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Abstract:

The most important utility in our lives as of today is automobiles, there is a lot of research and development is going in every section of the automobile field to give the safest possible vehicle to the world. One such is Brakes section; this is very important part in every vehicle, though we have most accurate and efficient brakes now-a-days, but they fail at the extreme conditions of heat , vibrations , high frequencies etc., this project is mainly concentrated on the aspects which are causing adverse affect to fail and create unusual  disturbances in the brakes. One such is brake squeal, an unwanted sound which is caused due to the vibration of the brake pads against the disc generating the high pitch noise. There are few other problems which leads into the high frequency problems, vibrations, tear in the brake disc etc.

Here in this project a detailed study of disc brake is taken into account by considering with two different materials cast iron and aluminium alloy. The performance of brake is studies using normal stress analysis, vibration analysis and thermal analysis. The main problem of squeal can be due to the combination of vibration in brake set-up from callipers to the brake discs. And can also due to the uneven surfaces of the brake disc which causes due to the improper heat dissipation in the brake disc, all this problems are kept into consideration and this analysis are carried out for brake disc with two different materials as mentioned. A simple change in the design of brake disc has also been done for the maximum heat dissipation and this design also studied in this extreme conditions. And these two type brake disc are compared in all its possibly calculated attributes and the best one is concluded.

Introduction:

An automobile is a creation of history when they started and now it has become a crucial part of the world. Automobile is a wheeled motor vehicle used for transporting passengers, good etc. There has been a lot of improvement in the automotive field in all ways from the past few decades. The main aim of the automotive department is to provide safest vehicle from its design to the material used for each component. Every single thing is decided on basis of the effect of it on the human lives. The vehicles we use are very efficient when compared with older generation vehicles, the safety increases with the development and technology. But there are few problems which are yet to be solved. One such is about brakes, as we know BRAKES are the most important part in the every moving body, we have seen very drastic improvement in the methods of braking system. In olden days the brakes were handled by hand and now we have disc brakes and hydraulic brakes.  But the whole concept of brakes is working on same principle of kinetic energy is converted into heat energy.

We find brakes very commonly used in cars, bikes, aeroplanes, automated machines etc. Brake is a device which decelerates the vehicle or machine by converting its kinetic energy into other form of energy, which will bring the vehicle down to the rest. We have disc brakes now which require very less amount of effort and time to stop the vehicle due to its accuracy and sensitivity; this are widely used in vehicles now-a-days. The drum brakes were used for very long time and we use even now, these were also very efficient brakes but due to the very common issues of changing the brake pads very often due to the short hand braking or improper usage, this has been replaced by disc or hydraulic in few machines. But we have found very common issues in disc brakes due to the brake rotor and brake pads. Due to the high friction while short braking we get unwanted noise brake squeal, though it doesn't have much effect on the performance of the vehicle, but it may fail the brake due to the tear of brake disc or brake pads. A detailed study of each problem will be studied in further report taking disc brake system.

History of Brakes:

Invention of brake has started with the automated machines; brakes came into light mainly when the motorised wheeled vehicles came into existence. Brakes were not only used in the vehicles, these are used in other machines as brake lever to stop the motion rotor and so on. It has been an essential part of the moving systems.

Brakes have developed a lot from first generation vehicles to present time. Early braking systems used steel rimmed wheels to stop the vehicle, which consists of curved wooden block designed to bear against the steel tire when operated by a single leverage system from the driver seat. But the brake shoe used was normal way of braking either in the horse drawn vehicle or steam locomotive. In 1895 Michelin Brothers move a step ahead to replace the steel rimmed wheels with the pneumatic rubber tire to come out with a new braking system as the brake shoes were no longer satisfactory.  A new method of braking system was required in those times as two early devices attempted to apply the friction force to the axle or to drum on axle or transmission shaft were not efficient as wanted. One method was use of wooden block inside a flexible contracting metal band which when pressed together would tighten the drum causing friction between the drum, which is connected to the wooden block and wheel, then the vehicle gets slow down. The other method was inner wheel or brake drum which will add an external contracting band to bear against the drum to bring the vehicle to rest.

In 1899 Daimler started cable operated braking system; a cable was wound around a drum and attached to the chassis, so that when the cable is tightened when car was moving forward, the rotation of drum will increase the tightness and grip of cable, so that it will reduce the amount of force required to pull the cable-lever on the pedal to stop the moving vehicle. This brake system worked well but still the braking efficiency was less, the added efficiency called servo assistance is still an important factor in drum brakes even today. The external brake was vulnerable to the atmospheric conditions like weathering and to un-even roads which caused a rapid loss of efficiency and wear of the brake shoe lining and on few times automatic brake use to happen due to the drum expansion. To overcome all these problems an internal shoe brake was developed were the expanding the brake shoes were placed the inside the brake drum, mainly to protect from the dust and weather.

Originally early brakes were operated by mechanically, i.e. the transformation by mechanical system was used to expand the brake shoes against drum by the driver's effort applied on the brake pedal. It works by pressing the brake pedal, which make cam to rotate by a lever connected to pedal, which forces the shoes to come on contact with the brake drum. And springs attached to both of the brake shoes to retain the original position when brakes are released. As the early brakes use to operate on lever supported cables and linkage system of fixed rods, equalising the same amount of brake pressure on the wheels has presented many problems , which were solved when hydraulic system was introduced, which used fluid to transfer the force applied to the brake pedal.

In hydraulic braking system the set-up of cylinders and pipe lines forms a closed system which is filled with fluid. The pressure generated in master cylinder will transmit equal force to the each wheel cylinder and then equal pressure is applied to all brake shoes. This hydraulic system is used with the disc brake as well. Disc brake is more efficient braking system which was used mostly sports car when introduced but now it has been a very common system in passenger vehicles. It has a disc and a calliper is attached to it which can be operated mechanically, hydraulically, pneumatically, electromagnetically.

Types of brakes:

The brakes are broadly explained as using friction, pumping or electromagnetism. But one brake system can also use more than one principle. As the project is based on the disc brake we will look forward only to discuss about the frictional brake.

Frictional brakes: These types of brakes are mostly rotating devices with a stationary pad attached with a rotating surface. These types of brakes are widely used even now in modern automotive braking system. Basically this are developed from band brakes to drum brakes then to the disc brakes.

