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: 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: Drum Brakes - Part2

In the previous article, we talked about the basic concepts that are related with brakes and terminology that is defined to understand brakes and its features. The previous blog can be found at: http://themechunicorn.blogspot.in/2014/04/brakes-general-part1.html
Now, in this part, we will start discussing about the components and construction of different braking systems, we will start with the simplest friction based drum brakes for vehicle and will continue towards disk brakes, aircraft drag brakes, jake brakes and will end towards electromagnetic brakes. This differentiation will be based on categories depending upon the vehicle i.e. we will first take brake systems used in cars, then aircrafts and then other vehicles.

The two images above show a basic drum-brake assembly for cars and motorcycle. These are the most common braking system till now for vehicles but are now being replaced by disc brakes at a very fast rate, the reason for this migration is quite simple, high brake fade, low peak force, less brake power when compared to disc brakes and less durability. The drum brakes work on a very simple principle of friction. The drum-brake assembly include the following:

1) Brake Drum - It is the brake cover that gets attached to the wheel while also serving as the friction surface for the brake system, the inner side of the brake drum is lined with frictional surface having a friction coefficient (µ) of anything between 0.4 to .45 while depending upon application, the µ might gets increases as high as 0.66. Brake drum also connects with the tire and is subjected to high torque when braking action is required.

2) Brake Shoe - It is the component that is attached with the brake lining material of the inner assembly and the actuation occurs here itself, the hydraulic slave cylinder is connected to both the brake shoes and when brakes are actuated, the slave cylinder pushes the brake shoe towards the brake drum and the shoe returning springs bring it back after actuation is completed.

3) Shoe Adjustment: It is the component through which you can set the initial position of the brake shoe! It is used to control the pedal play as well as to control the peak force, but increasing the initial value of shoe might result in reduced durability due to increased drag and more brake power.

4) Hydraulic Slave Cylinder: It is the actuator unit of the drum brakes, apart from hydraulic actuators like hydraulic cylinders, various drum brake designs also use mechanical actuation which is still commonly seen in motorcycles. Through a hydraulic pipe it is directly connected with the master hydraulic cylinder which in turn is connected with the brake pedal! As hydraulic systems are based on Pascal's law, the rest of the actuation method is nothing but a series of clever engineering architecture.

The brake power is directly related to the surface area of the brake pads or brake lining material in contact with the inner brake lining of the brake drum. Now, a days the application of drum brakes have been reduced considerably and are usually used as secondary braking system like the parking brakes while newer disk brakes have taken the place as primary braking system in the cars.

Thus, with this we conclude the information related to drum brakes, in next series of article, we will talk about other types of brakes and their constructions. Also, we will also bring in all the equations related to drum brakes and their designs in upcoming articles so that entrepreneuring designers can use the resources for designing their own drum brake systems and innovate!