SAE Teams – Charlie Walker

Tire and Wheel Selection

Introduction

The tires are the most important component of any racing vehicle; as they are the only way you can transmit controlling forces to the ground. Understanding the importance of this piece of the car, it was crucial that I selected the best tire and wheel package for our application.

Modeling

To begin this process, I needed to model the tires of interest so I could compare their characteristics. The model I chose was a simplified version of the Pacejka Magic Formula. The coefficients of this model are visualized below.

The model was simplified by removing the Curvature Coefficient ‘E’, which improved the R² value of the fit while reducing model complexity. An example of this model improvement on our chosen tire is shown.

Yaw Moment Diagrams

With the tire models developed, I needed a way to compare the wheel and tire options to see how they would affect the overall handling characteristics of the vehicle. For this, I chose to construct constant skid pad speed (25 mph) Yaw Moment Diagrams using the design specifications of our vehicle for each wheel tire combination.

Example Yaw Moment Diagram of Selected Wheel & Tire Package

These diagrams provide three crucial metrics which can be used to evaluate how the tires will impact cornering performance.

Maximum Lateral Acceleration: Represented by the X coordinate at the left and right extremities where there is no yaw moment on the vehicle, this predicts the maximum lateral g’s the car can hold in steady-state conditions.
Maximum Yaw Acceleration: Represented by the Y coordinate at the upper and lower tips, this predicts the maximum yaw acceleration the vehicle can undergo within grip limits based on the yaw moment created by the tires and the yaw inertia of the vehicle.
Steady State Control: Represented by the Z coordinate at the center of the diagram, this predicts the change in yaw acceleration per change in steering wheel angle and is a good metric of how responsive the vehicle is.

Extracting these datapoints from diagrams created with different wheel and tire combinations allowed me to compare the characteristics of my highest picks for tire and wheel setups. The main tire and wheel combinations I considered were R20’s on 7 inch wide OZ wheels and 8 inch wide Keizer wheels, as well as LC0’s on 7 inch wide OZ wheels.

The inclusion of different wheels proved to be quite important to the performance of the packages as predicted by the diagrams. While the OZ wheels are 28% lighter than the Keizer’s which increases responsiveness by lowering yaw inertia, they have lower cornering stiffness due to their smaller width which decreases responsiveness. Modeling these characteristics together allowed a more complete picture of their effect on the vehicle.

Ultimately, R20’s on OZ 7-inch wide wheels were chosen for this year’s vehicle. Though they don’t have the highest levels of max lateral acceleration or cornering control, they offered a good balance of these characteristics by being a close second for both of these metrics. They also showed the highest maximum yaw acceleration of the setups, very useful on the tight corners often found on FSAE tracks.

Other Factors

Another reason for the selection of the OZ wheels over TAMU’s typical selection of Keizer’s is the significant saving in manufacturing time and complexity at no cost penalty. This is because the OZ’s come as a single-piece wheel where Keizer sells wheel outers which need to be joined to custom wheel centers. When considering the cost of the high strength aluminum that would need to be purchased for these wheel centers, both wheels cost ~$350. The single-piece construction, however, reduces system complexity and saves the team ~40 hours of precision CNC machining time.

Another factor that was considered for the selection of the R20 was pre-season testing, where the drivers found the LC0 compound to be much less predictable than R20’s when using them on real track surfaces. Though this compound performed well once warmed up and scrubbed, they quickly dropped off as they wore down, or got out of their temperature envelope

Tire Characterization

With the wheel and tire package selected, I needed to figure out the best way for the suspension system to orient the tires for maximum performance. The first thing I looked at was camber angles.

As seen in the plots above, increasing camber improves cornering stiffness somewhat linearly, but this comes at the expense of limit cornering grip and longitudinal grip. Noting the large 2.5% drop in longitudinal grip between 2 and 4 degrees of camber, especially relevant with this year’s powerful 4-cylinder powertrain, I worked with the kinematics designer to keep the wheel in the range of 0.2 to 2.0 degrees of camber throughout wheel travel.

Another characteristic I inspected was tire temperature.

From this plot, it can be seen that the highest coefficients of friction occur between 131-138 Degrees F. Knowing this, we could adjust our camber angles on track to keep the tires in their best operating envelope.

Results

Ultimately this wheel and tire selection was 20% lighter than the previous team’s package, contributing to the lightest TAMU FSAE suspension system ever created, and allowed the vehicle to reach over 1.8 G’s of lateral acceleration on track.

