Braking Systems : Braking fundamentals

• Drum & disc brakes
• Coefficient of friction
• Lever/mechanical advantage
• Hydraulic pressure & force
• Brake fade
• Regenerative braking
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Drum & disc brakes

Drum brakes have a drum attached to the wheel hub, and braking occurs by means of brake shoes, expanding against the inside of the drum.
With disc brakes, a disc attached to the wheel hub is clamped between 2 brake pads.
On light vehicles, both of these systems are hydraulically operated. The brake pedal operates a master cylinder. Hydraulic lines and hoses connect the master cylinder to brake cylinders at the wheels.
Most modern light vehicles have either disc brakes on the front wheels and drum brakes on the rear, or, disc brakes on all 4 wheels.
Disc brakes require greater forces to operate them. A brake booster assists the driver by increasing the force applied to the master cylinder, when the brake is operated.
The antilock braking system prevents wheel-lock or skidding, no matter how hard brakes are applied, or how slippery the road surface. Steering stays under control and stopping distances are generally reduced.
It consists of a brake pedal, a master cylinder, wheel speed sensors, the electronic control unit or ECU, and the hydraulic control unit, also called a hydraulic modulator.

Coefficient of friction

Overview

Friction is a force that resists the movement of one surface over another. In some instances it can be desirable; but more often is not desirable.
It is caused by surface rough spots that lock together. These spots can be microscopically small, which is why even surfaces that seem to be smooth can experience friction. Friction can be reduced but never eliminated.
Friction is always measured for pairs of surfaces, using what is called a coefficient of friction.

• Low coefficient of friction for a pair of surfaces means they can move easily over each other.
• High coefficient of friction for a pair of surfaces means they cannot move easily over each other.

Coefficient of Friction

The coefficient of friction (also known as the frictional coefficient or the friction coefficient) is a scalar value used to calculate the force of friction between two bodies. The coefficient of friction depends on the materials used -- for example, ice on metal has a very low coefficient of friction (they rub together very easily), while rubber on pavement has a very high coefficient of friction (they do not rub together easily). It is interesting to note that, contrary to common belief, the force of friction is invariant to the size of the contact area between the two objects. This means that friction does not depend on the size of the objects.
The force of friction is always exerted in a direction that opposes movement. For example, a chair sliding to the right across a floor experiences the force of friction in the left direction.
Saying that rougher surfaces experience more friction sounds safe enough - two pieces of coarse sandpaper will obviously be harder to move relative to each other than two pieces of fine sandpaper. But if two pieces of flat metal are made progressively smoother, you will reach a point where the resistance to relative movement increases.
If you make them very flat and smooth, and remove all surface contaminants in a vacuum, the smooth flat surfaces will actually adhere to each other, making what is called a "cold weld". Once you reach a certain degree of mechanical smoothness, the frictional resistance is found to depend on the nature of the molecular forces in the area of contact, so that substances of comparable "smoothness" can have significantly different coefficients of friction.

Types of Friction

Static Fricton

Static friction occurs when the two objects are not moving relative to each other (like a desk on the ground). The coefficient of static friction is typically denoted as μs. The initial force to get an object moving is often dominated by static friction.

Kinetic Friction

Kinetic friction occurs when the two objects are moving relative to each other and rub together (like a sled on the ground). The coefficient of kinetic friction is typically denoted as μk, and is usually less than the coefficient of static friction.
Examples of kinetic friction:

• Sliding friction is when two objects are rubbing against each other. Putting a book flat on a desk and moving it around is an example of sliding friction.
• Rolling friction occurs when the two objects are moving relative to each other and one "rolls" on the other (like a car's wheels on the ground). The coefficient of rolling friction is typically denoted as μr.
• Fluid friction is the friction between a solid object as it moves through a liquid or a gas. The drag of air on an airplane or of water on a swimmer are two examples of fluid friction.

