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landing gear when the values listed in Table 1 arc
used in the shimmy analysis. An example of the
typical dynamic response of this landing gear is
provided in Figure 6 below for the 8 variable. (Note:
8 in this figure is in degrees.) It is noted that this
gear is very stable as there is little dynamic response
to the initial 5 degree deflection of 0.
Y I I
FIGURE 6
The Fighter B data sCt is one of the most
complete data sets for a landing gear that the author
poswsses. This set contains 11 charts that show the
nonlinear variation of 11 of the input parameters to
the shimmy analysis. Also included arc charts 12 and
13 which show the load stroke curve of the shock
strut and the load on the gear as a function of
aircraft forward ground speed.
In an earlier paper (7). an investigation was
conducted to determine the overall effect of these
nonlinear vuiations on the prrdiotcd stability
boundaries of the analysis in comparison to the
experimentally determined shimmy stability
boundaries of the gear. The manner in which this
investigation was conducted was to have the analysis
execute 5 knot increment runs starting with 15 knots
and incrementing up to 150 knots. At each speed
increment, the analysis would determine the load on
the gear from chart 13. Depending on the particular
parameter, the analysis would either then calculate the
parameter directly or it would determine the stroke
position from chart 12 and then calculate the desired
pwameter. After all I1 parameters were so
calculated, the analysis would execute and the
dynamic response of the gear would be determined.
From the analysis results. the shimmy speed was then
taken to be the lowest speed at which the analysis
indicated sustained limit cycle oscillation of the gear.
2-1
This procedure was repeated at increments of 0.05
degrees of torsional Geeplay from 0.5 to 1.2 degrees.
As a comparison. a static analysis of the gear was
also performed to evaluate the prediction variations.
The static analysis was conducted by selecting the 11
parameter values at the static stroke position of the
gear and incrcmenting the taxi speed in 5 knot
increments from IS to 150 knots while holding these
11 parameters constant. Again the shimmy speed was
taken as the lowest speed at which the analysis
indicated sustained limit cycle oscillation of the gear.
The comparison between the dynamic and static
analyses predictions are shown in chart 14. Also
included in this charr arc the actual experimentally
determined shimmy boundaries of the gear. The
lower experimental boundary shows when shimmy
onset occurred in the gear and the upper experimental
boundary indicates strong limit cycle oscillation
shimmy.
It is particularly interesting to note that the
dynamic analysis boundary follows the contour of the
shimmy onset boundary quite closely and consistently
errors slightly on the conservative side. Whereas, the
static analysis boundary lies above the shimmy onset
curve below 0.85 degrees of freeplay and ermrs
increasingly on the conservative side aa the torsional
freeplay increaser from 0.85 degrees to 1.20 degrees.
Both the dynamic and static analyses indicated the
shimmy frequency to be 27 HZ and this was
confiied in experimental measurement.
The overall implication of these fmdmgs seems to
suggest that the dynamic modelling of the gear as
described above will significantly improve the
~mcy of ths adyrir prsdiotions and that nonlinear
paramcter variation ir on important consideration in
obtaining an accurate shimmy analysis of a landing
gear.
The Fighter C data set in Table I is provided for
the 4 inch stroke position which corresponds to the
static stroke position of the gear. Figures 7.8.9, IO,
11, 12, 13, and 14 show typical dynamic response of
this nose gear. Figures 7, 8, 9, and 10 arc plots of
the y - L*Q or lateral displacement variable at the
point A for the taxi speeds of 80, 90, 95, and 100
knots respectively. (Note: In these figures what is
called the x - L*Q variable is identical to what is
referred to as the y - L*Q variable in this paper.)
Figures 11. 12, 13, and 14 are the plots of the 0 or
torsional rotation about the strut vertical axis variable
at these same taxi speeds. (Note: C3 in degrees.)