Page 210 - Steam Turbines Design, Applications, and Rerating

Chapter
11

Campbell, Goodman, and

SAFE Diagrams for Steam

Turbine Blades

Rotating blades of axial steam turbines are subjected to a variety of
steady-state and transient mechanical loads and stresses. Steady-state
stresses are due to the centrifugal force of the blade weight and the
force of steam striking the blade. Transient stresses are attributable to
several sources but are primarily due to blade excitation at a frequency
equal to the natural frequency of the blade. Transient stresses are
more rigorously defined as alternating, cyclic, or vibratory stresses.
Steady-state stresses are routinely calculated at critical points on
the blade by using principles from the mechanics of deformable bodies
and mechanical systems design. Both normal and shear stresses are
calculated and are compared to material and historically determined
acceptable limits.

11.1 Goodman Diagram

The purpose of a Goodman diagram is to serve as a stress analysis cri-
terion of static and fatigue failure. A Goodman diagram is a graph that
has the ultimate strength of a material plotted on the horizontal axis
and the endurance limit plotted on the vertical axis. These two points
are then connected by a straight line. This line is a failure line (factor
of safety = 1.00), which means stress levels below it are safe and stress
levels above it are likely to fail. Manufacturers such as Dresser-Rand
use the yield point of the material as the steady-stress failure limit
instead of the ultimate strength. By connecting the yield point with the
endurance limit by a straight line, one obtains a Soderberg diagram,
which is more conservative than the Goodman diagram (see Fig. 11.1).
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