Personal computers can now do many jobs that formerly required
a large mainframe computer. An example is NASA Lewis Research
Center's program Analysis of RotorDynamic Systems (ARDS), which
uses the component mode synthesis method to analyze the dynamic
motion of up to five rotating shafts. As originally written in
the early 1980's, this program was considered large for the mainframe
computers of the time.
ARDS, which was written in Fortran 77, has been successfully ported
to a 486 personal computer. Plots appear on the computer monitor
via calls programmed for the original CALCOMP plotter; plots can
also be output on a standard laser printer. The executable code,
which uses the full array sizes of the mainframe version, easily
fits on a high-density floppy disk. The program runs under DOS
with an extended memory manager. In addition to transient analysis
of blade loss, step turns, and base acceleration, with simulation
of squeeze-film dampers and rubs, ARDS calculates natural frequencies
and unbalance response.
ARDS-PC was used to analyze a magnetic-bearing-supported rotor
(a small rotordynamics demonstrator rotor) as it experiences a
sudden increase in imbalance or drops onto backup bearings. ARDS
draws an outline of the rotor configuration, which appears in
the figure above for the example rotor. This rotor was modeled
with 9 elements, resulting in 10 rotor stations. Concentrated
masses were attached to the shaft at 5 of the stations. An electromagnetic
bearing was at station 3, and a bronze bushing supported the shaft
at station 8. Magnetic bearings are customarily used with "backup"
bearings that can support the rotor if the magnetic bearing fails.
For this example, a backup bearing in the form of a loose bushing
was modeled in addition to the magnetic bearing at station 3.
No contact occurred in the backup bearing during normal (magnetically
suspended) operation; therefore, the backup bearing was nonlinear
in that the stiffness was zero until the radial clearance was
taken up. It was then assumed to have a constant stiffness in
the radial direction; the tangential force was calculated as the
radial force times a friction coefficient. This bearing model
was built into ARDS. Each computer run used 100 time steps per
revolution. On the 50-MHz 486 computer used, 4000 time steps took
slightly less than 2 min calculation time.
A blade loss in a turbine engine introduces a sudden imbalance
that can be many times the normal operating imbalance. Under this
condition, the magnetic bearing supporting the rotor can become
overloaded to the point that the backup bearing comes into operation.
As the bearing makes contact, the situation is similar to that
of a turbine wheel contacting its outer shroud. The following
figure shows 10 revolutions of a blade loss transient with an
active linear magnetic bearing and a friction coefficient of 0.4
assumed for the backup bearing. This figure is an orbital plot
of the rotor at station 3, the magnetic bearing location. The
imbalance is applied to the rotor at station 5. The plot shows
that the rotor flies out, hits the backup bearing, bounces off,
and repeats this behavior for the entire time period plotted.
The final figure plots the dynamic behavior of the rotor when
the magnetic support fails and the rotor drops onto the backup
bearing. The rotor walks up the side of the bearing, although
the more sensitive scale for the horizontal axis in this figure
exaggerates this motion. The vibratory motion eventually dies
down. Excitation forces can be combined: for example, a turn combined
with blade loss and base acceleration.
Previous articleLast updated May 5, 1997
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