Band brakes: A simple type of brake, works on a principle that a band is wrapped round the rotating drum. When a force is applied on the lever, the restraining torque is found from the difference in tension between the two ends of the belt. The principle of operation of the band brake is same as for belt drives.

This is external type braking system, as we see in picture the brake shoe are mounted on the drum.

Ref: http://school.mech.uwa.edu.au/~dwright/DANotes/brakes/intro/intro.html

Drum shoe brakes: This type of brake usually mean the brake shoe is mounted to press the inside surface of the drum. Two brake shoes are connected with a calliper set-up; it has lining on it which will create a frictional force when pressed towards the moving surface of the vehicle.

These types of drum brakes are still used in modern cars due to the some cost and engineering benefits. These are applied to the rear wheels of today cars.

Ref: http://school.mech.uwa.edu.au/~dwright/DANotes/brakes/intro/intro.html

Disc Brake: these most widely used brake of these days, A disc is mounted on the wheel or axle and brake pads are placed within the jaws of the calliper, this is give the necessary friction when it will grip on the brake disc.

Ref: http://static.howstuffworks.com/gif/disc-brake3.jpg

Characteristics of brakes:

Brakes are described on basis of several characteristics as

Peak force: The maximum force obtained to decelerate the vehicle is called peak force. Few times this can be more than the traction limit of tires, then the wheel gets skid

Continuous Power dissipation: As we know that the brakes get hot in use and get fail when the temperature gets too high, the maximum amount of power that dissipates through the brake without failure is the continuous power dissipation.

Fade: Due to the over heat of the brakes the surface of the brake pads or disc get fade which will cause decrease in the effectiveness of brakes. Few time's even cooling will have big effect on to fade.

Power: when a very less force leads to the braking force, which is higher than the other brakes in similar class then it's stated as powerful brake, which is due to the sensitivity of the brake system.

Durability: Friction brakes have the lining which has wear surfaces, these to be renewed periodically.  Like brake shoes, pads or brake disc. Even if wear surface due to brake shoe generates high peak force this will lead to wear quickly.

Weight: In some circumstances brakes are often mounted on wheels, this can disturb the traction significantly. Here weight means brake itself or an additional support structure

Noise: generally brakes create some minor noise when applied, but sometimes create a high pitch noise called squeal or grinding noise.

Principles of braking system:

Brakes work on simple principle to slow down the moving vehicle by applying an external force, it may use more than one component; directly or indirectly several components effect on the momentum of the moving vehicle. Various types of process are used for braking effect. Frictional brakes are most commonly used these days, these works on the simple mechanism of changing the kinetic energy into the heat energy, which is done by only factor friction. Friction is created when a stationary brake pad grips on the moving brake disc with a force applied.

This type of braking system is also used in the disc brakes; the stationary brake pads rub on the disc rotor which moves relatively in its own axis.

Basic laws of braking system:

Braking system can be explained by two simple Newton laws; which will explain the whole concept of the braking system

As we know that the Newton's second law "The net force on an object is equal to the its mass times its acceleration and points in the direction of the acceleration"

F = m* a

The law is used to find out the net force required by brake pads to bring the moving vehicle to rest, tough there are many other factors to be considered for calculation of brake force which will be discussed further.

It can also be explained through Newton first law "Every object remains at rest or in motion in a straight line at constant speed unless it is forced to change its state by an external force" if we check this law, an external force (brake force) is required to change the state of the vehicle (motion to rest).

As this law explained the evaluation of the brake force and system of braking, a further law explains how the brake force will stop the vehicle.

Law of thermodynamics: "Energy can neither be created nor be destroyed; it will be converted from one form of energy to other form."

This explained the frictional force (brake force) is converted into the heat energy.

Factors considered while Braking:

There are many factors to be considered for the high braking efficiency and performance; here we will see the few important factors which have a more effect on braking efficiency.

1. Condition of disc rotor: An uneven disc or ruffed disc rotor will decrease the braking effect; it has to be very well maintained as few a times due to dust and weather a extra layer is formed on the disc surface which will have a negative effect on the braking concept. Or wear of disc rotor due to overheat.

2. Pressure on brake rotor: A sufficient amount of brake pressure is to be maintained to get enough frictional force to stop the vehicle. If less pressure is applied it will directly affect the brake efficiency as force acting on the two rubbing surface will become less.

3. Contact surface: The area of contact between the brake pads and disc rotor should be more then the high friction is obtained. If lining of brake pads or surface of disc rotor is uneven then area of contact will be less, which will affect the brake efficiency.

4. Tyres: The design of tyre also have a normal affect on the brake efficiency, the more the contact of tyre to the road surface the good will be the braking system. Worn tyres will have less braking action and will not allow vehicle to stop the required point and may also skid, braking action is found high in new tyres due to its more contact with the road surface.

There are other factors which also play an crucial part in brake efficiency like aerodynamics, heat dissipation, weight of body etc.,

Causes of failure:

The most commonly found causes for the brake failure are

1. Oil or grease on the brakes will cause failure as it interferes with the friction. If we found oil in brakes mean the oil seal has failed and is why oil is leaking.

2. Overheat of brakes to great degree, which will develop a hot spot on the rotor and drums. This spots will resist the friction from brake shoe and pads, therefore braking power is lost and brake fails.

3. Brake squeal which indicates the tear in the brake pads, by the time the brakes start making a grinding sound, they would have worn out past the pads to rotors. This will require to change more than just brake pads for new one, which will increase replacement cost as well.

4. Improper wheel alignment or disturbance in the steering system will also lead into the failure of brakes. Even if the mass of vehicle will get out of its range due to extra load will cause a brake failure due to the uneven load distribution.

DISC BRAKE

Introduction: Disc brakes came into existence in 1890's in England. But due to the poor state of roads and dusty conditions the disc and pads use to get rust and get wear, so the system got non-viable at that time. But later it was fully adopted in 1950's with new innovations in the previous design. Many companies started using it in their cars as it was better when to compared with drum brakes, the main reason as it has overcome the brake fade problem by providing the resistance to the brake components and overall performance is better when compared with drum brakes.  Disc brakes become popular in sports cars due to its braking performance. Now it has been common in commercial vehicles as well, as it's used at front of the vehicles, as the front brakes perform most of the braking effort.

