FSAE Outboard Suspension Design

This is the second year that I am my Formula SAE team's Lead Suspension Engineer and this past summer I designed and developed our latest car's (named F32) outboard suspension. This subsystem on the car includes the hub & wheel center assemblies as well as the uprights. Looking back on it, it was a tremendous learning experience and had greatly developed my design and analysis skills.

Final Front Outboard Suspension Assembly Design

Below is a basic diagram of the design process that I followed while designing this. I find that this is a helpful diagram for teaching new engineers on the team the basic steps that should be taken when designing. This is also the order in which I will step through in this post.

Diagram of The Design Process

Objective

For this system of the car, the objective was to efficiently design a robust and serviceable outboard suspension assembly. To me, efficiently designing something is when just the right amount of iterating is performed and it something that I honestly need to practice more. I found it very easy to get stuck in an endless cycle of iteration trying to optimize as much as possible. There came a point when I had to call it quits and stop iterating. This is perhaps the greatest thing I learned throughout designing this system.

Constraints

My first constraint was time. For suspension group, I had set a group design freeze date of August 20th. Since design was being started back towards the end of May, I had broken up mine and other group members work into smaller groups and created a timeline (seen below) to ensure our deadline would be met. In the timeline I am designer 1. For the design of the outboard assembly, I had a total of 7 weeks of design time as seen below.

Group Timeline

The next constraint was space. There are two main contributors for the amount of space I could work with. The first being the size of the wheel shell and the other being the location of the outboard suspension kinematic points. For F32, we decided to go with a 16" tire which gave me a cylinder of about 9.5" in diameter to fit everything within. After determining the amount of space I had to work with, I then identified the maximum loading expected to be seen by the different components in the system. The loads were provided by our vehicle dynamics group which ran lap time simulations of the car to generate tire contact patch forces expected to be seen by the car. I took all of these forces and compiled them into a spreadsheet where I went through and found the scenarios which generated the highest amount of forces in the different suspension components through static analysis. The full breakdown of these maximum loads can be seen below.

Maximum Force in Front and Rear Suspension Components

There are also other design constraints that I had taken into consideration while designing including cost. The team has a tight budget so it is important to design economically. I did this by using sponsored items when possible and choosing materials/parts that primarily met my major needs. There were many materials and parts used in this assembly that were not my "dream" picks but I picked them because they had a good performance to cost benefit. If cost were not an issue then different choices would have been made. Another constraint followed throughout this design was the design for manufacture-ability. All of the custom metallic parts in the assembly are machined in-house by fellow team members so it is important that the parts I design can not only be machined by machinists of a certain skill level, but must also not exceed the capabilities of out machines. There are a few other small constraints followed throughout this design but these are the major ones that I felt should be identified.

Final Design

For time and length purposes, I will not be showing multiple iterations of the design, analysis, and evaluation steps but will be going over the steps taken to help me arrive at the final design.

Hubs and Wheel Center Design and Analysis

It is important to note that the following goes over the design process for the front hub and wheel center, the same steps were taken for the rear but are not shown for sake of length. There are images of the final designs for both front and rear at the end.

Exploded View of Hub and Wheel Center Assembly (Front)

To start with, I had gone through the process of selecting wheel bearings as these will help determine the geometry of everything else. The first step in this, was determining the maximum amount of force that is expected to be seen in each bearing for both the front an rear. This was done by performing a static analysis as seen in the diagram below. In the diagram, B1 and B2 are the bearing locations which act as the supports in the system and the tire contact patch force is applied at Fx,y,z.

Diagram of Static Analysis of a Wheel Hub

Resulting from my calculations, I had determined that the maximum amount of radial and thrust load any one wheel bearing should see on the entire car was 4500 lbf and 1000 lbf respectively. As SKF is one of our major sponsors, I went through their catalogue and selected a deep groove ball bearing with and inner bore of 80mm and an outer race diameter of 100mm. The reason I chose a deep groove ball bearing opposed to a tapered roller bearing is that the thrust loads seen are low enough to where a deep groove can be used and the expected lifetime of the rotating components on the car are also low enough where the thrust loading can be sustained for my use case. All of the rotating components of the wheel assemblies are designed to a 40 hour running time life. To ensure the bearings would last, I used SKF's bearing life calculator and the bearings I selected came in with an expected life of 41.3 hours.