When an object is pushed along a surface with coefficient of friction μk and a perpendicular (normal) force acting on that object directed towards the surface of magnitude N, then the energy loss of the object is given by:
U = N μk d
Where d is the distance travelled by the object whilst in contact with the surface. This equation is identical to Energy Loss = Force x Distance as the frictional force is a non-conservative force.
Note: this equation only applies to kinetic friction, not rolling friction.
Physical deformation is associated with friction. While this can be beneficial, as in polishing, it is often a problem, as the materials are worn away, and may no longer hold the specified tolerances.
The work done by friction can translate into deformation and heat that in the long run may affect the surface's specification and the coefficient of friction itself. Friction can in some cases cause solid materials to melt.
Friction may occur between solids, gases and fluids or any combination thereof. See aeroscentics and hydroathletics.

Reducing Friction

A common way to reduce friction is by using a lubricant such as oil that is placed between the two surfaces, often dramatically lessening the coefficient of friction. The science of friction and lubrication is called tribology. Superlubricity, a recently-discovered effect, has been observed in graphite: it is the substantial decrease of friction between two sliding objects, approaching zero levels - a very small amount of frictional energy would be dissipated due to electronic and/or atomic vibrations.
Lubricants to overcome friction need not always be thin, turbulent fluids; acoustic lubrication occurs when sound (measurable in vacuum by placing a microphone on one element of the sliding system) permits vibration to introduce separation between the sliding faces. World War II Panzer tank treads lubricated by their own squeak provide the most famous, if serendipitous, example.

Anti-Friction Technology

AF coatings (anti-friction coatings) have been successfully used for years as an element of heavy-duty lubrication. Typically used for applications where a permanent lubricating film is needed for metal-to-plastic or plastic-to-plastic lubrication, AF coating technology offers an economic solution to a wide range of engineering problems.
The usage of AF coatings, such as Molykote® brand or other prominent anti-friction coating brand, is most successful when requirements for wear and corrosion protection and optimal coefficient of friction are properly met. A low, high, or even constant coefficient of friction is achievable, if the appropriate application and type of AF coating is utilised.
A firm, completely dry, and non-contaminating lubricating film results once it is properly prepared and applied. The AF coating generally consists of the resin (epoxy, phenolic, and silicone) - a base material, which adheres well to the surface. Solid lubricants such as MoS2, PTFE, polyamide, polyethylene, and Graphite are set in this base material, passing on the anti-friction properties of an AF coating.
Water-dilutable AF coatings, coatings low in solvents, as well as non-combustible or electrostactically sprayable AF coatings, are now being offered to help save energy and meet environmental protection regulations.
Many products using AF technology offer corrosion protection in excess of normal industrial requirements, while some are unaffected by fuels, solvents, or oils.
Application is typically simple: preferably by spraying, dipping, or brushing on thoroughly degreased metal surfaces. The drying and curing times are short (between three minutes for air-drying and sixty minutes) for oven cured coatings.

Lever/mechanical advantage

Levers In physics, a lever (from Old French levier, the agent noun to lever "to raise", c. f. levant) is a rigid object that is used with an appropriate fulcrum or pivot point to multiply the mechanical force that can be applied to another object. This is also termed mechanical advantage, and is one example of the principle of moments. The principle of leverage can also be derived using Newton's laws of motion and modern statics.

Early studies

The earliest remaining writings regarding levers date from the 3rd century BC and were provided by Archimedes. Give me the place to stand, and I shall move the earth is a remark of Archimedes who formally stated the correct mathematical principle of levers (quoted by Pappus of Alexandria).
In ancient Egypt, constructors used the lever to move and uplift obelisks weighting more than 100 tons.

Force and levers

The force applied (at end points of the lever) is proportional to the ratio of the length of the lever arm measured between the fulcrum and application point of the force applied at each end of the lever. Mathematically, this is expressed by M = Fd.

The three classes of levers

There are three classes of levers representing variations in the location of the fulcrum and the input and output forces.

