Case 42: Torsional vibration problems can be costly

The results are hammering of the gears and fretting of the splines

It was then I learned that ifcii torsional vibration failures don't occur often, but when they do, they can be very costly to solve.

Torsional vibrations occur when a mass is twisted and released on a shaft and continues to vibrate, much like twisting a mass on the end of a coiled spring and releasing it. The vibration "dies out" unless a torsional frequency that coincides with one of the systems natural frequencies is present. When that occurs large vibratory amplitudes are possible and the system is said to be in resonance.

Fig. 1 consists of a pump, gearbox and diesel engine simplified into a two-mass system. The model considers the lowest of many natural frequencies; in this case, the lowest frequency is the most important.

The engine operates at 2,900 rpm and has a major harmonic of 4. This system is too close to resonance since 4 times 2,878 rpm = 11,513 cpm. Designing to keep resonance away from the operating range is usually the best approach.

The magnifier method1 can be used to approximate the resonance amplitude with engine damping only present (M= 25).

The 4th order excitation of this engine is ± 5% of the 6,300 in.-lb mean torque:
The mean torque on the gears at 2,900 rpm is 6,300 in.-lb and the vibratory torque is ±8,502 in.-lb.

"When the vibratory torque exceeds the mean torque such as is the case here, the gears and splines separate from their respective contact surfaces; they then cyclically load and unload at the resonant frequency. This results in "hammering" of the gears or fretting of the splines.

A complete analysis and torsional testing of this system are needed. Determining the engine excitation into a system is complicated2 and harmonics higher than the 4th order will, in fact, have to be considered

It follows that the services of an experienced torsional specialist are needed because a poorly thought-out modification may simply move the problems to another point in the system.

LITERATURE CITED

1    Sofronas, A., Analytical Troubleshooting of Process Machinery and Pressure Vessels: Including Real-World Case Studies, ISBN: 0-471-73211-7, John Wiley & Sons, p. 125.

2    Den Hartog, J. P., Mechanical Vibrations, 4th Edition, McGraw-Hill, p. 197.