Week-11 Challenge: Braking

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

Ans 1 :

The braking performance is one of the most important concerns in vehicle safety. In urban area driving, a significant amount of energy is consumed in braking. Electrification of vehicles makes it feasible to recover some of the energy lost in braking. A hybrid braking system was developed to ensure the efficient braking of the vehicle and recovering the braking energy. The design and control objectives of such a hybrid braking system are to ensure sufficient braking force to quickly reduce the vehicle speed, properly distributing the brake force to the front and rear axle, and also recover as much braking energy as possible. So understanding of braking energy of a driving cycle is important. Now, it is also important to mention that braking energy also depends upon the type of driving cycle i.e. the higher number of time the vehicle will have rapid speed changes and will come to rest then the braking energy will automatically rise for that particular drive cycle than other driving cycle where the rapid speed changes don't occur.

The function of the braking system is to retard the speed of the moving vehicle or bring it to rest in the shortest possible distance whenever required. The vehicle can be held on an inclined surface against the pull of gravity by the application of a brake. Brakes are mechanical devices for increasing the frictional resistance that retards the turning motion of the vehicle wheels. It absorbs either kinetic energy or potential energy or both while remaining in action and this absorbed energy appears in the form of heat. While moving down a steep gradient the vehicle is controlled by the application of brakes. In this case, brakes remain in action for a longer period making it imperative to dissipate the braking heat to the atmosphere as rapidly as possible.
Automobiles are fitted with two brakes; the service or foot brake and the emer­gency or hand brake. The foot brake is used to control the speed of the vehicle and to stop it, when and where desired, by the application of force on the brake pedal. The hand brake, applied by a lever, is used to keep the vehicle from moving when parked. Hand brakes are called emergency brakes because they are applied when the service brake fails. Virtually all vehicles are now equipment with 4-wheel brakes. The front brakes must operate without interfering with the steering action.
The brakes must be capable of decelerating a vehicle at a faster rate than the engine is able to accelerate it. Normally brakes have to absorb three times the amount of engine horsepower energy in its equivalent form.

Kinetic energy is the force that keeps the vehicle moving. This energy is provided by the engine in order to accelerate the vehicle from a standstill to desired speed. Kinetic energy is dissipated as heat by the brakes during application of breaks (Fig. 28.1). The kinetic energy of a vehicle during braking is given by

GOVERNING EQUATION:

Braking Energy =

Where,

m - Mass of vehicle (kg)

v - Velocity of vehicle (m/s)

CODE:

clc
clear all
close all
%Program to find the Braking energy for the drive cycle

drive_cycle=xlsread('drive_cycle'); %Loading the drive cycle
speed=drive_cycle(:,2); %Speed values extracted
time=drive_cycle(:,1); %Time values extracted
vf=[]; %Final speed array
vi=[]; %Initial speed array
m=600; %Mass of vehicle
%For loop for picking the initial and final speed of deceleration
for i=1:(length(speed)-1)
if speed(i)>speed(i+1)&&speed(i+2)<speed(i+1)&&speed(i-1)<speed(i)
vi=[vi,speed(i)];
elseif speed(i)<speed(i+1)&&speed(i+2)>speed(i+1)&&speed(i-1)>speed(i)
vf=[vf,speed(i)];
end
end
vf=[vf,0]; %Adding zero to the last value of Final speed
B=(0.5.*m.*(vi-vf).^2)/1000; %Calculating the Braking energy for each step down
x=sprintf('Total Braking Energy = %0.2fkWh',sum(B)); %Formating the data into string.
disp(x) %Displaying the total braking energy

%Plotting drive cycle
plot(time,speed,'linewidth',2)
title('DRIVE CYCLE')
xlabel('TIME')
ylabel('SPEED')
grid on

Explaining the code:

• Line 6: Loading the drive cycle.
• Line 7-8: Extracting the speed and time values.
• Line 9-10: Initializing the initial and final speed as an array.
• Line 11: Mass of the vehicle.
• Line 13: For loop to get the initial and final speed of deceleration.
• Line 14-18: If and else if condition to compare the values and identify if it’s decelerating or not and storing it in variable vi (initial speed) and vf (final speed).
• Line 20: Adding zero to the final speed array, since in every drive cycle the value of final speed will be zero (vehicle goes to rest).
• Line 21: Calculating the braking energy.
• Line 22: sprintf command to formatting the data into a string for display. Sum(B) add all the elements inside the variable B.
• Line 23: Displaying the string.
• Line 26-30: Plotting the drive cycle. Labeling the plot with title, xlabel and ylabel.

RESULT:

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

Ans 2:

The electric motor can't develop braking torque at high speed similiar to starting because once the electric supply is pulled off from the motor,it acts as a generator and due to the flux weakening effect of the electric generator produces low torque as expected.