First-class levers
	Examples: Seesaw (also known as a teeter-totter) Crowbar (removing nails) Pliers (double lever) Scissors (double lever) An oar when used for rowing, steering, or sculling
Second-class levers
	Examples: Wheelbarrow Nutcracker (double lever) Crowbar (forcing two objects apart) The handle of a pair of nail clippers
Third-class levers
	Examples: Human arm Tongs (double lever) (where hinged at one end, the style with a central pivot is first-class) Catapult and fishing rod (catapults that act as a see-saw, catapulting their load when something of great mass lands on the board on the opposite side of the fulcrum are first-class levers. Third-class catapults would be similar to the following: take a bobby-pin and bend it so that it looks like the upper-case letter "L." Then, take one arm and staple it to a wooden board. Then bend the free arm towards the stapled arm, and if released, this can be used to send things flying! You have just made yourself a third-class catapult.) Any number of tools, such as a hoe or scythe The main body of a pair of nail clippers, in which the handle exerts the incoming force

Mnemonic

A mnemonic for remembering the three classes of levers is the word flex, where the letters f-l-e represent the fulcrum, the load, and the effort as being between the other two, in the first-class lever, the second-class lever, and the third-class lever respectively.

Mechanical advantage

In physics and engineering, mechanical advantage (MA) is the factor by which a machine multiplies the force put into it. The mechanical advantage can be calculated for the following simple machines by using the following formulas:

• Lever: MA = length of effort arm ÷ length of resistance arm.
• Wheel and axle: A wheel is essentially a lever with one arm the distance between the axle and the outer point of the wheel, and the other the radius of the axle. Typically this is a fairly large difference, leading to a proportionately large mechanical advantage. This allows even simple wheels with wooden axles running in wooden blocks to still turn freely, because their friction is overwhelmed by the rotational force of the wheel multiplied by the mechanical advantage.
• Pulley: Pulleys change the direction of a tension force on a flexible material, e.g. a rope or cable. In addition, pulleys can be "added together" to create mechanical advantage, by having the flexible material looped over several pulleys in turn. More loops and pulleys increases the mechanical advantage.

Mechanical advantage

Consider lifting a weight with rope and pulleys. A rope looped through a pulley attached to a fixed spot, e.g. a barn roof rafter, and attached to the weight is called a single fixed pulley. It has a MA = 1, meaning no mechanical advantage (or disadvantage) however advantageous the change in direction may be.
A single moveable pulley has a MA = 2. Consider a pulley attached to a weight being lifted. A rope passes around it, with one end attached to a fixed point above, e.g. a barn roof rafter, and a pulling force is applied upward to the other end with the two lengths parallel. In this situation the distance the lifter must pull the rope becomes twice the distance the weight travels, allowing the force applied to be halved. Note: if an additional pulley is used to change the direction of the rope, e.g. the person doing the work wants to stand on the ground instead of on a rafter, the mechanical advantage is not increased.
By looping more ropes around more pulleys we can continue to increase the mechanical advantage. For example if we have two pulleys attached to the rafter, two pulleys attached to the weight, one end attached to the rafter, and someone standing on the rafter pulling the rope, we have a mechanical advantage of four. Again note: if we add another pulley so that someone may stand on the ground and pull down, we still have a mechanical advantage of four.
Here are examples where the fixed point is not obvious:
A man sits on seat that hangs from a rope that is looped through a pulley attached to a roof rafter above. The man pulls down on the rope to lift himself and the seat. The pulley is considered a movable pulley and the man and the seat are considered as fixed points; MA = 2.
A velcro strap on a shoe passes through a slot and folds over on itself. The slot is a movable pulley and the MA =2.
Two ropes laid down a ramp attached to a raised platform. A barrel is rolled onto the ropes and the ropes are passed over the barrel and handed to two workers at the top of the ramp. The workers pull the ropes together to get the barrel to the top. The barrel is a movable pulley and the MA = 2. If the there is enough friction where the rope is pinched between the barrel and the ramp, the pinch point becomes the attachment point. This is considered a fixed attachment point because the rope above the barrel does not move relative to the ramp. Alternatively the ends of the rope can be attached to the platform.
Inclined plane: MA = length of slope ÷ height of slope. Generally, the mechanical advantage is calculated thus:
MA = (the distance over which force is applied) ÷ (the distance over which the load is moved)
also, the Force exerted IN to the machine × the distance moved IN will always be equal to the force exerted OUT of the machine × the distance moved OUT. For example; using a block and tackle with 6 ropes, and a 600 pound load, the operator would be required to pull the rope 6 feet, and exert 100 pounds of force to lift the load 1 foot, therefore:

