Before analyzing the many parameters associated with suspension geometry, I familiarized myself with the SAE vehicle axis system. This allowed me to generate simulated vehicle motions with which to evaluate the suspension package with. These critical motions included:

• Pitch which refers to vehicle rotation about its lateral centerline, mainly occurring during acceleration and braking. 

• Roll which refers refers to vehicle rotation about its longitudinal centerline, mainly occurring during cornering.

• Heave which refers vehicle travel in the up and down direction, usually caused by bumps and uneven road surfaces.

Another aspect that is useful to examine is the effect of steering, which was another motion included in my analysis. These simulated scenarios were analyzed independently and combined, covering many vehicle cases that would occur in a racing scenario.

As mentioned, the suspension must provide the car's aerodynamic components with a stable platform, and for this reason, the simulated motions of the vehicle were created in collaboration with the aerodynamics subteam. Plots of aerodynamic efficiency versus pitch, roll and heave were provided to me by the aerodynamics subteam, as well as information about ground clearance for front wing and floor. This allowed me to set boundaries for the motions I would use to simulate suspension characteristics and enable the aerodynamic package to operate at its best.

Suspension design is often very difficult since there are many degrees of freedom and managing all of them simultaneously can be very resource intensive. Duke Motorsports uses OptimumK, a software that allows us to computationally derive suspension configurations based on our kinematic goals. In years past, suspension simulations would take hours for each iteration, which often led to underdeveloped packages due to time constraints. To mitigate this issue, the design process was separated into two components: outboard (the points connected to the wheels) and inboard (the points connected to the chassis). This greatly reduced computing time and allowed for more iterations to be run, leading to an overall more refined package. Outboard points were done first to reduce wheel assembly design lead times.

There is only so much space inside of the wheel to place a plethora of components including uprights, wheel hubs, brake rotors, brake calipers and sensors. This means that suspension point geometry not only must result in favorable vehicle characteristics, but also leave enough room to package the other components. These two tasks are often conflicting. For this reason, an important part of the suspension design process is a constant feedback loop with the wheel assembly team.

There are several key geometric parameters to consider when dealing with outboard suspension geometry, particularly in the front suspension. 

• Caster: The angle of an imaginary line through the upper and lower ball joint with respect to vertical in a side view. This angle creates favorable camber gain when steering.

• Mechanical Trail: The distance between the tire contact patch and the point where the imaginary caster line intersects the ground. This affects steering effort by acting as a moment arm in lateral loading.

• Kingpin Inclination (KPI): The angle between an imaginary line through the upper and lower ball joint with respect to vertical in a front view. This angle creates unfavorable camber loss when steering.

• Scrub Radius: The distance between the tire contact patch and the point where the imaginary KPI line intersects the ground. This affects steering effort by acting as a moment arm in longitudinal loading.

While increasing caster is favorable from a kinematics standpoint, it makes steering more difficult for the driver. In a similar way, KPI creates unfavorable camber loss, so it would make sense to minimize this, but doing this would cause higher scrub radius, again affecting the driver's steering effort. A tired driver makes the rest of the car design irrelevant, so it is important to balance these effects.

Using the test cases created earlier in collaboration with aerodynamics and the goals developed during tire analysis, I converted these to geometric goals that I would be able to use in OptimumK to drive suspension evolution. For example, achieving the target camber would be affected by KPI and Caster, so I set numeric goals for these geometric parameters which in turn affected dynamic camber. This allowed me to more finely tune individual characteristics, which helped reduce processing time and iteration variability. 

Bounding boxes were provided by the packaging team, and I used these to start the first iteration. After the optimization program was done running, I was able to simulate the dynamic behavior in OptimumK's simulation module. This enabled me to graphically compare kinematic behavior with the tire and aero goals. These graphs allowed me to adjust geometric goals and their weighting to drive the optimization program to create arrangements that better aligned with my goals. Once I found a configuration that I was happy with, I sent the set of 3D points to the packaging team for verification. Most of the time, they had feedback and provided new bounding boxes. These changes were often required if the points were too far outboard, leaving not enough room for the brake caliper, or if the combination of caster and scrub radius resulted in unsustainable steering effort. This process was repeated until both parties were equally satisfied, thus setting our outboard suspension geometry.

The inboard side of the suspension has a bit more spacial freedom than outboard, as the chassis is slightly more accommodating to suspension point changes. However, there are different types of constraints, like drivetrain halfshaft clearance, chassis node placement and aerodynamic floor clearance. Inboard geometry also consists of four points, compared to two for outboard, which adds more complexity. It often takes much longer to set inboard geometry for this reason, and there is a lot of overlap between geometry changes that may be beneficial in one motion, but detrimental in others. 