Components: A disc brake assembly consists of a

1. Cast-iron disc (disc rotor) that rotates with the wheel.

2. Calliper assembly attached to the steering knuckle (operated mechanically or hydraulically).

3. Friction materials (disc pads) that are mounted to the calliper assembly.

Operation: (Hydraulically powered)

Disc brakes prove to be efficient when compared with drum brakes even the working principle is same for both systems. The basic principle of braking system "The kinetic energy is converted into heat energy" 

When brake pedal is pressed, the hydraulic pressure is applied on the piston; it pushes the brake pad to get in contact with the disc. As the pressure increases the calliper pushes the outside pad to get in contact with the disc. Due the friction generated between pads and disc will create the braking force as the pads gets in contact fully with the disc rotor. But if we study the disc brakes widely, it shows that it does not use the much of the friction between the lining and rotor to increase the braking power as drum brakes does, they likely cause a pull between them.

Disc brakes have constrained self-energizing action, there has to be sufficient hydraulic pressure to get the required braking force. The braking force can be increased by changing the size of calliper piston. Even less heat dissipation occurs as the friction surface is exposed to the air, which also reduces the braking fade. 

Design of disc rotor: generally disc rotors are either solid or ventilated. The ventilated type disc rotor has cooling fins in the middle of the disc to ensure good cooling. Proper cooling ensures longer pad life and it also prevents fading. Some ventilated rotors have spiral fins which allow more air flow and better cooling. These fins are mounted on side of the vehicle and directional. Spiral fins are used in the front of the vehicles as front brakes take most of the braking action as more heat generates.

Ref: https://pontiworld.com.au

Design of calliper: The calliper are used as floating calliper or fixed calliper design, and these are mounted on the axle or attached to the wheel.

Floating calliper type: The calliper are used as floating calliper or fixed calliper design, and these are mounted on the axle or attached to the wheel.

this type of calliper requires less parts than the other type and it's also less in weight and economical. Based on requirement it consists of one or two pistons. The piston is either side of the calliper. Hydraulic pressure from the main cylinder is generated and the piston thus press the brake pad towards the disc, then instantly an equal hydraulic pressure is generated at the other side and right brake pad pushed towards disc rotor and vehicle stops due to the braking force.

Fixed calliper type: The calliper are used as floating calliper or fixed calliper design, and these are mounted on the axle or attached to the wheel.

This type of calliper design has piston on both sides of the calliper, which provides the equal force to each brake pad. These fixed calliper types can set-up either one or two pistons on each side. The two pistons can generate a more braking force and a compact design, as these absorb and dissipate more heat, due to its size and weight. This design is capable for greater number of hard stops of short brakes without the effect of brake fade.

Materials used for component:

The material used for disc rotor plays an important role in braking force. The material should be tuff enough to stand on high pressures and high friction forces. Generally cast iron is used for disc rotor commercially, but ceramic discs are used for high-performance vehicles and heavy automobiles. Recent study shows that aluminium alloys also do a great job as disc. Now we will discuss in detail about the commonly used materials cast iron and aluminium alloys.

Cast iron:

Grey cast iron alloy is used for the manufacturing of disc rotor; it has superior properties and various advantages over other materials, as it best suitable for manufacturing and machining when compared with other materials which lead to the graphite lubricating the cut and breaking the chips. It contains 2.5%-4% of carbon and greater than 2% of silicon.  This material has good wear resistance and galling which leads to self lubricating due to the graphite flakes. The graphite microstructure of grey cast iron allows less shrinkage. The silicon percentage in the grey cast iron makes the material corrosion resistance and increases its fluidity when casting which also makes material easy to weld.

Compared with other alloys of the cast iron, grey cast iron has low tensile strength , the good point about this material is the shock and impact resistance is almost doesn't exist.

Here we will see the properties of the grey cast iron for ASTM 60,

Tensile strength    62.5 Kpsi

Compressive strength 187.5 Kpsi

Shear modulus of rupture 88.5 Kpsi

Modulus of elasticity ( Tension ) 20.4 - 23.5 Mpsi

Modulus of elasticity ( Torsion ) 7.8 - 8.5 Mpsi

Endurance Limit 24.5 Kpsi

Brinerll Hardness 302 H_b

Specific heat 447 j/kg deg

Ref: http://www.engineershandbook.com

Characteristics of Grey cast iron:

Wear resistance: Grey cast iron works as excellent resistance to sliding friction wear, it is widely used for manufacturing of sliding components, most of the automobile components are made up of this item, it's all because of the low coefficient of friction, resistance to the galling it has which is due to the effect of graphite flakes . This will help the disc rotor to withstand for high friction forces.

Thermal conductivity: The important merit of grey cast iron is its high thermal conductivity, due to its flake graphite structure, heat dissipates occurs in material with good rate. This will increase the cooling of the disc rotor

Machinability: Due to the ferrite graphite structure, grey cast iron is simplest and easiest alloys for machining and casting. This will make easy to get the typical designs of the disc rotor with spiral and fins

Damping capacity: Grey cast iron has high ability to absorb vibration energy and also damping vibrations, which is due to the high percentage of the graphite flakes it has in it. It also has great property to resist high frequency vibrations. This will help disc rotor

Aluminium Alloys:

Aluminium is the important alloy of aluminium alloys, were the other metals are copper, silicon and magnesium. It has less tensile strength and low melting pointing. It has good casting characteristics due to its great levels of silicon (4-13%) in it. It is widely used as disc rotor due to its corrosion resistance.  But this is quite expensive when compared with cast iron. Though is in light in weight, has good electrical and thermal conductivity. It does also can be recyclable. All these properties brought a change in many industries to change their traditional materials i.e., aluminium alloys.

Characteristics of aluminium alloys:

Light weight: The best part of this material is its light in weight, actually its one third of steel in weight, due to its specific weight of 2.7 g/cm3. The more the energy consumed by aluminium the high will be the load capacity of the vehicle.  This will decrease the vibrations and also increases the brake efficiency due to its light weight.

Properties of the aluminium alloys:

Density     2600-2800 kg/m3

Melting point 660 deg

Elastic modulus 70-79 Gpa

Poisson's ratio 0.33

Tensile Strength 230-570 Mpa

Yield Strength 215-505 Mpa

Percent Elongation 10-25%

Thermal expansion coefficient 20.4 -25.0 10-6 /k

Thermal conductivity: it's used in most of the high conductivity line like power transmission, it has twice of the copper in the properties, and it's a good conductor of heat and electricity. This will increase the heat dissipation of the disc rotor.

