on a papermachine roll, the almost 6 mils displacement will most likely cause evenly spaced marks on the paper. If on a machine tool spindle workpiece, surface finish will certainly be bad.

Now consider low speed machines (speeds lower than 1000 rpm). For an "alert velocity" of 0.3 in/sec, on a 600 rpm fan or roll, it will take almost 10 mils. A cooling tower fan running 300 rpm will take 19 mils! A 19 mil orbit due to rotor unbalance or shaft/coupling misalignment will result in a large amplitude at the gear box's gearmesh frequency. The same will be true for a 9 mil orbit that will give a velocity of approximately 0.15 in/sec. The velocity units work well for gearmesh frequency and, therefore, lead the analyst to think there is something wrong with one of the gears. Instead, the gearmesh trouble actually originates with the large displacement orbit that does not seem too bad in velocity terms. In a paper mill, a large diameter dryer roll running 100 rpm will require an outstanding 57 mils before the velocity reaches 0.3 in/sec. Paper quality can be negatively affected with a displacement of 18 mils, which could lead the analyst to think the velocity amplitude is alright as it is -- only 0.1 in/sec (under 3 mm/sec).

It is suggested that such low speed machines show too many problems as indicated by the vibration at gearmesh frequency (number of teeth x rpm). As the number of teeth on large gears are many, the velocity reading will be read accurately. No correction factor is needed as the gearmesh frequency is usually several thousand cpm (where velocity is an accurate indicator). But the trouble probably originates with the large displacement orbit of the shaft's centerline around the axis of rotation (see section on gear vibration). If the large displacement orbit is properly measured and thereby revealed, the correction for vibration at gear mesh frequency will most often call for balancing or shaft alignment, instead of working on the gearmesh.

Low frequency vibration is very common on slow speed rolls driven by a gear system. The low speed roll requires a displacement reading to show how serious it is, and the vibration at gear mesh frequency requires a velocity reading! To make the situation more confusing, low frequency readings require either special pickups or the use of a "correction factor." A fan may be running at 875 rpm (where the correction factor is negligible). But its spectrum peak at ½ x rpm (437.5 cpm) will appear to be very small and, therefore, be ignored. But if the required correction factor is used for this low frequency, the ½ x rpm will reveal that something is loose. Something loose on a running machine cannot be safely ignored!

Various types of instruments are now popular for not only measuring vibration amplitudes but also for storing the readings for use with a computer. Velocity is the most common unit used. But too often, the user is not conscious of the fact that velocity cannot be a reliable guide for judgements based on vibration for low speed machinery.

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