Week-11 Challenge: Braking

1. To Calculate the energy required for braking for a defined driving cycle:

Braking is a dynamic state of a vehicle where it slows down that is, decelerates from a certain velocity. The vehicle's velocity will decrease over a certain period of time and this can occur until the vehicle reaches rest or to another velocity level. In either case, the vehicle is still in motion and as a result, it possesses kinetic energy. When a vehicle accelerates either from rest or while in motion, its kinetic energy will increase and the opposite occurs when a vehicle decelerates. The kinetic energy carried by an object in motion of mass, m and velocity, v is given by,

Ek= (1/2)*m*(v^2)---------------------------------------------------------------------------(1)

If we were to determine the change in kinetic energy, we can find the kinetic energy at the starting velocity and at the final velocity and subtract the former from the latter. This can be simplified by re-writing the kinetic energy equation as:

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

where,

vf= Final Velocity.

vi= Initial Velocity.

So, as we said above, 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 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 brake is the mechanical brake which inhibits motion through friction brake pads. A mechanical brake applies friction force to convert the kinetic energy of the vehicle into thermal energy which then dissipates into the atmosphere. Braking system which doesn't use friction are referred to as Regenerative Braking System. In regenerative braking system, the kinetic energy is converted into other forms of useful energy, which can be stored for later use, increasing fuel efficiency.

Calculation of Braking Energy:

For calculating the energy required for braking drivecycle data is prepared in the Excel sheet, which drivecycle data includes time and speed.

Below in the attachment is the Excel sheet of drivecycle data which includes time and velocity.

Graphical representation of the drive cycle is represented in the attachment below.

From the drivecycle data, there are following different situations of deceleration or braking of which the energy has to be calculated:

a) First Braking:

Initial speed= 25kmph

Final speed= 15kmph

Time= 4sec

b) Second Braking:

Initial speed= 35kmph

Final speed= 30kmph

Time: 1sec

c) Third Braking:

Initial speed= 45kmph

Final speed= 23kmph

Time= 5sec

d) Fourth Braking:

Initial speed= 62kmph

Final speed= 15kmph

Time= 7sec

e) Fifth Braking:

Initial speed= 45kmph

Final speed= 10kmph

Time= 5sec

f) Sixth Braking:

Initial speed= 75kmph

Final speed= 40kmph

Time= 4sec

g) Seventh Braking:

Initial speed= 50kmph

Final speed= 5kmph

Time= 12sec

The Braking power calculation is done used by excel calculator which is also present in the attachment below.

Therefore, from the results of Excel calculator, the total braking energy required= 0.023663 kWh= 85.1868 Kj.

2. To understand why electric motors cannot develop braking torque at higher speed similar to starting:

Electric motor cannot develop braking torque at high speed similar to starting, because braking torque is applied in the opposite direction of the rotation. Also, there are two major reasons for a motor developing higher starting torque compared to braking:

a) Due to Transients:

At starting the motor draws a large current dueto transients. As torque is proportional to square of current, therefore torque value is also high at the starting of motor. When we apply brakes, at this time current value is less therefore, torque values are also less.

b) Torque speed characteristics:

From Torque-speed characteristics, when speed increases, torque should decrease to maintain power constant. At the time of starting speed is very low therefore torque value is high. At the time of braking, speed value is high therefore torque value will be lower. From the Torque-speed characteristics, we need to understand the concept of regenerative braking mode of the motor.

Regenerative Braking:

Regenerative braking is a form of braking in which the kinetic energy of the motor is returned to the power supply system. Regenerative braking takes place whenever the speed of the motor exceeds the synchronous speed. This braking method is called regenerative braking because here the motor works as generator and supply itself is given power from the load, that is, motor. The main criteria for regenrative braking is that the motor has to rotate at a speed higher than synchronous speed, only then the motor will act as a generator and the direction of current flow through the circuit and direction of the torque reverses and braking takes place. Sometimes, after accelerating we cannot 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 motor voltage is too close to back emf and therefore current cannot increase more. This situation does not occur at the beginning of acceleration because most of the torque is used to increase the kinetic 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.

Peak acceleration torque and peak deceleration torque are not equal for electric vehicle motor. Acceleration is usually higher, at low speed we get higher torque but at high speeds, the value of torque gets lower. So, we cannot say that the motor would produce the same value of torque during deceleration as that produced during acceleration. Since we operate the motor in field weakening region or we are operating the motor above base speed, we must know that the torque is lower. So, electric motor cannot develop braking torque at high speed similar to starting. Since the torque of an EV motor is not as high as the acceleration torque, therefore regenerative braking cannot happen so effectively that we can get all the power back to the battery.