This performance, combined with the system’s reliability to give our drivers ample practice time, contributed to the team’s success at competition; earning 5th in skidpad and 5th overall out of over 100 teams at FSAE Michigan.

Brake System Design

2023 SAE Baja Car at Endurance After Passing Brake Check

Introduction

As the sole brakes engineer for TAMU Baja, I designed, manufactured, and tested a reliable, lightweight braking system for use in the 2023 vehicle.

Design Philosophy

At the beginning of the season, I helped establish a design philosophy to guide all team members as they make engineering compromises throughout the season.

Throughout the season, I referenced this guide to ensure I was creating a system in accordance with the agreed-upon vision for the car.

Braking Force Calculations

As the balance and strength of the braking system are a product of many design choices, I constructed an Excel Braking Calculator to ensure my design would be able to lock all four tires as I experimented with design changes.

From the data shown above, the calculator would create a brake proportioning plot.

As the brake designer, my objective is to design a system that is balanced such that the ‘Proportioning’ line points straight at the intersection of the ‘Lock’ lines. As well, it must provide enough mechanical advantage so a driver can reach this wheel lock with reasonable pedal force.

To help understand how to read these figures, some examples of proportioning plots for different systems are shown below.

Pedal Configuration

For the brake pedal configuration, I considered two main options: top mounted with linear master cylinders, and bottom mounted with pivoting master cylinders.

To help me choose between these, I constructed a decision matrix based on the overall team design philosophy. In this matrix, categories that could be numerically justified such as Mass, CG, and Logistics (which was based on cost) had normalized scores based on sample designs for each configuration. Other scores were chosen based on empirical research and intuition.

As shown, the matrix resulted in the selection of a bottom-mounted pedal.

Component Selection

The selection of master cylinder model was quite easy, as options for pivoting master cylinders required by my design are limited. Ultimately, the Tilton 78-Series master cylinders were chosen for their quality and availability of product information.

The calipers chosen were the Wilwood GP200. These were preferred to the PS-1 calipers used by previous teams because they were lighter and offered larger bore diameter options.

For the selection of master cylinder and caliper bore diameters, I chose the smallest master cylinder diameter and largest piston bore diameter to maximize my hydraulic advantage. This allows me to reduce the size of my pedal and rotors for easier packaging while still maintaining sufficient braking strength.

Rotor Thermal Simulations

Because the frictional coefficient of the brake pads, and consequently braking force, is dependent on temperature, I performed some thermal simulations to estimate my rotor temperature (roughly equal to the pad temperature).

For these simulations, I calculated the heat power needed to slow the car from straight-line speed to cornering speed based on the linear and angular momentum change from this deceleration, then subtracted the work done by rolling resistance. To estimate the convective coefficient, I used a flat-plate correlation equation from “The Fundamentals of Heat and Mass Transfer” along with the average center velocity of the disc. The bulk temperature was chosen to be 60 Fahrenheit based on typical weather in Woshugal MX Park where the vehicle would compete. Finally, I found the time required to perform this deceleration based on my braking force calculations.

For the numerical simulation, I applied the heat power for the time needed to slow the car and allowed 5-second cooling intervals between. I then selected a node in the friction surface region to generate a Temperature Vs Time Curve. In this plot, the friction surface converges to a temperature of approximately 420 Fahrenheit.

Although many assumptions were made for this simulation, my resulting coefficients and temperatures were all within a reasonable range based on other thermal simulations and tests of Baja SAE brakes.

Comparing the convergence temperature of 420 Fahrenheit with the Friction Coefficient Vs Temperature data for my selected brake pad suggested that I could nearly maximize the friction potential

Friction Coefficient Vs Temperature of My Chosen Brake Pad

Manufacturing & Testing

Successfully Passing Brake Tech on First Attempt

Off Road Suspension Force Calculations

After a promising review of my braking system design during the SAE Baja design season, the team leaders saw my potential for further involvement. They entrusted me with a crucial task: analyzing the forces within the suspension links to assist the designers. I tackled this challenge head-on with a methodical approach, First simplifying the suspension system of each corner into a quarter-car model.

From this model, I developed a free-body diagram (FBD) and equations of motion (EOMs) for each suspension corner.

I then wrote a Python script that implemented Euler integration to solve these EOMs, determining the position of both sprung and unsprung masses at each time step. This, in conjunction with the tire’s spring rate, allowed for the calculation of forces exerted on the wheel under various bump scenarios.

