A client recently approached us as they were considering modifications to a fleet of off-road trucks, including softening the rear suspension. They asked us to look at the safety implications of doing this; in particular, whether there would be an increased risk of vehicle rollover.
One method which has gained recent popularity for assessing the risk of rollover involves calculation of the static rollover threshold (or “SRT”). The SRT is a measure of the lateral acceleration required to overturn a vehicle. A small SRT indicates the vehicle is more likely to rollover, particularly when going around corners or undertaking sudden emergency manoeuvres. Factors which can lead to a small SRT include heavy loads carried at high heights, and soft suspension (especially the torsional stiffness). This should be unsurprising and relatively intuitive.
The SRT can be calculated from a fairly limited number of parameters regarding the vehicle dimensions and mass, CG location, and suspension stiffnesses. Typical default values can be used where detailed information is not available, however this does result in decreased accuracy and confidence in the predictions.
In this instance, CMP was able to obtain accurate measurements on the suspension components and hence calculate vertical and torsional stiffnesses with reasonable confidence. Intuitively it was expected that reducing suspension stiffness would reduce the rollover stability of the vehicle. After running an analysis, it was somewhat surprising when the initial results seemed to suggest that reducing the rear suspension stiffness had almost no effect on the SRT.
However, after concluding a more in-depth examination of the calculations and the underlying physics involved, it was clear that the results were valid and the explanation for this was relatively straight forward (even if not initially obvious).
Although there are other possible situations in which vehicle rollovers occur (eg high lateral winds), they most often occur during cornering manoeuvres. When a vehicle experiences lateral acceleration during cornering, more weight is carried by the tyres on the outside of the corner, and less weight is carried by the tyres on the inside of the corner. At sufficiently high levels of lateral acceleration, the inner tyres will tend to lift off the ground.
However, this lift-off does not occur simultaneously – typically the axle with the highest roll stiffness will lift off first, and SRT calculations include the flexibility of tyres, suspension and chassis to allow for this effect. In this particular instance, the roll stiffness of the rear suspension was much higher than the front suspension.
As a result of this difference in flexibility, the inner rear tyres would tend to lift off the ground before the front tyres when subjected to an overturning moment. Significantly, once the inner rear tyres have lifted off, the torsional stiffness of the entire vehicle is effectively governed by the front suspension stiffness.
Hence, softening the rear suspension had negligible impact on SRT as it was controlled by the front suspension.
The animation below illustrates this general principle: initially the body of the vehicle rolls on the suspension as lateral acceleration is applied. At a critical point, one of the rear wheels lifts off the ground. From this point onwards, the chassis and front suspension continue to flex until eventually the inner front wheel also lifts off the ground. Increasing the lateral acceleration will ultimately lead to the vehicle toppling over.