Brakes: Design your own Disk Brakes - Part7

We all know drum brakes are an important part of life and learning to design them is extremely important but with the time of upgrading brakes into disc brakes, it is even more important that one must know the design aspects of disk brakes. In this article we will show how you can design your own disk brake and all the calculations and equations involved.

The above image represents a simple disc brakes and to understand the equations, one must understand the image above and now key to defining elements:

F = Force applied by the slave cylinder on the brake shoe

r = radius from center of disk to center of the brake pad

r_o = radius from center to outer surface of the brake pad

r_i = radius from center to inner radius of the brake pad

θ₁ = angle from horizontal to heel of brake pad

θ₂ = angle from horizontal to toe of brake pad
P_max = maximum applied pressure (depends on frictional material)
P = Uniformly distributed pressure along brake pad
Now, one more things to take into account is, in disc brakes there are 2 conditions that persists! 1) Uniform Pressure: which is applicable for new brakes & 2) Uniform Wear: which comes after a certain amount of use. Now, Work done is directly proportional to P_max X r_i therefore, W = k.P_max.r_i and since W & k are constants, let, W/k = K = P_max.r_i, Also, K = P.r, therefore,
P = P_max.r_i/r
Now, the force applied on the brake pads (F) is equal to

F = 

Replacing P with equation above and doing integration for θ, we get;

F = 

Again, doing integration for radius r, we get;

F = 

The equation above gives the force, now for torque;

τ = 

Replacing P with Pmax equation and integrating for θ, we get;

τ = 

Again, integrating for radius r, we get;

τ = 

Thus, the above equation gives torque for the disc brakes for uniform wear system!

Now to get equivalent radius (r_e) = τ/µF 

All the above equations hold good for Uniform wear system when work done is dependent on radius but when the brakes are new, then P = P_max because of which the new equations becomes;

F = 

Integrating for θ and solving for P, we get;

F = 

Thus, the final equations comes out to be;

F = 

Also for Torque (τ), the equations changes as;

τ = 

Integrating for θ and solving for P, we get;

τ = 

Thus, the final equation on integration of r comes out to be;

τ = 

With, this all the design equations have been discussed for the disc brakes, again, we know Torque = Force X Perpendicular length

Therefore, The Force applied by the force to stop the car will be F_brake = τ / r_e

Using this, we can solve any linear motion problem and calculate stopping distance and find time to decelerate the vehicle from velocity v to 0 using equations of motion.

Brakes: The Drag Brakes - Part5

Drag brakes as the name suggest are completely different braking system, both in characteristics and functioning! As the name suggests, it produces a force which opposes the motion of the vehicle. Drag in normal terms can be described as the force which is applied on a component of vehicle which does not fall in its aerodynamic foil. The ambient air at high speeds, due to relative motion of the vehicle against air, produces a massive amount of air channel in front of vehicle through which the vehicle has to go through else it'll hinder the top speed capacity of the vehicle. After a lot of research in the field of aerodynamics, the researchers mentioned that the shape of the "falling water drop" is the most aerodynamic shape and if somebody might have noticed, the shape of Airfoil is also shape of drop only.
The most common application of drag brakes is aircraft, the common name of drag surface is spoiler in aircraft which is present above the flap and even flap functions somewhat as the drag brake. These are together called as control surfaces and they include: flaps, rudder, aileron, slats, spoilers and elevators which control the 6 degrees of freedom of the aircraft!

Courtesy to NASA

The basic concept of functioning is very simple, when flaps and spoilers are deployed, they work as resistance to the air flowing through the flat surface thus making air as the working medium to stop the vehicle.

The same concept has been used in cars for a very long time, the spoilers in cars does the same thing. There are two types of spoilers, 1) Fixed geometry: which is usually used to create downforce 2) Variable Geometry: also called as Retractable spoilers, they serve as both drag brake system as well as downforce producing system.

Both above images show different types of spoilers.

The above image shows a very conventional drag method to stop high speeding cars like the high tuned drag racing cars! In them, the designers and enthusiasts used to install the parachute behind the car with a deployment circuit through which the driver can deploy it whenever he wants to stop the car. Drag brakes in automotives have been very useful especially in the stopping distance timings of super cars like Bugatti Veyron. They make sure that the Peak force of the friction brakes are always under control!

So, with this we end with the types of braking system and their functioning, in next series we will start with the calculations involved in designing if each of the braking system and we will start from drum brakes.

