Page 195 - Steam Turbines Design, Applications, and Rerating

174 Chapter Ten

characteristics within the bearing oil film due to the relative motion
between the journal and the bearing.

10.7 Foundations
The most common foundation designs are relatively massive, reinforced
concrete structures that present a high impedance to the turbine at the
connection points. In this respect, they are dynamically similar to the
special bases that support the turbine during vibration response tests
run in the factory. The experience has been that the factory test results
have been predictive of subsequent operation in the field.
From this standpoint, concrete foundations are preferable to fabri-
cated steel structures that tend to exhibit resonant frequency behavior
that may be difficult to predict and more difficult to modify after the
structure is in place. Local foundation resonances will affect turbine
response, because they introduce low dynamic stiffnesses into the total
bearing support system.

10.8 Impedance
The total bearing support structure is complex. Thus, its dynamic char-
acteristics are difficult to represent with a mathematical model. On the
other hand, experience indicates that good correlation is obtained
between rotor dynamic analyses and unbalanced vibration response
tests when a simple approximation of support stiffness is used.
In the past, support stiffness was based on static deflection, either
measured or calculated. More recently, impedance tests have been
made to determine the dynamic stiffness for various turbine designs.
In the case of new designs, impedance tests have been made on scale
models and later verified by tests on the full-scale prototype. A typical
impedance plot is shown in Fig. 10.6 for the drive end bearing support
of a high-speed turbine. The exciting force was applied at the bearing
location, and the motion was measured at the same location and in the
same direction. The ratio of driving force to vibration velocity is the
direct or driving point impedance.
The ordinate scale is the mechanical impedance ratio, which is
pounds of force divided by velocity in inches per second. The abscissa is
frequency, in Hz. The diagonals that slope downward to the right are
dynamic stiffness ratios, which are pounds of force divided by ampli-
tude in inches. The diagonals that slope upward to the right are effec-
tive mass lines in pounds of weight. Each valley in the impedance plot
is a resonant frequency, and each peak is an antiresonant frequency. At
the resonant frequencies, the supporting structure presents a lower
impedance (dynamic stiffness) to the rotor-bearing, oil film system at