4569846498

Modelling and analysis of suspension systems 139
to the designer are spring and damper calibration. Therefore the preceding
analysis would suggest that the softest springs possible, to position the
resonant frequency as low as possible, are preferred.
In a purely technical sense this is indeed true; however, our vehicles are to
have as their primary purpose the transport of people. People in general
have a susceptibility to motion sickness for very low frequency motions;
this places a practical lower limit on our resonant frequency of something
around 0.5 Hz, or 3 rad/s. Given that the human frame is primarily engineered
for walking, a more typical value for the resonant frequency of the
body mass on the road springs is just over 1 Hz, this being the frequency at
which we walk for the majority of the time. This is one of several reasons
why babies may be readily nursed to sleep in cars; the motion of the
vehicle gives an acceleration environment not unlike being held in the arms
of a walking adult.
Our real vehicle systems are rarely so straightforward to address as this, however.
Real vehicle suspensions have vertical and longitudinal compliance
behaviour. Suspension components rotate as well as translate and the sprung
mass has rotational as well as translational freedoms. Modern multibody
system analysis software allows us to describe the individual components
of the system and will automatically calculate the contribution of, for
example, sprung mass pitch inertia to the acceleration solution for the body.
The software also allows the linearization of the system about an operating
point and the calculation of modes of vibration of the system. For example,
the longitudinal compliance typically snubs out under hard braking and the
fore–aft isolation suffers; proprietary software will allow the calculation of
fore–aft resonant frequencies under cruise and braking conditions and their
comparison by an intelligent user will explain (and perhaps generate solutions
for) harsh behaviour over small obstacles while braking.
At no stage with added complexity do the basic rules for dynamic systems
break down; there remains a subresonant, stiffness-dominated regime, a
resonant, damping-dominated regime and a post-resonant, mass-dominated
regime. The software user who keeps a grasp of these basic concepts, while
allowing the software to undertake the task of assembling the equations of
motion and solving them, is productive within an engineering organization.
4.1.3 Handling load control
The simplest possible representation for a vehicle, Body 2, manoeuvring in
the ground plane is shown in Figure 4.6. If we break from the full 3D vector
notation the following pair of differential equations describes it fully:
Σ M2z Izz˙
2z
Σ F m ( V˙
V
)
2y 2 2y 2x 2z
(4.28)
(4.29)
These equations, their significance and a more formal derivation are well
described in the seminal IME paper (Segel, 1956). The formulation states
that yaw acceleration is the applied yaw moments divided by the yaw inertia
of the vehicle, and that lateral acceleration is the applied lateral forces