In cornering, a car will experience roll, which is generally is suboptimal for aerodynamics performance. When this happens, the outside suspension compresses, and the inner suspension extends, so counteracting these opposing motions will lessen the roll angle and improve aerodynamic performance. This is the goal of the anti-roll bar, which counteracts opposing suspension movement through torsion. The suspension forces create a net torque on the anti-roll bar, and material properties of the bar itself create a reaction torque. This cancels out the roll motion of the vehicle, and adjusting how much torque is transmitted into the bar determines how much reaction torque there is, which is an ideal way to tune roll stiffness.

At this point in the design cycle, suspension kinematics had been finalized, and I was able to use some of the geometric characteristics of the car to calculate a target roll stiffness. To do this, I once again utilized the target roll gradient, the rate at which roll angle increases with G-force, in combination with the vehicle's roll moment. The body of the vehicle rolls since the distance between the roll center and center of mass acts as a moment arm, creating a roll moment during cornering. Using this, I calculated an angular stiffness by dividing the roll moment by the target roll gradient. Now, I had an idea of the roll stiffness that was required to maintain ideal aerodynamic performance during cornering.

After determining the target roll stiffness, the next task was to determine how much of the roll stiffness must be provided by the anti-roll bar. Roll stiffness can be broken down into three components: tire stiffness, suspension spring stiffness and anti-roll bar stiffness. The tire and spring act in series while the anti-roll bar acts in parallel, all of which can be theoretically modeled as springs. Using formulas for springs in series and parallel, I determined how much roll stiffness was contributed by the tire and spring, and the remaining deficit to the roll stiffness target was to be provided by the anti-roll bar. This number would be used to dictate design and material choices.

There are a number of potential design choices for anti-roll bars, but nearly all designs feature a tube or bar, which reacts against vehicle roll through torsion. To create this effect, cantilevers are attached to the moving parts of the suspension by drop links, creating a torque on the torsion bar.

Given the overall architecture, I was able to model the torsion bar and cantilevers as springs in series with torsional stiffness and bending stiffness respectively.  This required me to convert cantilever bending stiffness to angular stiffness, and doing so allowed me to examine how material and dimension changes affected overall stiffness relative to the design target.

The anti-roll bar not only has to meet the stiffness target outlined above, but also had to be packaged as to not interfere with other critical systems of the car. In the front, this mostly related to cockpit clearance rules, and in the rear, engine and exhaust accessibility. For this reason, I selected a U-bar style design, which was easily attached to the bellcranks and had a minimal overall area.  

Sizing of the torsion bar and cantilevers were the factors I examined most closely. I briefly considered material choices as well, but settled on mild steel construction due to cost constraints and manufacturing timelines that impacted the rest of the team. With this in mind, I created an Excel tool that allowed me to iterate through several combinations of cantilever and torsion bars, and eventually settled on a rectangular cross section for the cantilevers, and a hollow rod as the torsion bar. 

Changing roll bar stiffness can be achieved by altering the material or overall layout, but changing these parameters is not practical. The other important variable that can be changed is applied torque. Since the reaction torque from the torsion bar depends on the applied torque from the suspension, changing the length of the cantilever can be used to adjust stiffness. To achieve this effect, I added a series of additional mounting holes at different distances to the torsion bar on the cantilever. Bolting in the drop link to a different hole would create a different amount of roll bar stiffness. 

An additional benefit that led me to choose a simple steel cantilever U-bar was manufacturability. The cantilevers were thin enough to be waterjetted, and the torsion bar was dimensioned so that it aligned with existing steel stock. This meant extremely low cost, and a manufacturing process that only involved welding the components together. To align the cantilevers properly, the torsion bar was first fixed to the chassis using bearings and mounts. These bearings allow free rotation but isolated the bar against bending or translational movement. The cantilevers were then attached to the bellcranks via rod ends, which allowed me to see angle of the cantilever relative to the torsion bar. Once I had adjusted the linkage such that the cantilever was correctly positioned both laterally and angularly, the components were welded together.