Ductility and recyclability: Due to the lower density and melting point, the material is considered as ductile, this will help to the complicated design, as we need in the disc rotor with spiral fins and groves for the air dissipation. Recyclability is also one great factor of aluminium as it consumes only 5% of the energy to melt it, and it doesn't affect its original quality of aluminium.

Corrosion resistance: This is the main factor which made it to select for disc rotor manufacturing. It has a natural property of corrosion resistant as it surfaces form an oxide coating on it. While using as disc rotor further surface treatments like lacquering and anodising are done to increase its resistance towards corrosion.

Major problems with Disc Brakes:

The disc rotor of Disc Brakes is more exposed to the air, due to which there are very frequent chances of getting damaged. Usually this damage of disc rotor is explained in four common ways warping, cracking, rusting and scarring. Few a times the damage takes the disc into the unsafe area then the new disc is replaced with damaged ones. But sometimes using simple machining and other process this damages can be overcome. As scratches or damage on disc rotor can be removed by removing the thin layer on the disc on lathe machine if after that the thickness of the disc falls in the safe dimensions for the braking force.

Warping: This is caused due to the excessive heat of the friction area of the disc rotor, due to excessive shorthand braking, uneven cooling of disc may also causes warping. If braking pads get into contact of disc excessively this will lead to warping after certain times, this warping is most commonly found in the racing cars as brakes are used very frequently due to speed and used at high gear times. There are few methods which can avoid the warping, braking at lower gear which will help to reduce the braking load on the brakes, and less heat is generated. The more the braking load, the more the heat generated and more the chances of improper cooling to take place. Changing the disc design with more fins can few times avoids warping. Improper installation of disc rotor may also leads to the warping as only the overwhelmed disc will come in contact with the brake pads.

Cracking: This is found mainly in the drilled disc. Cracking occurs mostly around the edges and holes of the disc, due to the uneven expansion in severe environments. As the uneven expansion take place and the braking load varies every time the brake is applied which will lead to the cracking. And in several situations the disc will fail and no possible repair can be done. Even cracking can be overcome by maintaining proper the cooling of the disc and proper heat dissipation. If cracking is become severe then there might be a chance to replace the disc rotor.

Rusting: This is found in the vehicle which are not used for period of time, the regular use keeps the friction area clean, but when not in use the friction area and slots get rusted and it reduces the braking power, due to which the strength of the disc also falls down and at this conditions disc should replace with new one.

Scarring: Scarring occurs if something hard gets in contact with the disc while moving, which forms a hard spot on the disc, which reduces the braking power and weakens the brake. Generally this happens when the brake pad service life come to end and still its attached to the brake set-up then the steel support of the brake pad get in contact with the disc which creates a hard scratch. These scratches will form black slots when a vehicle come in use, and reduces the structure strength. This can be avoided by regular checking of brake pads checking life of the friction layer, machining the disc to remove the layer on surface of disc which removes the scratches.

There are few phenomenal problems which has been a challenging task in braking department like brake squeal, brake judder and brake dust. These problems can be dangerous when they get on excessively. Change of design, material, brake assembly setup all these have been checked extensively to find out the perfect solution for these problems, this project is undertaken based on this problems. Lets discuss in detail about these problems and what are the methods being simplified to overcome it.

Brake Squeal: squeal mean noise, this brake noise is a vehicle system problem due to the regularity and severity. The noise generated is mainly because of brake and suspension components together. This is not considered as the main problem to the vehicle were performance is the initial objective, but it's not so proper for the road use. This noise is mainly between the pad and disc during the braking. But squeal can also be combination of disc, calliper and brake pads. To avoid squeal under the braking condition is not so possible, if we are assuming brake to absorb very high energy inputs.

Actually this brake squeal came into account when front wheel drive and metallic brakes arrived. These metallic pads are harder than asbestos counterparts, and thus more squeal is observed if there are more irregularities and roughness on the rotor surface or if you found looseness between the pads and callipers. Few types of calliper designs are more noisier, if the pads of this callipers are not fitted so tightly and the calliper itself move around when brakes are applied. The more the brakes play the more are the chances of noise. Fixing the squeal problems in wrong way can lead to the squeal more worse.

Brake squeal also occurs due to vibration of brake pads towards the disc rotor when vehicle is moving at low speed, this may not affect the braking performance much but will lead to the replacement of brake pads, this is very common problem which most of the vehicles are facing now.  Lot of methods are used to reduce the level of noise,  simple methods like having chamfers to the linings, applying grease between the pads and calliper, adding the brake shim between  the brake back plate and brake pads etc., these may help in some way to reduce the noise.

Ref: http://www.aa1car.com/library/bsqueal.htm

While using the methods to reduce the brake noise, have to assume the vehicle suspension system which acts more on the braking system, but at the end the squeal is avoided by trial and error method. Although we see an efficient improvement in understanding the actual reason for the brake squeal, it has been difficult to solve it. It was easily verified through the design and study to overcome the squeal, but it was different case practically. The failure was mainly caused because of the dynamic behaviour of the braking system and due to the gap between braking components. The easiest way was using high temperature grease to the back of pad to create the damping medium between pad and piston. High friction brake pads generate the high energy at the friction surface which will lead to more brake squeal. Some brake pads generate less noise rating, due to the lower friction co-efficient. The unbalances static and dynamic values, reduction in the friction between pads and disc is also observed.

Brake Judder: This is very common complaint in most of the vehicles. The brake disc should be warped and replacement is the only sure for this problem if it gets too severe. This occurs mainly due to the uneven thickness of the rotor. Driver feels this affect when brake is applied which is due to the back-force vibration from the brake system; this effect is called brake judder.  This effect a lot on the brake performance may also cause a brake failure. This phenomenon is classified in two types of brake judder.

