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: Design your own Drum Brakes - Part6

Well, we are nearly at the end of series with few more articles to go! Till date, we have already discussed nearly everything about construction, advantages, disadvantages and uses of each braking system but we, The Unicorn, understands that just understanding is not enough for anyone that is why we also make you understand how you can design the system yourself! As our motto says, Educate, Excel and then Innovate! To innovate you need to learn everything including how to design the system and the equations involved. In this article we will discuss the design aspects and equations involved in designing drum brakes.

To understand the design aspects of drum brakes, we have to understand the image above! First of all, as assumed we will say that direction of rotation of wheel is clockwise. Now the key to defining elements:

F = Force applied by the actuating device on each of the brake shoes.

P_max = Maximum Pressure applied

c = total displacement of heel and toe of the brake shoe

a = displacement from center of drum to the center axis of the brake shoe

r = radius of the drum from center of drum

b = displacement from center axis to the pivot point

Θ₁ = angle from center of pivot point to heel of shoe lining

Θ₂ = angle from center of pivot point to toe of shoe lining
Θ = average angle to distribute forces along the whole length of the shoe
and let µ = frictional coefficient of the shoe lining material

Since, the rotation is clockwise, the right shoe lining will attack first and its effect will be more than the trailing left shoe! and to calculate the force applied, we need to calculate the moment of inertia applied due to frictional force and also due to normal force acting on the shoe lining.
let's take k = P_max/SinΘ₂ therefore, k = P/sinΘ
equating both, we get; P = P_maxsinΘ/sinΘ₂ (where P is Uniformly distributed Pressure)
Now, Let M_f be the Moment of Inertia due to Frictional Force then,

M_f = 

Replacing P, we get:

M_f = 

Therefore, final formula after integration comes out to be:

M_f = 

Now, for calculating Moment of Inertia for Normal Force,

M_n = 

Replacing P in above equation,

M_n = 

After integration, final formula comes out to be:

M_n = 

Therefore, F = (M_f - M_n)/c

Also, Torque applied by the right shoe will be equal to

τr = 

replacing P, we get:

τr = 

The final equation becomes:

τr = 

Also, we need to add the force due to Left Shoe also called the trailing shoe;

For trailing shoe P'max = FcPmax/(Mf + Mn)

The torque applied by the left shoe will be:

τl = 

replacing P', the above equation becomes:

τl = 

The final equation becomes:

τl = 

The total Torque τ = τr + τl

Also, we know Torque = Force X Perpendicular length

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

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: 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: 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!