Please enjoy the 2-minute summary gallery below, or scroll further to explore my work in greater detail

Suspension Kinematics

The ultimate job of a suspension system is to control the behavior of all four tires in a way that maximizes the performance, drive-ability, and stability of the vehicle. In order to do this, the tires must be kept in an optimal combination of operating conditions, and the kinematic motions of the suspension linkages play a key role in controlling that window. A well designed suspension will maximize the time spent in the tires' "performance envelope" and manage that subsequent tire performance effectively.

 

In this page, I will discuss the process I used to develop the kinematic design for Clemson FSAE's 2020 vehicle, Tiger22.

Design Methodology

Tiger20 on the autocross course at FSAE Michigan 2019

In many FSAE vehicles, suspension geometry is often one of the first designs to get finalized. This is because the geometry and orientation of several downstream components are derived from the locations of suspension pickup points. For critical components such as the frame, this is critical for integration and ensuring that suspension points are placed on nodes to maximize installation stiffness. Switching the order of that process, and using chassis nodes to determine suspension points, is ill-advised.

For Tiger22, this remains the case. However, in past vehicle when suspension geometry is finalized first, other components such as the frame have to compromise their design in order to align with kinematic pickup points. These compromised designs are often heavier and more compliant than they need to be. In order to avoid this, I decided to include chassis and outboard design considerations to inform my design from the very beginning of the project.

With this in mind, my approach to the suspension design was to start by defining all of my kinematic behavior targets abstractly. This exploits the fact that there are infinite variations of a suspension that can achieve near-identical kinematic characteristics. Once these targets have been fully identified, I can focus on creating design iterations that meet all of the requirements while simultaneously pursuing secondary design objectives. By including these interactions in the early stages of design, I can help avoid design compromises further downstream. 

The non-nodal pickup point on the front upper control arm shown here (c. 2018) is an example of design compromise caused by finalizing suspension geometry without consideration of the downstream subsystems

Vehicle Modelling

The starting point for my vehicle model was the two track steady state vehicle model, using my  non-linear CSAPS tire model that can capture load, slip and camper effects in both longitudinal and lateral forces. The model has 7 degrees of freedom: yaw and side slip velocity, longitudinal acceleration, front/rear roll, ride height and pitch angle. Suspension stiffness has an effect on total roll and pitch motions (and by extension kinematics), but no direct effect on mechanical grip is captured. Tire compression is also neglected. This describes the basic model foundation, and as the design process moved forward, kinematic details such as roll and steer camber were added in as required. Final design evaluations take all variables in effect, but by increasing complexity in stages I can better evaluate the effects of individual design parameters without worrying about coupling with others.

In most cases, this vehicle model was used to generate GGV models of the car, which were then input to the lap time simulation to predict performance at FSAE dynamic events. You can learn more about the development of the lap sim here.

Camber Kinematics

The first objective in the design process was to select camber change targets for the vehicle. I defined camber change as "camper compensation", meaning the percentage of camber lost during body roll that is gained back. For example, 50% camber compensation means that for the amount of positive camber generated by body roll, half of it is gained back as negative camber from suspension travel. With the two variables of static camber and camber compensation (front and rear), I am able to abstractly define the full camber behavior of the vehicle.

The general design trade-off here is the compromise between cornering and longitudinal performance. Having small amounts of camber gain means that the camber changes very little under braking and acceleration, helping improve grip in those situations. However, that subsequently means that the positive camber gain in cornering is left unaddressed, hurting lateral acceleration performance. For high camber gain, the opposite is true.

To make sure these interactions were being captured, I started with a gut check design exploration:

This braking example demonstrates that increasing camber gain or static camber will decrease overall braking performance

This cornering example demonstrates that the more camber gain is present, the less static camber is required to achieve maximum cornering performance

With a gut check complete, it was time to move on to actual optimization. The goal here was not to select a final camber configuration just yet, but rather identify a target range of camber compensation to work with. This allowed flexibility for other downstream considerations such as steer-camber and desired vehicle balance.

A series of surface response plots were generated to evaluate the effects of static camber and camber compensation on FSAE dynamic event performance.  To simplify analysis, front and rear values were kept equal to each other, and steer camber effects were neglected. Again, the goal was simply to find a target range as a starting point. 

The Accel results track pretty well with the design exploration above. For maximum ideal rear end grip in a straight line, one would want zero static camber and zero camber change in squat.

Similarly, the Skid pad results track nicely as well. It is clear to see here the desire to have high static camber and low compensation, vice versa, or somewhere in between.

The Autocross and Endurance Event results show a slightly more complex relationship, due to the nature of both lateral and longitudinal performance requirements.

Finally, the total points prediction for all 4 dynamic events is shown below:

For the autocross and endurance event, as well as the total score, higher rates of camber compensation yielded higher overall points hauls. This suggests that, in suspension design, favoring cornering performance over braking and acceleration will have a greater effect on lap time. This makes intuitive sense for power-limited FSAE cars running on autocross courses with low speeds and small braking zones. It is interesting to note that the higher the camber compensation, the higher sensitivity to static camber.

 Based on these results, I selected a target range of between 60 to 80 percent camber compensation, with low static camber (0.25-.5 deg). Front and rear values would ultimately vary based on desired balance, steer camber, etc.

Steering and Kingpin Axis

The next design section to tackle was the kingpin axis. Unlike camber curves, this one is a little trickier because there are more opposing criteria that you are trying to achieve. KPA affects not only the performance due to weight jacking and steer camber effects, but also the balance and force feedback to the driver. With that in mind, my primary design criteria were the following, in order of highest to lowest priority:

1) Control the limit approaching behavior of self returning steer moment (MZ) in order to consistently communicate to the driver that they are approaching the limit. The baseline target is for the returning moment to peak at around 70 percent of where peak lateral force occurs, to allow the drivers enough bandwidth to anticipate the limit.

2) Manage the steer camber and jacking characteristics so that both vehicle performance (lateral acceleration) and vehicle balance (understeer gradient) is consistent across the full operating range.

3) Achieve a target max steering wheel force of 25 pounds (based on previous driver preference data)

4) Maximize outright lateral acceleration performance. 

Visualization of the variables being explored.

Source: Jambukar S., Sujatha C. (2020) Effects of Kingpin and Caster Offset on Braking Stability of Long Wheelbase Bus. In: Biswal B., Sarkar B., Mahanta P. (eds) Advances in Mechanical Engineering. Lecture Notes in Mechanical Engineering. Springer, Singapore

Before moving forward, it's important to know the characteristics of the steering rack used. Our team uses the NARRCO FSAE rack due to it's low cost and low weight

The first step is always to explore the design space, so I started with some simple spreadsheets to visualize the relationship between steering kinematics and resultant driver force

Steering force solver spreadsheet

KPI and Caster trade-off visualization

From there, the next step was to explore the MZ saturation behavior. I did this using a single axle cornering model, applying a total slip angle and solving for quasi-steady state equilibrium.

This enabled me to narrow in on the combination of settings required to achieve my MZ saturation target near the cornering limit (see bolded table entry)

However, with driver steering force there is another important consideration to make. If the majority of returning moment comes from the mechanical (caster) trail, there can be a loss of resolution, and natural MZ fall-off from the tire will pass unnoticed by the driver. So it's important to keep track of this.