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Modelling and analysis of suspension systems 163
Using the instant axes method the left and right steer axes can be computed
from the suspension’s compliance matrix. The process involves locking the
spring to prevent wheel rise and applying an incremental steering torque or
force. The resulting translation and rotation of the wheel carrier parts can
then be used to compute the instant axis, and hence steer axis of rotation for
each wheel carrier.
Note that the formulations of suspension output that follow are for a quarter
vehicle suspension model located on the right side of the vehicle using
the general vehicle co-ordinate system in this text with the x-axis pointing
to the rear, the y-axis to the side and the z-axis upwards. Needless to
say users must ensure the formulations are consistent with the vehicle
co-ordinate system and the side of the vehicle being considered to ensure the
correct sign for the calculated outputs. For each of the suspension characteristics
discussed a typical system variable calculation is provided. This will assist
users of MBS programs who need to develop their own calculations without
access to the automated outputs in a program such as ADAMS/Car.
4.5.3 Bump movement, wheel recession and half track change
As stated earlier it can be the practice to impart vertical motion to a suspension
system at either the wheel centre or wheel base. In the following
example the displacements at the wheel centre are used to determine the
suspension movement. The displacements at the wheel base would be corrected
for camber, steer and castor angle changes and dependent on the suspension
geometry. On the real vehicle the displacements of the tyre contact
patch relative to the road wheel would also result due to the effects of tyre
distortion. This is discussed later in Chapter 5.
Bump movement (BM) is the independent variable and is taken as positive
as the wheel moves upwards in the positive z direction relative to the
vehicle body. Similarly wheel recession (WR) and half track change (HTC)
are taken as positive as the wheel moves back and outwards in the positive
x and y directions respectively.
The displacements are obtained simply by comparing the movement of a
marker at the wheel centre (WC) relative to an initially coincident fixed marker
on the ground (FG). The displacements are shown in Figure 4.24 where the
MSC.ADAMS system variable format is used to describe the outputs.
4.5.4 Camber and steer angle
Camber angle, , is defined as the angle measured in the front elevation
between the wheel plane and the vertical. Camber angle is measured in
degrees and taken as positive if the top of the wheel leans outwards relative
to the vehicle body as shown in Figure 4.25.
The steer or toe angle, , is defined as the angle measured in the top elevation
between the longitudinal axis of the vehicle and the line of intersection
of the wheel plane and road surface. Steer angle is taken here as positive if
the front of the wheel toes towards the vehicle.
Both camber and steer angle can be calculated using two markers located
on the wheel spindle axis. In this case a marker is used at the wheel centre