Week-11 Challenge: Braking

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

Ans:

Objective: To calculate the energy required for braking.

A. Drive cycle pattern:

Below is the energy pattern for braking with a given drive cycle. It has Velocity on X-axis and Energy on Y-axis.

B. Energy required for braking:

The above pattern gives us the maximum value of energy required for a given drive cycle = 156kW.

C. Velocity:

The above pattern gives us the maximum value of energy required for a given drive cycle = 156kW.

https://docs.google.com/spreadsheets/d/1xdardHoB-w8oMU9xO9OFuY6A-DvvUizGeF_RMmZj4Ts/edit#gid=0

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

Ans:

Objective: To give the reason why electric motor can’t develop braking torque at high speed similar to starting? and How electric and mechanical brakes are coordinated?

A. Electric Motor Braking Torque Production:

• What you read as torque actual value is indeed the current read on the motor multiplied by a factor (torque sensitivity or torque constant) that we consider linear and constant.

Reasons why the torque actual is NOT the real torque:

1. If commutation, phasing, is not correct, an important part of the current is not useful torque, it just creates electrical and magnetic loses.
2. If current loop is not well configured or unstable, the current will be higher and with ripple, the real "useful mechanical torque" will be indeed lower.
3. Torque constant can vary due to several factors, like motor construction, temperature of the magnets (that affects its magnetic properties).

• Sometimes after accelerating you can't reach the maximum torque. The reason is that no matter how much the current loop wants to increase current (proportional to torque) by increasing the PWM duty cycle of the power stage, the Vmotor is too close to Vbemf and therefore current can't increase more.
• Whenever Friction torque + Additional loads = Motor Torque, the load remain in equilibrium (does not move, or moves under constant speed). Whenever Friction torque + Additional loads < Motor Torque, the load accelerates (Motor torque - Friction torque - Additional loads = Acceleration torque > 0). At high speeds, the BEMF is so close to Vbus that the applicable Motor torque gets limited. Then, the bigger the Friction torque + Additional load is, the smaller the Acceleration torque becomes.
• This can also occur if acceleration or speed is limited by some reason.
• This situation does not occur at the beginning of acceleration because most of the torque is used to increase the kinetical energy of the load (and motor). But when the speed is already high and no extra load is applied it is not possible to increase the torque.

• To Prevent:

1. Increase DC bus voltage.

2. Unlimit system acceleration.

3. Use a motor with less resistance and lower back EMF proportion.

The proposed solution is to add a torque demand limitation based on speed.

• Will improve user feeling when releasing brake when the vehicle is already accelerated.
• Will limit vehicle top speed (safety)

B. Electric and Mechanical brakes coordination:

• Recent braking technologies like ABS and many others have changed the complete co-ordination of the braking system.
• In mechanical braking the driver applies brakes, then the brake pedals come closer to the disc connected with the driving disc.
• In electrical braking; either series or parallel methods can be followed.
• In Series Electrical Braking, the braking involved is applied one after another but not at the same time.
• In Parallel Electrical Braking, the braking involved is applied at the same time.
• When the brake pedal is pressed, the hydraulic fluid reaches the brake piston and created the braking pressure on the wheels.
• The same kinetic energy is being used for generating more power using bi-direction motor which operates as a generator while braking.

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3. Make a MATLAB program that plots contour of given motor speed, torque, and efficiency values. Attach the code as a .m file attach a screenshot of all the plots:

Ans:

Objective: To make a MATLAB program that plots contour of given motor speed, torque, and efficiency values.

A. MATLAB Script:

B. Responses:

a. Torque-speed:

b. Efficiency:

C. Code sample for the script:

clear all
close all
clc
Velocity = linspace(1,1000);
Torque = linspace(1,250);
kc = 0.2;
ki = 0.008;
kw = 0.0001;
constL = 20;
[X,Y] = meshgrid(Velocity,Torque);
Output_power = (X.*Y);
Copper_L = (Y.^2)*kc;
Iron_L = X.*ki;
Windage_L = (X.^3)*kw;
Input_power = Output_power + Copper_L + Iron_L + Windage_L + constL;
Efficiency = Output_power./Input_power;
V = [0.7,0.75,0.8,0.85,0.875,0.9,0.91,0.92,0.93];

box off
grid off
contourf(X,Y,Efficiency,V);
colorbar
xlabel('Rotor Speed (rpm)')
ylabel('Torque Induced (N-m)')
zlabel('Efficiency')
title('Torque-Speed curve of induction motor')

figure
surf(X,Y,Efficiency)
colorbar
xlabel('Rotor Speed (rpm)')
ylabel('Torque Induced (N-m)')
zlabel('Efficiency')
title('Efficiency of a motor')

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