The other components that are designed to a 40 hour running life are the hubs and wheel centers. Since both of these components are rotating, they undergo cyclical loading and more of it compared to other components on the car so fatigue is a concern. To start the analysis process for fatigue, data from an IMU and wheel speed sensor was collected on our previous years car during endurance at competition. The IMU allowed me to determine an acceleration that can be later used to determine an equivalent load. To get an acceleration value, I ran the data through a custom MATLAB script that filtered the data then created a histogram of different acceleration values, result seen below.

Acceleration Values Compiled Into a Histogram

From this, the rainflow counting method is used which weighs the severity of different acceleration values along with how often it occurs. This results in a singular acceleration value with x, y, and z components which is used to determine an equivalent load for fatigue analysis. The equivalent load is in the form of a contact patch force which is determined through a lap time simulation with the previously found acceleration as the input.

The wheel speed sensor data is used to determine a cycle count expected for a 40 hour running life. This is done by using the same custom MATLAB script which sorts wheel speed data based on the amount of time spent at each speed, the results from this can be seen below. The frequency and speed of the car is then used to generate the number of cycles that is expected over the course of the cars driving life.

Graph Displaying Time Spent at Various Speeds Throughout and Auto Cross Lap

After this, I applied a FOS of 1.5 on the cycle count and determined a material allowable based on the S-N curve for 7075 Aluminum. This allowable would be used for both the hubs and wheel centers. I also determined the material allowable maximum stress for analyzing the maximum loading that each component can handle. Both the fatigue allowable and max stress allowable can be seen below.

Fatigue Allowable Results

Max Stress Allowable

With the material allowable determined, I did hand calculations for simple failure scenarios. Some of the calculations include thread tearout, bearing stress, axial and shear failure of bolts. An example of some of the hand calculations can be seen below for the wheel lugs.

Example Hand Calculations For Wheel Hub Lug Bolts

Along with these hand calculations I modeled the hubs and wheel centers alongside them. Running a finite element analysis (FEA) on them many times to do my best to optimize their strength and weight. Many different FEA setups were performed to properly analyze them but I will give an overview of the setup for the fatigue loading in the front. Below is the setup for the forces and supports.

Setup of Loads and Supports for Front Hubs and Wheel Centers

For this, a remote force is applied to the outside surface of the wheel shell located at the center of the tire contact patch. Bolt pretension is applied to the wheel lugs determined by the torque spec which was calculated prior. Cylindrical supports were applied to the wheel bearings with tangential motion free and radial and axial motion fixed. Another cylindrical support was applied to the outside surface of the rotor which was fixed in the tangential direction and free in the radial and axial directions. This same setup was also used with the entire assembly rotated 45 degrees so the wheel lugs form a square instead of a diamond. This is to analyze this assembly at the two extremes. After the supports and loads are applied, I applied a mesh to everything. The final mesh can be seen below and ended up being around 760k elements.

Example of Mesh Applied to Analyze Hubs and Wheel Centers

I also went through and specified all of the contacts in the assembly. With this done I ran the simulation and review my results. And example of the results from the final versions of the hubs and wheel centers can be seen below.

Results From a Fatigue Simulation on the Front Wheel Center

Results From a Fatigue Simulation on the Front Hub

I was pretty happy with all of the results from all of the different FEA setups that I did on these. There are some spots that go over the allowable according to the results but these are all cases of bearing stress. I performed hand calculations for all of the holes with bolts going through them which proved these red spots should not be of concern. Other simulations that I ran on the assembly was a max braking load case, max static loading, and as previously mentioned these load cases were all simulated with the assembly at 90 and 45 degrees.

Uprights

It is important to note that the following goes over the design process for the front upright, the same steps were taken for the rear but are not shown for sake of length. There are images of the final designs for both front and rear at the end.

