Project 1

THE DEVELOPMENT OF A FORWARD ENERGY-BASED FUEL CONSUMPTION MODEL OF A CONVENTIONAL VEHICLE

AIM

1. Compute the fuel economy numbers for the given vehicle (kmpl) on the urban cycle (UDDS) and highway cycle (HWFET). And to analyse and understand the vehicle operating points in terms of engine speed, torque, transmission speeds, pedal positions, gear, distance travelled, etc.
2. Build Simulink model using blocks and complete the vehicle Model

OBJECTIVES

1. Build Simulink model using blocks and complete the vehicle model.
2. Writing scripts in MATLAB to load all the variables required for running the Simulink model.
3. Tabulate the fuel economy numbers (kmpl) for UDDS and HWFET cycle.
4. Plot the time trace for engine, transmission input, transmission output and wheel speed on one plot.
5. Plot engine torque, engine power, fuel rate and fuel consumption using subplots.
6. Plot accelerator and brake pedal, gear command, vehicle desired and actual speed, vehicle distance using subplots.
7. Plot the engine operating points on the engine fuel map.
8. Generate the plots for both drive cycles.

THEORY

Forward-Modelling Approach

• The forward modelling approach is also known as cause-effect, engine-to-wheel or rear-to-front method. The direction of calculation is the same as the direction of positive power flow, from engine-to-wheel.
• This approach is based on vehicle dynamics equations and the behaviour of each powertrain components and their dynamic interaction.
• Moreover, a driver controller is required to control the vehicle to follow a desired speed and set the start of the calculations. The controller is implemented to model the driver that will either push the accelerator or the brake pedal to match the desired speed which enables to study the driver behaviour. The controller is used as part of a feedback loop that will determine the energy required to drive the vehicle.

Conventional Vehicle:-

Conventional vehicles use an internal combustion engine fuelled by gasoline or diesel to power the wheels. In this the heat engine uses the principle of heat release through combustion of a fuel with an oxidizer in a combustion chamber to create expanding gases which pushes against a piston creating force and torque output.

In this vehicle engine converts chemical energy stored in the fuel into heat which is used to produce useful work. Typically use fossil fuels like petroleum (petrol and diesel). The most popular type of engine is used in this system is 4 stroke reciprocating engines. Engine in cylinder process can be represented by ideal thermodynamic cycles such as Otto cycle, Diesel cycle. Otto cycle is a ideal cycle that describes the cycle process for spark ignited SI engine. and the Diesel cycle is the ideal cycle that describes the cycle process for a compression ignited

CI engine.

Energy and performance

In this system the power demand on the wheel need to instant supplied by the powertrain. In other word the power coming from the powertrain dictates the power demand on the wheels (as per performance viz, acceleration, speed etc is determined by it. In this vehicle the powertrain is consists of an engine connected to the wheels through a transmission therefore the power comes from

the engine through the transmission.

Conventional powertrain

The engine generates power by converting chemical energy stored into the mechanical energy by the process of combustion. This

process of energy conversion also has an efficiency and the energy input is in the form of fuel consumption.

- Instantaneous fuel consumption is given by

mf =Pe/ηe ⋅ ηt ⋅ QLHV

Where,

mf = mass flow rate in [kg]

pe = Power of engine

pt = power of transmission

nt = efficiency of transmission

ne = efficiency of engine

QLHV = it is the calorific value/ lower heating value of fuel.

This model includes a driver model that provides input commands acceleration and brake torque depending on the drive cycle and the actual speed of the vehicle. A control model that controls the engine torque to the desired range and changes the gear command and control brake torque

according to the driver input. The transmission model that gives the actual speed of the vehicle as feedback to the driver model. The model includes the engine, transmission, differential, wheel and vehicle dynamics models separately.

Pre-Processing

A MATLAB script has been created to load all the variables needed to run and post-process the Simulink model. Drive cycle selection is also done from here. Before running the Simulink vehicle model, the script is initialized at MATLAB to load all the variables in the workspace.

