Page 142 - Improving Machinery Reliability

114 Improving Machinery Reliability

the shaft. For this reason the transient stresses must be calculated and compared to
the endurance limit stress. It is not necessary that the transient stresses be less than
the endurance limit stress; however, the stresses must be sufficiently low to allow an
acceptable number of starts. If the transient stresses exceed the endurance limit, the
cumulative fatigue concept is applied to the stresses in excess of the endurance limit
stress to determine how many starts can be allowed for the system.
Cumulative fatigue theory is used to estimate the number of cycles a certain stress
level can be endured before shaft failure would occur. This is based upon a plot of
stress versus number of cycles (S-N curve), which defines the stress conditions at
which a failure should occur. The S-N curve is based upon actual tests of specimens
of a particular type of metal and defines the stress levels at which failures have
occurred in these test specimens. These S-N curves are available for most types of
shafting materials. Using the appropriate curve, the allowed number of cycles for a
particular stress can be determined. It is possible to calculate the number of total
startups that can be made with the system before a shaft failure is predicted. Since
the stress levels vary both in amplitude and frequency, a more complex calculation
must be made to determine the fraction of the total fatigue that has occurred. The
stress levels for each cycle are analyzed to determine the percentage of cumulative
fatigue and the allowable number of startups can then be determined.
The calculation of the allowable number of starts is strongly dependent upon the
stress versus cycles to failure curve and whether torsional stresses higher than the
torsional yield are allowed. In the design stage it is preferable to design the system
such that the introduced torsional stresses do not exceed yield. This can usually be
accomplished through appropriate coupling changes.

Impeller and Blade Responses

A design audit should also include an assessment of the potential excitation of
blade or impeller natural frequencies. Several papers document such
The impeller and blade response analysis should include:
1. The blade and impeller natural frequencies
2. The mode shapes
3. Interference diagram indicating potential excitation mechanisms and the natural
frequencies.

The interference diagram, which gives the blade and impeller natural frequencies
and the various potential excitation mechanisms, is the key to prevention of failures.
The resonances should be sufficiently removed from the major excitations in the
operating speed range.
In the design stage, it is possible to calculate the natural frequencies and mode
shapes using finite element method [FEM] computer programs. However, the accu-
racy of predictions depends to a great extent upon the experience of the analyst and
the complexity of the system.
Since the blades and impellers will usually be available in advance of the rotor
assembly, the most accurate natural frequency and mode shape data can be obtained