Braking

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

• We have to create a drive cycle excel file with random data of velocity concerning that time and plotted them to see the drive cycle

• Then import that file into Matlab.

• Then to create an array into the command window by entering code braking_energy
• Then write a code to calculate the braking energy and avg braking energy.

MATLAB Code:

% Brake Energy Calculation For a Drive Cycle

clear all
close all
clc

load drivecycle.txt                                % drive cycle file
time = drivecycle(:,1);                            % assigning the first coloumn of the drive cycle as time values in sec
speed = drivecycle(:,2);                           % assigning the second coloumn of the drive cycle as speed values in m/sec

figure
plot(time,speed, 'Color','r')                                   % drive cycle graphically
title('DRIVE CYCLE')                               % title
hold on
xlabel('time (sec)')                               % labelling x axis
ylabel('speed (m/sec)')                            % labelling y axis
grid on                                            % making grids ON

kerb_weight = 1400;                                % vehicle mass in Kg

brake_energy = (0.5.*kerb_weight.*speed.^2)./1000;           % braking energy calculation

figure
plot(time,brake_energy)                                      % plotting brake energy vs time graph
grid on                                                      % making grids ON
colorbar
title('BRAKE ENERGY vs TIME')                                
xlabel('time (sec)')                                         % labelling x axis
ylabel('brake energy (KJ)')                                  % labelling y axis

Workspace:

Output Graph:

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

Why electric motor can’t develop braking torque at a high speed similar to starting?

Types of Torque:

• Starting Torque:

Starting torque also referred to as locked rotor torque, is the torque that the motor develops each time it is started at rated voltage and frequency. It is the torque produced when power is applied to a motor at rest, i.e. when the motor is energized at full voltage and the shaft is locked in place. This is the torque used to start accelerating the load. The starting torque is indicated on the torque/speed curve shown above.

• Pull-up Torque:

This term is used for the lowest point on the torque-speed curve for an electric motor which is accelerating a load up to full speed. As the motor picks up speed, torque decreases slightly to the lowest point shown on the curve above. The torque available at this point is called pull-up torque.

1. Sometimes after accelerating you can't reach the maximum torque. The reason is that no matter how much the current loop wants to increase current (proportional to torque) by increasing the PWM duty cycle of the power stage, the Vmotor is too close to Vbemf, and therefore current can't increase more. Whenever Friction torque + Additional loads = Motor Torque, the load remains in equilibrium (does not move, or moves under constant speed).
2. Whenever Friction torque + Additional loads = Motor Torque, the load accelerates (Motor torque - Friction torque - Additional loads = Acceleration torque  > 0). Al high speeds, the BEMF is so close to Vbus that the applicable Motor torque gets limited. Then, the bigger the Friction torque + Additional load is, the smaller the Acceleration torque becomes.
3. This can also occur if acceleration or speed is limited by some reason.
4. This situation does not occur at the beginning of acceleration because most of the torque is used to increase the kinetical energy of the load(and motor). But when the speed is already high and no extra load is applied it is not possible to increase the torque.

Reasons why the torque actual is NOT the real torque:

• If commutation, phasing, is not correct, an important part of the current is not useful torque, it just creates electrical and magnetic losses. 
• If the current loop is not well configured or unstable, the current will be higher and with ripple, the real "useful mechanical torque" will be indeed lower.
• Torque constant can vary due to several factors, like motor construction, the temperature of the magnets (that affects its magnetic properties).

Maximum achievable torque depending on motor speed:

To prevent this:

• Increase DC bus voltage. 
• Unlimit system acceleration.
• Use a motor with less resistance and lower back EMF proportion. 

How electric and mechanical brakes are coordinated?

Types of Brakes:

Mechanical:

• Drum braking
• Disc braking
• Band braking
• Pawl & Ratchet braking

Electrical:

• Plugging type braking
• DC injection type braking
• Eddy current braking
• Dynamic resistor type braking
• Regenerative braking
• Sharing DC bus type braking

Mechanical Braking System:

Mechanical braking mostly used in scooters, motor vehicles, and motorcycles where small power is required. It is essential in manufacturing power transmission applications, material handling, etc. It delivers forces to the axle or a wheel in order to stop motion. It helps to reduce the speed of the system slowly by the mechanical process when compared to electrical braking. The working of a mechanical brake depends on the pedal. When the pedal is pressed, the brake shoes are pushed outwards and rotates against the drum which is connected to the wheels. Hence the machine or vehicle gets slow down and stopped. And when the pedal is released, it goes to a normal position due to the pullback action of spring shoes.

