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Modelling and analysis of suspension systems 199
1.0E00
60 mph
120 mph
Road amplitude (m)
1.0E02
1.0E04
1.0E06
0.1 1 10 100
Frequency (Hz)
Fig. 4.63
Road surface frequency content
where R and K are constants of 2.5 and 5 10 5 respectively. The value of
K varies with the nature of the road being studied. For novel applications or
for previously unknown markets, some measurement of road profiles is
desirable; for the developed western world the values given are generally
appropriate. For military applications, a value of 1 for R may be appropriate.
The very smoothest roads are unlikely to have R higher than 4.
It can be seen that the spectral content as seen by the car varies with vehicle
speed. Gillespie (1992) gives a ‘rational’ argument to suggest that spectral
content rises with speed squared. However, Hales (1989) gives a different
view, reproduced in essence here. The road surface is a process that may be
approximated by a straight line on a log–log plot and represented by
log[u(n)] log[K] R log[n] (4.89)
implying that
K
un ( )
(4.90)
n R
This is a spatial representation of the road profile, with n defined in
cycles/metre. It appears under the car at frequency of V n Hz, where V is
the forward speed of the car, thus
Vn ⇒ n
(4.91)
2
2V
We can write
gn ( ) 2V
un ( ) gn
( )
n
u( ) 2 V
(4.92)
if we acknowledge that g(n) g() – i.e. that the process is unchanged
whatever we choose to express it as a function of. Hence:
1 K 1 K
u( )
m
2 V n 2 U ( / 2V
)
m
K( 2V)
m
m1
(4.93)