Coordination of Electric and Mechanical Brake:

Braking is the change in the motion of a vehicle from a starting speed level to a lower speed level. The act of braking, if sustained for a sufficient time, can either bring a vehicle to a lower speed than it started with or it can bring it to complete rest. So, the act of braking brings about deceleration which is decrease in speed of the vehicle over a period of time which corresponds to the speed values at those times. Braking is an act which is desired in speed control applications and in case of vehicles, they are very much necessary to ensure the safety of the driver and the control of the vehicle. There are several methods for performing braking in vehicles whether they are conventional vehicles pr HEVs and EVs. Below is the types of brakes in practice:

Mechanical Braking:

In conventional IC engine vehicle, there is only one physical braking mechanism that can be performed and that is done with the brake pads and discs. The braking pad is pressed by the driver, which results in the application of the brake pads or discs onto the wheels of the vehicle. The friction that arises between the rotationg wheels and the stationary brake pads/discs will decrease the speed of the vehicle. Another method of braking in conventional vehicles is called Engine braking. In this method, the throttle or the accelerator pedal is released and the gear is changed to a lower gear in the case of manual transmission vehicles which will result in the deceleration of the vehicle. This occurs via the manifold effect whereby, the releasing of the accelerator pedal leads to the stopping of the fuel flow to the engine cylinder. This also stops the air flow resulting in a negative traction torque. In heavy duty vehicles example, trucks, lorries, engine braking is very useful because it helps to prevent the high heat build up in the brake pads/discs which would be generated if they were only used. So, engine braking is useful as it allows for the desired control while reducing wear and tear on the physical braking mechanism.

Electric Braking:

In motors and HEVs/EVs, various methods of braking exist. One method is using a 'brake motor' which consists of a DC rectifier, a magnet, springs and a friction disc. The mechanism of the brake motor involves the rectifier giving a signal to disrupt a magnetic field which will influence the springs to expand and apply a force on the friction discs which will come in to contact with the moving part that is in contact with the motor. When the vehicle is accelerating or moving with constant speed, the motor will receive its three-phase AC supply from the inverter and so the brakes are not applied. This DC rectifier relays no signal to the magnetic field so that the springs stay in their stationary position and do not force any contact on to the friction discs. However when the vehicle is not accelerating, the three-phase AC supply from the inverter is cut-off, causing the brakes to be applied. The DC magnetic field is disrupted by an air gap which causes the springs to get excited and expand and apply force on the friction disc to produce braking action. EVs and HEVs have the brilliant feature of regenerative braking which is where during the act of braking the motor begins to operate as a generator and instead produces electrical energy. Essentially, when a vehicle decelerates, the change in the kinetic energy of that vehicle is used to produce a torque on the motor and thereby producing electrical energy via the generator effect which can be stored by the battery or be diverted for another powering purpose. The electricity generated by the regenerative braking phenomenon is referred to as back emf because it produces a current that travels in the opposite direction to the conventional current. For regenrative braking to occur, the rotor of the motor has to rotate at a speed that is greater than the synchronous speed. This will result in the back emf being greater than the terminal voltage so that the potential difference is strong enough to influence the current to flow in the opposite direction. Using regenerative braking not only decelerates the vehicle, but also increases the efficiency and the energy savings of EVs and HEVs. ANother method of braking in EVs and HEVs is reffered to as dynamic braking. In this method of braking, the supply voltage powering the motor is disconnected and instead a resistor is connected. The absence of the resistor would result in significant frictional and windage losses which would decrease the efficiency of the vehicle and lead to longer braking times. This is not desirable because a good brake needs to bring the vehicle to rest within a certain amount of time and done in a safe manner. With the resistor fitted instead, the braking time can be reduced significantly. In addition, another braking method in motors and EVs/HEVs is referred to as terminal voltage reversal. In this method of braking, two separate voltage sources are used with different polarities as well as a switch. When the motor is running normally, the first voltage source is the main supply of power to the motor and creates a current flow in the conventional direction. When the braking action is desired, the switch is cosed to connect the second voltage supply in to the circuit and disconnect the first voltage source. Because the second voltage source has a reversed polarity, the current flow in the circuit to the motor is reversed thereby slowing the motor down by making its rotor rotate in reverse direction that is negative torque. This method is not always preferred due to the fact that it produces a severe braking and generates high levels of braking torque. So, a braking resistor is also used in the circuit and will come in to use whenever the second voltage source is connected to power the motor.

