Suspension & Steering
for Formula SAE
As Dynamics Lead, the design, manufacturing and assembly of the Formula SAE car's suspension was my responsibility. The overall goals for this subsystem were:
- Withstand the forces experienced from driving
- Maximize lateral force
- Provide a "flat" ride
- Provide steering feel without wearing out the driver's arms
- Have roll stiffness, toe and front caster adjustability
- Have low un-sprung mass
Vehicle Dynamics Modeling
I created a 4-DOF suspension model of the vehicle to simulate the behavior of the suspension as the car goes over bumps in the road. I derived the equations of motions and coded them in MATLAB to generate plots of interest. My goal with this simulation was to be able to optimize the rear ride frequency to minimize pitching over bumps.
I later modified this model to incorporate longitudinal dynamics, which provides a simulation of a drag race. This required inclusion of a drivetrain model and longitudinal tire model. This model is particularly useful because it contains the effect of weight transfer on longitudinal acceleration, which would allow the engineer to optimize different vehicle and suspension characteristics for acceleration.
Schematic and equations of motion for the 4-DOF half car ride model.
Additional equations required for the 4-DOF half car ride model.
Results of the FSAE car going over a small bump at 30 mph.
Varying rear ride frequency, this is the pitch angle of the FSAE car going over a small bump at 30 mph.
Visual representation of the scale of the bump.
Schematic of "drag race" model, which is just a 4-DOF half car ride model modified with:
- Driving torque on rear wheel
- Rear wheel slipping
- Traction force on rear wheel
Results of the FSAE car accelerating from a standstill over a smooth surface.
Longitudinal tire model used in drag race simulation.
Powertrain model used in drag race simulation.
Tire Analysis
Suspension design revolves around the tire, as it is ultimately responsible for making contact with the road. Using tire data from FSAE’s Tire Testing Consortium, my team and I developed simple tire models of different outputs that the tire generates to aid in our understanding of how tires work and to use in vehicle dynamics simulations.
Plot of tire data points vs. number of data points. By making several of these plots with different parameters on the y-axis, I was able to sort through the tire data and understand the conditions under which each test was done.
Lateral force curves of each tire in a turning scenario. I input my weight transfer calculations into the lateral force tire model to generate these curves.
Cornering Stiffness as a function of Vertical Load and Slip Angle.
Aligning Moment as a function of Vertical Load and Slip Angle.
Lateral Force as a function of Vertical Load and Camber Angle.
Aligning Moment as a function of Vertical Load and Camber Angle.
Kinematic Analysis
I created a model of our vehicle in ADAMS Car (using the FSAE template) to be able to analyze the kinematics of the suspension. This model was used to locate and adjust suspension parameters such as roll centers, camber and toe curves, suspension to wheel motion ratios, and anti-roll bar installation ratios. The plots shown below were the ones most useful in evaluating our suspension geometry.
SolidWorks sketch showing the hardpoint locations of this suspension. This is how I started the suspension design before creating CAD models.
Front and rear roll center vertical location as functions of roll angle.
Motion ratios (spring displacement : wheel displacement) of pushrod suspension.
Front and rear camber angles as functions of roll angle.
Front and rear toe angles as functions of roll angle.
Front Suspension & Steering
This assembly consists of double wishbone, pushrod actuated suspension with a 3-way adjustable torsion anti-roll bar. All the components were designed around coordinate points in 3D space, which were the suspension hardpoints. The bellcranks, anti-roll bar, and control arms were validated in FEA where the load cases were braking, turning and/or a combination of both.
The goal of the steering was to achieve a desired steering torque target, which was determined via calculation. The steering ended up being a lot heavier than I intended, but this could be alleviated by reducing the caster angle, of which the car probably had too much.
Front view showing the component breakdown of the front suspension and steering.
The front suspension as assembled on the car.
Rendering of the control arm welding jig. The spherical bearing cups bolted to the three posts, then the tubes were cut to length, crushed on each end to add a taper, grinded on each end to fit the curve of the bearing cups, and welded together.
FEA of the gusset plate on the lower control arm to simulate the effect of the suspension compressing.
The front pushrod suspension as assembled on the car.
The original design was to be machined out of aluminum, but Cumberland Additive offered to print some parts for us for free. After I did a quick re-design, I sent the files to them and they worked with me to get it printed. This cut down on our machining and allowed us to finish the car quickly.
FEA to determine the torsional stiffness of our front anti-roll bar. This was a previous design, which was replaced in order to increase manufacturing speed.
Rear Suspension
This assembly consists of double wishbone, pushrod actuated suspension with a 3-way adjustable torsion anti-roll bar. All the components were designed around the suspension hardpoints. The bellcranks and control arms were validated in FEA where the load cases were turning, accelerating and/or a combination of each.
This assembly originally had an anti-roll bar, but due to the car needing to be manufactured quickly, a different, larger rear sprocket had to be used, which caused the chain to interfere with the anti-roll bar location.
Rear view showing the component breakdown of the rear suspension.
The rear suspension as assembled on the car.
FEA of the bellcrank to simulate the effect of the suspension compressing.
Topology optimization of the bellcrank to minimize weight.