BRAKING BAD

Braking is the first element in a Formula Student car's cornering phase. If the car isn't slowed down at the right point and with the right force on the pedal, it will compromise the remaining phases - hitting the apex, taking the right line, carrying the optimum speed through the corner, getting the power down on exit and completing a clean run to the next turn. This can have a major impact on a car’s lap time. A good brake system design provides the suitable braking power for the car to make quick corners and faster straights. The greater the average deceleration over the braking phase, lesser the time required to slow the car down for a corner and better the average speed.

Redesigning the Brake System

Here are some points to keep in mind and objectives which will help in designing the brake system:

• Balance bar and spherical bearing mounted master cylinders offer better tunability over tandem master cylinders.
• Floating rotors provide allowances for thermal expansion and caliper alignment.
• Employing tire data to get the maximum braking performance and the optimum brake torque as well as the brake bias.
• Parallelly working on selecting off-the-shelf components like master cylinders and calipers.
• Maximizing convection of rotors to maintain optimum temperature.
• Validating the above simulations using sensors.

Even if the brake system is excellent, it is the driver’s effort on the pedal that matters in the end that effectively stops the car. We can find how much pressure a driver can apply on the pedals with the help of weighing scales.

The maximum deceleration of the car depends on the properties of the tire. We employed the tire data to determine the braking torque for the front and rear. Do take a look at our MathWorks blog on the brake model which explains modelling the brake system in Simulink/Simscape.

The only physical constraint present is the dimension of the rotors which depends on the rim inner diameter. Maximizing the rotor diameter helped us to reduce the forces on the wheel assembly and to reduce the operating pressure.

 

Off the Shelf components

Calipers and master cylinders are the major components of the brake system. From the above information - braking torque and rotor size, the caliper to be used and the operating pressures are determined. We used Wilwood GP200 for all 4 corners. A master cylinder is required in order to achieve the required pressure. Using the driver effort, the pedal ratio and the master cylinder to be used for the front and rear is found.. The Tilton 77/78 series worked best for us. Other factors that we considered to select these components were cost, weight and availability.

Tilton master cylinder and Willwood brake caliper

The pedal assembly was then designed in order to get the required ratio. Essentially, the brake pedal - master cylinder combination is an inversion of the slider-crank mechanism. Various pedal positions and lengths as well as the master cylinder position were iterated to get the ratio right.

Brake pedal assembly line model in Inventor

Simulation and Validation

The rotors take up the kinetic energy lost during braking as heat energy. It is important to maintain optimum temperature to avoid brake fade and prevent altering the mechanical properties of the components. We have chosen cast iron as it has high hardness, high thermal capacity and better strength. And based on the brake pad performance, the operating temperature was chosen. The rotor geometry was designed to have maximum convection coefficient. This was done by simulating it in ANSYS Fluent. Once the required rotor profile was achieved, the transient thermal simulation was done to find the steady state temperature on the FSG autocross track. Now, it is an iterative process of getting the required convection coefficient for the optimum temperature. The final design was checked for the structural integrity by doing a fatigue simulation.

Static structural simulation in ANSYS