Vehicle dynamics for a Formula Student car, 3rd at Formula Bharat 2020

Two seasons on a combustion Formula Student car's suspension and vehicle dynamics, from tyre data to track testing. In the second season I ran the vehicle-dynamics group.

CAD render of two Formula Student cars side by side: on the left the 2020 car with its tubular rear frame, on the right the 2021 design with a plate rear bulkhead carrying the rear suspension and drive — Fig.
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The team's 2020 car and the 2021 design, in CAD
Kind
CAD render
Source
GTU Motorsports, Formula Student

Role: Vehicle Dynamics Engineer
Team: GTU Motorsports, about 25
Period: Apr 2019 to Mar 2021
Team results: Formula Bharat 2020, 3rd overall with 745 points, full marks in Acceleration and Endurance; Formula Bharat 2021 (held virtually), 5th overall, 3rd in Engineering Design
Suspension: About 3 kg removed, part by part
Tools: SolidWorks, ANSYS Workbench, MSC Adams, Lotus Suspension Analysis, Excel

Two seasons

I worked on the car's suspension and vehicle dynamics for two seasons, on the 2020 car and the 2021 design (Fig. 1). The decoupled heave and roll suspension was designed for both and ran on track at Formula Bharat 2020; Formula Bharat 2021 was held virtually, and I defended the vehicle-dynamics design to the Engineering Design judges. The organiser's certificates from both events are with the team's results in the title block (Fig. 2).

The team's first decoupled suspension

I designed the team's first suspension with independent heave and roll springs and dampers, with no reference design to follow (Fig. 3). Fig. 4 shows the split: rockers drive a heave element when the wheels move together and a roll element when they move in opposition, so heave and roll each get their own stiffness and damping.

CAD drawing, front view: pushrods from the wheels to rockers, a heave spring-damper between the rockers, and the roll spring-damper inside its cage — Fig.
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The heave and roll units with their pushrods, in CAD
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CAD render
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GTU Motorsports, Formula Student

Fig.: 4
Title: Heave and roll, decoupled
Kind: Schematic, principle only, not to scale
Source: Drawn for this site
Note: In the accent, the element that works in each case. The roll element is the unit in the damper cage.

CAD render of the damper cage: two end yokes joined by four guide rods, with a spring-damper unit and rod ends held between them — Fig.
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The damper cage: one spring-damper held between two yokes on four guide rods, loaded in compression whether the rocker pushes or pulls
Kind
CAD render
Source
GTU Motorsports, Formula Student

The roll damper is mounted so that it compresses in roll one way and extends in roll the other. A damper works both ways, but a spring only pushes back in compression, so I designed a cage that always compresses the spring-damper, whether the rocker pulls it apart or pushes it together (Fig. 5).

More depth: the full-car Adams model, the motion ratios, the cage's linear-bearing iteration and the load cases

More depth: why the cage, with the mechanism animated

Major parts in FEA

I ran FEA on every major suspension part, 5 to 10 load cases each, before it was made. The heave and roll rockers show the sequence: designed on their shafts in CAD (Fig. 6), checked in FEA under the maximum heave and roll spring forces at the element eyes (Fig. 7), and held in position for welding by a fixture (Fig. 8).

CAD renders of two rocker shaft assemblies side by side. Left: a triangular lattice-cut rocker plate on a shaft. Right: a curved lattice-cut rocker plate on a shaft that ends in a clevis. — Fig.
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The heave and roll rockers on their shafts
Kind
CAD render
Source
GTU Motorsports, Formula Student
Note
Same order as the FEA; the CAD and the FEA model differ in detail at the shaft ends.

FEA stress plots of the heave and roll rockers on their shafts: blue low stress, red high, highest where the rocker plates meet the shafts — Fig.
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Heave and roll rockers in FEA
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FEA, stress contour, scale removed
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GTU Motorsports, Formula Student
Note
Load case: the maximum heave and roll spring forces at the element eyes. Colour shows stress; values withheld.

CAD render of a welding fixture: upright locating plates on a base plate holding the lattice-cut rocker plates and their shafts in position — Fig.
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Welding fixture for the rocker assembly
Kind
CAD render
Source
GTU Motorsports, Formula Student

Part by part, in many small steps, this took about 3 kg out of a suspension that was already light: the wheel centres, the damper cage, the damper extension shaft and the rocker shafts.

