In this brief article, we will discuss the Suspension Roll Rate, how suspension roll rate is derived and the effect of the Roll rate parameter on vehicle performance.

## What is the Roll Rate of a Suspension?

A Car’s suspension roll rate is defined as the stiffness of the vehicle in “Roll” motion. It is a quantity that gives a measure of the effect of all the stiffnesses involved in the car in resisting roll motion during cornering.

It is the amount of torque required to cause a unit degree of roll angle in the vehicle under steady state cornering (meaning that during cornering, there is no longitudinal acceleration in the vehicle)

## How is the Roll Rate Derived?

The Roll stiffness is an addition of the front and Rear suspension Roll stiffnesses. The Front/Rear Roll Stiffness is a result of several contributing factors like :

- Spring Rate
- Anti-Roll Bar Rate
- Bush Stiffnesses
- Tire Stiffness
- Chassis Twist mode stiffness

The Roll Stiffness of the front suspension is defined as the sum of the effects of the Spring stiffness, the suspension arm bushing stiffnesses, the Anti-roll bar roll Stiffness and the Tire stiffness, all acting at the wheel center. What this means is that you need to factor each of the suspension component stiffness as an effective rate that is experienced at the wheel center.

For e.g, The coil spring is at an offset from the wheel center. So 1 mm of vertical travel at the wheel center would result in say 0.6 mm (just as an example number) of spring compression. This implies that the motion ratio of spring is 0.6.

In a similar fashion, you need to calculate the wheel rate due to the effect of the control arm bushings and the effect of the anti-roll bar. All these effects need to be added and the resultant is called the Roll stiffness of the front/rear suspension.

The last effect that is due to chassis or BIW (Body in White) stiffness is not easy to know. It will need to be simulated in a Finite Element Analysis because the body is a result of 100’s of panel joineries like spot welds, and adhesives.

Total Roll Rate = Front Roll Stiffness + Rear Roll Stiffness + Chassis/BIW Roll Stiffness

## What is the importance of Suspension Roll Rate?

Vehicle Roll rate is important while optimizing the Chassis in the Mule Prototyping stage of a vehicle development program. At this stage in the vehicle program engineers are basically trying to mix and match and put together a suspension set-up and see what is the resultant effect of the springs, bushings, anti-roll bars and chassis.

Usually, there a set of Benchmark target values for Roll Stiffness that would have earlier been derived from either competitor vehicle chassis setups or the manufacturer’s own model from the past. Once the benchmark targets for vehicle roll-rate are known, then it is easy to make decisions when there is choice to be made between multiple components that would fit into the same function, like two coil springs with different spring rates that fit into the same top and bottom spring mounts. By doing this quick calculation, you would understand the impact of each coil spring into the front/rear suspension roll rate and then make an informed decision.

## Advanced Tools to calculate Roll Stiffness

The abovementioned calculation method would work in a lot of situations. But there would be many situations where changes in geometry would require a lot of input values, for e.g., the curvature and shape of the anti-roll bar. This would require many points of geometric data and become time consuming.

Instead, if the 3D CAD model of the components are available, it would be possible to feed in all these shapes, along with spring and bushing rates and then simulate the suspension movement to calculate and derive the roll rate. This sort of calculation is possible in specialized high-end softwares called “Multi-body dynamic softwares” and “Symbolic modeling softwares”. Eventhough these softwares are extremely expensive and also require High-performance computing hardware, many OEMs do find it worthwhile and do invest in acquiring these advanced softwares.

**Conclusion**

In this brief article, we have discussed the Suspension Bar, its features, advantages, and applications.

**References**