Electrical Braking System:

Electrical braking is used to reduce the speed of the machine depending on flux and torque. This type of braking is mainly used for functional braking to control the speed of the machine. It is easy to handle and comfortable. But it cannot be used for emergency braking and parking braking. The working of electrical braking depends on the electromagnetic force (EMF) acting on the brake shoes. The battery is used to generate an electric current which helps to energize the electromagnet mounted on the backplate. This results in activating the cam and expanding the brake shoes. Hence the vehicle or machine is stopped by braking the wheel.

Comparison between Electrical and Mechanical Braking:

1. Electrical braking systems are used for functional braking (controlling the speed; bringing the load to a standstill). Mechanical braking systems are used for emergency stopping or for parking.
2. Electrical braking is usually very smooth and comfortable. Mechanical braking is usually rough and uncomfortable.
3. No wear results from electrical braking. Mechanical braking on the other hand causes wear in the braking components and requires regular maintenance.
4. It is possible (but not always feasible) in electrical braking systems to return the regenerated energy back to the main supply. This is not possible in mechanical braking systems and the energy is always lost as heat, noise, and wear.
5. The electrical braking system cannot be used as a safety device. Most systems will require a mechanical braking system as a backup safety device.

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

MATLAB Code:

% PROGRAM TO PLOT CONTOUR LINES FOR THE DEFINED MOTOR SPEED, TORQUE AND EFFICIENCY

close all
clear all
clc

%SPEED & TORQUE ARRAY
w = linspace(1,1250,250);                 % SPEED ARRAY
T = linspace(1,100,250);                % TORQUE ARRAY

%MESHGRID
[X,Y] = meshgrid(w,T);                   % 2D COORDINATES FOR SPEED & TORQUE

%LOSS CONSTANTS
kc = 0.2;                                % COPPER CONSTANT
ki = 0.008;                              % IRON CONSTANT
kw = 0.00001;                            % WINDAGE CONSTANT
const = 20;                              % CONDUCTION CONSTANT

%MOTOR LOSS CALCULATIONS
l_copper = (Y.^2)*kc;                    % COPPER LOSS
l_iron = (X*ki);                         % IRON LOSS
l_windage = (X.^3)*kw;                   % WINDAGE LOSS

%OUTPUT POWER,INPUT POWER & EFFICICENCY CALCULATIONS
pout = X.*Y;                                            % OUTPUT POWER
pin = pout + l_copper + l_iron + l_windage + const;     % OUTPUT POWER
eff = pout./pin                                         % EFFICICNCY CALCULATION

%EFFICIENCY VALUES FOR CONTOUR
V = [0.70,0.80,0.85,0.90,0.91,0.92,0.925,0.93];         % DEFINES AN ARRAY FOR EFFICIENCY THE CONTOUR LIMITS 

%COMMANDS FOR READABILITY
figure
box off                                                 % REMOVES THE BOX OUTLINE AROUND THE AXES
grid OFF                                                % GRIDS ARE NOT SHOWN
contourf(X,Y,eff,V);                                    % CONTOUR COMMAND  
colorbar                                                % COLORBAR FOR BETTER UNDERSTANDING
xlabel('Speed rad/sec')                                 % X AXIS IS LABELLED
ylabel('Torque N/m')                                    % Y AXIS IS LABELLED
zlabel('Efficiency')                                    % Z AXIS IS LABELLED
title('Torque-Speed curve for the Induction Motor')     % TITLE OF THE PLOT

figure
surf(X,Y,eff)                                           % SURFACE COMMAND 
colorbar                                                % COLORBAR FOR BETTER UNDERSTANDING
xlabel('Speed rad/sec')                                 % X AXIS IS LABELLED
ylabel('Torque')                                        % Y AXIS IS LABELLED
zlabel('Efficiency')                                    % Z AXIS IS LABELLED
title('Efficiency curve for the Induction Motor')       % TITLE OF THE PLOT

Workspace:

Command Window:

Output Graph:

References:

1. https://doc.ingeniamc.com/wiki/motion-wiki/why-sometimes-i-can-t-reach-100-motor-torque-when-is-already-turning#:~:text=This%20situation%20does%20not%20occur,possible%20to%20increase%20the%20torque.
2. https://www.machinedesign.com/mechanical-motion-systems/article/21831982/whats-the-difference-between-friction-and-regenerative-car-brakes
3. https://learnmechanical.com/brake-system/