Piston Motion and Analysis in Advanced Powertrain Engineering

This study focuses on the piston motion and analysis in advanced powertrain engineering. It covers the aims and outcomes, equipment used, results, calculation and analysis, discussion, and concluding remarks. The study also includes gear ratio selection and its analysis.

6MV500
Advanced Powertrain Engineering
Student Name
Student ID Number
Institutional Affiliation
Instructor
Date of submission

TABLE OF CONTENTS
PISTON MOTION..........................................................................................................................2
INTRODUCTION.......................................................................................................................2
AIMS & OUTCOMES.................................................................................................................3
EQUIPMENT...............................................................................................................................3
RESULTS....................................................................................................................................3
CALCULATION AND ANALYSIS...........................................................................................3
DISCUSSION..............................................................................................................................6
CONCLUDING REMARKS.....................................................................................................11
REFERENCES...........................................................................................................................12
GEAR RATIO SELECTION........................................................................................................13
INTRODUCTION.....................................................................................................................13
AIMS & OUTCOMES...............................................................................................................15
ANALYSIS................................................................................................................................15
RESULTS..................................................................................................................................15
DISCUSSION............................................................................................................................15
1

LIST OF FIGURES
Figure 1 Piston motion for the crankshaft [source: Wikander,2004]..............................................3
Figure 2 The plot of the travel distance against angle [Matlab R2018b]........................................4
Figure 3 plot of speed on torque generation [Matlab r2018b].........................................................5
Figure 4 The road run test I [Matlab r2018b]..................................................................................6
Figure 5 The piston assembly [Maskinelement Handbook, 2003]..................................................7
Figure 6 The piston force balance...................................................................................................9
Figure 7 The piston side thrust load..............................................................................................10
Figure 8 The four-stroke engine balance.......................................................................................11
Figure 9 Estimated power and torque curves for the engine.........................................................16
Figure 10 The road run test............................................................................................................17
Figure 11 Plot of te RPM against the time [Matlab r2018b].........................................................17
Figure 12 The maximum possible top speed of the vehicle..........................................................18
Figure 13 [Wang]...........................................................................................................................20
LIST OF TABLES
Table 1 Experiment Table...............................................................................................................3
Table 2 Powertrain crank rotation...................................................................................................4
Table 3 Vehicle payload system parameters.................................................................................16
2

PISTON MOTION
INTRODUCTION
Piston motion is determined in terms of travel, speed, acceleration, and vibration. A
crankshaft connects a number of components that can be used to capture the drivetrain energy
during the rotational motion as well as combustion. The crankshaft is designed such that there is
a backbone centrally located to hold all the other components via a coaxial cylindrical rod. It is
referred to as the crankpin. The crankshaft turns the pistons up and down in a circular motion.
For the piston to spin evenly, other components are added to the crankshaft to help the engine
run smoothly. In the crankshaft, the crank pin transfers the force of the piston and connecting
rods into a rotational power. The piston velocity is given as the instantaneous rate of change in
the position of the system with respect to a reference variable. It is the first derivative of the
position curve. To determine the mean piston speed,
MPS ( ft per minute )= RPM∗2∗stroke ( inches )
12 (inches per foot )
¿ RPM∗stroke
6
The piston acceleration determines the force exerted with respect to the weight of the object and
the acceleration.
3

Figure 1 Piston motion for the crankshaft [source: Wikander,2004]
AIMS & OUTCOMES
(i) To determine the piston motion parameters and behavior for a particular engine
vehicle payload parameters
EQUIPMENT
(i) Engine simulation devices
RESULTS
Petrol mass and volume data
A 50ml density bottle was used and the warm up to room temperature.
Table 1 Experiment Table
Parameter Test 1 Test 2 Test 3 Test 4
Empty bottle 25.7 25.6 25.7 25.5
Bottle with petrol 62.3 62.3 62.3 62.3
CALCULATION AND ANALYSIS
For the powertrain crank rotation, the change in the rotation angle has an impact on the piston
motion and as a result, the travel distance and acceleration.
4

Table 2 Powertrain crank rotation
0 50 100 150 200 250 300 350 400
Angle
0
5
10
15
20
25
30
35
40
45
Travel Distance
Crankshaft Position-->Travel Distance
PowerTrain
Figure 2 The plot of the travel distance against angle [Matlab R2018b]
More information is provided on the speed versus the torque that is generated,
5