Regerative Braking:

Regenerative braking is an energy recovery mechanism that slows down a moving vehicle or object by converting its kinetic energy into a form that can be either used immediately or stored until needed. In this mechanism, the electric traction motor uses the vehicle's momentum to recover energy that would otherwise be lost to the brake discs as heat. This contrasts with conventional braking systems, where the excess kinetic energy is converted to unwanted and wasted heat due to friction in the brakes, or with dynamic brakes, where the energy is recovered by using electric motors as generators but is immediately dissipated as heat in resistors. In addition to improving the overall efficiency of the vehicle, regeneration can significantly extend the life of the braking system as the mechanical parts will not wear out very quickly.

Understanding how regenerative braking works first requires knowledge of how a conventional braking system operates. When you step on a vehicle's brake pedal, the discs and the brake pads create friction as they meet. In turn, the friction creates kinetic energy that dissipates into the environment in the form of heat.

Regenerative braking recovers some of the kinetic energy that would otherwise turn into heat and instead converts it into electricity. In this system, the motor drives the wheels during acceleration or cruising, but the wheels drive the motor while decelerating. This two-way energy flow allows the motor to act as a generator, resisting the rotation of the wheels and creating electricity to recharge the vehicle's battery.

There are two conditions when regeneration occurs:

1. When the driver applies the brake pedal

2. When the driver releases the accelerator pedal, and the vehicle is coasting

In both cases, the system creates electricity to recharge the battery. Drivers can view this regenerative effect on the vehicle's charging gauge, which shows it as energy flowing from the wheels to the battery.

The amount of electricity the system generates is proportional to the level of braking force. That means the stronger the braking force, the greater the electrical current. Ultimately, the amount of energy the system captures is dependent on the vehicle's speed and the duration of brake application.

When braking, the system automatically allocates some portion of the braking force to energy regeneration and some to the conventional brake system. This way, the system simultaneously achieves the dual purpose of slowing the vehicle down and recharging the battery for improved efficiency and greater electric driving range.

The most common form of regenerative brake involves an electric motor functioning as an electric generator. In electric railways, the electricity generated is fed back into the traction power supply. In battery electric and hybrid electric vehicles, the energy is stored chemically in a battery

, electrically in a bank of capacitors, or mechanically in a rotating flywheel. Hydraulic hybrid vehicles use hydraulic motors to store energy in the form of compressed air. In a hydrogen fuel cell powered vehicle, the electrical energy generated by the motor is used to break waste water down into oxygen and hydrogen which is recycled back into the fuel cell for later reuse.

The most common form of regenerative brake involves using an electric motor as an electric generator. The working of the regenerative braking system depends upon the working principle of an electric motor, which is an important component of the system. The electric motor gets activated when some electric current is passed through it. But, when some external force is applied to activate the motor (during the braking), then it behaves as a generator and generates electricity. This means that whenever the motor runs in one direction, the electric energy gets converted into mechanical energy, which is then used to accelerate the vehicle, and whenever the motor runs in the opposite direction, it performs functions of a generator, which then converts mechanical energy into electrical energy, which makes it possible to utilize the rotational force of the driving axle to turn the electric motors, which results in regenerating electric energy for storage in the battery and simultaneously reducing the speed of the car with the regenerative resistance of the electric motors. This electricity is then used for recharging the battery.

Coordination of Electric and Mechanical Brake :

Fig A : Regenerative brake

In an electric Motor, the Total Brake distribution is in two aspects which are Electrical Brake which is called Regenerative Brake, and Mechanical Brake or Classical Brake with a hydraulic cylindrical system. Brake Force distribution must be uniform, If the Regenerative braking power requirement is more than the charging limit of the battery or more than the regenerative capacity of the machine we must apply Mechanical brakes as well. In a practical case, the combination of these two is applied. So usually it is a combined response of Mechanical brake and Regenerative brake. The reason for how this braking force is combined, that particular phenomena are called Brake Control Strategies. There are two Brake Control Strategies, which are Series - In case of Series, we apply Mechanical brake and Regenerative electric brake one after another. We can apply only one brake strategy at a time either apply Regeneratively or apply Mechanical brake. The Series Brake Control Strategy has a further classification, that is based on whether we want the comfort of driver or Brake behavior compared to energy efficiency. Parallel - In the case of Parallel, we apply both brakes simultaneously. This Particular Parallel braking is going to happen both at a time. Electric Driven Intelligent Brake (EDIB) is a combination of Hydraulic brake or Mechanical brake along with a Regenerative brake. It is a Parallel braking technique. The Control criteria such that at low speed use regenerative braking higher and at high speed or during the initial braking period we actually combine the both.