Hot Judder: Due to the rigorous use of braking in vehicle from high speed to slow speed this effect Hot Judder is found. Excessive heat is generated in this process which will lead to an unbalances expansion in the brake components, and hot spots form on the disc rotor which will get black spot on continuous braking. Which will reduce friction force, braking performance etc., this generally happens when we use used brake pads with new brake pads, the heat dissipation will be different on both sides of disc which lead to the brake failure due to the thickness variation of the disc rotor. This can be rectified by machining the thin layer of the disc and maintaining the thickness in safe limits. Usage of wrong brake pads with low friction and sometimes design and manufacturing defects also leads to Hot Judder

Cold judder: Cold judder causes because of using the same brake pads, disc rotor, braking components for long time without any maintenance. This will let the disc to form layers on it, due to which the thickness of the brake disc varies and it will effect when brake is applied. It creates the vibrations and creates the reverse brake force due to the uneven thickness. Failure in the maintenance and the design or manufacturing leads to the cold judder. This will lead to scratching as well when brake pads are not changed for long time.  Severity and regularity of this will lead to brake failure and have to be replaced with new set of the brake components.

Common factors of brake hot and cold judder:

Design of brake components:

The design attributes of brake components is important step, the proper design, sufficient surface finishing, machining of edges and groves getting finest smoothness of the surfaces is crucial in performance of the braking. Using of low quality of brake pads which will give lower friction and cannot perform well in high performances and also causes high vibrations. And proper fitting of brake pads and disc is common problem faced when brakes are repaired, the surface of brake pads should be parallel accurately with the disc rotor. If not, this will lead to slip and cause vibrations which lead to brake failure.

High vibrations: The vibrations with high frequency are common cause for the brake squeal. This causes due to the damaged or worn our disc, when brake is applied the brake pads come on contact with the uneven disc surface which create the vibrations due to the moments of up and down when in contact. At high speed due to the continuous vibrations and resonance of this effect will lead to the high squeal and brake failure as well.

Heat dissipation:  As we all know the basic principle of the braking system is, kinetic energy is converted into the heat energy. For good braking performance there should be more heat dissipation.  The more heat gets dissipated the less will be the phenomenal problems and properties of the braking materials will not change. The design of the disc rotor should be carefully taken so that the heat dissipation should be at good rate, this can be done by having vents, groves and fins.

Friction materials: the friction material should be well binded; the good quality of frictional materials will also give the good braking performance and also this will reduce the brake squeal. Cheap friction brake pads will remove the friction material on regular use and this will lead to the disc damage when the brake pad support gets in contact with the disc. New technologies are being used to reduce the squeal effect, a new friction material which when gets in contact with disc will leave a thin layer on the disc which will smoothen the surface and reduce the brake squeal.

Reduction of brake squeals:

Avoiding the brake squeal completely is quite impossible, but there are few factors which should be considered to reduce the brake squeal. At high braking conditions when brakes have to absorb the high energy only trial and error method can reduce the noise. But in real system in dynamic conditions have to assume the suspension system as well in settling the brake system. Many methods are being followed so far, but simple mistakes will lead to the high pitch voice so a careful inspection of every time should be taken to reduce this sound. The few methods which can benefits are:

Ref: http://www.carbibles.com/images/brakesqueal.jpg

1. Lower friction brake pads can be used which will generate high energy and there are chances of high brake squeal but most of times these are well known for generating lower noise.

2. Design of brake rotor, by increasing the surface finishing, machining the edges and fins well for good heat dissipation and using some good damping materials between brake pad and brake supports for high vibration reduction.

3. Well in time maintenance should be done and brake pads should be changed if they will bring damage to the disc rotor. And a copper slip can also be applied just to avoid the contact between grease and the brake pads.

Properties brake disc should satisfy:

Damping:

"Damping is the energy dissipation property of a material or system under cyclic stress", in bold way damping is explained as restricting the vibrations caused by dynamic oscillations or noises created by various moving parts by dissipation of some energy. If a body is in motion dynamically, a series of vibrations are found in every part of system which in directly or indirectly effects on the performance of the system, thus to reduce the vibrations in the system these damping is used. For examples a rubber sheets used under the heavy machines or a rubber layer between two components is also used for damping purpose. Achieving perfect damping is really important at industrial levels. A system is said to be well damped when it cannot vibrate. The levels of damping can be stated as, critical damping- if object doesn't vibrate at all in dynamic motion and takes shortest time to come in rest without oscillations. Under damping- if objects oscillate to and fro to come in rest after dynamic motion then it means the damping stability not as much required then its state as under damping. Over damping- In over damping there will not be any oscillations but the systems take a little more time than critical damping to come in rest that is due to the heavy friction which does not allow the mass of system to move freely.

This damping more necessary in braking system, because the most familiar problem brake squeal is caused due to the improper damping as well, the whole braking system starts vibrating along with suspension set-up which will lead to brake squeal and a high pitch of noise will be created due to resonance of vibrations. The damping capacity should be more for the component material. The relative ability of a material to absorb vibration is evaluated as its damping capacity. Now will see the damping properties of the material used for disc rotor which is grey cast iron and aluminium alloys.

Grey Cast Iron: objects made of materials with high damping capacity can reduce the noise such as squeal. Vibration is a severe problem; this can also cause failure or not truly satisfactory operation result. The exceptional damping capacity of grey cast iron is an most important characteristic of this material. This is why grey cast iron is used mainly for machine components and vehicle components like cylinder, brake components etc, Damping capacity of this material is higher when compared with the other cast irons and steel, this is because of the flake graphite structure of grey iron and also because of its unique stress-strain factors. The damping capacity varies when the strength increases as graphite present in iron is of lower strength and they start absorbing more energy. Heat treatments also work better to increase the damping capacity.

Aluminium Alloys: damping capacity of this material is quite low when compared with the cast iron, but this is preferred because, there are very few chances of variation in material properties. This is used for very fine finishing objects and also benefit is its light weight. As these have very high corrosion resistance and less tensile strength, it has good damping capacity. This is add-on material as a disc rotor with good damping and material properties which fulfil most of the braking rotor requirements.

There are different types of damping, which are used as per its suitability

Passive damping: if the energy is dissipated within the system. For example using dampers at joints and machinery support, these damping materials will absorb the energy.

Active damping: if the energy dissipated is by external means then its active damping. Like actuators used in system will help to neutralize the vibrations.

Viscous damping: if the vibration energy is converted to thermal energy, this is mainly used for accurate damping resistance, a piston is used which is fitted in the fluid medium cylinder. The fluid will absorb the vibrations and try to restore to its original position.

