Week-11 Challenge: Braking

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

Breaking energy= 1/2mv^2

Where

m=Mass (Vehicle +load)kg

V=initial-final velocity m/s

Velocity m/s	kmph	Mass	Braking Energy
0	0	5000	0
6	21.6	5000	90000
8	28.8	5000	160000
10	36	5000	250000
12	43.2	5000	360000
16	57.6	5000	640000
18	64.8	5000	810000
26	93.6	5000	1690000
28	100.8	5000	1960000
50	180	5000	6250000
60	216	5000	9000000
40	144	5000	4000000
30	108	5000	2250000
26	93.6	5000	1690000
20	72	5000	1000000
18	64.8	5000	810000
15	54	5000	562500
10	36	5000	250000
6	21.6	5000	90000
4	14.4	5000	40000
2	7.2	5000	10000
0	0	5000	0
			total energy	31912500

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

i)Electric motor cant develop braking torque at hig speed because torque is inversely proportional to the square of the rotor speed therefore at high speed torque will be less.

ii)

there are four main braking modes: pure electric braking mode, motor and engine braking mode, motor and hydraulic braking mode, and hydraulic braking mode. In order to facilitate the kinetic analysis, the hybrid vehicle drive system model is simplified, as illustrated in Figure 5. where J_e is moment of inertia of the engine; J_ISG is moment of inertia of the ISG; J_cvt is moment of inertia of the CVT; J_C1 is moment of inertia of the clutch I; J_C2 is moment of inertia of the clutch II; J_PMSM is moment of inertia of the PMSM; J_w is moment of inertia of the wheel; J_O1 is moment of inertia of the final drive I; J_O2 is moment of inertia of the final drive II; m is the vehicle mass; r is the tire radius.

Figure 5. Equivalent diagram of the system model.

(1) Pure Electric Braking Mode

When the motor is braking clutch I is engaged and clutch II is disconnected. The engine and the hydraulic braking systems do not participate in the braking action and the required braking torque is provided by the motor. The equivalent to the moment of inertia on the wheel is:

Jv=((JISG+JC1)⋅icvt+JCVT)⋅iO1+JO1+JO2+JPMSM⋅iO2+Jw+mr2

(14)

The dynamic equation of braking is:

⎧⎩⎨⎪⎪TbICE=0Tbh=0TbISG⋅icvt⋅iO1+TbPMSM⋅iO2=Jvωw∙

(15)

where T_bICE is the engine drag resistance torque, T_bh is the hydraulic braking torque, T_bISG is the ISG braking torque, T_bPMSM is the PMSM braking torque, and ω˙w is the wheel angular acceleration.

(2) Motor and Engine Braking Mode

When the motor and engine are involved in braking, clutches I and II are engaged. The required braking torque is provided by the motor and the engine. At this time, the equivalent to the moment of inertia on the wheel is:

Jv=((Je+JISG+JC1+JC2)⋅icvt+JCVT)⋅iO1+JO1+JO2+JPMSM⋅iO2+Jw+mr2

(16)

The dynamic equation of braking is:

{Tbh=0(TbISG+TbICE)⋅icvt⋅iO1+TbPMSM⋅iO2=Jvωw∙

(17)

(3) Motor and Hydraulic Braking Mode

During motor and hydraulic braking modes, clutch I is engaged and clutch II is disconnected. The required braking torque is provided by the motor and the hydraulic braking system. At this time, the equivalent to the moment of inertia on the wheel is:

Jv=((JISG+JC2)⋅icvt+JCVT)⋅iO1+JO1+JO2+JPMSM⋅iO2+Jw+mr2

(18)

The dynamic equation of braking is:

{TbICE=0TbISG⋅icvt⋅iO1+TbPMSM⋅iO2+Tbh=Jvωw∙

(19)

(4) Hydraulic Braking Mode

During hydraulic braking mode, clutches I and II are disengaged and the required braking torque is provided by the hydraulic braking system. The equivalent to the moment of inertia on the wheel is:

Jv=JCVT⋅iO1+JO1+JO2+JPMSM⋅iO2+Jw+mr2

(20)

The dynamic equation of braking is:

⎧⎩⎨⎪⎪TbICE=0TbISG=TbPMSM=0Tbh=Jvωw∙

(21)

Based on the kinetics analysis of the braking mode, there are three types of braking torque that need to be coordinated during braking mode switching. The motor, the hydraulic, and the engine braking systems are three different systems with different dynamic response characteristics; therefore, the sequences and moments of the three joint systems are different. Because mode switching is completed instantaneously, the braking torque varies sharply during the intervention and exit from braking. If there is no coordinated control, it will cause torque fluctuation and seriously worsen the ride comfort of the vehicle.

4.2. Coordination Control Strategy for Mode Switch

According to whether or not the hydraulic braking system is involved in braking, the braking mode-switch type is divided into two categories (Figure 6). Braking mode-switch coordination control strategies are developed for the different braking mode-switch types.

Figure 6. Braking mode switch classification.

(1) Type one: braking mode switch without hydraulic braking system participation. In this type of mode switching it is necessary to control the engagement of the clutch and the change rate of the motor torque. Thus, the fluctuation caused by mode switch can be reduced.

(2) Type two: braking mode switch with hydraulic braking system participation. Due to the different dynamic response characteristics of the motor and the hydraulic braking systems, this switch mode is difficult to coordinate. The idea of coordinating control is to take full advantage of the characteristics of the braking systems. The hydraulic system can provide large and stable torque, and the motor braking system’s torque response is quick and accurate, reducing the fluctuation of the vehicle.

The overall coordination control flow chart is shown in Figure 7. T_{bm_req}, T_{bh_req} and T_{bICE_req} are the target motor, hydraulic and engine braking torques allocated by the braking force control strategy.

Figure 7. Flow chart of overall coordination control.

First, according to current speed, SOC, CVT ratio, and brake pedal, the braking force distribution control strategy allocates the target motor, hydraulic and engine braking torques; then, according to the braking mode boundary conditions the vehicle controller determines whether the braking mode should switch or not. If mode switching happens, the vehicle controller determines the type of mode switch and then selects the corresponding coordination control strategy and controls the clutch, motor and hydraulic torques to reduce the mode switch fluctuation. Finally, the vehicle controller determines whether the coordination control is completed, and if it is completed, the vehicle will enter a new braking mode.

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.

clc

clear all

close all

omega=Linspace(0,1500);

T=Linspace(0,200);

kc=0.2;

ki=0.0065;

kw=0.0001;

[X,Y]=meshgrid(omega,T);

copper_loss=(Y.^2)*kc;

iron_loss=X.*ki;

windage_loss=(X.^3)*kw;

con=25;

o_p=X*Y;

input_power=copper_loss+iron_loss+windage_loss+o_p;

eff=(o_p)./(input_power);

n=Linspace(0.65,0.95,10);

contour(X,Y,eff,n)

xlabel('rpm')

ylabel('torque')

title('Efficiency')