In HEVs/EVs, the total brake distribution is in two aspects which are electric 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 methods are applied. So, usually it is combined response of mechanical brake and regenerative brake. The reason for how these brake forces are combined, that particular phenomena is called brake control stategies.

Control Strategies:

From the above mentioned various braking methods, it is obvious that both mechanical and electrical braking is useful and both have their benefits and drawbacks. In regards to a vehicular application, depending on the type of vehicle either one of both types are utilised. In the case of conventional vehicles, only mechanical braking consisting of friction braking and engine braking is utilised whereas in HEVs/EVs, both are utilised. In HEVs/EVs using both mechanical and electrical braking means that the braking application can get the advantages of both types and minimize the disadvantages as much as possible. HEVs and EVs use controls strategies for controling the braking method and deciding which brakes to apply and when to apply them. These control strategies are referred to as braking modes and they will find a compromise between the mechanical and electrical braking methods to see which is the most efficient at its job. For instance, at lower speed levels, it may be more suitable to use mechanical brakes that is friction braking because these brakes will be more than capable to brake the vehicle and not generate too much heat and thus will not produce too much wear and tear for the brake pads/discs. However at higher speed levels, it would be more suitable to use electrical braking. This is because electrical braking is more effective, it won't generate nearly as much heat as mechanical brakes would. Electric braking also is more efficient and energy saving because at higher speeds, more kinetic energy will be carried by the vehicle and thus, regenerative braking can occur to convert that kinetic energy into electrical energy to be stored back in the battery. If mechanical brakes were used instead, high amounts of heat would be generated and would lead to wear and tear of the brake pads/discs over time. The high heat generation also means that the dissipation of the kinetic energy is wasted into energy that cannot be reused which reiterates its inefficiency compared to the electric brakes. In addition, the electric brakes would be smoother and more gradual and not sudden like the mechanical brakes which would make the braking action more comfortable and safer for the passengers. So, these control strategies that is braking modes will know from the vehicle data, which type of braking is the best to use depending on its current state of motion. There are various braking modes for different situations the vehicle may face and by utilising these control strategies, the vehicle can be operating at the highest efficiency at all times and make the best use of the two braking mechanisms without damaging or sacrificing one for the other. During the initial braking time, mechanical brakes are used in larger proportion than regenerative braking. Inorder to ensure the directional stability and enough efficiency in the process of braking, ECE R13 braking regulations constituted by the United Nations Economic Commission for Europe put forward explicit requirements for front and rear braking force of dual-shaft vehicle. Under various loading conditions, we must ensure that the braking strength is satisfied. There are two different brake control strategies namely, series and parallel control. The series-parallel regenerative braking control strategy of hybrid electric vehicle is designed according to the basic idea of parallel braking control strategy as well the characteristics of regenerative braking system of hybrid electric vehicle and the working characteristics of key components of regenerative braking system such as driving motor and power battery.

Series Braking System:

Series braking system consist of a braking controller which controls the braking forces on the front and rear wheel. The purpose of this strategy is to minimise stopping distance and give optmize the driver feel. the shortest braking distance and good braking feel requires the brake force on front and rear wheel to follow ideal brake force distribution. The main principle of series braking system is to recover the braking energy as much as possible in the condition of meeting the total braking force fot the given deceleration. Here, mechanical brakes and regenerative brakes are applied one after another.

Parallel Braking System:

Parallel braking system includes both electrical and mechanical braking system which produces braking force in parallel and simultaneously. This kind of braking system has a conventional mechanical braking which has a fixed ratio of brake force distribution on front and back wheel. Here, mechanical brakes and regenerative brakes are applied simultaneously.

Electric Driven Intelligent Brake:

The Electric Driven Intelligent Brake (EDIB) is a combination of hydraulic brakes or mechanical brakes along with regenerative brakes. It is a parallel braking technique. The control criteria such that at low speed use regenerative braking higher and at high speed or during initial braking period we actually combine the both. EVs and HEVs use regenerative braking, thereby charging the battery using the bidirectional converter. For this the kinetic energy of the vehicle is converted into electrical energy. It works by controling the reactive force from the pedal in order to unify the feeling when stepping down on the pedal and the sense of deceleration. When the brake pedal is applied the reactive force on it is sensed by the stroke sensor. This information transmitted to the ECU which in turn controls the motor. The motor engages the piston and amplifies the friction brake's pressure. Through optimum control of the friction brake's hydraulic pressure, the energy regeneration outcome is maximised. It works in such a way that initially both are working and at low speed and high torque which is retardation regenerative braking is done.