Structural damping: the energy loses from the system is absorbed by the system itself, such damping phenomenon is known as structural damping.

Stiffness of braking system:

Heat dissipation

FINITE ELEMENT METHOD:

FINITE ELEMENT METHOD is an computer based, approximate method for solution of engineering field problems such as, structural, electric field, fluid flow, thermal etc, this is an simple technique of finding out the solution by dividing the complex objects into the small parts. This is the most commonly used method for analyzing the engineering problems, and this is worldwide accepted method. Most difficult problems are solved by this method all small parts of the object are connected adjacently by nodes and their performance for the variables like temperature, loads, stress-strain etc.,

Now-a-days lot of work is going on FEM to solve the problems which were unsolved due to lack of technology and proper methods. And a wide area of applications has increased for most of the products as this method is used to verify the suitability as strength when it's used. The best feature of this method is implementation. Its easy and implement and watch the scenario how the product is going to affect.

Leading software for doing this method is ANSYS, which is used in this project for analysis of the disc brake. This is easy to use and it's easy to deal with complex designs and design which has more boundary conditions and nodes. Almost every engineering field industries use this tool because of its idealness in dealing with complex geometries with ease. This method is also used in the other field like medicine analysis, bio-medical etc. This method is based on the numerics and equations; the approximation is calculated and implemented in the analysis for the accurate solution. Now we will see in depth how this method is carried out and what are the important aspects while dealing with design in this method?

http://www.me.mtu.edu/~bettig/MEEM4405/lecture01.pdf

STEPS IN FINITE ELEMENT METHOD:

1. Element equations developments

2. Discretization of solution domain into finite element mesh

3. Element equations assembly

4. Defining boundary conditions

5. Unknown modal solutions

6. For each element there should be a solution and quantities related to it.

In every finite element analysis, there is few common steps noted, such as the main structure is divided into the number of small structure, this small structure is called ELEMENT. And the phenomenon used to divide the components into elements is called NODES. All these nodes can be formed from different points and they form a grid called MESH. Then when we come to nodal solutions, boundary conditions and assembly solutions all these will remain same.

Initially mathematical calculations are done to get started with the analysis with some approximation values. There are two phases in this mathematical calculation

a. Derivations of element phase, in complicated structures the element matrices are developed. The formulas used for numerical calculations of each element are developed.

b. The formulas developed are used to do calculations and write the numerical matrices of each element.

In this analysis we will be using some FEM terms which are necessary to know before using.

1. Continuum: If similar elements are in sequence in a physical body and are analysed, then it is called continuum

2. Discretization: Dividing the structure into small elements is known as discretization.

3. Nodes: The link between the two adjacent elements is called nodes

4. Elements: The each small structure generated when a complex structure is divided is called element.

5. Degree of freedom: neutralizing the attributes like displacement, rotation in axis to explain the deformation of complete finite structure.

6. Natural coordinate system: if coordinate system is used by having numbers without any dimensions at a particular point on the element, and where the value of magnitude number should not increase unity then that system is called natural coordinate system

7. Local coordinate system: if coordinate system is used only for a element then that system is called local coordinate system

8. Global coordinate system: if the coordinate system used for an element is also used to study with the whole structure then that system is called global coordinate system.

9. Displacement functions: These are the functions which are simple and where we assume values for each element.

10. Variables: problems which are unknown in the system are called variables

Finite element method description:

As discussed earlier, the complex structure is divided into number of small parts which are stated as elements. This can be done after uploading the design file into Ansys. And these elements are connected each other with Nodes. The unknown points on the structure are known as nodal points. If we got a few elements we can take displacement functions to explain about the elements.

We can also represent the complex structure for analysis in trigonometric functions or polynomial equations. This are used when whole system is based on few common attributes then it will be easy to manipulate the system variables easily rather than changing to every element. To form the equations we use principles of mechanics such as potential energy is calculated to make it in equilibrium state. The external loads on the system are stated through loaded elastic body energy and internal energy on system summation is done through displacement. When displacement to each element is given and connected each element with other with nodes, and when we combine all these and main equations for equilibrium of entire structure.

Procedure for analysis of Brake Disc:

The 3D model of disc is loaded in Ansys. And as the structure of disc is complex discretization is done which mean disc is divided into the certain number of small elements. During this process we should be very careful so that the actual design of disc should not change when its divided into elements, which is called continuum.

Procedure to follow for elements:

Generally elements will be a bar or line, it all depends on the type of the structure. If the structure is complex we will get problem when we apply loads due to the elements types used in it. So in some cases we have to use different types of elements which when connected will give the actual structure, in this case similar type of element will not give the original design.

Number of Elements: the more accurate solution we need the more should be number of elements. As we divide the structure into the number of elements and will constrain the degree of freedom the more will be the performance of components on that attributes will be.  Because few times less number of elements will not show the actual solution due to insufficient effect of conditions on every element, this happens usually for complex designs. For simple structures we can move on with less number of elements as it will not have problem when load is applied as the type of element will be similar in most of cases.

Types of element: The type of problem we have will decide the type of elements we use. While analysis of structure the set of elements will be depend on set of loads. If the loads are in as original directions then only the bar type elements will give the solution. In some cases we have to use different types of elements just to maintain the actual structure which is to be analysed.

Element Size: The required solution of the analysis is depending on the size of the element. There are few important things to be verified while doing analysis as the elements should not get converge in the solution, every element has their own solution at its node, this will make solution easy as mathematical calculation of each element is time consuming and there are chances of parallax errors. It's not necessary that we should take all elements of same sizes, if we are taking a structure the elements will be of different sizes, like we use small size elements at places were the expected stress is more to get the accurate solution. Even in complex structure like tapered sides, field variables are required to get the very clear mesh region. A simple axiom is used while deciding the element size that is 'Aspect ratio'. The ratio of biggest dimension to the smallest is defined as Aspect ratio in an element. If this ratio is almost unity then best results are obtained.