80 82 84 86 88 90 92 94 96 98 100
Speed
20
21
22
23
24
25
26
27
28
Torque
Speed on Torque Generation
PowerTrain
Figure 3 plot of speed on torque generation [Matlab r2018b]
6

60 80 100 120 140 160 180 200
Time(sec)
0
2
4
6
Power(Watts)
Road Run Tests
Power
60 80 100 120 140 160 180 200
Time(sec)
0
20
40
60
Speed(km/h) Speed
60 80 100 120 140 160 180 200
Time(sec)
0
5000
10000
Revolutions per minute(RPM)
RPM against Time
Figure 4 The road run test I [Matlab r2018b]
DISCUSSION
There are different automotive components that rely on the lubrication that is applied on the
engine for it to operate and every experience affects more than one regime of lubrication for a
7

single cycle. The key operating tribological parameter that is used in the powertrain system is the
lubricant film thickness that seeks to separate the interaction among components especially those
that are moving on the crankshaft in rotary motion. The lubrication is defined as a means of the
relative magnitude of the lubricant film compared to the combined surface roughness that
connects to more combined surface roughness for different surfaces. The ratio difference is
equated as,
The equation represents the film thickness, h, and the root mean square surface roughness, rms.
The piston is combined as shown in the illustration below,
Figure 5 The piston assembly [Maskinelement Handbook, 2003]
For an internal combustion engine the piston assembly is made of the ring pack that contains a
set of metallic rings. The aim of the piston is to maintain an effective gas seal between the
8

combustion chamber and the crankcase. The internal combustion engine is founded on the piston
which is critical in the transformation of the energy that is generated by combustion of the fuel
and the air mixture to form useful kinetic energy.
It is paramount to lubricate the regime for the ring by having the total load acting in the
ring in radial direction due to the sum of the hydrodynamic lubrication force and the solid to
solid interactions along the asperities of the surface. It is given as,
FR =FH + Fc
One other parameter considered, especially in the energy transformation, is the friction force. It
determines how much energy is lost during the transformation. In the piston crankshaft design,
the total friction force is observed to act on the ring in a tangential direction. It is obtained as the
sum of friction forces between the asperities and the shear force about the HDL regime.
As a result the friction force is directly proportional to the piston velocity, such that
f μ=μf ∗S p
Sp= πLN
60 sin θ [ cos θ
√ R2−sin2 θ −1 ]
f μ= μf∗πLN
60 sin θ [ cos θ
√ R2−sin2 θ −1 ]
9

The computation of frictional forces takes into account the coefficient of the friction in the piston
as well as the global frictional losses. The cyclic integral of friction is, therefore, obtained as,
The engine friction is affected by the stroke –to-bore ratio as these two parameters are in
constant competing effect. The crankshaft bearing friction and power cylinder friction is
considered. It is determined that the stroke-to-bore ratio decreases, the bearing friction increases
because the larger piston area transfers larger forces to the crankshaft bearings. It is clear to note
that the corresponding shorter stroke results in the decreased power-cylinder friction originating
at the ring/cylinder interface. From the data analysis, data on the angle and travel, it is possible to
determine the piston force balance as,
10
Fmep =W cycle , friction
V stroke
=∮ Pμ ( θ ) d ( θ )
V stroke
W cycle , friction=∮ Pμ ( θ ) d ( θ )

Figure 6 The piston force balance
To determine the piston side thrust load, two statuses are considered namely the full load
and the half load. For instance, the full load may be at 3800 rpm and the half load at 2000 rpm.
11

Figure 7 The piston side thrust load
The piston motion considers a number of aspects of speed such as acceleration, velocity, and
torque. The four stroke engine has a piston moving upwards and downwards at different angles.
The governing function is given as,
Sp= ds
dt =
ds
dθ ∗dθ
dt
Sp= ds
dt =
ds
dθ ∗2 πN
60
s ( θ )=acos θ+ √l2−a2 sin2 θ
Sp= πLN
60 sin θ [ cos θ
√ R2−sin2 θ −1 ]
12

Figure 8 The four-stroke engine balance
CONCLUDING REMARKS
The effect of the crankshaft rod on the intake stroke will draw harder on the cylinder head
from 900 from section A to section B. The compression stroke has the piston travel from section
B to 900 at section C in the shorter rod. The system is observed to travel slower from 900 at
section C and to section D. It is bound to change the ignition timing requirement against the short
rod as piston spends more time at the top.
13
S p= π LN
60 sinθ [ cos θ
√ R2−sin2 θ −1 ]

