Suspension behaviour related to a static toe variation

From this evaluation it is possible to have an idea on the routes to follow when setting up the vehicle, a negative camber angle will move the lateral acceleration limit to higher values, while a positive angle will move the limit towards lower values.

The negative camber condition will reach the same side-slip angle at higher accelerations, increasing the limit of grip of the vehicle. The main differences between the configurations become clear only as the vehicle reaches the grip limits, for small side-slip angles the difference is, basically, unnoticeable. By watching these graphs, it is possible to understand that negative camber angles will be, most likely, better than positive values concerning the cornering behaviour, due to the fact that a reduction in understeer is obtained, this is a good confirmation of the slightly negative value of static camber used by the design condition.

approaches the limit is similar between the three conditions, all the cases it seems to be gradual in their variation.

Figure 6.25: Lateral force in function of the average side-slip angle on the front axle

Lateral force is evaluated also in function of the average side-slip angle, on the front axle the value of force will be lower for a negative toe angle when keeping the average side-slip angle constant in the comparison, the rear axle will not be affected by variations in toe at the front.

The graph in Figure 6.25 is useful to understand the cornering stiffness of the vehicle, this parameter reflects the ability of the tire to resist deformation in shape during a cornering event: It can be obtained by computing the slope of the curve that plots lateral force in function of the side-slip angle: This relation is valid for slow slip angles, hence why the first part of the graph is characterized by a linear behaviour: Thanks to the fact that the lateral force is related to the side-slip angle only by the cornering stiffness in this phase.

Case Difference in slope from neutral angle

Toe Angle -1 -20,15%

Toe Angle +1 +8,60%

Table 6.3: Differences in slope in reference to the neutral case

A comparison between the cases where the alignment was modified from the neutral condition is shown in Table 6.3, the variation in percentage confirms what was seen in the graph. A negative toe angle will reduce the cornering stiffness and vice versa, a negative toe angle value will have a clearly

less pronounced slope leading to a decrease in cornering stiffness. The effect of the positive toe angle is to increase the cornering stiffness, when moving towards positive values the percentage variation in absolute value will be less pronounced than what happens towards negative values.

Figure 6.26: Average Side-Slip angle evolution for different toe angle values

By plotting the average side-slip angle in function of the lateral acceleration in Figure 6.26 it is possible to see that toe largely affects the side-slip value that the wheels will experience, a negative toe value will show higher side-slip angles and a lower peak lateral acceleration. The effect is very pronounced, the difference when applying a positive toe angle is less relevant but will deliver lower angles and higher peak accelerations, the rear axle will be more uniform in shape between cases.

Figure 6.27; Difference between the two side-slip angles as the toe angle varies

In this case the most relevant graph is the one in Figure 6.27, this graph tells that a negative toe angle will likely increase understeer, due to the fact that the difference between the two side-slip angle absolute values is higher. A positive static toe will instead reduce the understeering phenomenon.

Camber angle is also largely affected by the value of toe angle, as it is seen in Figure 6.28 on the front, it is so affected that the variation is higher than the one experienced by directly acting on the static camber, camber angle variation follows the sign of the toe variation.

Figure 6.28: Real front camber angle variation with respect to lateral acceleration, for different toe values

Like what happened with camber, the toe angle will change as the steering motion continues, as it can be seen in Figure 6.28: On the front axle differences between tests will become smaller as the test goes on. The values of toe and camber found on the rear axle are very small, so small that it is possible to say that the variation in toe is negligible on the rear axle as the toe angle is changed.

Inclination angle also gives a good inside on how the suspension reacts to static toe variations, results are presented in Figure 6.29.

Figure 6.29: On the left the actual toe angle value variation is shown for the left front wheel, on the right the same is done for the right front wheel

Figure 6.30: Inclination angle variation on the front axle as toe angle is changed

Inclination angle results clearly show that the toe angle will also affect the value of static camber, sign of toe and camber will be the same on the outer wheel and vice versa.

As the static value is defined differences will be high, the differences among configuration will become smaller as the manoeuvre proceeds.

At higher steering angles the effect of static toe on the inclination will be reduced, being that the suspension has largely changed its geometry compared to the case in the beginning. Results are shown in Figure 6.30

Figure 6.31: Roll angle variation with lateral acceleration, again shown for the three variations in static toe

Roll angle shows a straightforward evolution with lateral acceleration, it will be reduced by negative toe and increased by positive toe, the variation is minimal between the three tests, results are seen in Figure 6.31.

Figure 6.32: Understeer behaviour as the toe angle is changed

Figure 6.33: Side-slip angle computed at the centre of the vehicle model, as the toe angle is changed

By looking at the graph in Figure 6.32, it is possible to see that the situation is clearer compared to the tests about camber angle variation. The differences between the tests are larger, toe-out will decrease the lateral acceleration values that are reached at a given steering angle but will make the behaviour more gradual compared to the other two tests.

In this case the best compromise seems to be the neutral condition. The graph showing the body side-slip angle in function of lateral acceleration is showed in Figure 6.33. Toe-in condition will reach a given value of side-slip angle at higher values of lateral acceleration compared to the other two tests.

From this evaluation it resulted that toe leads to large changes in how the vehicle reacts to different manoeuvres, especially at low steering angles. By looking at the graphs the condition of neutral toe seems to be the best compromise, being always in the middle between the two, obviously the tune depends on the vehicle mission, some changes in toe can bring changes in behaviour that in some conditions are beneficial, while in others they are not.