Week-11 Challenge: Braking

1. For a defined driving cycle, calculate the energy required for braking.

ANS:

The objective is to calculate the energy required for braking for a defined driving cycle.

The energy required to stop an electric vehicle is called as Braking energy.

We use two types of braking in electric vehicle:

1) Electric braking

2) Mechanical braking

The above two brakings are necessary to halt the vehicle from a given speed to zero speed.

The energy required for braking is given as follows:

`E=1/2mV^2`

where,

m= mass of the vehicle in Kg

V= final velocity in m/s

Let us create a Drive cycle, which is generally a speed vs time graph.

The below snap shows the drive cycle.

For the above data cycle we need to calculate the average Braking energy required. This can be done by converting the data points from drive cycle to the excel format as shown in below figure.

From the above excel sheet, we can calculate the braking energy required at various speed using the formula `E=1/2mV^2`.

Hence the average value of braking energy for the overall drive cycle is 0.05584 KWh.

2. Why electric motor can’t develop braking torque at high speed similar to starting? How electric and mechanical brakes are coordinated? 

ANS:

There are mianly 2 major reasons for a motor to develop a higher starting torque compare to braking.

1. Due To Transients:-

At the starting the motor, it draws a large current due Transient . As we know that torque is proportional to square of current, hence the  torque value is also very high at this moment.

When brakes are applied to motor at that time current value recides within the range hence the  Torque values is also recides within the range.

2. Torque speed characteristic:-

From Torque speed characteristic we know that when speed is increased torque should decrease to maintain the constant power. At the time of starting of motor, the speed is very low hence the value of torque is very high.Similarly, at the time of braking of a motor, the speed value is high hence there will be a low torque value present. Therefore at the time of motor braking, available value of torque will be lower. The braking operation happens in the motor which is been distributed as per proportion in the 'REGENERATIVE BRAKING' and the 'BRAKE ENERGY'.

Hence we can conclude that the electric motor can’t develop braking torque at high speed similar to starting.

Coordination of electrical and mechanical brakes:

As we can see in several vehicles, the mechanical brakes uses the pedals which helps us to engage or disengage the brakes. Currently there are many life-saving braking technologies are available in the market such as EBD, ABS, BA and many more. All these latest technologies play a vital/major role in stopping the vehicle and coming back to the rest position at a high speed. In general when the driver applies the brakes the brake pads come closer to the disc connected with the driving disc. The brake pad usually offers inefficient braking.

There are two generic methods by which the vehicle could be braked in the ELECTRIC BRAKES.

1.Series - In this method, the mechanical braking and regenerative braking are applied one after another.

2.Parallel - In this method, the Mechanical Braking or the Regenerative Braking both are applied Parallely.

At lower speeds, regenerative braking are used and at the higher speeds mechanical brakes are used.

Whenever the brake pedal is pressed the hydraulic fluid reaches the brake piston and creates braking pressure on the wheels and the same kinetic energy is being used by regenerative braking for generating the more power using Bi-directional motor which operates as a generator while braking. An example of the proposition of mechanical braking and regenerative braking is NISSAN LEAF EDBI.

NISSAN LEAF EDIB (ELECTRONIC-DRIVEN INTELLIGENT BRAKING)

EDIB (Electric Driven Intelligent Brake) controls the regenerative brake and friction brake to support both of these requirements. Further, it also controls the reactive force from the pedal in order to unify the feeling when stepping down on the pedal and the sense of deceleration.

3. Make a MATLAB program which plots contour of given motor speed, torque and efficiency values. Attach the code as a .m file attach a screenshot of all the plots.

ANS:

We Know that contour is a graphical technique of representing 3-dimensional surfaces. 

% A MATLAB PROGRAMM FOR PLOTTING CONTOUR PLOT OF MOTOR SPEED, TORQUE
clear all
close all
clc

% SPEED ARRAY
w = linspace(0,1000)

% TORQUE ARRAY
T = linspace(0,300)

% LOSS COEFFICIENTS
kc = 0.18;  % COPPER LOSSES
ki = 0.006; % IRON LOSSES
kw = 0.000015; % WINDAGE LOSSES

% MESHGRID
[X,Y] = meshgrid(w,T)
copper_loss = (Y.^2)*kc
iron_loss = X*ki
wiindage_loss = (X.^3)*kw
cons = 20

o_p = X.*Y
input_power = (copper_loss)+(iron_loss)+(wiindage_loss)+(o_p)+cons
Eff = (o_p)./(input_power)
n = linspace(0.7,0.95,10)
box off
grid off
contour(X,Y,Eff,n)
title('SPEED TORQUE CHARACTERISTICS')
xlabel('SPEED RAD/s')
ylabel('TORQUE N/m')

 Program Desciption:

• Here in the code first two inputs are given as speed and torque using linespace command.
• Motor constants namely copper loss, Iron loss, Windage loss and motor constants are assigned.
• The meshgrid is used to evaluate functions 2 variables and 3-D mesh/surface plots.
• The output power is calculated by multiplying speed and torque.
• Then all the losses are calculated and the input powers are also calculated.
• Then the efficiencies are calculated. And then contour graph is plotted between Speed, Torque and Efficiency.
• Title are given and labels are given.

Workspace:

Output Graph:

From the output graph, we can see that only at a particular speed and torque value, the efficiency is at maximum i.e. 95%.

Where the  Speed x = 151 rad/s @ 30 N-m Torque. As the Speed increases we'll get reduced efficiencies.