The automotive brake system works on three fundamental theories: Pascal's Law, leverage and friction. When all three of these theories are applied, we can begin to understand car brakes.
Pascal's Law deals with the way fluids act in a closed hydraulic system. Without this closed hydraulic system, no pressure can be developed in the brake system. Archimedes broadened our knowledge of the principles of using leverage to do work in the 400s B.C. Without applying these principles, enough force cannot be applied to the system to do the work in the first place. Principles of friction and thermodynamics allow us to determine the proper materials to use in a brake pad or shoe and design the system as whole to operate in usable temperature range.
Pascal's Law
Pascal's Law states that, because fluids are virtually non-compressible, any force applied to a closed hydraulic system will be felt equally and instantly throughout the entire system. It goes on to show that when a force is applied to one cylinder of a closed system, the output is directly proportionate to the ratio of the input to output pistons.
If we look at how the brakes stop your car, it becomes apparent that the forces required are many times the force that can be applied to the brake pedal by the driver. So, when designing the brake system, we need ways of multiplying the driver-applied force. One of the ways this is done is to increase the size of the output piston; in this case, the caliper piston. If a typical input piston size in the master cylinder is 1 inch, and a typical output piston size is 2 inches, we double the output force.
Now for the downside. We also double piston travel on the input side when we double output piston size. This means if the input piston is half the size of the output then the input must travel twice as far to make up for the added volume behind the output.
So, it's a trade-off. We can multiply the force the driver applies to the system by increasing the output piston size. But when we do that, we also increase pedal travel. The design process is in a delicate balance here.
Leverage
We have increased the force of the driver's input, but it is not enough. We need another way to increase that force. Leverage is used to do that. A lever and fulcrum is a simple machine that increases output force by trading it for distance.
The use of leverage to increase driver input force is in the brake pedal assembly itself. This type 2 lever assembly gives us a typical brake pedal ratio of 3 to 1. The distance from the fulcrum to the input end is 9 inches, and the distance from the fulcrum to the output end is 3 inches. As a result, this ratio triples the output force from the input force.
For example, if the driver applied an input force of 100 pounds, the output would be 300 pounds. So, just as with Pascal's Law, the output is directly proportionate to the input to output ratio.
Friction
All this brings us to the final piece of the puzzle. Friction can be defined as the resistance of motion relative to objects in contact with each other. More simply put, the amount of force required to slide one object over another. This force varies according to weight and material type. Some materials weigh less or are, by nature, slicker.
If we can understand the moving vehicle to be a kinetic energy source, then to stop that energy, we must convert it to another type of energy. The first law of thermodynamics addresses conservation of energy and states we can't add to or take away from energy, we can only convert from one form of energy to another. In the automotive brake system, we do this by converting the kinetic energy of the moving vehicle into heat energy.
The material in a brake shoe or pad should be hard enough to resist wear, but soft enough to generate good friction. An example to start with is a billiard ball rubbed on a glass table top. Since both objects are hard, less friction is developed and less heat is generated. How about a rubber block on a concrete floor? We are getting closer, but the rubber block will wear rapidly. A lot of friction, but no durability.
This is why the automotive friction material is a composite of materials, including carbon and bronze. Carbon is hard and has good wear characteristics; bronze is soft and has good co-efficient of friction characteristics. These materials allow us to generate maximum energy conversion with good durability.
Conclusions
Pascal's Law gives us the ability to transmit force to the brake components and increase that force. Leverage allows us another increase in applied force, and friction allows us to use that force to convert kinetic energy to heat energy and slow the vehicle down.
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