CENTRO DE DISTRIBUCIÓN INTERMEDIA

The double wishbone or double A-arm suspension is a little more difficult to solve than the simple rigid arm. As before, it is necessary to establish a motion ratio between the suspension bump velocity and the angular velocity of the arm which operates the spring or damper, or operates the pushrod to the rocker for a racing car. Figure 4.11.1(a) shows the basic configuration.

If the bump camber coefficient of the suspension is already known, then a particularly simple method is possible. The bump camber coefficient eBC is the rate of change of wheel camber angle g with

suspension bump, arising from suspension geometry: eBC¼

dg dzS

ðrad=mÞ

For a suspension bump velocity VS, then for a reasonably constant eBC, usually a good approximation

for the present purpose, the wheel camber angular velocity is dg

dt ¼ eBC dzS

dt ¼ eBCVS

The vertical velocity of B is therefore

VB¼ VS eeBCVS¼ VSð1  eeBCÞ

Hence, the motion ratio RB/Sof ball joint B to suspension bump is

RB=S¼ 1  eeBC

Realistic values are e¼ 0:1 m and eBC¼ 1 rad=m, which will give RB/Sa value of 0.9, a substantial

deviation from 1.0 which should certainly be included in the analysis.

In the absence of prior information on the bump camber coefficient, a velocity diagram may be considered, as in Figure 4.11.1(b). This is more easily constructed by initially assuming an angular velocity vABfor the lower link, rather than a bump velocity of the wheel. A and C are fixed points,

therefore appearing at the origin of the velocity diagram. The tangential velocity of B relative to A is vABlAB, and the line ab in the velocity diagram is perpendicular to link AB, the length of ab being the

tangential velocity at the diagram scale. This establishes point B. Line cd is perpendicular to CD, and bd is perpendicular to BD; the intersection gives point d.

To obtain the velocity of F, at the bottom of the notionally rigid wheel, in the position diagram project line DB and drop perpendicular from F, giving E. In the velocity diagram, the rigid wheel with the wheel upright is solved by scaling. Hence

be db¼

BE DB

giving point e. Draw the perpendicular from e. DBEF is a left turn, so dbef is also to the left. Use

ef de¼

EF DE

to give point f. Finally, drop the perpendicular from f to the vertical axis, giving point g.

This completes the velocity diagram to some convenient scale for some angular velocity vABof the

lower arm. This methodology may, of course, form the basis of a computer program where repeated analysis is desired.

The velocities of interest may now be read from the diagram.

(1) The vertical velocity of the point F, i.e. the suspension bump velocity, VS, is represented by ag

(VS¼ VG=A).

(2) The wheel scrub (lateral) velocity VWSis represented by fg.

(3) The tangential velocity of D relative to B, VD/B, is represented by bd.

(2) The camber angular velocity

dg dt ¼

VD=B

lDB

(3) The bump camber coefficient eBC¼ 1 VS dg dt ¼ VD=B lDBVS ¼  ldb lDBlag

(4) The basic roll centre height (unrolled)

hRC¼1₂T

lfg

lag

In the present context, it is the velocity ratio that is of interest. The lower arm may then be analysed as a rocker output for the damper drive, as was the rigid arm, to give the overall damper motion ratio.

4.12 Struts

The strut suspension is a the usual choice nowadays for the front of passenger cars. The use of a strut at the rear is a little unusual, but has featured in several cases.

The usual strut incorporates the damper into the body of the strut, and has a surrounding spring. An alternative design, the damper strut, has only the damper in the strut body, with the spring acting separately on one of the arms. Geometrical considerations are the same, although, of course, in the latter case it is the arm which must be analysed for the spring motion ratio.

Overall, the method of analysis is similar to that of the double wishbone suspension. Figure 4.12.1(a) shows a strut suspension. This is in fact the simpler version where the strut axis passes through the ball joint at B.

If the bump camber coefficient is already available, then the vertical velocity VZBof B is given by

VZB¼ VSð1  eeBCÞ

where

e¼ XF XB

The tangential velocity of B is then

VB=A¼

VZB

cos f1

and the damper compression velocity VDis

Hence RD¼ VD VS ¼ ð1  eeBCÞ cosðf1þ u2Þ cos f1

Realistic values may give a motion ratio below 0.9, in contrast to the naive expectation of a value close to 1.0.

The velocity diagram is shown in Figure 4.12.1(b). Construction begins by assuming an angular velocity vABfor the bottom link:

VB=A¼ vABl1

perpendicular to AB, giving point b representing VBin the velocity diagram. Velocity VB/Cis the vector

sum of longitudinal and tangential components, so construct a line through b perpendicular to CB and through c parallel to CB to intersect, giving point d. Point d represents the velocity of point D, which is

to give e and f, and drop the perpendicular from f onto the vertical axis to give g. Point f represents the motion of the base of the wheel, and g represents its vertical component.

From the velocity diagram can be obtained: (1) the suspension bump velocity represented by ag; (2) the wheel scrub velocity (fg);

(3) the tangential velocity of B relative to D (db). Hence, the following may be calculated:

(1) the motion ratio R of the lower arm to suspension bump R¼vAB

VS

¼ VA=B lABVA=G

(2) the camber angular velocity

dg dt ¼

VB=D

lBD

(3) the bump camber coefficient eBC¼ dg=dt VS ¼ VB=D lBDVS ¼  lbd lBDlag ½rads1_=ms1_

(4) the basic roll centre height (unrolled)

hRC¼12T

lfg

lag

On front suspensions in particular, the damper axis is frequently aligned such that it does not pass through the ball joint at B, but rather inside or outside it. In that case the preceding analysis is still applicable, with the following provisos:

(1) The angle u2used is that of the damper axis, not that of the steering axis CB.

(2) To obtain e and f still use the steering axis line CB extended.