Week-11 Challenge: Braking

AIM:

1. For a defined driving cycle, calculate the energy required for braking.
2. To define why electric motor can’t develop braking torque at high speed similar to starting and how electric and mechanical brakes are coordinated.
3. To make a MATLAB program which plots contour of given motor speed, torque and efficiency values.

DESCRIPTION:

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

Here 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.

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. To define why electric motor can’t develop braking torque at high speed similar to starting and how electric and mechanical brakes are coordinated.

"Electric motor can't develop braking torque at high speed" - Reason:

Now Speed torque characteristics of motor is shown below,

Here it is clearly shown in the first graph that till the motor reaches the critical speed it has constant torque and once it reaches the critical speed, the curve is having a down slope which is a constant power region. And this graph denotes the accelerating operation of the motor. For the deceleration or braking operation of the motor, this graph is mirrored down which will be having the speed (+ve) and torque (-ve).

For example,

we can say that an EV can achieve 0-100 kmph in 10sec. Acceleration operation goes this way, with low speed and high torque Constant torque region is achieved which has accelerating power and by reaching the critical speed it shifts to constant power region and thus it easy for an EV to reach 0-100 kmph.

As said the breaking operation graph will be th mirrored image of above plot. So we cannot say that the motor producing 7Nm torque for acceleration can also produce -7Nm for breaking. Because we are operating in the field weakening region, and operating above the base speed. Thus Peak Acceleration torque is greater than the Peak Deceleraion torque. Thus for acceleration it has high torque with low speed and for deceleration it has low torque for high speed.

Electric and mechanical brakes are coordination:

There are two brake control strategies namely, SERIES & PARALLEL.

SERIES:

Brakes will be applied one after the another so which they are connected in series. Either one brake stragety at a time either Regenerative braking or Mechanical braking at a time.

PARALLEL:

In case of parallel both the brakes are applied simultaneously, Both at a time.

ELECTRIC DRIVEN INTELLIGENT BRAKE:

And Nissan has developed a practical brake strategy called ELECTRIC DRIVEN INTELLIGENT BRAKE developed by Nissan leaf.

Technology Functionality:
After stepping on the brake pedal, the system produces natural and adequate braking force that corresponds to the operation. The amount of energy regeneration also needs to be increased as much as possible. 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. To make a MATLAB program which plots contour of given motor speed, torque and efficiency values.

MATLAB program:

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; %Eff of the motor
V = [0.70,0.80,0.90,0.91,0.92,0.925,0.93]; %Efficiencies to be plotted
box off
grid off
contourf(X,Y,Efficiency,V);
contourcbar
title('Speed-Torque-Efficiency Characteristics of Motor');
xlabel('Speed (rad/sec)');
ylabel('Torque (Nm)');

Program Description:

• Here in this program first two inputs were given. They are Speed & Torque using linspace command.
• Then the motor constant values are assigned namely Copper loss, Iron loss, Windage loss and Constant motor.
• Then meshgrid is used to evaluate functions of two variables and three-dimensional mesh/surface plots.
• Output Power is calculated by multiplying speed and torque.
• Then all the loss were calculated and the input powers were also calculated.
• Then comes the efficiency were calculated. And Contour graph is plotted between Speed, Torque and Efficiency.
• Title were given and labels were given.

Workspace:

Plot:

This clearly shows that maximum efficiency of 93% is achieved by 691.1rad/sec and at 147Nm. The lowest Efficiency is achieved at 223 rad/sec and at torque of 105.3Nm .And this Contour plot clearly gives the idea on Speed, Torque and Efficiency relationship of the motor. The color indicates the efficiency denoted in the right side with the colorbar.

Google Drive Link:

Matlab file : https://drive.google.com/file/d/1ImtQTmGNxlzEkUYsYR5Rv6Y97lSEeb-w/view

CONCLUSIONS:

1. For a defined driving cycle, the energy required for braking is calculated.
2. Why electric motor can’t develop braking torque at high speed similar to starting and how electric and mechanical brakes are coordinated were dicussed.
3. A MATLAB program which plots contour of given motor speed, torque and efficiency values is coded.