Please enjoy the 2-minute summary gallery below, or scroll further to explore my work in greater detail
Suspension performance is critically dependent on the kinematic control of linkages in 3-D space. However, since a truly rigid body does not exist, suspension links inevitably deform under the various loads cases seen on the track, which can affect the performance and stability of the vehicle. Further adding to the challenge is the opposing criteria of minimizing mass of suspension components, which will decrease their stiffness.
Compliance is a notoriously ignored phenomenon in the Formula SAE community, to the frustration of many design judges who have made it a core topic of technical discussion. The Clemson FSAE team has been historically guilty of this, but over the last couple of years I have led a foray into the exploration of its effects in a push to develop more informed design targets. In this page, you will see my discussion on my development work to date, as well as the critical validation steps that need to be made and future development routes that I would like to explore.
Clemson FSAE's 2019 car, Tiger21, was the first to be developed with suspension compliance targets in mind.
For this initial foray into compliance exploration, I wanted to focus my efforts on two significant areas affecting performance and stability: camber and toe compliance in cornering scenarios. This is not to say that there aren't other important areas of compliance management; for example, vertical force load paths in the suspension and mounting are often some of the most egregious sources of compliance! Camber and toe errors simply have a more directly calculable effect on the performance and stability of the vehicle, and provide a solid foundation for a first exploration.
That's not to say that other sources of compliance were ignored, either! The first and most significant step in controlling compliance comes from managing load paths from the suspension into the chassis. No amount of link sizing optimization will mitigate the deflection of a rod end in bending, mounted in single shear to a non-nodal cantilevered frame post. I won't go into too much detail here, but there are other pages on this site where you can read more about the conceptual, packaging and mounting decisions made across the suspension to minimize compliance
One quick example of load path management - when exploring different spring concepts for the Tiger22 decoupled suspension, the final decision was to use an anti roll bar mounted to the pitch rocker. One of the driving factors behind this decision was that by consolidating most of the loads onto one of the rockers, we'd minimize the torsion loads, and therefore deflection, across the rocker shaft.
Load paths being set aside, the approach to selecting compliance targets began with exploring the effects of compliance on steady state performance, cornering response, and vehicle control. Alongside that, I used suspension load cases and basic sizing calculations to build a rough correlation between a compliance target, and the subsequent weight of a suspension sized properly to achieve that. Since compliance was a new area, we did not have previous data or targets to inform a threshold for how much compliance is too much compliance. Instead, my approach was to consider the compliance and weight trade-off hand in hand, and balance their respective points of diminishing returns to select final targets.
Toe Compliance Analysis
Since steering is the direct cornering "control" input at the driver's disposal, toe (or steering) compliance has a significant effect on vehicle behavior deviations. For both front and rear, toe compliance has a direct effect on the slip angles achieved in a corner, which can drastically alter vehicle balance or outright performance if not managed properly.
My initial analysis was done with a linear bicycle model using the Bundorf Cornering Compliance concept pioneered by R. Thomas Bundorf (Bundorf, R. and Leffert, R., "The Cornering Compliance Concept for Description of Vehicle Directional Control Properties," SAE Technical Paper 760713, 1976). This is because the 2 degree of freedom bicycle model is a powerful tool to explore basic control and stability parameters, and using cornering compliance to describe front/rear axle performance makes incorporating added compliance very straightforward.
The following figure was generated using a step-steer simulation to explore the effects of compliance on cornering response time. It is apparent that increasing compliance overall hurts response. However, increasing understeer compliance has a much larger effect in improving response! This is because the rear axle provides the stabilizing yaw moment in a corner, and the stronger it is relative to the front the faster it will be able to "catch" the car.
Under-steer, however, is a double edged sword. Firstly, there are other ways to achieve understeer, such as tuning the lateral load transfer distribution or static camber alignment. In addition, excessive under-steer hurt peak lateral performance capacity due to the front axle saturating much sooner than the rear. Lastly, vehicle balance is a key drive-ability parameter, and we have testing data informing our understeer gradient targets based on driver preference. Straying away from that target would need some serious justification.
To explore the control of the vehicle, step steer inputs are inadequate in capturing the hysteresis effects of compliance. FSAE tracks typically feature several slalom sections, and this would be an area where hysteresis can have a large effect. The use of a linear model enabled a frequency response analysis to capture the on-center behavior of the car in such a situation.
This bode plot captures the frequency response of the vehicle for an average FSAE track slalom speed, across a range of typical slalom steering input frequencies