% Project 1 - Conventional Vehicle Model
% By - Ullekh Gambhira 

% Description:

%% Initialization File
% Initialization file for loading the variables for the Conventional vehicle simulation model

%% Vehicle Parameters
M = 1500;       % Vehicle weight [kg]
Cr = 0.015;     % Rolling resistance coefficient
Rw = 0.35;      % Rolling radius [m]
Cd = 0.33;      % Drag coefficient
Af = 2;         % Frontal area [m2]
rhoa = 1.225;   % Air density [kg/m3]
Vwind = 0;      % Wind velocity [kmph]
g = 9.81;       % Gravitational acceleration [m/s2]
theta = 0;      % Slope [deg]
myu_road_tire = 1; % Coefficient of friction between tire - road interface

%% Powertrain Parameters 
FDR = 3.73;                         % Final Drive Ratio / Diff Ratio
DiffEff = 0.99;                     % Differential efficiency (assumed independent of operating conditions)

NumGear = 4;                        % Number of gears in transmission
TransGear = [1:NumGear];            % Transmission Gears
TransRatio = [3.06, 1.62, 1, 0.7];  % Corresponding Transmission ratios
TransEff = 0.90;                    % Transmission efficiency (assumed independent of operating conditions)

TC_SR = [0, .5, .6, .7, .8, .87, .92, .94, .96, .97, 1];   % Torque Converter Speed Ratio (Matlab default) -> TurbSpd/PumpSpd  
TC_TR = [2.232, 1.5462, 1.4058, 1.2746, 1.1528, 1.0732, 1.0192, 1, 1, 1, 1];   % Torque Converter Torque Ratio (Matlab default) -> TurbTrq/PumpTrq
TC_Cf = 1e-4 * [.72558, .66322, .63463, .59042, .51331, .4144, .29287, .22444, .12186, .04386, 0]; % Torque Converter Capacity Factor (Matlab default) -> PumpTrq/PumpSpd^2 [Nm/rpm^2]

load Vehicle_Data/Engine_data_1_9L_Saturn_95kW
load Vehicle_Data/Trans_Shift_map

%% Driver Parameters
Kp = 10;                    % P gain for driver PI model
Ki = 1;                     % I gain for driver PI model
Drive_Cycle_Select = 2;     % Drive cycle selection

% Drive cycle values in m/s

if Drive_Cycle_Select == 1
    load DriveCycles/UDDS;
    
elseif Drive_Cycle_Select == 2
    load DriveCycles/HWFET;
    
elseif Drive_Cycle_Select == 3
    load DriveCycles/FTP;
    
elseif Drive_Cycle_Select == 4
    load DriveCycles/US06;
    
elseif Drive_Cycle_Select == 5
    load DriveCycles/NEDC;
    
elseif Drive_Cycle_Select == 6
    load DriveCycles/WLTP;
 
end

time_end = cyc_time(end);
vel_end = cyc_vel(end);

The Drive Cycle can be selected from this MATLAB Script, By changing the variable Drive_Cycle_Select

SIMULINK MODELLING

• The Simulink model for the convection model is created using 3 main subblocks for the driver model, control model and powertrain block.
• The actual vehicle speed is given as feedback to the driver block, and the driver block gives the controller block the required acceleration or brake output, while the controller block provides control signals for engine torque, gear shifting and brake torque to the Powertrain model.

DRIVER MODEL

• Driver Model is a basic PI controller that generates accelerator and brake pedal outputs to match the desired and actual vehicle speeds.
• The PI controller controls the error between the required drive cycle and actual vehicle speed by providing acceleration and brake pedal output to the controller.

Scope in Driver Model:- For UDDS cycle

Scope in Driver Model:- For HWFET cycle

CONTROLLER MODEL

The ‘Controller’ block is the brains of the vehicle, representing the electronic controls units. Based on the driver inputs, it generates desired engine torque, desired transmission gear and desired brake torque. These inputs are fed to the ‘Powertrain’ block which represents the drivetrain of the vehicle

Graph created from Scope in controller Model:- For UDDS cycle

Graph created from Scope in controller Model:- For HWFET cycle

• Engine Control Unit

In this control model We use engine control unit in that give input Engine speed through creating look up table. in that table we give input Maximum torque and map speed then also create 2nd look up trable in that give input ct torque and map speed then it substracts and multiplied. the engine speed also give to ideal contro speed to integrate from this we meet output of engine required torque.