3. To make a Matlab program which plots contour of given motor speed, torque and efficiency values:

A contour plot that shows the characteristics of the speed, torque and the efficiency of a motor is referred to as an efficiency map. Contour plots are very useful as they make it very easy to understand which operating states result in the highest efficiencies of the motor. In this way, a manufacturer can design a motor knowing which applications it will be useful for depending on the speed, the torque it achieves at that speed and the efficiency of the motor which operates at those values. Inorder to plot this, we need the specifications of a motor. In this question we are taking generic values for the specifications of the motor as well as for the losses that occur in the motor operation. In Matlab script, we begin with the clear all, close all and clc commands. Then we create arrays for the speed and the torque of the motor using the linespace command. These arrays are then used to create 2D grid coordinates using the meshgrid command. These coordinates will help in the creation of the cotour plot. Inorder to find the efficiency of the motor, we need to consider the various losses occur in the motor's operation. The various losses are:

Copper Loss:

Copper Loss= (I^2)*R.

Where, R= Armature Resistance

We can say that torque is proportional to current. So, the copper loss can be considered as, kc*(T^2). Where, kc is to take care of resistance of brushes and also take care of flux and its effect.

Therefore, Copper losses= kc*(T^2)-------------------------------------------------(1)

Iron Loss:

Iron losses are nothing but magnetic losses, which is denoted as

Iron Loss= ki*w

Where, ki is the factor based on the magnetic field effect. For permanent magnets have constant magnetic field and this iron losses is based on the value ki and this is going to change according to the speed. At various speed there will be different value of back emf and thaat is going to affect the iron loss.

Iron Loss= ki*w-------------------------------------------------------------------------(2)

Windage Loss:

This is a mechanical or friction or windage loss. This is based on size of shape of motor and the amount of windage losses that the motor is going to experience is given below,

Windage Loss= kw*(w^3)---------------------------------------------------------------(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*(T^2))+(ki*w)+(kw*(w^3))+C------------------------------------(4)

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.

Below attachment is the Matlab program to plot the Motor Speed-Torque Contour.

We also need to calculate the efficiency of the motor using the data we currently have. Since efficiency is defined as the ratio of the output power to the input power, we can calculate the efficiency of the motor by determining the input and output power of the motor. The output power of the motor can be calculated by multiplying the angular speed with the torque.

Mathematically, Output Power, Pout= T*w----------------------------------------------------(5)

Then, we can calculate the input power supplied to the motor by adding the output power to the energy losses. Mathematically,

Input Power, Pin= Pout+(Copper Loss)+(Iron Loss)+(Windage Loss)+Constant Loss-------(6)

Since efficiency as said above, the ratio of the output power to the input power , we can calculate the efficiency of the motor by:

`eta`= (Pout)/(Pi+(Copper Loss)+(Iron Loss)+(Windage Loss)+Constant Loss)------------(7)

Explanation for above Program:

Step-1: Assign Input of Speed and Torque in an array using linespace command and allocate consatnt values for four losses (Copper Loss, Iron Loss, Windage Loss and Constant Motor Loss).

Step-2: Mesh the Speed and Torque values using meshgrid command.

Step-3: Calculate the Output power by multiplying speed and torque values.

Step-4: Calculate Copper loss, Iron loss, Windage loss using above formulas.

Step-5: Calculating Input power by adding output power and four losses (Copper loss, Iron loss, Windage loss and Constant Motor Loss).

Step-6: The ratio of output power and input power we can get the efficiency.

Step-7: Now set the effeciencies for which a contour will be plotted. The range of contour effenciency is to plot from 70% to 93% effenciency. V is the mapping of those effenciency points.

Step-8: Plot the contour effenciency using contour command and plot speed, torque, effenciency and V.

Contour:

Contour (Z) creates a contour plot containing the isolines of matrix Z, where Z contains high value on the X-Y plane. Matlab automatically selects the contour line to display. The column and row indices of Z are the X and Y co-ordinates in the plane, respectively. Contour(X, Y, Z) specifies the X and Y co-ordinates from the values in Z.

Step-9: Now plot a contour of power output. Plotting contour of 8kW and 10kW of a motor.

Step-10: Run the program and get the Motor Speed-Torque Efficiency Contour Plot.

Result:

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 efficiency as 95%, because where the height is maximum and another point is denoted outermost contour line contains group of effinciencies which is lowest value of efficiency as 70%, because where the height is at the lowest point. Increasing efficiency order is going inward and decreasing efficiency order is going outward. The yellow line shows the 8kW and 10kW power.