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Modelling and analysis of suspension systems 169
The instant centre is found by intersecting lines projected along the transverse
arm and perpendicular to the axis of the strut. The roll centre is found
by projecting a line between the wheel base and the instant centre. The
point at which this line intersects the centre line of the vehicle is taken to
be the roll centre. All calculations are assumed to take place in the same YZ
plane as the wheel centre. The first step is again to set up expressions for
the gradients GR1 for the line perpendicular to the strut and GR2 for the
line projected along the transverse arm:
GR1 (BY AY )/(AZ BZ ) (4.44)
GR2 (DZ CZ)/(DY CY) (4.45)
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) (4.46)
ICZ CZ GR2 (ICY CY) (4.47)
Rearranging these two equations gives:
AZ GR1 ICY GR1 AY CZ GR2 ICY GR2 CY
(4.48)
ICY (GR1 GR2) GR1 AY GR2 CY CZ AZ (4.49)
This allows the instant centre to be located using:
ICY (GR1 AY GR2 CY CZ AZ)/(GR1 GR2) (4.50)
ICZ AZ GR1 (ICY AY) (4.51)
The gradient of the line joining the wheel base to the instant centre GR3,
can be expressed as
GR3 (ICZ WBZ)/(ICY WBY) (4.52)
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 (4.53)
RCZ WBZ GR3 (RCY WBY) (4.54)
The roll centre height RCH, can be defined by:
RCH RCZ RZ (4.55)
where RZ is the z co-ordinate of the road.
As stated earlier the calculation of the instant centre and roll centre position
can be implemented either by programming in the input deck with the
VARIABLE statement or by preparing a user-written FORTRAN subroutine.
By way of example these methods are demonstrated for a front suspension
system only. Using the VARIABLE statement it is possible to program the
equations laid out for the double wishbone system as shown in Table 4.6.