• (force IN 100 × distance IN 6) = (force OUT 600 × distance OUT 1)or,
• WORKin = WORKout

This requires an ideal simple machine, meaning that there are no losses due to friction or elasticity. If friction or elasticity exist in the system efficiency will be lower; Workin will be greater than Workout
Mechanical advantage also applies to torque. A simple gearset is able to multiply torque.

Type of mechanical advantage

There are two types of mechanical advantage:

• Ideal mechanical advantage (IMA)
• Actual mechanical advantage (AMA)
  

Ideal mechanical advantage

The ideal mechanical advantage is the mechanical advantage of an ideal machine. It is usually calculated using physics principles because we have no ideal machine. It is 'theoretical'.
The IMA of a machine can be found with the following formula:
IMA = DE / DR
where DE equals the effort distance and DR equals the resistance distance.

Actual mechanical advantage

The actual mechanical advantage is the mechanical advantage of a real machine. Actual mechanical advantage takes into consideration real world factors such as energy lost in friction. In this way, it differs from the ideal mechanical advantage, which, is a sort of 'theoretical limit' to the efficiency.
The AMA of a machine is calculated with the following formula:
AMA = R / Eactual where
R is the resistance force,
E Actual is the actual effort force.

Hydraulic pressure & force

Overview
Hydraulic brake systems use a incompressible fluid, such as brake fluid or oil, to transmit forces from one location to another within the fluid. Most automobiles use hydraulics in the braking systems.Pascal's law states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container.
Hydraulic pressure is transmitted through liquid. Since liquid is effectively incompressible, pressure applied to a liquid is transmitted without loss throughout the liquid. In a braking system, this allows a force applied to the brake pedal to act upon the brakes at the wheels.
Hydraulic pressure can transmit increased force. Since pressure is force per unit area, the same pressure applied over different areas can produce different forces - larger and smaller.
This system has cylinders of different sizes. When the brake pedal is pressed, the force against the piston in the master cylinder applies pressure to the fluid. This same pressure is transmitted throughout the fluid, but it has a different effect on each piston in the other cylinders. The top cylinder is smaller than the master cylinder, so the force it exerts will be less than the force applied to the master cylinder. The middle cylinder is the same size as the master cylinder so the force from it will be the same too. The bottom cylinder is larger than the master cylinder, and so is its force.

Pressure

Pressure is the application of force to a surface, and the concentration of that force in a given area. A finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a thumbtack can easily damage the wall, even though the force applied is the same, because the point concentrates that force into a smaller area.
More formally, pressure (symbol: p or P) is the measure of the normal component of force that acts on a unit area, see also stress (physics):
p = F/ A
where:

• p : is the pressure
• F : is the normal component of the force
• A : is the area

Often 'F' is taken to be the magnitude of the mean vector force normal to the surface of area A upon which it exerts; the "surface" not necessarily being a that of a body, but for example the cross sectional area of a conduit.
The gradient of pressure is force density.
Pressure is sometimes measured not as an absolute pressure, but relative to atmospheric pressure; such measurements are sometimes called gauge pressure. An example of this is the air pressure in a tire of a car, which might be said to be "thirty PSI", but is actually thirty PSI above atmospheric pressure. In technical work, this is often written as "30 PSIG" or, more commonly, "30 psig", though other methods which avoid attaching this information to the unit of pressure are preferred. 1
In the human body, pressure is measured by baroreceptors.
"Pressure is a scalar quantity, but teachers and authors do not appear to believe this in their hearts." (McClelland, 1987)

Scalar quantity

Let us look at a static gas; one that does not appear to move or flow. While the gas as a whole does not appear to move, the individual molecules of the gas, which we cannot see, are in constant random motion. Because we are dealing with a nearly infinite number of molecules and because the motion of the individual molecules is random in every direction, we do not detect any motion. If we enclose the gas within a container, we detect a pressure in the gas from the molecules colliding with the walls of our container. We can put the walls of our container anywhere inside the gas, and the force per area (the pressure) is the same. We can shrink the size of our "container" down to an infinitely small point, and the pressure has a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has a magnitude but no direction associated with it. Pressure acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular to the surface.