Brakes: Electromagnetic Brakes - Part4

Dear readers, I am sorry for the delay in 4th part of the brake series. Today we are going to talk about EM Brakes or Electromagnetic Brakes. We have already covered the basics, about disk brakes and about drum brakes in previous articles and they can be found in http://themechunicorn.blogspot.in/. So, let's come to the topic of EM Brakes, EM Brakes are usually seen in heavy vehicles like trams, trains etc. They serve as an alternative to friction brakes. The various advantages of EM brakes include high CPD (Continuous Power Dissipation) i.e. it's ability to remove excess heat energy very quickly thus increasing life span of system and reducing maintenance costs. In recent years, with development of hybrid and electric cars, the EM brakes have been used in  them also, and their functioning and construction is very different from conventional disk or drum friction brakes.

As can be seen from the image above, the EM brakes have a electric coil which produces controlled magnetic pole and energizes the Armature to have an opposite pole and with continuous change in strength, the magnetic forces push the armature towards the friction disk which produces the required braking action.

Now we will explain each component and their role in functioning of the EM brakes.

Lead Wire: It is the electrical wire that brings 24V or 12V DC from battery/alternator to the EM brakes coils.

EM Coil: On application of DC, the coil produces a magnetic force and pole on the concepts of Faraday's law of Electromagnetic Induction and Faraday-Maxwell Equation and also on Fleming's Right-Hand thumb rule.

Braking Spring: It is the return spring, after application of brakes and de-energizing of coils, the return brake springs detaches the armature from friction disks.

Friction disks: They are circular disks with friction material linings on outer surface, they are usually made of aluminium and are hollowed inside for maximum ambient air displacement and increased cooling effect on friction disk.

Hub: The component which attaches to the output shaft and finally with wheels.

The whole EM brake assembly is mounted on anti-vibration mountings in chassis and is fixed together with 3 fixed bolts. The EM brakes have a lot of advantages over conventional friction brakes and can be easily equipped with many other technologies like KERS (Kinetic Energy Regeneration System) to increase the efficiency and overall power of the whole vehicle.

Brakes: Disk Brakes - Part3

In last 2 articles we covered the basic terminology and basic knowledge of brakes and in second the concepts of working principle behind the drum brakes. Our previous articles can be found on http://themechunicorn.blogspot.in/. In this article we will continue our trend with working principle of disk brakes for automobiles in bikes. Well, the disk brakes have quickly become a spotlight feature in nearly all cars and motorbikes. The reason is simple, more power, more peak force capability and surely reduced weight! Disk brakes are usually found and known as hydraulic disk brakes, while mechanical disk brakes are also present, but hydraulic disk brakes are more powerful, durable and requires very less maintenance. Also, unlike drum brakes, the disk brakes have less reciprocating/moving components and due to use of hydraulic fluid as the working medium, the disk brakes are more responsive in nature.
In construction:

The above image shows a typical single hydraulic cylinder hydraulic disk brake. In the simplest of words, the caliper holds 2 brake pads which are of frictional material and when the pressure is applied by the piston, the brake pad rubs against the disk and because of this frictional combination, the braking action is achieved. Well, there are actually 3 types of hydraulic disk brakes, single cylinder configuration, dual cylinder configuration and full disk configuration. While, the first 2 configurations are differentiated by the no. of cylinders disk caliper will be housing, the full disk configuration is rather based on surface area the brake pad will be covering! In cases of single and dual cylinder disk brakes, the brake shoe is covering a particular angled surface area of the disk, while in case of full disk configuration, a full 360^o brake pad is used.

The first image shows the full disk configuration, while the second image is the common single cylinder hydraulic disk brake. The only reason, the full disk configuration aren't popular is because of the low durability due to high surface area contact and unbalanced forces acting on the actuation rod.

Now, we will explain each component of the single cylinder disk brake.

1) Hub: Like the brake drum in drum brakes, the hub is the component of disk brakes that is connected with the wheel of the vehicle.

2) Rotor/Disk: It is the metallic disk that's been abraded to produce a frictional surface over it. The disk has to be designed in such a way that it can withstand all the frictional heat and should implement best methods of aerial cooling or ambient cooling.

3) Brake Pads: The brake pads are made of frictional material like graphite or carbon composites. the brake pads serve the same feature as served by brake shoes in the drum brakes, but are more durable in construction and usage.

