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Modelling and analysis of suspension systems 197
The preceding results were all generated using an undamped eigensolution.
However, for vehicle ride work, the influence of the dampers is critical.
Moreover, the dampers are typically highly non-linear devices. Therefore,
a further treatment of the existing MSC.ADAMS model is required once
the modal ‘positioning’ (i.e. the undamped frequencies for primary ride,
wheel hop and fore–aft compliance) is established.
In terms of the modelling approach the only modification here is a change
in the motion applied to the jack where the function now represents a sinusoidal
input with fixed amplitude but with a frequency that increases as a
function of time as illustrated in Figure 4.61. The motion input is referred
to as a frequency sweep, sometimes described as a ‘chirp’ – for reasons
which are obvious if the resulting signal is audible.
The following motion statement is an example of a suitable input function
where the amplitude of the road input is fixed at 10 mm and the frequency is
increased using the following function from zero to 20 Hz after 80 seconds.
MOTION/20, JOINT 20, TRANS
,FUNCTION 10.0 * SIN(TIME/8 * TIME * 360D)
Using this simulation we can produce a time history plot showing the
change in vertical acceleration of the sprung and unsprung masses of
the quarter vehicle model as the simulation progresses. Examination of the
response shown in Figure 4.62 reveals that excitation of a system resonance
(a ‘mode of vibration’) occurs at two points during the simulation. The first
of these corresponds with the natural frequency of the body and the second
with the natural frequency of the unsprung mass.
Another interpretation of the results obtained here is to perform a Fast
Fourier Transform (FFT) so that the results can be plotted in the frequency
rather than the time domain as shown in the lower half of Figure 4.62. The
simulation was allowed to run for 81.91 seconds with an output sample rate
of 100 Hz, giving 8192 points including the zero time point. A single buffer
transform was performed on the entire record for each of the signals.
Although flawed, this method is adequate for identifying frequency peaks.
However, for quantifying amplitude content the underlying presumption
Jack
part
Motion input
z r
Frequency sweep
Time (s)
Fig. 4.61
Input of frequency sweep via jack motion