4569846498

200 Multibody Systems Approach to Vehicle Dynamics
m
x(t)
k
c
u(t)
Fig. 4.64
Single-degree-of-freedom ride model
If a single degree of freedom ride model is considered (Figure 4.64) for the
purposes of positioning the ride mode, then the frequency domain relationship
between ground input, u, and displacement of the vehicle body, x, is
given by
2 2 2
x( )
k c
u( )
2 2
( k
m)
c
2 2
(4.94)
The acceleration environment is the prime concern in ride studies.
Assuming harmonic solutions (i.e. made up of sine waves), we may write
x˙˙( )
x( )
˙˙( x )
u( )
u( )
(4.95)
u( )
2
u( )
Thus we have all that is needed to calculate a harmonic acceleration
response of the car over a typical road profile. If the acceleration response
is compared to the curves in ISO2631-1:1997, then some direct measure of
ride comfort can be made.
Figure 4.65 shows a prediction of the same vehicle travelling at 60 and
120 mph on the same road, with threshold figures based on 1 hour exposure
to the vibration environment. Considering Figure 4.65, it may be supposed
that a better riding vehicle could be made by positioning the primary ride
resonance at a lower frequency in order to better match the shape of the
threshold curves and thus improve the aggregate ride over the frequency
range of interest. Notwithstanding the difficulty in general that lower ride
frequencies mean larger suspension motions, if we presume these difficulties
can be overcome, another difficulty remains – the problem of motion
sickness.
Figure 4.66 shows the acceleration response for a 0.2 Hz primary ride car,
which has a much lower exceedance of the perception threshold. However,
superimposed on the graph is a motion sickness threshold for 5% of the
population at 1 hour’s exposure. It can be seen that in the region substantially
below resonance for the 1 Hz car, the motion sickness threshold
exceedance is entirely in the region in which the vehicle does not amplify
road inputs; in other words, motion sickness is induced by irregularities in