Brakes in Motorsport

In this article, I will look into the functionality of brakes, brake system operating conditions, the brake proportioning, rules on brakes, design of brakes, the parts that consist the braking system, the influence of coefficient of friction on ideal brake force ratio and tips on designing the brakes. Please feel free to skip to the part most relevant to you.


Functionality 

The objective of the brakes is to convert the kinetic energy that is associated with the vehicle into another form of energy, commonly heat and dissipate it into the atmosphere (although there is now regenerative braking that converts the kinetic energy into electrical energy to store for later use.
Since braking uses friction, a lot of heat is generated in the braking system, typically in the hundreds of degrees (in the order of 300 degrees Celsius).

For a motorsport practice, the functions of the race car brake system are to decelerate the vehicle in a controlled manner and, when appropriate, cause the vehicle to stop completely.


Brake System Operating Conditions

The above sentence seems pretty simple that the brake system has to decelerate the car and make it stop. However, this needs to be achieved all in sorts of varying conditions:
  • Environment - Wet or dry roads, straight line or braking on a curve, rough or smooth roads, cold or hot conditions and a split friction surface.
  • Operational circumstances of vehicle - How long are the brakes applied for? How frequently are they applied and what type of G force is being produced by the brakes?
  • Driver behaviour - Is the driver skilled and will push the brakes to the limit or a novice?
  • Brake system condition - Wet or dry brakes as well as new or worn components and lining.
This makes it clear that the brakes must be able to operate reliability and predictably under a number of diverse and extreme set of conditions since the brake system forms the most important accident avoidance system on any vehicle.

Saying this is is extremely important to remember that the effectiveness of the brakes are always ultimately limited by the amount of traction available through the tyre-ground contact patch. No matter how good the brakes seem to be on the car, if the tyres lose grip with the road surface, the car will skid and the brakes will be useless (which is why cars have ABS).


Design of a Brakes System

The brakes system consists of the following methodology:
  • Energy source - These are the components that generate, store and release energy to the braking system.
  • Wheel brakes - These generate the braking toque that creates the brake force at the wheel-road interface.
  • Modulation system - The elements that manage the distribution of braking effort for optimum braking.
  • Transmission system - These are the components through which the energy travels through.
To design a brake system, you should consider the following fundamentals:
  1. Establish the braking force distribution between the front and rear axles.
  2. Size the master cylinder, front/rear wheel cylinders and energy transmission system.
  3. Design of foundation brakes bearing in mind thermal performance, wear, noise and so on...
  4. Produce the pedal assembly and vacuum boost system.
Ultimately, all the stages are related so a system based design methodology is used to ensure a safe and reliable design. To produce a outline of the brake design, we need to know the following basic vehicle parameters:
  • Vehicle mass with driver
  • Wheelbase
  • Height of centre of gravity with driver
  • Tyre and rim size
  • The coefficient of friction between the tyre and ground
  • Maximum vehicle speed
  • Static weight distribution with driver

Brake System Components

  • Pedal assembly - The pedal assembly transmits a force and movement to the master cylinder through a linkage.
  • Foundation brakes - Is the brake going to be disc (axial) or drum (radial)?
  • Regulating valves - The regulating valves enables a degree of control to be exercised in distributing the braking effort between the front and rear axle.
  • Master cylinder - These are the components that initiates the controls braking.

Brake Proportioning

Introduction

If we know the coefficient of friction between the ground and the tyres, it is possible to determine the maximum rate of deceleration the two axle vehicle can undergo due to the brakes without the tyres slipping. To determine this, the front and rear axles need to be known which are not usually equal.
As well as this, to efficiently utilise the available adhesion between the ground and tyre, the braking effort must be split between the front and rear axle in a controlled and intelligent manner. If this does not happen, then any of the below can potentially happen:
  • For a given pedal pressure, the vehicle is not able to brake enough to provide the desired deceleration.
  • The front axle loads resulting in a loss of steering.
  • The rear axle locks causing the car to become unstable which can cause it to spin.

Static Axle Loads

To work out the static axle loads, there must be some assumptions:
  • The centre of gravity of the vehicle lies on the longitudinal centre line of the vehicle.
  • The loads on the wheels mounted to the same axle are equal. Therefore, instead of looking at specific wheel loads, axle loads will be used.
  • The vehicle is moving along a flat, level road with no camber.
With this, by creating two free body diagrams, equations can be derived to work out the maximum braking force of a vehicle.


Influence of Coefficient of Friction on Ideal Brake Force Ratio

The coefficient of friction will have a significant effect on brake forces developed at the front and rear axles. 
  • If the coefficient of friction increases, the rear axle will have too high a proportion of braking effort, causing the rear axle to lock first.
  • If the coefficient of friction decreases, the front axle will have too high a proportion of braking effort causing that axle to lock first.
Ideally, for optimum braking, both axles should lock at the same time.


Rules

For motorsport, rules make up everything. Here are some rules on the brakes for Formula Student:

The car must be equipped with a braking system that acts on all four wheels and is operated by a single control.B7.1.1 It must have two independent hydraulic circuits such that in the case of a leak or failure at any point in the system, effective braking power is maintained on at least two wheels. Each hydraulic circuit must have its own fluid reserve, either by the use of separate reservoirs or by the use of a dammed, OEM style reservoir.B7.1.2 A single brake acting on a limited-slip differential is acceptable.B7.1.3 The brake system must be capable of locking all four (4) wheels during the test specified below.B7.1.4 “Brake-by-wire” systems are prohibited.

Design

  • Pedal box - For the pedal box, the typical installation uses two master cylinders.
  • Master cylinder - There is usually one master cylinder per brake circuit. There is a range of piston sizes to choose which, along with the input force, will determine the brake line pressure.
  • Brake pedal - The brake pedal ratio should be determined before designing it since this will affect the input force on the master cylinder.
  • Balance bar - This is a bar that used to finely adjust the brake ratio (the bias between the front and rear braking effort).
  • Calliper  - The choice of calliper will depend on factors such as the size, mass, cost, pad choice, disc, size, availability, bite, coefficient of friction, temperature range, wear, fade and the thermal capacity in conjunction with the brake disc.
  • Brake disc - The brake disc has to integrate with the wheel assembly (which often rules out motorbike rotors). Factors that need to be included in the design of the brake disc are the choice of materials (cast iron, stainless steel, aluminium or carbon ceramic), ease of manufacture, cost and pad availability, mounting method (floating to reduce thermal stress?), hole/groove patters (which allow hot gases to be vented between the pad and disc, cleans the pad surface and increases bite), thermal capacity, warping, what brake fluid type to use and whether the design of the disc for both front and rear will be the same or not.
Diagram of Brake Force

Tips on Designing the Brakes

  • High temperature brakes will not work at low temperatures.
  • Do not make the pedal force to high.
  • Depending on the track layout depends on what braking your vehicle requires. For example, you do not want to overheat your brakes as the brake fluid will boil causing the pedal to become soft.
  • The track surfaces vary and weather can change. For this reason, always try to build in a bias adjuster.