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Modelling and analysis of suspension systems 195
wheel vertical motion. Some practitioners quote this as a motion ratio of
1.43:1 and some as 0.699:1. It is very important the definition of motion
ratio as quoted is understood before the number is used since it is not
always true that the spring moves less than the wheel.
Using the motion ratio, the wheel rate due to the spring can be seen to be
31.96/1.43 2 15.63 N mm 1 . Reassessing the classical calculations, the
estimated ride frequency is now 0.874 Hz, with a ride rate of 14.24 N mm 1 .
The estimated frequency is now less than that calculated using the full
model (which was 0.954 Hz), suggesting there is some additional stiffness
or reduced mass in the mode of vibration. Examining the model again, the
so-called ‘ride rate’ (k eqv ) can be taken directly (Figure 4.60). In the case of
this particular suspension geometry, the ride rate is 14.97 N mm 1 . The difference
between the two ride rates may be attributed to additional rates
arising from the suspension bushes; these are commonly referred to as
‘parasitic’ rates. Although that term implies something undesirable about
them, they are generally small and do not degrade the suspension behaviour
unduly.
It may be noted, however, that the difference between the two results is not
fully accounted for by the difference in wheel rate. For this particular
example, using the analytical solution for the two-mass solution we may
calculate ‘effective’ masses and stiffnesses for each mode of vibration. In
the results from the full linkage model, these effective masses and stiffnesses
are reported in the results file. They are known as ‘modal’ mass and
stiffness values. For the model in question, these values are given as:
Primary ride mode: 17.2232 N mm 1 479.355 kg
Wheel hop mode: 177.019 N mm 1 38.552 kg
It is clear then that there is some other stiffness influence on the ride rate
within the model that is not readily apparent to the user. Similarly, the mass
is larger than the mass associated with the body alone. This acknowledges
5000.0
MOTION_12.Element_Force.Z
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4500.0
Force (newton)
4000.0
3500.0
3000.0
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100.0 50.0 0.0 50.0 100.0
Analysis: Last_Run
Length (mm)
2003-08-05 20:38:59
Fig. 4.60
Wheel rate measured from full linkage model