In 3 dimensional structure, as 3 co-ordinate systems are used the elements are also taken in 3 dimensional and analysis is carried out. In 2 dimensional elements the analogous elements can be used, these type of elements are called tetrahedron elements. Few problems are indentified if we use the one or two coordinate system, this problems can be analysed by using Axis symmetry method. In complex structure as we see the curvature on the design, the elements are also taken in that shapes, then these elements are known as high order because of its geometrical structure. And on the flat surfaces the elements are taken as straight line elements this can be solved easily and these elements are called linear elements

Analysis and Results:

The careful evaluation of every single step carried out in analysis should be considered to get the solution. In this project we will see the detail overview of the analysis of disc brake, the main causes of the project is to avoid the brake noise problem, so our analysis should be more concentrated on this aspect. As we discussed earlier in report the actual cause for the brake squeal is vibrations generated in the dynamic conditions of the system and also the effect of the load and vibration together create some problems which are to be solved. The original design of brake disc is of Honda Accent, whose proper dimensions re taken and compared with the modified design. Initially the modifications are done with own aspects and a design is evaluated which was held to be more expensive and time consuming for the manufacturing then a small changes are done on the actual design to get the maximum heat dissipation then at the end the scenario of original design and the latest modified design are compare. To see the performance of disc rotor we use it of two materials, grey cast iron and aluminium alloys are used. Both are analysed under similar conditions and their total deformation, thermal stress (heat dissipation) and equivalent stress is calculated.

Description of Analysis:

The best thing in analysis using Ansys is it's easy to manipulate the conditions and implement the analysis. This can also be defined in other terms as trial and error method. Here initially the modified disc rotor is taken, which is designed for the maximum heat dissipation to avoid the total deformation.

Steps for analysis

1. Results of modal analysis are evaluated on original disc.

2. Design is evaluated till the required result is obtained

3. Material of components is changed and compared to get the most suitable material for components in stated conditions

4. The thickness of disc is reduced by 1mm and complete is analysis is carried to check whether its in safe region with different material and design after worn out by 1mm.

MODIFIED DESIGN 1:

3-D design of brake disc:

This is initial design of brake disc which is made for high heat dissipation. The cranks in this design are increased for more cooling and a complex fins are incorporated inside for cooling aspects to overcome the deformation of disc. As we see in this design 6 fixed supports are shown the total deformation is shown on 6 modes separately with their own load conditions of 200mpa load through brake pads.

Brake Disc with Load Conditions:

This is Load conditions image, as we see the red surface is the area where the load of 200Mpa is applied through the brake pads. Then effect of this is evaluated by deformation and stress. This design is generated for the maximum heat dissipation to reduce the brake squeal.

Total deformation at mode 1:

The deformation in z-axis is taken here, and we see that the minimum deformation is 0m which is shown as dark blue area, and the severe area is shown in red where we had maximum deformation that is 5.9196m. The reported frequency at mode 1 is 3899.3 Hz

Total deformation at mode 2:

The deformation in z-axis is taken here, and we see that the minimum deformation is 0m which is shown as dark blue area, and the severe area is shown in red where we had maximum deformation that is 5.8181m. The reported frequency at mode 1 is 3915.4 Hz

Total deformation at Mode 3:

The deformation in z-axis is taken here, and we see that the minimum deformation is 0m which is shown as dark blue area, and the severe area is shown in red where we had maximum deformation that is 5.4012m. The reported frequency at mode 1 is 4031.6 Hz

Total deformation at mode 4:

The deformation in z-axis is taken here, and we see that the minimum deformation is 0m which is shown as dark blue area, and the severe area is shown in red where we had maximum deformation that is 5.7455m. The reported frequency at mode 1 is 4054.7 Hz

Total deformation at Mode 5:

The deformation in z-axis is taken here, and we see that the minimum deformation is 0m which is shown as dark blue area, and the severe area is shown in red where we had maximum deformation that is 4.4267m. The reported frequency at mode 1 is 5722.5 Hz

TOTAL DEFORMATION

There total deformation by applying conditions for the vehicle to be in dynamic motion, then this is the affect on brake disc.

Here we see the red area on the edge of disc, that is were the maximum deformation id found. The minimum deformation is 0mm and the maximum is 49488mm.  As we see the red tag on the red area as MAX, which means this is the more affected area, and if case an extra load is applied on the disc in that area there are chances of brake failure.

Equivalent Stress of Brake Disc:

Here we see the stress analysis of Brake Disc at that conditions, the blue ares is the less effected stress area which is here 124.81 Mpa and the maximum area is shown with the red mark on the disc which is a sensitive area were the stress found is 1.1872e+5Mpa, any further stress in this area will worn out the disc as the disc conditions will come out of the safe limits.

Thermal Analysis of Brake Disc

Due to the heat generated at the conditions givens, the heat flux is the amount of heat flown into  the disc, as we see in the analysis above the blue area is the less heat is found that is  1.6929e-9 and the red mark shown on the disc surface is the area were maximum heat energy is found. This is 6.3918 e-3. This shows the surface area which comes in contact with brake pads have more heat flux.

Vibration Analysis:

As we see here the vibration frequency is increasing with increase in the amplitude, which is nothing but the speed of the vehicle. Minimum was 500 Hz and maximum frequency found is 3500 Hz.. tough the deformation has shown the difference at different points with different modes. There is no change in the phase angle with change in the frequency. This having an frequency range of 3500 Hz.

The total deformation for Mode 6 will also similar as mode 5, hence we calculate the total deformation of brake disc with all direction in the geometrical axes and the maximum deformation is calculated and graphed for the clear understand view of the total deformation.

If we evaluate this graph we see the deformation is almost same at node 1 and 2 due to its load axis is similar and same with mode 3 and 4, and also with mode4 and 5, as we see the bit larger difference in 5 and 6 which is due to the excessive load in the particular direction and due to the vibration energy.

Hence with the above solution from the total deformation and the vibration analysis the brake disc will be in safe limits at general conditions. Until the excessive load is applied on the red areas which are more effected due to the load analysis. But the manufacturing and machining costs will be very high for this. As the finite spiral fins are incorporated inside the disc flange for the good cooling purpose can create a problem when it is taken commercially as it indirectly increase the labour charges which will affect the product final cost. So this design is further modified in other way for the best possible.

Modified Design 2:

This design is modified in totally separate way when compared with the previous design, this is much more similar to the actual design of Honda accent, As we know that the heat dissipation will be in tangential when the braking is applied so the cranks on the disc are design so as the tangential and more heat dissipation take places in actual direction.

In this analysis we compare the result of new design with two different materials Aluminium alloys and grey cast iron. As each material has their own possible advantages, but with new design let's see which material type will give the maximum possible justice to the bake disc.

