Week-11 Challenge: Braking

1)

formula for calculating the energy required for braking

E = 1/2*m*(vi-vf)^2

here m=mass,vi=initial speed,vf=final speed

here i have created my own drive cycle and calculated the braking energy using the formula ,the calculated braking eneergy are in KW

2)

below screenshot indicates the speed torque characteristic of ac motor

From the above screenshot, we have two region, 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 power region as the power generated by the motor will be at it's 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.

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

Mechanical Braking System

*in mechanical braking, the frictional force between the rotating parts and the brake drums produces the required braking

coordination of these brakes in vehicles

*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 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 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)

% 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_l = (Y.^2)*Kc;% Copper losses equation
I_l = X*Ki;     % Iron losses equation
W_l = (X.^3)*Kw;% Windage losses equation

Input_power = Output_power + C_l + I_l + W_l + 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');

*from the above screenshot it can be seen that the speed and torque varies as the efficiency increases,this is due to the motor losses that occur

*greater the motor efficiency, lower speed-torque combination is required to overcome the motor losses