Week-11 Challenge: Braking

Aim:

• To calculate the energy required for brakingbased on a specific drive cycle.
• To explain Why electric motor can’t develop braking torque at high speed similar to starting? How electric and mechanical brakes are coordinated? 
• To 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.

Q No 1)  For a defined driving cycle, calculate the energy required for braking.

Answer:

The driving cycle taken into consideration is the UDDS cycle which stands for Urban Dynamometer Driving Schedule.Although the data is taken for a total driving time for 1370s,for simplicity sake on 150s, of driving time is considered.The speed which is in miles per hour ha sbeen converted into meter per sec.

The drive cycle is given below:

Take equation for kinetic enegry from braking is given as.

`E = 1/ 2 m ( V_ i − V_ f )^ 2`

Where,

m = Mass of the vehicle in Kg.

Vi = initial speed of the vehicle in m/s

Vf = final speed of the vehicle in m/s

from the driving cycle 10 braking points were obtained.The mass is set at a constant 1500 kg.The energy required for the braking is given in the table below.

Therefore,the total energy required for braking is 

The excel sheet file of the Drive cycle and braking data is provided below.

Q No 2) Why electric motor can’t develop braking torque at high speed similar to starting? How electric and mechanical brakes are coordinated? 

Answer:

Let us consider the torque speed characteristic.

From  this curve we have two regions,constant torque and constant power region.At the start the motor achieves the peak torque till it reaches a certain motor speed range from where it will rapidly drop.The reason due to the drop in torque is due to the motor shaft reaching critical speed and the area where the peak torque is constant is known as the constant torque region of the motor.The region where the torque decreases is known as the constant power region as the power generated by the motor will be also its peak.

Since the torque produces at the constant power region is very low,it is not possible to develop enough braking torque in this region.The braking torque produce increases as the speed decreases.

How electric and mechanical brakes are co-ordinated? 

In electric vehicles,tow types of braking system is used electric brake system and mechanical brake system.

Electric braking System:

In electrical braking,the winding of the motor is used to produce a braking torque.A braking torque is developed during the braking operation.This braking torque opposes the motion of the rotating member or shaft.This is achieved by suitably changing the electrical connections of the motor.The motor operates on a Speed-Torque characteristic,depending upon the method of braking employed.

 Mechanical braking:

In mechanical braking the frictional force between the rotating parts and the brake drum produces the required braking.To achieve this mechanical equipment,such as brake lining and brake drums,are required.Whether electrical and mechanical,the braking of the drive should stop the motor at the specified point of time and position.

The electric braking system used in EVs and HEVs is regenerative braking.This method uses the motor as a generator during braking,developing a retarding torque,which acts on the running motor and halts it.The kinetic energy and potential energy,minus the losses of the motor are returned to teh mains and the motor runs at a constant speed.Thus,regenerative braking eliminates the tendency of the load to accelerate the motor.

Mechanical braking systems used can be either disc or drum brake system.Where in case of a disc brake system friction pads rub aganist a disc when th ebrake pedal is applied and the kinetic energy is converted into heat and slows th evehicle down.In a drum brake a set of brake shoes which are th efriction materials press aganist a drum.

Since the braking torque is very less at high speeds,mechanical brakes are applied to slow down the vehivle.As the motor reaches the constant torque region and regenerative braking system take effect where the motor acts as a generator and the negative torque produced charges the battery pack.

Q No.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.

 Answer:

An efficiency map of an electric motor is a contour plot of torque and speed.It is used to describe the speed and torque combinations required at different efficiency ranges.In order to model the efficiency contour we must consider the losses that occour in electric motors and these losses are:

• Iron or Core Losses: Iron losses are made of two components which are hysteresis losses and eddy currents.Hysteresis losses occour as we switch the electromagnets in our motor ON and OFF,and depends on the magnetic properties of the iron material used in the motor.Eddy current losses depend on many variables,including the thickness of the laminations in the stator,the frequency at which the motor operates,the flux density and the material's resistivity.The iron losses are proportional to the square of the lamination thickness.
• Copper or Variable Losses: Copper losses are due to the resistence of the copper conductors and the current that was ask them to carry,and they lead to heating of the conductors.Of course,because copper is heavy,we want to use as  little of i tas possible,minimizing cross-sectional area.This increases resistance and therefore increases losses and heating.
• Windage Losses: The loss caused by air friction between rotor and surrounding air is called windage losses.It occours due to air resistance to the armature.Higher the speed of the motor more will be the windage losses.

Based on these three losses the MATLAB to plot the efficiency contour is below.

     % Motor efficiency counter.
clear all
close all
clc

% Defining the speed and torque as arrays.
x = linspace(1,1000); % Motor speed in rad/s
y = linspace(1,250); % Motor torque in N-m

% Motor loss constant
Kc = 0.2; % copper losses constant
Ki = 0.008; % iron losses consatant
Kw = 0.00001; % windage losses contant
Conl = 20; % constant motor losses

[X,Y] = meshgrid(x,y); % To create a 3D array
Output_power = (X.*Y); % power equation
C_1 = (Y.^2)*Kc; % copper losses equation
I_1 = X*Ki;      % Iron losses equation
W_1 = (X.^3)*Kw; % windage losses equation
Input_power = output_power+ C_1 +I_1 + W_1 +Conl;
Z = output_power./Input_power; % Efficiency
V = [0.7,0.8,0.85,0.9,0.91,0.92,0.925,0.93]; % Mapping the contours of the efficiency

%Plotting the contour
box off
grid off
Contour(X,Y,Z,V);
xlabel('Speed in rad/d');
ylabel('Torque in N-M');
legend('0.7,0.8,0.85,0.9,0.91,0.92,0.925,0.93');
hold on

Explanation of Code,

• First the clear all,close all and clc commands are written to clear all variables in workspace,to clear all plots and to clear te workspace respectively.
• The speed and the torque are defined as two dimentional linearly spaced arrays using the linspace command.
• The constant of the motor losses are defined.
• The 2-D arrays of the speed and torque are then defined as 3-Dimensional arrays using the meshgrid command.
• The output power equation is defined as the product of speed and torque.
• The equations of the motor losses based on the speed and torque are defined.
• The input power is defined as the sum of output power plus motor losses.
• The efficiency is then defined as the ratio of output power to input power.
• In order to map the contour  for different efficiency ranges an array is defined which consists of the efficiencies from 0.7 to 0.93.
• The graph is plotted using the counter command to plot the speed,torque and efficiency.

The counter plot of the above MATLAB program is given below

From the plot it can be observed that the speed and torque varies as the efficiency increases.This is due to the motor losses that occour.The dark blue line represent the contour 70% efficiency and the bright yellow lone represents the contour 93% efficiency.

For example at 70% efficiency,the torque reaches it's peak value of 250 N-m when the vehicle is at very low speed but the torque decreases signifcantly as the speed increases for the same efficiency.And at a motor efficiency of 93% the speed and torque required is much less compared to an efficiency of 70%.

Greater the motor efficiency,lower the Speed - Torque combination is required to overcme the motor losses.

Conclusion:

• The energy required for braking of a vehicle based on drive cycle is calculated.
• The co-ordination between electric brakes and mechanical brakes and why braking torque is less at hig speed are explained.
• The MATLAB program to plot the Speed,torque and efficiencies contour is written and the graph is plottd.