Torsional Vibration of Turbomachinery

Following calculation of the transient torque responses in the machine shafts, it is often necessary to estimate the amount of fatigue life expenditure in the shafts (if any) as a result of the torsional disturbance being analyzed. Generally the shaft torsional response is a complex waveform made up of several frequency components as illustrated in the case studies in Sec. 9.4.
Fatigue is a complex subject and an imprecise science. This chapter gives only a very brief introduction to this topic. References are cited for those readers wishing to study this subject in more detail.
Fatigue is the tendency of materials to crack and then finally fracture under repetitions of stress or strain at a level considerably less than the ultimate static strength of the material. Fatigue is an important subject because it is the largest cause of failures in metals. Fatigue failures are often catastrophic and often occur suddenly and without warning. The fracture surface is usually brittle-like in form even in ductile materials and is often characterized by striations or beachmarks that are formed during crack growth. The applied cyclic stress state may be axial (tension-compression), flexural (bending), torsional (twisting), or a combination of these. The cyclic stress may alternate with a zero mean level, alternate about a mean level, or vary quite randomly with amplitude and frequency. For an applied tensile stress, the fracture surface is generally perpendicular to the direction of the applied force. A fatigue crack will generally initiate on a free...