Graph created from Scope in Engine control Model:- For UDDS cycle

Graph created from Scope in Engine control Model:- For HWFET cycle

• Transmission Control Unit

• The transmission control block controls the gear shifting using the study flow Variable chart.
• The Gear shifting is Controlled according to the vehicle speed and throttle input
• The gear command is passed to the Transmission block to select the desired gear ratio.

• Brake Control Unit

Brake Control unit Produce required brake torque according to the brake pedal input and passes the brake torque in to the wheel block in the transmission model.

POWERTRAIN MODEL

• The powertrain model includes all the components that convert the power of the engine into vehicle.
• This includes Engine, Transmission, Differential, Wheels and the vehicle body dynamics subsystems.

• Engine Model

• Based on the Engine speed The required torque from the controller is saturated between Max torque curve and min torque curve and passes the Engine torque to the Transmission block.
• The 2D lookup table is used to calculate the fuel flow rate based on engine speed and engine torque. The fuel flow rate is then integrated to find the fuel consumption.
• Estimated fuel flow rate, fuel consumption, engine torque and engine speed are passed to the MATLAB workspace using the to workspace block.
• Engine fuel flow rate and Fuel consumption are scoped.

Scope in Engine Model:- For UDDS cycle

Scope in Engine Model:- For HWFET cycle

• Transmission Model

In these model we take engine torque, gear selector from controllerb for transmission of gear ratio. The ratio is multiply by transmission input torque and then the transmission efficiency positive torque and negative torque gives transmission input speed. In this case torque converter connects the engine to transmission it is part of transmission. In it basically engine dynamics and that is decoupled.

Graph created from Scope in Transmission Model:- For UDDS cycle

Graph created from Scope in Transmission Model:- :- For HWFET cycle

• Torque Converter

The gear selection from the transmission control unit is multiplied by the engine torque in this block, and the efficiency and engine dynamics of the torque converter are applied in this model.

Scope in Torque Convertor:- For UDDS cycle

Scope in Torque Convertor:- For HWFET cycle

• Differential Model

The transmission output torque is multiplied by the differential ratio and differential efficiency in this block and the torque is transmitted to the wheel as the axle torque.

• Wheel Model

• The brake torque from the control model is subtracted from the Axle torque and divides from the rolling radius to determine the Tractive force.
• The Wheel speed is calculated from the vehicle velocity and saved in the workspace.

• Vehicle Dynamics

• The longitudinal dynamics of the vehicle along with the road load is represented in the ‘Vehicle Dynamics’ block
• In this takes tractive force and road load. It is dictates vehicle speed based on tractive force and road load.

the dynamic equation for calculating road load is

M_eq dv_veh /dt = (η λ_tot / R_w) T_M – (1/2 * ρ_a A_f C_d (V_veh + V_wind)² + C_r M g cosϴ + M g sinϴ)

ρ_a - Air Density

A_f - Frontal Area

C_d - Drag Coefficient

C_r - Rolling Coefficient

M - Mass of Vehicle

g - Acceleration due to gravity

θ - Slope

Graph created from Scope in Vehicle dynamics Model:- For UDDS cycle

Graph created from Scope in Vehicle dynamics Model:- For HWFET cycle

POST-PROCESSING

A MATLAB script is Created to analyse data and to generate plots. Here we rename the variables loaded from the model, do some basic post-process calculations and generate results and plots.

% Project 1 - Conventional Vehicle Model
% By - Ullekh Gambhira 

% Description:
% The following file is to used with the Initialization file and Simulink
% results for post-processing of the data.
% The file is incomplete, has some examples of how the data is imported
% into a readable format, data analysis and plotting examples.
% Based on the project task, use commands in a similar format as given
% below, to analyse the data and generate required plots.
% You can change variable names if desired

%% Post-Processing File
%  File for post-processing the Conventional vehicle simulation model data