Ans 3 : MATLAB Program to Plot Motor Speed-Torque Contour Efficiency :

clear all
close all
clc

w = linspace(0,1000);
T = linspace(0,250);

% motor constants
kc = 0.2; % for copper loss
ki = 0.008; % for iron loss
kw = 0.00001; % for windage loss
conL = 20; % for constant motor losses

% making mesh
[X,Y] = meshgrid(w,T);
OutputPower = (X.*Y); % Torque x Speed = Power
B = (Y.^2)*kc; % copper loss
C = (X.^3)*kw; % winding loss
D = X*ki; % Iron loss
InputPower = OutputPower + B + C + D + conL;
Z = OutputPower./InputPower;

% Set the efficiencies for which the contours will be plottted
V = [0.70 , 0.75 , 0.80 , 0.82 , 0.85 , 0.87 , 0.89 , 0.90 , 0.92];
box off
grid off
contour(X,Y,Z,V);
xlabel('Speed(rad/s)')
ylabel('Torque(N.m)')
hold on
V = [8000,10000];
contour(X,Y,OutputPower,V);

Explanation:

To plot contour line for a given Motor. A Motor have various types of losses happening inside. The various types of losses are:

Copper Losses - I^2R , where R is the Armature resistance and we say that Torque is proportional to Current, this copper loss can be consider as .where is to take care of resistance of brushes and also take care of ux and its effect.

Copper losses = kc⋅T2kc⋅T2

Iron Losses - Iron Losses are nothing but Magnetic losses, which is denoted as , where factor is based on the Magnetic eld effect. For Permanent Magnets have constant Magnetic eld and this Iron losses is based on the value of and this are going to change according to the Speed. At Various Speed have different value of Back EMF and that is going to affect the Iron Losses.

Iron Losses = ki⋅ωki⋅ω

Windage Losses - This is a Mechanical or friction of Windage losses. This is based on size of shape of Motor and the amount of windage losses that the motor is going to experience.

Windage Losses = kw⋅ω^3

Constant Losses - This is denoted as C.

Total Losses - The Total Losses are considering the above four losses and denoted as,

Total Losses =kc⋅T^2+ki⋅ω+kw⋅ω^3+C

All Motors are model as per the above equation of losses. This above equation is not only applicable for Permanent Magnet DC Motor, but other motors as well like induction motor.

MATLAB program for calculating the losses of the EV motor:

In this MATLAB script, we create arrays for the speed and the torque of the motor using the ‘linspace’ command. For the speed, consider a range of values from 0 to 2000 radians per second whereas for the torque, consider a range of values from 0 to 300Nm. These arrays are then used to create 2D grid coordinates using the ‘meshgrid’ command. These coordinates will help in the creation of the contour plot. To find the efficiency of the motor, we need to consider the various losses that occur in the motor’s operation. These are:

• Copper losses
• Iron losses
• Windage losses
• Conduction losses

These various losses are dependent on the speed and the torque of the motor. They each also have a characteristic constant of proportionality which are all assumed for the following calculations and represented as 'K'. In each calculation, the speed and the torque are represented respectively as ω and T.

• Copper losses = KCu⋅ω2
• Iron losses =KFe⋅T2
• Windage losses =Kw⋅T3

The values of coefficients are taken as general values. Conduction losses are assumed to be 18 Joules.

Finally, we plot the contour with the 'contour' command. Besides, an array for the efficiency values we want to plot for is created called 'W' and is assigned for values ranging from an efficiency level of 0.75 to 0.95. This array is used in the creation of the contour. Axis labels and a title are also made for better readability.

Output:

clear all
close all
clc
% Speed Array
omega = linspace(0, 300, 100);
% Torque Array
T = linspace(0, 2000, 100);
% Meshgrid
[X,Y] = meshgrid(T, omega);

% Loss Coefficients
cu = 0.17; % Copper coefficient
fe = 0.006; % Iron coefficient
win = 0.000015; % Windage coefficient

% Losses
cu_loss = cu*(Y.^2); % Copper Losses
fe_loss = fe*(X.^2); % Iron Losses
win_loss = win*(X.^3); % Windage Losses
cond_loss = 18; % Conduction Losses

% Output Power
P_out = (X.*Y);
% Input Power
P_in = P_out + (cu_loss) + (fe_loss) + (win_loss) + (cond_loss);
% Efficiency
n = ((P_out)./(P_in));

% Efficiency values for contour
W = linspace(0.75, 0.95, 10);
% Contour Plot
contour(X,Y,n,W)
xlabel('Angular Speed, rad/s')
ylabel('Torque, Nm')
title('Speed, Torque and Efficiency characteristics of Motor')

Result:

The above Plot shows the Motor Speed-Torque Efficiency Contour Plot. A Point is denoted in innermost contour line is group of efficiencies which is highest value of the efficiency as 93%, because where the height is maximum and another point is denoted outermost contour line is contain group of efficiencies which is the lowest value of efficiency as 70%, because where the height reduces. Increasing efficiency order as going inward and Decreasing efficiency order as going outward. The yellow line shows the 8kw and 10kw Power.