Week-11 Challenge: Braking
1.For a defined driving cycle, calculate the energy required for braking.
1. Energy required for Braking based on a driving cycle.
The driving cycle taken into consideration is the UDDS cycle which stands for Urban Dynamometer Driving schedule.Data of 150 sec of driving time is considered.
The speed which is in miles per hour has been converted to meters per second.
The drive cycle is given below.
The equation for kinetic energy from braking is given as.
E= 1/2.m(Vi-Vf)^2
where,
m= mass of the vehicle in kg.
Vi= initial speed of the vehicle nn m/s.
Vf= Final speed of the vehicle in m/s.
From the drive cycle 10 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 16.8 KW .
The google sheet file of the drive cycle and braking data is provided below.
https://docs.google.com/spreadsheets/d/1GRL3EbKjw2ZEqSRhGD8shqhbSIyW2EK5p_sTP7Dz-g4/edit?usp=sharing
2.Why electric motor can’t develop braking torque at high speed similar to starting? How electric and mechanical brakes are coordinated?
Electric motor braking:
1. The electric motor braking is also known as regenerative braking, which is known as energy recovery mechanism that
slows down a moving vehicle or object by converting its kinetic energy into a form that can be either used immediately
or stored until needed.
2. When a break pedal is applied ,power supply to the motor is cut-off and the motor will be in rotation due to inertia.
3. During the rotation, inside the magnetic field a Back emf is generated which produces a negative torque and that is
used as the brakes to reduce the vehicle speed.
4. Also the current flows in reverse direction,using a bi_directional inverter we can store the current back into the
battery.
5. This process of braking by the effect of negative torque produced and where the motor acts as generator in producing
the current out of the motors rotation and storing back into the battery is called Regenerative braking.
Speed and torque charaterstics of a Dc motor:
1. From the above figure we can see the speed and torque behaviour of a electric motor.
2. During the initial low speed the torque is high which is the constant torque region.As speed builds up, after the
critical speed point the torque gradually decreases which is known as contant power region.
3. So during high speed the motors will be at contant power region abd while braking,due to high speed of the motor
the negative torque produced will be less.
4. But while starting the motor ,the speed will be very less and at this stage the motor will be operating in constant
torque region and this is the reason for high accelerating torque during the start of motor.
5. From this we can conclude that the braking torque produced at high speed motor operations will be lesser than the
starting torque of an electric motor.
6. Also there are other reasons like battery limitations due to which we cannot get high braking torque.
7. The rate of discharge is always higher than the rate of charging due to battery's chemical compositions.
Combination of Electric and Mechanical brakes:
1. Motor of electric vehicle is able to be used to brake regeneratively,so braking energy can be recycled.
2. Braking stability of electric vehicles with electro-hydraulic hybrid braking system can be influenced by braking force
distribution between hydraulic braking force and regenerative braking force.
3. Electric cars have regenerative braking and this does substantially reduce the need for hydraulic braking.
4. But there are some limitations like, the maximum deceleration with the engine alone is far smaller than with the brake
assistance. So you still need an ordinary frictional brake system to make the car stop instantly if required.
5. When the regenerative capacity is less than the actual braking required,mechanical brakes are applied at those times.
Brake control strategy:
1. When the brake pedal is pressed the control signal is sent to both the hydraulic cylinder and power converters for producing
both frictional braking and regenerative braking.
2. There are two ways of applying the combination of brakes and they are classified as,
series-The regenerative braking and frictional braking are applied one after another.
parallel-The regenerative braking and frictional braking are applied at the same time.
3. The series braking and parallel braking is choosen based on two parameters, one is drivers comfort and the other one is based on the efficiency.
4. This parallel combined braking technology is further developed as EDIB, which is Electric Driven Intelligent Braking.
5. The above figure represents the Electric Driven intelligent braking system, where we see both the regenerative brakes and the frictional brakes
are applied at the same time.
6. After braking the speed reduces from higher speed values and at this moment the % of composition of the combined braking changes.
7. Hence after brake application the speed is reduced to low speeds. Here torque will be high and the motor will be operating at constant torque region.
8. Now at this point the % of frictional brake application is reduced and regenerative braking is increased because at this point more negative torque can
be generated and thus higher electric power generated out of this braking can also be fed back to the battery.
9. Thus using this technology in braking an electric driven vehicle certainly increases the stopping power and also contributes to higher efficiency figures.
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.
An efficiency map of an electric motor is a contour plot of torque and speed .It is used to describe the speed and torque combination
required at different efficiency ranges .In order to model the efficiency contour we must consider the losses that occur in electric
motors and these losses are:
1. Iron or Core losses: Iron losses are made of two componenets which are hystersis and eddy currents.Hysteresis losses occur as we
switch the electromagnets in our motor on and off and depends upon 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 resistivity.The iron losses are proportional to the square of the lamination
thickness.
2. 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.ofcourse,because copper is heavy, we want to use as little of it as possible,
minimising cross-sectional area.This increases resistance and therfore increases loses and heating.
3. Windage looses: The loss caused by air friction between rotor and sorrounding 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.
clear all
close all
clc
%The torque and velocity range of the motor
T = linspace(0,250);%torque
W = linspace(0,1000);%velocity
%copper loss constant
kc = 0.2;
%iron loss constant
ki = 0.008;
%windage loss constant
kw= 0.0001;
%constant motor loss
c= 20;
%creating 2D array for torque and velocity
[X,Y] = meshgrid(W,T);
output_power = (X.*Y);
%Loss calculation
copper_losses = kc*(Y.^2);
iron_losses = (X).*ki;
windage_losses = (X.^3)*kw;
%power and efficiency calculations
Input_power = output_power + copper_losses +iron_losses +windage_losses + c;
Efficiency = output_power./Input_power
%Efficiency curves value range
V = [0.70,0.75,0.80,0.85,0.875,0.90,0.91,0.92,0.93]
%plotting the contour for speed ,torque and effieciency
box off
grid off
contour(X,Y,Efficiency,V);
colorbar
xlabel('motor speed(RPM)');
ylabel('Torque(NM)');
zlabel('Efficiency');
title('contour of given motor speed,torque and efficiency')
Explanation of the code,
1. First the clear all, close all and clc commands are written to clear all variables in workspace, to clear all plots and to clear
the workspace respectively.
2. The speed and torque are defined as 2_dimensional linearly spaced arrays using the linspace command.
3. The constants of the motor losses are defined.
4. The 2-D array of the speed and torque are then defined as 3-D arrays using the meshgrid command.
5. The output power equation is defined as the product of speed and torque.
6. The equation of the motor losses based on the speed and torque are defined.
7. The input power is defined as the sum of output power plus motor losses.
8. The efficiency is then defined as the ratio of output power to input power.
9. 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.
10. The graph is plotted using the contour command to plot the speed,torque and efficiency.
The contour plot of the above MATLAB program is given below.
From the plot it can be observed that the speed and torque varies as the effeiciency 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 efficency of 70%.
Greater the motor efficiency, lower the speed_torque combination is required to overcome the motor losses.
Conclusion:
1. The energy required for braking of a vehicle based on a drive_cycle is calculated.
2. The co-ordination between electric brakes and mechanical brakes and why braking torque is less at high speed are explained.
3. The matlab program to plot the speed, torque and efficiencies contour is written and the graph is plotted.