4569846498

168 Multibody Systems Approach to Vehicle Dynamics
GR2 (DZ CZ)/(DY CY) (4.33)
where AY, AZ, BY, BZ, CY, CZ, DY, DZ are the y and z co-ordinates of
points A, B, C and D.
The co-ordinates of the instant centre ICY and ICZ, can be established from
two simultaneous equations based on the upper and lower arms:
ICZ AZ GR1 (ICY AY ) (4.34)
ICZ CZ GR2 (ICY CY ) (4.35)
Rearranging these two equations gives:
AZ GR1 ICY GR1 AY CZ GR2 ICY GR2 CY (4.36)
ICY (GR1 GR2) GR1 AY GR2 CY CZ AZ (4.37)
which allows the instant centre to be located using:
ICY (GR1 AY GR2 CY CZ AZ)/(GR1 GR2) (4.38)
ICZ AZ GR1 (ICY AY) (4.39)
The gradient of the line joining the wheel base to the instant centre GR3,
can be expressed as
GR3 (ICZ WBZ)/(ICY WBY) (4.40)
where WBY and WBZ are the y and z co-ordinates of the wheel base.
This allows the roll centre to be located using:
RCY 0.0 (4.41)
RCZ WBZ GR3 (RCY WBY) (4.42)
The roll centre height RCH, can now be defined by
RCH RCZ RZ (4.43)
where RZ is the z co-ordinate of the road.
The methods used to determine the instant centre and roll centre position
for a McPherson strut suspension are based on the construction shown in
Figure 4.30.
A
Centre line
Instant centre
B
C
D
Roll centre
y
z
Roll centre height
Wheel base (WB)
Fig. 4.30 Instant centre and roll centre positions for a McPherson strut
suspension