Week-11 Challenge: Braking

1. For a defined driving cycle, calculate the energy required for braking.
2. Why electric motor can’t develop braking torque at high speed similar to starting? How electric and mechanical brakes are coordinated?
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.

AIM :-

• To Calculate the energy required for braking based on a specified drive cycle.
• To explain why electric motors cannot develop braking torque at high speed and also how electric and mechanical brakes are co-ordinated.
• To write a MATLAB program to plot the contour of a motor’s speed, torque and efficiencies.

1. ENERGY REQUIRED FOR BAKING BASED ON A DRIVING CYCLE :-

The driving cycle taken into reference is the UDDS cycle which stands for Urban Dynamometer Driving Schedule. the data is taken for a total driving time for 300sec. for simplicity. The speed which is in miles per hour has been converted to meters per second.

The drive cycle is given below.

As we know that the equation for kinetic energy from braking is given as,

E=1/2 m(V_i-V_f)^2

Were,

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.

Form the drive cycle 11 braking points were obtained. The mass is set at a constant 1500 Kg. The energy required for braking is given in the table below.

Therefore, the total energy required for braking is 529.39 KWhr.

If the time required to reach from max speed to zero (0) is 10 sec. then,

Power required is P=E/t W.

i.e., 529391/10 = 52.93KW.

2. WHYELECTRIC MOTORS CANNOT DEVELOP RAKING TORQUE AT HIGH SPEEDS. HOW ARE ELCETRIC AND MEHCANICAL BRAKES C0-ORDINATED: -

As you can see, an Induction motor does not generate max torque at zero speed but at certain speed much like an internal combustion engine.

But the thing is, these characteristics are obtained when we run the motor directly from a rated supply. Fortunately, we do not run motors directly from supply. We use Motor Controllers in-between the motor and the supply.

Motor Controllers provide lots of advantages over running from direct supply, Speed Control, regenerative breaking, smooth starting to name a few.

Motor controllers employs one of several control techniques like PWM, space vector modulation, variable frequency etc to control motor torque, speed, power output. They can also make a motor produce max torque at any speed below rated speed.

Let us consider the torque speed characteristics.

From this curve we have two regions, constant torque and constant power region. At the start the motor achieves 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 region as the power generated by the motor will be at its’ peak.

Since the torque produced at the constant power region is very low, it is not possible to develop enough braking torque in this region. The braking torque produced increases as the speed decreases. And so maximum torque output can be maintained up to the rated speed. When rated speed is reached, motor hits it's power limit, so further increase in speed requires torque to be decreased.

How are electric brakes and mechanical brakes co-ordinated?

In electric vehicles, two types of braking systems are used electric brake system and mechanical brake system.

Electric Braking System: - 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 the mains and the motor runs at a constant speed. Thus, regenerative braking eliminates the tendency of the load to accelerate the motor.

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 charging the electrical connections of the motor. The motor operates on a speed-torque characteristic, depending upon the method of braking employed.

Mechanical Braking System: - In mechanical braking, the frictional force between the rotating parts and the brake drums produces the required braking. To achieve this, mechanical equipment, such as brake linings 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.

Mechanical braking systems used can be either disc or drum brake system. Where in case of a disc brake system friction pads rub against a disc when the brake pedal is applied and the kinetic energy id converted to heat and slows the vehicle down. In a drum brake system, a set of brake shoes which are the friction materials press against a drum.

ELECTRICAL BRAKING	MECHANICAL BRAKING
Little maintenance and dust free operation due to absence of mechanical equipment.	It requires frequent maintenance. Adjustment of brakes and replacement of linings due to wear and tear.
The energy due to rotating parts can be converted into electrical energy.	Energy of rotating parts is wasted as heat in friction.
This energy can be utilised or turns into mains during braking.	Here heat is generated during braking.
Braking is smooth.	Braking is not smooth.
High initial cost.	Low initial cost.
Safer but takes long time than mechanical braking in sudden brake appliance.	Less safe compare to electrical braking.
Frication free	Friction plays a major role in mechanical braking.

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

These two brakes are used as parallel as shown below.

3. MATLAB PROGRAM TO PLOT THE CONTOURS OF A MOTOR’S SPEED TORQUR AND EFFICIENCES:-

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 ranges. In order to model the efficiency, contour we must consider the losses that occur in electric motors and these losses are,

• Iron or Core Losses: Iron losses are mase of two components which are hysteresis and eddy currents. Hysteresis losses occur 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 resistance of the copper conductors and the current that we 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 it as possible, minimising cross-sectional area. This increase 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 occurs due to air resistance to the armature. Higher the speed of the motor more will be the windage losses.

Based on these 3 losses we can plot the contour through the matlab program (script file) as below.

% motor efficiency contour.
close all
clc
%defining the speed and torque as arrays.
x = linspace(1,1000); %motor speed in rad/sec.
y = linspace(1,250); %motor torque in Nm.
%motor loss constant.
Kc = 0.2;     %constant copper losses.
Ki = 0.008;   %constant iron losses.
Kw = 0.00001; %constant windage losses.
Conl = 20;    %constant motor losses.
%now make mesh.
[X,Y] = meshgrid(x,y); %to create a 3D array.
Output_Power = (X.*Y);%power equation P=speed * torque.
C = (Y.^2)*Kc; % equation for copper losses.
I = X*Ki;      %equation for iron losses.
W = (X.^3)*Kw; %equation for windage losses.
Input_Power = Output_Power + C + I + W + Conl;
Z = Output_Power./Input_Power; %efficincy.
V = [0.7,0.8,0.85,0.9,0.91,0.92,0.925,0.93]; %mapping the contours of the efficiency.
%ploting the contour.
box off;
grid off;
contour(X,Y,Z,V);
title('contour for motors speed torque and effeciency');
xlabel('Speed in rad/sec');
ylabel('Torque in N/m');
legend('0.7,0.8,0.85,0.9,0.91,0.92,0.925,0.93'); 

The contour plot of the above program is given below.

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

For example, at 70% efficiency, the torque reaches its peak value of 250 N-m when the vehicle is a very low speed but the torque decreases significantly 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%.

Grater the motor efficiency, lower speed-torque combination is required to overcome the motor losses.

Conclusion:

• the energy required for braking based on a specified drive cycle is calculated.
• Why electric motors cannot develop braking torque at high speed and also how electric and mechanical brakes are co-ordinated are explained.
• MATLAB program to plot the contour of a motor’s speed, torque and efficiencies with the graph plotted.