There are many parameters to consider when setting inboard suspension points, but a few key ones to discuss are:

• Front View Swingarm Length: This represents the length of an imaginary line from the wheel center to the intersection points of the projected upper and lower control arms (instant center). This dictates the rate of camber gain in roll, but can have opposite effects in heave.

• Roll Center: This is the point around which the vehicle's axle rotates about, and can be geometrically located by finding the intersection points between lines drawn from the left and right instant centers to the opposite tire's contact patch. This affects weight transfer in cornering, as well as chassis and suspension loading.

• Jacking Force: Camber gain from swingarm geometry can cause jacking forces as the wheel orientation directs lateral force components vertically. A similar effect results from higher roll centers due to vertical suspension loading. Jacking force needs to be mitigated while still preserving ideal tire camber characteristics.

• Anti-Geometries: Suspension configurations that results in a torque that cancels out some percentage of the dive motion under braking or squat motion under acceleration. Increases suspension loading while improving platform control.

There are many tradeoffs to manage with these parameters, and is a major reason why simulation software like OptimumK is so critical in suspension development. For example, poor dynamic camber may require shortening swingarm length, but doing so would also cause instability over bumps and in braking. 

This process is very similar to the one taken to set outboard points. I set up the optimization module with geometric goals based on my kinematic targets, and run the module to set a baseline. I can simulate these in the previously mentioned test cases, which allows me to adjust the kinematic goals. Once I have a set of points I am happy with, I send them to the chassis subteam so they can check for compatibility with our tube frame chassis and other vehicle systems. The main points for me to look out for when setting suspension geometry is proximity to chassis nodes (points where multiple tubes intersect), and in the rear, clearance to the halfshaft and diffuser. This process usually generates more refined bounding boxes, which I can then use in my next set of optimizations. This process takes a while due to the four different subsystems (vehicle dynamics, chassis, powertrain, aerodynamics) that need to check off the design.

The team uses a double wishbone suspension design, consisting of two triangular controls arms, a tie rod and a pushrod. The control arms exist in space as three points in a triangular shape, but to fix them to the chassis and wheel, there needs to be a system in place that allows them to be fixed in lateral and longitudinal movement, but still free to pivot about the chassis and wheel independently. To achieve this, I selected high load ball joint rod ends, which would need to be fixed to the control arms as well. On the outboard side, a bearing carrier was designed and FEA optimized to weld into the suspension arms and bolt into the upright. On the inboard side, the rod ends were screwed into the suspension tubes and bolted into the chassis mounts. 

I did not cover tie rods and push rods here, but I did work on optimizing, packaging and manufacturing those parts as well.

An item that is often overlooked in FSAE suspension is the effect of compliance and suspension loading. Suspension linkages must be sufficiently stiff to minimize compliance, which is often the main reason simulations don't align with reality. Any deformation or deflection in the suspension changes the geometry, which usually has negative effects on handling. To combat this, our team created a suspension forces calculator, allowing us to decompose lateral and longitudinal forces exerted by the tire into components in each suspension arm. This was done using matrix algebra, as the suspension arm positions can be represented as unit vectors in 3D space, as can the forces applied to the wheel. These individual suspension arm forces informed the material choices and sizing of the suspension arms to maintain sufficient margin of safety under worst case loading. This ensures reliability and eliminates the chance of suspension failure. 

In addition to calculating suspension arm material and sizing, this data was used to analyze compliance. Using Solidworks, I modeled the entire corner assembly and applied the calculated loads through a virtual point representing the tire contact patch. This simulates cornering forces being transmitted through the tire and into the suspension, and allowed me to observe how much the system deflected. One of the key causes of compliance I noticed was excessive hardware usage. Each suspension arm featured a turnbuckle style adjustment system to account for manufacturing error, but was the limiting case for system compliance. I elected to remove this part of the design, which reduced deflection and retained more of the designed kinematic effects. 

Once all the kinematic and mechanical design work was completed, manufacturing was the next step. There were three main components to consider as mentioned earlier in this section — the control arm, the bearing carrier, and the rod end. Control arms were measured and cut using a bandsaw. However, there needed to be a way to attach the threaded rod end into the control arm, as well as a way to grip it using a wrench to correctly fasten them together. To solve this issue, I created threaded, hexagonal inserts to attached to the tube. This enabled a way to both attach the rod and and tighten it into place. 

On the wheel side, there needed a way to accommodate two converging suspension arms, as well as a way to allow free steering and vertical movement of the wheel. This is the job of the bearing carrier, which, as the name suggests, fixes the spherical bearing to the suspension arms. This part had to appropriately handle the loads experienced in the two attached suspension arms, without being excessively heavy. I constructed the part geometry based on the control arm angle, and used Solidworks to conduct an FEA using the previously mentioned suspension loads. The optimized bearing carrier was milled, before being welded to the control arms using a specialized jig to eliminate manufacturing errors. Finally, the control arms were bolted to the chassis, and then to the uprights.