Practical Solutions to Machinery and Maintenance Vibration Problems
Chapter 10, Gear Vibration
Section 3, Gearmesh Vibration at Gearmesh Frequency
This source for gearmesh vibration is most often caused by the orbiting of the shaft at its operating speed due to unbalance, misalignment, bent shaft and so on. This orbiting was described earlier to show that it increases the 1 x rpm vibration in the imaginary line connecting the centerline of the mating gears. However, if the resulting orbit is large enough, the vibration at gearmesh frequency is increased.
Usually the gear's 1 x rpm velocity amplitude is larger than at gearmesh frequency (rpm x number of teeth) and gearmesh harmonics. Similar to vibration amplitudes from deteriorating rotating element bearings, gearmesh-related amplitudes are usually very small. For example, 0.1 in/sec (approximately 2.5 mm/sec) is acceptable at 1 x rpm but is considered bad for gearmesh frequency.
Sideband difference frequencies around gearmesh-related peaks are usually equal to 1 x rpm of the offending gear. Sometimes the sidebands differ by 2 x rpm of the offending gear. It is suspected that most often the 1 x rpm differences are the result of a gear with either an eccentric pitch circle or "running eccentrically" due to the orbit created by unbalance or misalignment. If sidebands with a difference frequency of 2 x rpm also occur, shaft/coupling misalignment is suspected.
On one old papermachine, a dryer roll was rotating at only 100 rpm. The roll was badly out of balance. A slow roll showed a shaft eccentricity of less than 9 mils. But at 100 rpm operating speed, a large unbalance resulted in orbiting of the shaft supporting the gear -- enough to run eccentrically by slightly over 1/8 of an inch!
The amplitude at the gearmesh frequency of over 8000 cycles per minute is large anyway and, of course, very noisy. But when vibration intensity becomes large enough, it will travel far enough and with enough energy to "reach" some part to resonate. In this situation, it resonated a section of the very heavy cast iron gear case. With the increased magnification of resonance, it is easy to imagine the vibration intensity and noise.
Changing to new gears made no difference, since the problem didn't emanate from improperly manufactured gears. The only solution was to reduce the large orbit at the 100 rpm running speed. This could only be done by getting at its source, by balancing and straightening the remaining bend.
In another situation at considerably higher speed, the same problem occurred. This time it involved a high speed pump shaft with a gear at one end and a cantilevered impeller at the other end. The 11,000 plus rpm of the shaft was orbiting (displacement) about 1.5 mils at 1 x rpm and diagnosed as unbalance. (The impeller was properly balanced on the shaft, but in this case, the ball bearing races were eccentric beyond tolerance, causing a new unbalance by displacing the weight of the rotor assembly off center.) If there were no gears at one end, it probably would not have resulted in enough vibration due to unbalance to cause trouble; but as previously described, the unbalance orbit was magnified in the direction of the imaginary line connecting the center of the mating gears. This large elliptical orbit at 1 x rpm resulted in a high vibration (velocity) at gearmesh frequency. There was also indication of resonance to the mesh frequency. But the writer put that aside as a separate problem from the one caused by unbalance.
Field balancing was possible as this pump could be run without liquid flowing. Corrections were made on the impeller by hand grinding. It was actually very surprising that, as the balancing progressed with its resulting smaller and smaller 1 x rpm shaft centerline orbit, the vibration at gearmesh frequency decreased proportionately. When the rotor assembly's vibration amplitude was decreased to tolerance, the vibration at gearmesh frequency was also within tolerance.
1. Unbalance, misalignment and so on causes a shaft centerline orbit at 1 x rpm.
2. The orbit displacement is magnified in the imaginary line connecting the centers of the mating gears.
3. The enlarged orbit at 1 x rpm also enlarges the vibration at gearmesh frequency. If the orbit is large enough, the gearmesh vibration can be excessive even if no resonance is present.
4. Sidebands surrounding gearmesh peaks point to the offending gear.
5. If resonance to gearmesh frequency is present, it magnifies that vibration.
6. When there's excessive vibration at gearmesh frequency, first analyze and remove sources for large orbits at lower frequencies such as at 1 x rpm. If there is no sign of sources for large orbits, the problem may be within the gear's machined concentricity or defective gearmesh.
This textbook contains only part of the information in our Practical Solutions seminar.