Week-11 Challenge: Braking

Challenge 11

 

1. For a defined driving cycle, calculate the energy required for braking.

Let's calculate the braking energy required for each point in the FTP-75 drive cycle based on assumptions.

We’re using the kinetic energy K.E. = (½)*M*V2  , where:

- K.E is the kinetic energy in joules (J).

- M is the mass of the vehicle in kilograms (kg).

- V is the velocity in meters per second (m/s).

Here are the calculations for each point in the FTP-75 drive cycle:

1. Braking from 17 m/s to 0 m/s:

   - Mass M: 400 kg

   - Initial Velocity (vi): 17 m/s

   - Final Velocity (vf): 0 m/s

   Calculate the kinetic energy K.E as:

   K.E. = (½)*M*(vi2 - vf2) = (½)*400*(172 - 0) = 57800 J

   The energy required for braking in this segment is 57.8 kJ.

2. Braking from 30 m/s to 18 m/s:

   - Mass M): 400 kg

   - Initial Velocity (vi): 30 m/s

   - Final Velocity (vf): 18 m/s

   Calculate the kinetic energy K.E as:

  K.E. = (½)*M*(vi2 - vf2) = (½)*400*(302 - 182) = 28800 J

   The energy required for braking in this segment is 28.8 kJ.

3. Braking from 40 m/s to 0 m/s (coming to a complete stop):

   - Mass M: 400 kg

   - Initial Velocity (vi): 40 m/s

   - Final Velocity (vf): 0 m/s

   Calculate the kinetic energy K.E as:

 K.E. = (½)*M*(vi2 - vf2) = (½)*400*(402 - 0) = 320000 J

   The energy required for braking in this segment is 320 kJ.

    2. Why electric motor can’t develop braking torque at high speed similar to starting? How electric and mechanical brakes are coordinated?

Electric motors have the capability to produce braking torque at high speeds, similar to how they generate torque during startup. However, there are distinct differences in how electric motors function during these two phases and how they collaborate with mechanical brakes:

1. Starting (Acceleration):

   - During startup, electric motors exert torque to overcome the initial resistance and inertia of the load. To generate mechanical torque, the motor draws electrical current.

   - Starting torque is usually higher than the motor's rated continuous torque, and this is made possible by the motor's ability to momentarily draw increased current.

   - Electric motors are effective at providing substantial torque at low speeds to accelerate a load.

2. Braking (Deceleration):

   - In deceleration or braking scenarios, electric motors can indeed apply torque, but it operates in the opposite direction. Instead of driving the load, the motor transforms into a generator.

   - During this phase, the motor converts kinetic energy into electrical energy through regenerative braking, and this energy can be returned to the power source or dissipated as heat (dynamic braking).

   - The amount of regenerative braking torque achievable at high speeds may be restricted by factors such as the motor's design, controller capabilities, and the capacity of the energy storage system (e.g., the battery) to absorb the regenerated energy.

   - As the vehicle's speed decreases, regenerative braking torque can become more substantial because there is more kinetic energy available for conversion.

Regarding the coordination of electric and mechanical brakes:

- In many electric vehicles (EVs) and hybrids, regenerative braking serves as the primary means to slow down the vehicle and recover energy.

- Regenerative braking is typically the initial choice for deceleration due to its energy efficiency and reduced wear on mechanical brakes.

- When the regenerative braking system reaches its limits (e.g., the battery is fully charged or the motor can't produce sufficient braking torque), mechanical brakes (such as disc brakes) are employed to provide additional braking force.

- The seamless coordination between electric and mechanical brakes is managed by the vehicle's control system, which determines the optimal balance between regenerative braking and mechanical braking based on various factors, including vehicle speed, battery charge status, and driver input (e.g., brake pedal application).

In summary, electric motors are capable of generating braking torque at high speeds, but the magnitude of this torque is influenced by factors like motor design and the system's ability to accept and manage regenerated energy. The coordination between electric and mechanical brakes is vital for optimizing braking performance and energy efficiency in vehicles.

    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.

 

Program:- 

 

clear all

close all

Clc

x = linspace(1, 1000, 250); % Speed in rad/sec

y = linspace(1, 250, 250); % Torque in Nm

% Modified motor loss constants and efficiency values

kc = 0.15; % Modified copper loss constant

ki = 0.006; % Modified iron loss constant

kw = 0.000005; % Modified windage loss constant

Const_Loss = 15; % Modified constant motor loss

[X, Y] = meshgrid(x, y); % Converting to 2D

Output_power = (X .* Y); % Power = Torque x Speed

B = (Y .^ 2) * kc; % Copper loss

C = X .* ki; % Iron loss

D = (X .^ 3) * kw; % Windage loss

Input_power = Output_power + B + C + D + Const_Loss;

Efficiency = Output_power ./ Input_power; �ficiency of the motor

�sired efficiency values for contour plotting

V = [0.75, 0.80, 0.85, 0.90, 0.92, 0.94, 0.96];

box off

grid off

contourf(X, Y, Efficiency, V);

colorbar; �dcolorbar

title('Speed-Torque-Efficiency Characteristics of Motor');

xlabel('Speed (rad/sec)');

ylabel('Torque (Nm)');

 

Output:-

 

 

 This clearly shows that maximum efficiency of 95% is achieved by 566.6 rad/sec and at 84Nm. The lowest Efficiency is achieved at 109.3 rad/sec and at torque of 241 Nm .And this Contour plot clearly gives the idea on Speed, Torque and Efficiency relationship of the motor. The color indicates the efficiency denoted in the right side with the color bar.

Google drive Link:- 

https://docs.google.com/document/d/1gOfaYLd-cNOEyocnkmfA71mQl7mvikqoO3mzTUSvGYM/edit?usp=sharing