%% Renaming variables
Time = out.tout;
Acc_Pdl = out.Acc_Pdl;          % Accelerator pedal [%]
Brk_Pdl = out.Brk_Pdl;          % Brake pedal [%]
Gear_Cmd = out.Gear_Cmd;        % Transmission gear
Trans_In_Spd = out.Trans_In_Spd*30/pi;  % Transmission input speed [rpm]
Trans_Out_Spd = out.Trans_Out_Spd*30/pi;% Transmission output speed [rpm]
Eng_Trq = out.Eng_Trq;          % Engine brake torque [Nm]
Eng_Spd = out.Eng_Spd*30/pi;    % Engine speed [rpm]
Eng_Fuel_Consump = out.Eng_Fuel_Consumption;    % Engine fuel consumption [g]
Veh_Dist = out.Veh_Dist/1000;   % Distance traveled by vehicle [km]
Veh_Spd = out.Veh_Spd*18/5;     % Vehicle speed [kmph]
Eng_Fuel_rate = out.Eng_Fuel_rate;

%% Data Analysis
Eng_Pwr = Eng_Spd*pi/30*Eng_Trq/1000;   % Engine brake power [kW]
rho_petrol = 0.7197;                    % Density of petrol [kg/L]
kmpl = Veh_Dist(end)./(Eng_Fuel_Consump(end)/1000/rho_petrol);    % Fuel economy [kmpl] 


%% Plotting vehicle characteristics time trace
figure (1)
subplot(3,1,1)
hold on
grid on
plot(Time, Acc_Pdl, 'linewidth', 1, 'Color', 'black');
plot(Time, Brk_Pdl, 'linewidth', 1, 'Color', 'red');
ylabel('Pedal [%]')
xlim([0, Time(end)]);
legend('Accel','Brake');
subplot(3,1,2)
hold on
grid on
plot(Time, Trans_In_Spd, 'linewidth', 1, 'Color', 'black');
plot(Time, Trans_Out_Spd, 'linewidth', 1, 'Color', 'red');
ylabel('Speed [rpm]')
xlim([0, Time(end)]);
ylim([0, 6000]);
legend('Trans Input','Trans Output');
subplot(3,1,3)
hold on
grid on
plot(Time, Gear_Cmd, 'linewidth', 1, 'Color', 'black');
xlim([0, Time(end)]);
xlabel('Time [s]');
ylabel('Gear');

%% Plotting engine operating points on engine fuel map
figure('Name','Engine Operating Points');
hold on
grid on
title('Engine Operating Points','fontsize',12);
p1=plot(Eng_map_spd*30/pi,Eng_max_trq,'linewidth',2,'color','r');
p2=line([Eng_map_spd(end)*30/pi Eng_map_spd(end)*30/pi],[0 Eng_max_trq(end)]);
set(p2,'linewidth',1,'linestyle','--','color','k');
p3=line([Eng_map_spd(1)*30/pi Eng_map_spd(1)*30/pi],[0 Eng_max_trq(1)]);
set(p3,'linewidth',1,'linestyle','--','color','k');
[c,h] = contour(Eng_map_spd'*30/pi,Eng_map_trq,Eng_fuel_map');
clabel(c,h);
xlabel('Engine Speed [rpm]');
ylabel('Engine Torque [Nm]');
title('Engine Fuel Consumption Map [g/s]');
p4 = plot(Eng_Spd,Eng_Trq,'.','color','k');
legend([p1 p4],{'Max Curve','Operating Points'});
axis([Eng_map_spd(1)*30/pi Eng_map_spd(end)*30/pi 0 Eng_map_trq(end)]);

RESULTS

Fuel Consumption Of both cycles are tabulated

CYCLE	AVERAGE SPEED Kmph	MAXIMUM SPEED Kmph	ECONOMY Kmpl
UDDS	31.35	91.99	16.89
HWFET	77.68	96.92	26.23

PLOTS OBTAINED FOR UDDS CYCLE

PLOTS OBTAINED FOR HWFET CYCLE

OBSERVATION FROM BOTH PLOTS

Brake requirements are lower, more accelerator pedals are applied on the highway drive cycle, and gear shifts often occur
because the drive cycle is smoother.

CONCLUSION

• 
  Hence, the forward energy-based fuel consumption model of a conventional vehicle has been successfully Simulated using
  MATLAB and Simulink.
• 
  Analyses and understands vehicle operating points based on engine speed, torque, transmission speed, pedal positions, gear,
  and distance travelled.
• 
  Post process calculations were performed and the required graphs were successfully plotted.
• 
  Successfully calculated vehicle fuel efficiency numbers (kmpl) for the given city cycle (UDDS) and highway cycle (HWFET).