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Modelling and analysis of suspension systems 241
m 5 {A G5 } 1
{F J51 } 1
Z
Z 1
[I 5 ] 5/5 {α 5 } 1/5 [ω 5 ] 1/5 [I 5 ] 5/5 {ω 5 } 1/5
J Y 5
{F J 51 } 1
J
Static analysis
Dynamic analysis
X 5
O 5 G 5
5
H
H
{F H54 } 1 m 5 {g} 1
{F H54 } 1
X 1 Y 1
O 1
Fig. 4.78
Free-body diagrams for static and dynamic analysis of the tie rod
of a two-force body type scale factor, as used for the static analysis with the
tie rod Body 5, can be employed here. Figure 4.78 shows free-body diagrams
for both a static and dynamic analysis of the tie rod. For the static
analysis it can be seen that with the assumption that gravity is ignored the
reaction forces at J and H act along the axis of the tie rod allowing a scale
factor to be used. For the dynamic analysis it can be seen that the inertial
forces do not allow such an assumption and that a set of six equations of
motion for Body 5 will be required for the solution.
If at this stage we ignore the mass effects of the damper assembly we can
represent the force {F C37 } 1 acting on Body 3 at point C using as before a
scalar. Since the line of action of {F C37 } 1 is known to act along the line C–I
it is possible to define the force using the magnitude of the magnitude |F C37 |
factored with the unit vector {l CI } 1 , acting along the line from I to C, as
follows:
{F C37 } 1 F s {l CI } 1 (4.339)
where F s is the magnitude of the force |F C37 | with a sign assigned that is
positive if the force acts towards point C from I. In this analysis, and under
normal driving conditions, F s will be positive.
A consideration of the complete suspension system indicates that the following
set of 25 unknowns must be found to solve for dynamic forces:
F A31x , F A31y , F A31z
F B31x , F B31y , F B31z
F D43x , F D43y , F D43z
F E21x , F E21y , F E21z
F F21x , F F21y , F F21z
F G24x , F G24y , F G24z
F H54x , F H54y , F H54z
F J51x , F J51y , F J51z
F s
Each moving body, Bodies 2, 3, 4 and 5, yields six equations of motion that
can be used to solve the dynamic analysis. Using the same approach as