A blade anti-roll bar

For the same layout I designed a blade anti-roll bar, so roll stiffness can be retuned in minutes with the same parts. Fig. 9 is the bar in CAD and one blade arm in FEA, flat and turned; Fig. 10 is why turning it works: flat, the blade bends about its thin side and is soft, on edge about its wide side and is stiff.

The plates at the blade roots set the angle (Fig. 11), and FEA at three positions, the two extremes and the middle, found the limits of its roll-stiffness range.

The blade bar and the caged roll spring are two ways to give the car its roll stiffness: the bar for a layout with plain dampers on the rocker shafts, the cage for a roll spring-damper. One or the other, never both.

CAD render of the blade anti-roll bar, a torsion tube in two sleeves with a tapered blade arm at each end; below, two FEA results of one blade arm, held at the bar and loaded at the blade tip, with the blade flat and turned — Fig.
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Blade anti-roll bar in CAD, and the blade arm in FEA with the blade flat and turned
Kind
CAD render; FEA, stress contour, scale removed
Source
GTU Motorsports, Formula Student
Note
Fixed at the bar, loaded at the blade tip. Colour runs from blue, low stress, to red, high; values withheld.

Fig.: 10
Title: The blade bar in plan, and the blade in section
Kind: Schematic, principle only, not to scale
Source: Drawn for this site
Note: b: blade width; t: blade thickness. Bending axis dash-dot, load in copper.

CAD render of one end of the blade anti-roll bar: the tapered blade arm on the torsion tube, and a perforated plate beside a teardrop plate that index the blade's angle — Fig.
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The blade arm and the plates that set its angle
Kind
CAD render
Source
GTU Motorsports, Formula Student

More depth: the bars it replaces, the sizing and the strength load cases

The rear bulkhead

With the chassis department I co-designed the rear bulkhead: a water-jet plate assembly that carries the suspension and drivetrain mounts. It was designed to stiffen the rear in torsion and shorten the car's frame. Fig. 12 is the assembly in CAD, with the rockers, the spring-dampers and the drive it carries; Fig. 13 is the 2021 design it belongs to.

CAD render of the 2021 design's rear bulkhead assembly, cropped to the plates that carry the rockers and both spring-dampers, with the drive sprocket and brake disc below — Fig.
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The rear bulkhead assembly I co-designed with the chassis department, in CAD: the plates that carry the rockers, the spring-dampers and the drive
Kind
CAD render, cropped
Source
GTU Motorsports, Formula Student

CAD render of the team's 2021 Formula Student design: orange space frame, black side bodywork, the seat, and a plate rear bulkhead carrying the rear suspension and drive — Fig.
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The 2021 design in CAD
Kind
CAD render
Source
GTU Motorsports, Formula Student

Tyre data

When the team's attempt in MATLAB stalled, I analysed the Formula SAE Tire Test Consortium data in Excel for one question: how much grip the tyres gain or lose at each level of weight transfer. Fig. 14 is the relation, not the data: two tyres sharing a load make more side force than the same two once load moves from one to the other.

The suspension and its load cases were set to manage that transfer in cornering, and I left the workflow so later team members could reuse it.

Fig.: 14
Title: Why weight transfer costs grip
Kind: Relation, not data
Source: Drawn for this site
Note: Tyre data are licensed to Tire Test Consortium members and are not shown.

Testing and setup

I planned the instrumentation in Fig. 15: damper potentiometers on the heave and roll units, steering angle, an IMU and wheel speed, with scale pads for corner weights; the key says what each one was for.

On track I ran the setup work against the model's targets: corner weights, and bump and rebound settings for the heave and roll dampers.

Sensor key
Sensor	Measures	Used for
1Damper potentiometers, heave and roll units	Damper travel and velocity	Damping settings; heave travel for ride height
2Steering angle	The driver's steering input	Reading the car's response against the input
3IMU, near the centre of gravity	Lateral acceleration and roll angle	The roll gradient
4Wheel speed, at the uprights	Speed of each wheel	Vehicle speed
5Scale pads, one under each wheel	The load on each wheel	Corner weights

Fig.: 15
Title: Sensor plan
Kind: Schematic, principle only, not to scale
Source: Drawn for this site

Running the group

I split the group's work, two engineers on a team of about 25, across suspension design, tyre analysis and steering; ran the design reviews and the simulation and FEA checks; coordinated with the chassis, powertrain, steering and braking groups; and trained team members in ANSYS and Adams.