4) Hydraulic Slave Cylinder: Just like the drum brakes, Slave Hydraulic Cylinder also works as an actuator in disk brakes. The pressure created inside the cylinder serves as the way to move the brake pads towards the disk.

5) Caliper Return Springs: They are mediocre to high tension springs that helps in bringing back the brake pads to their original position when the pressure from the main and slave cylinder is removed.

6) Caliper: It is the main housing in which the brake pads, hydraulic slave cylinders and caliper return springs rests and helps the whole braking system to stay rigid and in required position.

While designing a hydraulic disk brake, a lot of things need to be taken care of and every design has its own specifications, the angle covered by the brake pads, the radius of brake pads, position of them from top, frictional coefficient of the disk caliper, and many more considerations need to be taken care of while designing the braking system. In the coming series of continuing articles, we will also discuss all the equations required to design hydraulic disk brakes and their derivations, so stay tuned. Remember, educate, then excel and then only innovate.

Brakes: The General - Part1

In these series of blogs, we are gonna discuss everything and anything about brakes, starting from terminology and basics involved in first blog to its calculations and how entrepreneur designers can design their own locomotives. Since Brakes are one of the most important 3 mechanisms of any locomotive, other being power generation and steering mechanism; So, we will give time and explain everything about them gradually! So, let's start with the basics! What is a brake? In easiest words, a system or device that reduces or halts motion. Taking example of cars; brakes reduces the speed of a moving car and eventually brings it to a complete halt. Now, there are various types of braking methodologies, 1) Friction Brakes: The brakes use friction to bring out braking action and usual example include drum brakes, disk brakes, hydraulic disk brakes & pneumatic disc brakes. 2) Pumping Brakes: which use engine and engine's components friction as the required braking action! The most popular ans simple type of Pumping brake is Jake Brake which open the exhaust valve during the expansion stroke of Engine. 3) Electromagnetic Brakes: They bring about the braking action using electromagnets, they are commonly installed in hybrid/electric vehicles and is also the basis of KERS (Kinetic Energy Regeneration System) in cars. 4) Drag Brakes: These types of brakes find their application in vehicles which require deceleration through a fluid medium like air or water; the easiest example is the flaps in the wings of aircraft.

courtesy to www.images.google.com

The above image shows a typical disc-drum arrangement in a modern car and the various components involved in them! In the continuing articles we will explain functioning and detailed information about each component but for basics, I believe, its the best way to understand the braking system. Now, let's talk about some terminology one should know while studying brakes.

1) Peak Force: The peak force is the maximum amount of decelerating effect that can be achieved by the system. The peak force is usually greater than the traction limit value of tyres which results in wheel skid when brakes are applied with full force. The peak force depends on the friction coefficient between the friction components of the braking system and the time of actuation or in drag brakes case: the angle of attack i.e. at which angle the actuated component is to the streamlined fluid.

2) Continuous Power Dissipation: It is commonly affiliated with friction brakes, on actuation a lot of heat energy is produced in the system and after a particular temperature the braking system might breakdown! Thus, the maximum amount of power a braking system can dissipate without breaking down is called as Continuous Power Dissipation. The dissipation is dependent on temperature and speed of ambient cooling air.

3) Brake Fade: Because of increase in temperature, the brakes efficiency might reduce, which is technically termed as Brake fade. It is dependent on the design, and cooling system of brake plays a very important role in determining the Brake Fade of the system.

4) Smoothness: It is more of a physical term than technical term for brake application. It's all about the experience of the driver, if the brakes are harsh, worn out and exert unequal force will produce skids and would be unappreciated by the driver as such system will make him experience that he is driving on a camel.

5) Power: It is the amount of brake force the system produces with respect to the application of brake pedal! In other way, it is the ability of the system that how fast can it reach its Peak Force.

6) Drag: It is the incomplete detachment of one braking component with another because of which the unwanted braking action might be there even during full pedal release. The common causes of drag are misaligned brake shoes, broken springs, over-extended actuator wire or piston failure etc.

7) Durability: Brake systems have frictional parts that wear out at every application of brake and might needs to be replaced from time to time. The durability of systems with higher peak force is lesser.

Well, these are the most important terminology one must know in order to understand braking and braking systems! The braking system is specifically mounted on either wheel or trans-axle depending on application of the braking system. One thing that one must also know is that braking system which may/may not include supporting structure adds into weight of the body thus, it also plays an important factor depending on application. With this, we end our first article on basics of brakes and keep tuned for the next article which will briefly explain each component of braking systems and application-wise differences in them.