Week-11 Challenge: Braking
- For a defined driving cycle, calculate the energy required for braking.
Braking energy is the kinetic energy that needs to be dissipated to slow down or stop a moving vehicle. It can be calculated using the formula: Braking Energy = (1/2)mv^2, where m is the total mass of the vehicle (including payload) in kg, and v is the initial velocity minus the final velocity in m/s. During a drive cycle, the required braking energy needs to be calculated for each second of time to slow down or stop the vehicle.
Here I have taken the drive cycle data from a website the link is attached below. We have used NEW YORK CITY DRIVE CYCLE for our calculation.
This Excel file is also attached below for better reference. And with this data we have plotted a graph between time and speed which is miles per hour. Which is converted into meter per sec for calculation purposes.
The graph is given below,
Now we are going to calculate Braking energy by this vehicle during this whole driving cycle.
Parameters:
M : Mass : 800kg
Vf : Final velocity : Here the minimum velocity obtained after braking is considered as final velocity.
Vi : Initial velocity : Here the maximum velocity obtained before braking is considered as initial velocity.
Formula:
33 decelerations were made during this driving cycle, So 33 braking energy is to be calculated and sum it up to get the Total braking energy.
Calculations:
This calculated word document is also attached with below.
Google Drive Links:
Website from which have downloaded drive cycle data : https://www.epa.gov/vehicle-and-fuel-emissions-testing/dynamometer-drive-schedules
Drive cycle data as Excel file : https://drive.google.com/file/d/1GAZjVzSOIHk08YBt8XuS8sY0_u0TYw8o/view
Calculations in Word document : https://drive.google.com/file/d/1rH35X1-z_nAcGmSa58NZB1VrzJHtD_nX/view
2. Why electric motor can’t develop braking torque at high speed similar to starting? How electric and mechanical brakes are coordinated?
electric motors can develop braking torque at high speeds, but the amount of braking torque decreases as speed increases. This is because the back EMF (electromotive force) generated by the motor increases with speed, which counteracts the applied voltage and reduces the amount of current flowing through the motor. As a result, the torque produced by the motor decreases.
To compensate for this, electric vehicles use regenerative braking, which converts the kinetic energy of the vehicle into electrical energy that can be stored in the battery. When the driver applies the brakes, the motor operates as a generator, producing a braking torque that slows down the vehicle and generates electricity at the same time.
Electric and mechanical brakes are coordinated in a way that ensures safe and efficient braking. Typically, the electric motor handles most of the braking at low speeds, while the mechanical brakes take over at higher speeds. The transition between electric and mechanical braking is controlled by the vehicle's electronic control unit (ECU), which monitors the speed and position of the motor and wheels and adjusts the braking force accordingly.
DC motor Torque vs Speed Characteristic
Here for both in case of AC or DC there is no torque at maximum speed, gradually the torque decreases at high speed as the speed tends to be maximum speed. This situation does not occur at the beginning of acceleration because most of the torque is used to increase the kinetic 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 as well as to develop braking torque. The braking operation happens in the motion which is been distributed as per proportion in the Brake Energy and the regenerative braking.
There are two types of braking:
(i)Mechanical Braking: Mechanical brakes all act by generating frictional forces as two surfaces rub against each other. The stopping power or capacity of a brake depends largely on the surface area of frictional surfaces as well as on the actuation force applied. Mechanical brakes are assemblies consisting of mechanical elements for the slowing or stopping of shafts in equipment drives. They use levers or linkages to transmit force from one point to another. Braking slows or stops the movement of the coupled shafts. There are several types of mechanical brakes.
1) Band brakes: These are the simplest brake configuration, have a metal band lined with heat and wear resistant friction material.
2) Drum brakes: These are commonly used on automobile rear wheels, work when shoes press against a spinning surface called a drum.
3) Disc brakes: These are constructed of brake pads, a calliper, and a rotor. During operation, the brake pads are squeezed against the rotor.
(ii) Electrical Braking: Electric brakes are devices that use an electrical current or magnetic actuating force to slow or stop the motion of a rotating component. They are used in industrial and vehicular braking applications that require fast response times and precise tension control. The magnet in the backing plate has 2 conductor wires which tap directly into the wiring. When electricity is on, it magnetizes the brake magnet. The magnet is attracted to the drum face. When it contacts this area, the friction causes it to rotate, which moves the actuating arm, and pushes the shoes out against the drum. Those shoe have a special brake pad material on them that resists the heat caused by that friction. When the shoes press against the inside of the drum, they prevent the hub, and consequently the wheel that's touching the ground.
A very beautiful electric braking scheme called Regenerative Braking is now being employed for electric braking. Here during the braking action, the motor is operated as generator. As we know that during generating action, a counter torque is produced. So this counter torque opposes the motion of motor and motor comes to halt. Moreover, the brake energy is converted to electrical energy which can be fed back to the source using power converters.
Electric and Mechanical brake coordination:
There are mainly 2 ways by which the Electric Vehicles could be braked:
- Series- Regenerative braking and mechanical braking both are applied one after another.
- Parallel- Regenerative braking and mechanical braking both are applied simultaneously.
When brake pedal is pressed the hydraulic fluid reaches the brake pistons and created the braking pressure on the wheels and the same kinetic energy is been used by the Regenerative Braking for generating more power using the Bi-directional motor which operates as a generator while braking.
MATLAB CODE:
clear all
close all
clc
x = linspace(1,1000,250); % Speed in rad/sec
y = linspace(1,250,250); % Torque in Nm
% Motor loss constants
kc = 0.2; % Copper loss constant
ki = 0.008; % Iron loss constant
kw = 0.00001; % Windage loss constant
Const_Loss = 20; % Constant motor loss
[X,Y] = meshgrid(x,y); % Converting to 2D
Output_power = X.*Y; % Power = Torque x Speed
B = (Y.^2)*kc; % Copper loss
C = X.*ki; % Iron loss
D = (X.^3)*kw; % Windage loss
Input_power = Output_power + B + C + D + Const_Loss;
Efficiency = Output_power./Input_power; % Efficiency of the motor
V = [0.70,0.80,0.90,0.91,0.92,0.925,0.93]; % Efficiencies to be plotted
figure;
contourf(X,Y,Efficiency,V);
colorbar;
title('Speed-Torque-Efficiency Characteristics of Motor');
xlabel('Speed (rad/sec)');
ylabel('Torque (Nm)');
OUTPUT:
This program defines the speed and torque range using the linspace command, and then computes the efficiency of the motor for each combination of speed and torque values using the provided loss constants. A contour plot is then created using the contourf function, with the efficiency values specified by the V vector.
To run this program, save the code as a .m file and run it in MATLAB. The resulting plot should appear in a new figure window.
explanation:
This program calculates the efficiency of an electric motor at different combinations of speed and torque values. The motor losses are calculated based on copper loss, iron loss, windage loss, and constant motor loss, and the efficiency is calculated as the ratio of output power to input power.
The output of this program is a contour plot that shows the efficiency of the motor as a function of speed and torque values. The contour plot is generated using the 'contourf' function in MATLAB, which creates a filled contour plot with color-coded contours representing different efficiency values. The colorbar function is used to add a colorbar to the plot.
The x-axis of the plot represents the speed of the motor in radians per second, while the y-axis represents the torque of the motor in Newton meters. The title of the plot is "Speed-Torque-Efficiency Characteristics of Motor", and the x and y-axis are labeled accordingly.
The variable V represents the different efficiency values to be plotted, ranging from 0.70 to 0.93. These values are used as contour levels for the plot.