Week-11 Challenge: Braking
- For a defined driving cycle, calculate the energy required for braking.
Braking is the process of controlling the velocity of an object by inhibiting its motion. An object in motion possesses Kinetic energy and to bring the object to a stop this kinetic energy must be removed. Removing the kinetic energy can be accomplished by dissipating the energy to the atmosphere through friction or by converting it into another form of energy. The most common type of braking is a mechanical brake which inhibits motion through friction brake pads. A mechanical brake applies a friction force to convert the kinetic energy of the vehicle into thermal energy which then dissipates into the atmosphere.[2] Braking systems which don't use friction are referred to as regenerative braking systems (RBSs). In RBSs, the kinetic energy is converted into other forms of useful energy, which can be stored for later use, increasing fuel efficiency.
Vehicles are generally having 2 brakes , the service or foot brake and the emergency or hand brake.
Driving cycles are the patterns representing the journey of any vehicle.
The energy present in an object in motion is given by the following equation:
where,
• mass of the object in kilograms (kg).
• velocity of the object in meters per second (m/s).
• kinetic energy in joules (J)
2) Why electric motor can’t develop braking torque at high speed similar to starting?
Solution: The electric motor can't develop braking torque at high speed similiar to starting because once the electric supply is pulled off from the motor,it acts as a generator and due to the flux weakening effect of the electric generator,the generator produces low torque as expected.
The regenerative braking torque produced by the electric motor is proportional to the speed of the tire. Without regenerative braking torque control, in a high-speed situation, the tire will slip. If your vehicle does not have a sufficient amount of brake torque, it will not be able to stop as effectively as it otherwise could.
Here it is clearly shown in the first graph that till the motor reaches the critical speed it has constant torque and once it reaches the critical speed, the curve is having a down slope which is a constant power region. And this graph denotes the accelerating operation of the motor. For the deceleration or braking operation of the motor, this graph is mirrored down which will be having the speed (+ve) and torque (-ve).
The breaking operation graph will be th mirrored image of above plot. So we cannot say that the motor producing 5Nm torque for acceleration can also produce -5Nm for breaking. Because we are operating in the field weakening region, and operating above the base speed. Thus Peak Acceleration torque is greater than the Peak Deceleraion torque. Thus for acceleration it has high torque with low speed and for deceleration it has low torque for high speed.
How electric and mechanical brakes are coordinated?
In a electric Motor the Total Brake distribution is in two aspects which are Electrical Brake which is called Regenerative Brake and Mechanical Brake or Classical Brake with hydraulic cylindrical system. Brake Force distribution must be uniform, If the Regenerative braking power requirement is more than the charging limit of the battery or more than regenerative capacity of the machine we must apply Mechanical brakes as well. In practical case the combination of these two is applied. So usually it is combined response of Mechanical brake and Regenerative brake. The reason for how these brake force are combined, that particular phenomena is called Brake Control Strategies. There are two Brake Control Strategies, which are
To plot contour line for a given Motor. A Motor have various types of losses happening inside. The various types of losses are
Copper Losses - I^2⋅R">I^2*R⋅, where R is the Armature resistance and we say that Torque is proportional to Current, this copper loss can be consider as kc⋅T^2">kc⋅T^2.where kc">kc is to take care of resistance of brushes and also take care of flux and its effect.
Copper losses = kc⋅T^2">kc⋅T^2
Iron Losses - Iron Losses are nothing but Magnetic losses, which is denoted as ki⋅ω">ki⋅ω, where ki">ki factor is based on the Magnetic field effect. For Permanent Magnets have constant Magnetic field and this Iron losses is based on the value of ki">ki and this are going to change according to the Speed. At Various Speed have different value of Back EMF and that is going to affect the Iron Losses.
Iron Losses = ki⋅ω">ki⋅ω
Windage Losses - This is a Mechanical or friction of Windage losses. This is based on size of shape of Motor and the amount of windage losses that the motor is going to experience.
Windage Losses = kw⋅ω3">kw⋅ω^3
Constant Losses - This is denoted as C.
Total Losses - The Total Losses are considering the above four losses and denoted as,
Total Losses = kc⋅T2">kc⋅T^2 + ki⋅ω">ki⋅ω+ kw⋅ω3">kw⋅ω^3 + C
All Motors are model as per the above equation of losses. This above equation is not only applicable for Permanent Magnet DC Motor, but other motors as well like induction motor
MATLAB script to Plot Motor Speed-Torque Contour Efficiency :
The above Plot shows the Motor Speed-Torque Efficiency Contour Plot. A Point is denoted in innermost contour line is group of efficiencies which is highest value of the efficiency as 88%, because where the height is maximum and another point is denoted outermost contour line is contain group of efficiencies which is the lowest value of efficiency as 67%, because where the height reduces. Increasing efficiency order as going inward and Decreasing efficiency order as going outward. The yellow line shows the 6kw and 7.5kw Power.