Exploded View (Left) and Side View (Right) of Front Upright

Since the wheel bearings and hubs had already been designed and the outboard kinematic points were already determined by this point, a lot of how the upright would look was already decided. It was my job to bring everything together and figure out caliper mounting. For the material, 7075 T7 was used for the upright and 7075 T6 for the camber shoe and camber shims. Ideally, T6 would have been used for the upright as it has a greatly UTS and yield strength for nearly identical density. T6 was not used for the upright as sourcing for the proper sized stock was rather difficult and it started to cut too much into the available design time that I had. For everything in this sub-assembly, it has the allowables seen below.

Material Allowables For Uprights and Camber Shoe & Shims

After determining allowables, I identified the different worst-case load cases that the upright is expected to see. Below are the different load values. There are three load cases that cover the maximum loading at each outboard point (the UBJ, LBJ, and steering/toe) and also maximum braking torques.

Max Loads For Front Uprights

Max Braking Torques for Front and Rear Uprights

With the loads and material allowables, I began doing some simple hand calculations for key geometry. The first hand calculations I did was to determine the minimum tang thickness at each of the three ball joints. For this, I did a bearing stress and shear stress calculations for the tangs and this can be seen below.

Tang Thickness Hand Calculations for Front Upright

Next I made sure the bolts I planned on using, AN3 10-32, would not shear with a hand calculation seen below.

Bolt Shear Stress for Highest Loaded Ball Joint on the Front Upright

The next hand calculations I did were not for determining structural capabilities of the upright but instead were calculations to ensure the desired range in camber adjustment could be achieved. Camber is one of the many things we tune on the car and being able to discretely and rapidly adjust it is important. My aim was to achieve a max positive camber of +1 degree and a max negative camber of -3 degrees. Below are the results from my calculations which uses the distance between the upper and lower ball joints and a changing y-distance on the UBJ to determine camber with different camber shim thicknesses.

Camber Calculations for Front Upright

Following these hand calculations I did lots of FEA on them and did many iterations to make optimize weight, strength, and rigidity. Many load cases were analyzed for in with FEA but I will go over the setup for max loading at the UBJ and also maximum brake torque.

The first thing I did to setup the FEA simulation, was import geometry and assign the different parts of the assembly their appropriate materials. Next, I went through and defined all of the different contact regions. Following this I setup the loads and supports to constrain the upright. Below is the setup for the max loading at the UBJ.

Loads and Supports Setup for the Front Upright (Max Load at UBJ)

For this setup, there are two cylindrical supports and three applied loads. The first set of cylindrical supports are applied to the inner faces of the wheel bearings. For these, tangential motion is free and radial and axial motion is fixed. The next set is applied to the inside of the brake caliper mounting holes. For these axial and tangential motion are free and radial motion is fixed. The three load s are applied to each of the ball joints. The next setup is to analyze for max braking torque and can be seen below.

Loads and Supports Setup for the Front Upright (Max Forward Braking Torque)

Similar to the last setup, there is a set of cylindrical supports on the inner face of the wheel bearings with tangential motion free and radial and axial motion fixed. Opposite to the last setup, the three ball joints in this one are fixed supports. The load being applied for this one is a moment applied to the working surface of the brake pads. The two bolts mounting the caliper also have an applied pretension of 1500lbf each. After setting up the loads and supports for each of these, I created a mesh for each setup. Images of both can be seen below.

Mesh of Max Ball Joint Load Case (Left) and of Max Brake Torque Setup (Right) for Front Uprights

With all of this setup, I ran many simulations of the upright to do my best to optimize for strength, weight, and rigidity. After many iterations I arrived at the design that has been seen in all of the previous images. Some of the results can be seen below.

Max Steering Front Upright Results

Front Camber Shoe Results

Max Braking Front Upright Results

Similar to the results of the hubs and wheel centers, the peak stresses on the uprights are in the holes where bolts go through. Though they fail according to FEA, I have hand calculations to back up that these should not be a concern and pass with plenty of margin.

Final Results

Overall, this experience had not only taught me a lot about designing and analyzing a complex assembly but it also taught me the importance of communication, time management, and also the importance of not over-iterating. I found myself getting caught in a loop of iteration trying to make my design perfect where perfect is neither achievable or necessary. There comes a point in the iteration process that there are minimal performance benefits with increasing amounts of time required. Below I have decided to include more pictures of the final results for both the front and rear outboard assemblies and some of the parts that have been machined at the time of writing this.