Hydrostatic pressure

Hydrostatic pressure is the pressure due to the weight of a fluid.
where:

• ρ (rho) is the density of the fluid
• g is the acceleration due to gravity
• h is the height of fluid above the point being measured

Units

The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N·m-2 or kg·s-2·m-1). This special name for the unit was added in 1971; before that, pressures in SI were expressed in units such as N/m²
Non-SI measures (still in use in some parts of the world) include the pound-force per square inch (PSI) and the bar.
The cgs unit of pressure is barye (ba). It is equal to 1 dyn·cm-2.
Pressure is still sometimes expressed in kgf/cm² or g/cm² (often as kg/cm² and g/cm² without properly identifying the force units). The technical atmosphere (symbol: at) is 1 kgf/cm².
In the United States air pressure is still measured in inHg — inches of mercury (as in the mercury barometer). Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, because it gives the same numbers as the older millibar (mbar).
The standard atmosphere (atm) is an established constant. It is approximately equal to typical air pressures at sea level and defined to be standard atmosphere = 101 325 Pa = 101.325 kPa = 1013.25 hPa.
Non-SI units presently or formerly in use include the following:

Atmospheres

Manometric units:

• Centimetres, inches and millimetres of mercury
• Millimetres, centimetres, metres, inches and feet of water

Customary and foot-pound-second units:

• Kips, tons-force (short), tons-force (long), pounds-force, ounces-force, and poundals per square inch
• Pounds-force, tons-force(short) and tons-force (long) per square foot

Non-SI metric units:

• bars and millibars
• Kilograms-force (kiloponds), grams-force, tonnes-force (metric tons-force), newtons and dynes per square centimetre
• Baryes = dyn/cm² and technical atmospheres = kgf/cm²
• Kilograms-force and tonnes-force per square metre

Brake fade

In automobiles, fade, or brake fade is the reduction in stopping power caused by a buildup of heat in the braking surfaces (and in the case of drum brakes the change in dimension of components in response to heat). It occurs most often during high performance driving or when going down a long, steep hill. Owing to their configuration this is more prevalent in drum brakes. Disk brakes are much more resistant to brake fade and have come to be a standard feature in front brakes for most vehicles but the brake rotors can become warped due to excessive heating.
Brake fade and rotor warping can be reduced through proper braking technique; When running down a long downgrade that would require braking simply select a lower gear (for automatic transmissions this may necessitate a brief application of the throttle after selecting the gear). Also, periodic, rather than continuous application of the brakes will allow them to cool between applications. Continuous light application of the brakes can be particularly destructive in both wear and adding heat to the brake system.

Regenerative braking

Regenerative braking is any technology that allows a vehicle to recapture and store part of the kinetic energy that would ordinarily be lost when braking. A simpler technology that can only convert the energy to heat but which uses similar principles is known as dynamic braking. Both are most commonly seen on electric or hybrid vehicles. Braking is accomplished by electrically switching motors to act as generators that convert motion into electricity instead of electricity into motion. Traditional friction-based brakes must also be provided to be used when rapid, powerful braking is required. Estimates currently see 30% efficiency; however, the actual efficiency depends on numerous factors, such as the state of change of the battery, how many wheels are equipped to use the regenerative braking system, and whether the topology used is parallel or series in nature.
Electric railway vehicles feed the recaptured energy back into the grid, while road vehicles store it for re-acceleration using flywheels, batteries or capacitors. Older dynamic brake systems generally used the electricity to provide heat or just passed it through large banks of resistors to dissipate the energy.