While time and budget constraints within the Baja SAE competition made physical testing of my code before vehicle design impossible, I was committed to achieving meaningful validation. To do so, I sought the expertise of Chris Bachman from Cal State, who had previously conducted similar calculations for a Baja SAE vehicle and successfully correlated them with strain gauge testing. His results demonstrated a strong agreement between calculated and measured forces on the track, providing a valuable benchmark. To establish consistency with his findings, I ran a simulation using the vehicle parameters from his research, yielding similar results. This cross-validation, even in the absence of direct physical testing, instilled confidence in the accuracy and reliability of my code.

Having established the wheel forces, the next step was to dissect their distribution through individual suspension links. To accomplish this, I employed Skyciv, a structural analysis software.

Despite its primary application in civil engineering, Skyciv’s low solve time and ease of setup for 1D beam elements made it well-suited for finding the stress distribution throughout the suspension system as a whole.

The resulting force data at each pickup point allowed the suspension designers to execute solid body FEA (Finite Element Analysis). This validated the strength of their links and informed their design decisions, ultimately contributing to the team’s success in the Baja SAE competition.

Chassis Design

Introduction

For my first season on an FSAE team, I was able to contribute as a chassis engineer. During that season, my subteam and I defined our engineering needs, made design choices accordingly, and successfully manufactured and validated our design through real-world testing.

Need Statement

“A readily adaptable, cost-effective chassis that will optimize rigidity and weight.”

High-Level Design Choices

For the vehicle chassis, a few defining decisions had to be made at the beginning of the design cycle. These choices included the configuration and material.

Configuration: Spaceframe

Material: 4130 Chromoly Steel

Torsional Rigidity

As seen in the plot, there is a point of marginal returns where it is not necessary to increase the chassis stiffness further. This occurs around 90% of full vehicle stiffness or 1960 lb*ft/deg chassis stiffness, which was chosen as our rigidity goal.

Manufacturing and Validation

Welding Jig.

Simulation Validation

Physical testing gave a torsional rigidity of 2307 ft*lb/deg, representing only a 2% error from the simulation’s prediction.

Outcomes

Although this frame did become somewhat heavy from the extra frame members required to house the team’s dual-battery system, it was extraordinarily rigid which allowed the suspension team to precisely tune their setup. As well, its ability to accommodate this unique battery was rewarded by the design judges; helping the car place in the top third of teams in the design event in TAMU’s first year competing in this category.

Learnings

With this being my first major collegiate design project, it is nearly impossible to summarize the amount of hands-on engineering knowledge I gained from this experience. Beyond all the engineering drawings, fastener types, and manufacturing processes, I learned something much deeper from this design: how to manage an engineering project in the real world. With no rubric or answer key to fall back on, me and my team had to decide what the best answers were for ourselves and be confident enough to follow through with them.

Safety Systems

Introduction

Like many racing series, the Formula SAE competition requires safety equipment for drivers to race. I was responsible for a few safety systems on our car, specifically the impact attenuator, firewall, and head restraint.

Impact attenuator

For the impact attenuator, I had the option of making a custom device or using one of the two standard attenuators. Because a custom attenuator demands extra testing time and budget while offering nearly no performance benefit, a standard attenuator was the obvious choice.

Between the two standard attenuators shown above, the honeycomb aluminum design was chosen over foam because of its smaller footprint, allowing the Aero team more space to design their nosecone.

Firewall

For the design of the structure, I utilized the Solidworks sheet metal tool, adding bends to avoid interference with the chassis. To attach the firewall, riv-nuts were used in the spots where the firewall would need to be removed and installed frequently to ease this process.

The final product was fabricated from a dual-layer system of aluminum and Nomex 410 paper.

Head Restraint

The final safety system I oversaw was the driver head restraint. It is required by rules that the mounting of this device is capable of sustaining 900N of rearward load and 300N of shear load.

For the construction of the headrest itself, I utilized HPDE backing, Confor Impact foam, and a vinyl cover. To assemble the final product, I was able to reach out to a previous team member to do all upholstery work free of charge.

Outcome

Each system obtained approval from the inspectors, making our car the first TAMU FSAE EV to pass the rigorous tech inspection.

Learnings

While the designs were primarily rules-defined, it was an enjoyable experience to explore how to adhere to those rules while creating lightweight and user-friendly products. This is a skill I could use in industry, where many designs have to be effective while following some set of rules or codes.