Alternating vibrations and stresses in turbomachinery

E veryone knows the story of bridges that simply collapsed as they were crossed by an infantry regiment marching in cadence. The Tacoma bridge in the USA collapsed six months after it was commissioned in 1940, under the effect of a steady but not particularly high wind. It had already withstood slightly slower or stronger winds without damage. These accidents are the result of resonance, the coincidence of a structure's natural frequency and an excitation frequency.

These vibratory phenomena are also frequently at the root of mechanical incidents encountered on turbomachinery. Calculating the eigenmodes of components, and knowing the excitations likely to be applied to them during operation, can significantly improve equipment reliability and availability.

The development of computing resources has enabled us to calculate frequencies and eigenmodes with ever greater precision, thanks in particular to finite element techniques. Numerous software packages have been developed, some general, some specific to particular studies, such as the torsional analysis of a shaft line. On the other hand, while knowledge of excitation sources has greatly improved, it is still sometimes insufficient to explain and, above all, anticipate the complex vibratory phenomena encountered on rotating machines.

The aim of this article is to use two very different examples, chosen from the field of turbomachinery, to present the methodology to be applied to carry out the most complete possible vibration analysis of mechanical components.

The moving bearings of steam turbines, which are very rich in eigenmodes, are often subject to high excitations linked to steam flow. Designers have developed numerous techniques to provide damping, in particular, to reduce the effect of these disturbances and ensure the fatigue life of these components.

The dynamic bending study of a turbomachinery shaft line is essential to avoid any surprises during commissioning. A low rotor vibration level is an important parameter in ensuring high availability and longevity of rotating machines. It also guarantees the preservation of internal clearances, and therefore efficiency.

Theoretical developments are extensively explained in numerous technical books and are not repeated in this article. However, the study of a simple vibratory system subjected to forced excitation is briefly presented.

Acceptability criteria are given for guidance only. They are the result of experience or imposed by rotating machine construction codes.