Pumps and Systems, January 2007

## Example 1

Vertically mounted pumps can resonate as a total structure in a "rocking" mode, as shown in Figures 1 and 2 below. This is one of the toughest unsolved vibration problems at several plants.

Figure 1. Vibration modal plot of shaft centerline motion (as seen from above the base). Figure 2. Vibration modal plot of shaft centerline motion (as seen extended to below the base)

Typically in such situations, the source for the vibration is in one or more of the pump impellers mounted below the concrete support. The impeller may be in a state of single plane static imbalance. However, as it is mounted on a long cantilevered shaft, the static imbalance creates a large "false couple" to the total machine.

This couple's rocking motion causes the whole pump structure to "wobble" at the rotor's 1 x RPM. Normally, the total vertical pump's structure is not resonant to its own RPM. However, note how the structure above the concrete support is relatively heavy, especially at the drive motor. That heaviness lowers the total structure's natural frequencies. Sometimes the natural frequency to its couple mode of shaking causes large amplitude at the top of the structure (the drive motor), and its pivot point, below, near the concrete base.

Actually, the amplitude at the bottom end of the cantilevered shaft would also have large vibration amplitude, but with the analyst standing on the concrete, that large amplitude below is not usually noticed. It is too easily diagnosed as very large amplitude at the top of the drive motor with smaller and smaller amplitudes read further down near the concrete base. The analyst concludes too quickly that the large amplitude at the top could be corrected by single plane balancing the fan at the top of the motor.

This never works! Either the single plane imbalance in the out-of-balance impeller is corrected at that impeller or the total vertical pump structure has to have its resonance to couple "rocking" corrected. This is not as easy as it sounds, because it is difficult to determine where to apply a brace to stiffen the rocking motion.

It does not work to attach a horizontal brace to the top of the machine and brace it to, for example, a nearby column. The resonance to couple motion is the result of the "spring system" of the pump's vertical axis and the bottom of the pump's horizontal axis.

Instead, it is much easier to use a dynamic absorber to cure the vibration. The absorber (sometimes referred to as a tuned absorber) is mounted at the top of the total assembly, responding to vibration in the direction of the resonance.

Figure 3. Dynamic absorber used to reduce amplitude due to resonance "rocking motion."

##### Example 2

A large gear's outer rim completely fractured several times a year. The gear's diameter (see Figure 4) was approximately one meter (approx. 3.3-ft). There were several identical gears in the same paper machine. Each one would fracture several times a year, resulting in extremely high production as well as rebuilding costs. The manufacturer took no responsibility, as calculations indicated that the gear's strength was several hundred percent greater than what was required.

Figure 4. This gear cracked and caused a system shutdown every 3 months (on average).

For over 20 years, the problem did not exist. Fracturing started when the machine's operating speed was increased less than 10 percent. The gear's operating speed was under 200-rpm. However, there were over 100 gear teeth per gear. The very small RPM increase resulted in a gearmesh increase of well over 1000-cpm. The new gearmesh amplitude/frequency resonated the angle between the rim and gear's main disc. This resulted in a node that finally resulted in a crack (see Figure 5). The crack kept lengthening until the rim was weak enough to break off (several inches) (see Figure 6). This shut down the whole paper machine.

Figure 5. Crack occurring at the angle between the outer gear ring and the gear's main body.

Figure 6. Large section of outer gear breaks off to cause a machine "wreck."

It took many months to get the manufacturer to accept that the gear was resonant (at the angle between the rim and the hub). However, they finally replaced the gears with a different design, and the new design had no resonances with gearmesh or any other machine frequencies.