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Modelling and analysis of suspension systems 191
Quarter vehicle body
or
sprung mass
m b
k s
Suspension
spring
m b 472 kg
m t 39.1 kg
k s 36 190 N/m
k t 160 000 N/m
Unsprung mass m t
Tyre
spring
k t
Fig. 4.56
Two degree of freedom quarter vehicle model
4.9.1 Case study 4 – Dynamic ride analysis
In this case study we adapt the quarter vehicle model shown in Figure 4.51
for a ride analysis. Before considering the output from the simulation simple
manual calculations can be performed to check and confirm the
MSC.ADAMS results. These calculations can find the natural frequencies
for the body on the suspension and for the unsprung mass between the road
spring and the tyre spring. Figure 4.56 shows a two degree of freedom
quarter vehicle model with the data used to support the calculations.
The undamped natural frequencies for the body, f b , and unsprung mass, f t ,
can be estimated using the following equations. Note that for the body we
determine an equivalent stiffness k eqv to represent the combined contribution
of the road and tyre springs:
kk s t
keqv
(4.69)
k k
s
t
f
b
1
2
k
eqv
m
b
(4.70)
f
t
1 ks
k
2 m
t
t
(4.71)
Performing the calculations using the data given results in values as follows:
k eqv 26 639 N/mm
f b
f t
1.196 Hz
11.15 Hz