Design of Modified Design 2:

In this design as discussed above the crank angle is changed to 9 angles between two cranks, which will give 40 cranks on the disc surface and it is shaped in tangential direction which will allow maximum amount of heat dissipation. Here we see the new design modification.

Here in this design the Dimensions carried out are outer diameter 241.1 mm and the Inner diameter 182.20 mm. The Hole diameter 17mm at angle of 72 deg. And the cranks shown are having 9 deg differences between each other and they are in tangential direction.

Boundary conditions:

Here we see the red area shown is the surface were the load is applied which is 100 Mpa and this also have affect of the fixed supports at the 5 holes on the disc. And further analysis is carried out at this condition.

TOTAL DEFORMATION OF BRAKE DISC OF GREY CAST IRON:

Here in this analysis we see the deformation is more at area were the red tag shown that is 36215mm and minimum is 0mm. We the area is less when compared with previous design. So this area should be carefully evaluated so that no more loads are applied.

TOTAL DEFORMATION OF ALUMINIUM ALLOYS

Here we see in this analysis the minimum deformation is 0mm which is mainly they are fixes with supports and we see the possible maximum deformation is red area with a tag showing MAX which is found as 56243mm. That small area has to be inspected so that no more extra load is applied which may cause the brake failure. But so far this is in safe limits.

Equivalent Stress of Grey Cast Iron:

In this stress analysis we see the brake surface area is very clear and only the corner shown on disc with red tag is the danger zone, that is were the maximum stress is calculated that is 1.3757e+008pa and the minimum stress on the disc due to the dynamic analysis is calculated as 1.8074e+005Pa. An another careful analysis to reduce the stress at this corner will made the design strong enough for commercial use.

Equivalent Stress of Aluminium Alloys:

Here also the maximum stress is found at the corner of the disc, that is 1.3938e+008pa and the minimum stress found is 1.9047e+005pa. This design is in safe limits as of the equivalent stress when the possible load is applied on it.

Thermal Stress of Grey Cast Iron:

Firstly the temperature effect is shown on the disc, as we know that the temperature difference on the each side of disc will not be same. So in this case at different temperature will see the effect of the disc at one side 951 deg and on other side 950 deg of temperature is applied.

The red tag is the side on which 951deg is applied and on the other blue side 950 deg, definitely the area with more heat will shows the more difference in the performance.

HEAT FLUX OF GREY CAST IRON:

In grey cast iron we see the maximum heat flown is found at the red tag that is 1.3623e-002 w/mm2 and the minimum heat flow which is at most of the area of the disc is 1.0897e-007 w/mm2

HEAT FLUX IN THE ALUMINIUM ALLOYS:

Here in Aluminium Alloys the maximum heat flux found is 4.5845e-2w/mm2 , that is at the red tag shown, and the minimum heat flux is 3.6673e-7 w/mm2

A detail evaluation of heat flux is carried out for the grey cast iron by taking the heat generated in steps from zero to the maximum and again to the zero as vehicle comes to rest and disc should retain its properties. Here the temperature is divided into 25 steps from 0 to 950 and heat Flux is evaluated two separate graphs one with minimum heat and other with maximum heat flux with that temperature conditions.

MINIMUM HEAT FLUX CALCULATED:

MAXIMUM HEAT FLUX CALCULATED:

VIBRATION ANALYSIS:

Comparing the Results:

Here we analysed the new modified design to find out thermal stress and normal stress with two different materials Grey cast iron and Aluminium Alloys. Now let's compare the each result for both materials with see which one is performing better when compared with other.

Total Deformation:

Material      Minimum ( in mm )   Maximum ( in mm )
Grey cast Iron      0       36215
Aluminium Alloys    0       56243
			

Here if we see in this table the minimum deformation is same for both the materials. But there is much difference in the maximum deformation; Aluminium is showing more deformation than grey cast iron which due to its ductility and less tensile strength properties. Which can be rectifies by hardening methods.

Equivalent Stress:

Material       Minimum ( in mm )  Maximum ( in mm )

Grey Cast Iron 1.8074e+005Pa 1.3757e+008pa

Aluminium Alloys 1.9047e+005pa 1.3938e+008pa

Here we see that, there is no much difference in the stress evaluations of both the materials. Both the minimum stress and maximum stress are almost equal. The material doesn't make difference to the normal stress analysis at these conditions.

Thus we have seen the comparison of the grey cast iron and Aluminium Alloys at load conditions of 100Mpa from the brake pads. By the total deformation and equivalent stress values we see that the grey cast iron suits best but Aluminium is lacking only at the deformation only which can be strengthen by hardening methods, then it will be almost equal to the grey cast iron in its properties, and also it will be less in weight and which will reduce the brake squeal noise to some extent. The more the mass of the disc the more are the chances of less vibration and more squeal.  Hence both materials can suit at these conditions with an extra strengthening its properties.

Thermal Analysis:

The amount of heat flown into the disc due to the temperature conditions at the dynamics state is evaluated here; we will see the heat flux of grey cast iron and Aluminium Alloys here

Heat Flux:

		
Material    Minimum      maximum
Grey cast iron   1.0897e-007 w/mm2   1.3623e-002 w/mm2
Aluminium Alloys 3.6673e-7 w/mm2     4.5845e-2w/mm2
			

Here we see the Heat flux values if we see its  more in aluminium but that difference is very small which will not make an much difference on the disc. We can improve the material properties by add-on methods to have good heat flux ability. The less the heat flux, the good will be the material, which will not show any phenomenal change in it within limits. This at this conditions the chances of brake squeal are less but still it may be more when compared with grey cast iron. As per this design we see the heat dissipation is more and deformation is quite less when compared with the original design.

Conclusion:

Changes in the design and material of brake disc will definitely increase the disc ability to stand on the extreme conditions. But to avoid the brake squeal completely is not possible. As we discussed earlier the brake squeal is caused because of the dynamic instability of brake system and suspension system. Along with the disc the brake system and suspension system should also be made to get stabilize at the extreme conditions. The main part of disc, the further developments in it will reduce the brake squeal. Therefore the further changes in design for more heat dissipation and less deformation will reduce the brake squeal as that will make the disc to get stabilize as the change in its dimension will be less and the effect of heat will be less which will make a perfect disc to perform in the extreme conditions.

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