Week-11 Challenge: Braking
1. Braking based on drive cycle
2. Electric Motors Cannot Develop Braking Torque
Let us consider the torque-speed characteristics which 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 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 at its peak.
| Electrical Braking | Mechanical Braking |
| The winding of the motor is used to produce braking torque | The frictional force between the rotating parts and the brake drums produces the required braking. |
| To achieve electrical braking, suitably change the electrical connections of the motor. | To achieve mechanical braking, mechanical equipment, such as brake linings and brake drums is required |
| Electrical braking requires less maintenance | Mechanical Braking requires regular maintenance |
| Dust-free operation due to the absence of mechanical equipment | Adjustment of brakes and replacement of brake linings due to wear and tear |
| The energy of rotating parts can be converted to electrical energy. This can be utilized or returned to the mains during braking | The energy of rotating parts is wasted as heat in friction. Heat is generated during braking |
| Braking is smooth, without snatching | Depending on conditions, braking may not be smooth |
| Equipment of a higher rating than the motor rating may be required in certain braking applications | Equipment like brake shoes, brake lining, brake drum are required |
| To produce holding torque, electrical energy is required for the operation | Mechanical braking can be applied to hold the rotating part or shaft at a particular 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 the 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 systems, Where in the case of a disc brake system friction pads rub against a disc when the brake pedal is applied and the kinetic energy is 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.
- 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.
3. Contour Program
% Motor efficiency contour.
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 constants
Kc = 0.2; % Copper losses constant
Ki= 0.008; % Iron losses constant
Kw = 0.00001; % Windage losses constant
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/s');
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:
- First, the clear all, close all, and clc commands are written to clear all variables in the workspace, to clear all plots, and to clear the workspace respectively.
- The speed and torque are defined as 2-Dimensional linearly spaced arrays using the linspace command.
- The constants of the motor losses are defined.
- The 2-D arrays of the speed and torque are then defined as 3 Dimensional arrays using the
- mesh grid 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 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 vary as the efficiency increases. This is due to the motor losses that occur. The dark blue line represents the contour's 70% efficiency and the bright yellow line represents the contour's 93% efficiency.
For example, at 70% efficiency, the torque reaches its peak value of 250 N-m when the vehicle is at 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 are much less compared to an efficiency of 70%.
Greater the motor efficiency, a lower speed torque combination is required to overcome the motor losses.
CONCLUSION :
- The energy required for braking a vehicle based on a drive cycle is calculated.
- The coordination between electric brakes and mechanical brakes and why braking torque is less at high speed are explained.
- The MATLAB program to plot the speed, torque, and efficiencies contour is written and the graph is plotted