When the ignition is turned on, the flame travels very fast and there is a chance that there
will be a detonation. A power stroke is bound to occur when the piston is pressed down further
into the bore in a rod/crank pin angle. It is determined that at any crank angle from 200 to 750 in
section A with less force exerted at the crank pin with a shorter rod. The piston will be higher in
the bore for any given crank angle from 900 in section A to section B. The result of the piston
motion is an increase in the cylinder pressure. When the long rod is used, less time is spent to
move the piston from 900 in section A to section B. The reduced time enables exhaust to escape
via the power stroke process to the vehicles exhauster ejection system.
Cylinder-to-cylinder variation in radial engines and resulting vibrations has been known
for a long time. Now, advanced software enables us to perform a qualitative evaluation of the
impact of rod-crank system’s kinematics on engine performance. Based on the engine operations,
the cylinder and piston are connected to the crankshaft using a connecting rod. In the four stroke
engine operation, the piston travels to the upper limit that is the top dead center and to the lower
limit that is the bottom dead center. The piston strokes are said to be intake, compression, power,
14

and exhaust. The piston intake stroke section has the crankshaft which turns and pulls the rod
and piston down into the cylinder. It creates a low-pressure suction and the atmospheric pressure
pushes the air-fuel mixture. The stoichiometric mixture is given that the 15:1 air to fuel ratio is
such that the gasoline will not burn unless it is mixed with air. The engine is divided into several
cylinders. The engine front has a camshaft, timing cover, and the vibration damper. The camshaft
is driven by timing gears or sprockets using a timing chain or a belt. The timing cover seals
against the instance of the oil leakage. It manages to keep elements out of engines with a timing
belt. The vibration damper, on the other hand, is responsible for all the vibrations in the engine
front as it is separated by the thin rubber strip or the harmonic balancer. The piston motion is
therefore changed to the rotary motion by the connecting rod and crankshaft. The flywheel gives
momentum to the crankshaft and smoothers impulses that are perceived between the power
strokes. The camshaft and valve train control the engine’s intake and exhaust flow.
REFERENCES
Czarnigowski, J., Jakliński, P., & Wendeker, M. (2010). Fuelling of aircraft radial piston engines
by ES95 and 100LL gasoline. Fuel, 89(11), 3568–3578. doi:10.1016/j.fuel.2010.06.032
Gęca, M., Litak, G., Wendeker, M., Jakliński, P., Czarnigowski, J., & Pietrykowski, K. (2009).
Diagnostics of a combustion process in the aircraft radial engine. PAMM Proceedings in Applied
Mathematics and Mechanics, 9, 677–678. doi:10.1002/pamm.200910308
Pietrykowski, K., & Gęca M. (2014). Simulation studies of the aircraft radial engine. Logistyka,
6, 8645–8653. Pietrykowski, K. & Tulwin, T. (2015). Aircraft Radial Engine CFD Cooling
Model. SAE Int. J. Engines, 8(1), 82–88. doi:10.4271/2014-01-2884
Siebert, H. W. (n.d.). Approximate Formulas for Piston Travel in Radial Engines. Journal of the
Aeronautical Sciences, 7(10), 434–437. doi:10.2514/8.1194
Tulwin, T. (2016). A coupled numerical heat transfer in the transient multicycle CFD aircraft
engine model. Procedia Engineering, 157, 255–263. doi:10.1016/j.proeng.2016.08.364
15

GEAR RATIO SELECTION
INTRODUCTION
In this experiment, the focus is on the Yamaha R6 Engine code-5SL from 2003-2005.
The power train is responsible for the transfer of power from the engine point to the drive
wheels. It enables the vehicle to be controlled while providing higher levels of the engine torque
especially when turbo speed is needed and it also controls the speed of the engine. In mechanics,
torque defines a rotational or twisting force that causes motion. The torque is responsible for the
motion in a vehicle such that it is able to convert energy from one form to another and as a result
it takes the engine power and makes the drive axle propel the wheels and tires in rotary motion.
The experiment also seeks to achieve proper gear setting. Gears in a powertrain or a drivetrain
are considered to the levers. Energy is lost to another form especially heat during propulsion but
the gear set ensures energy is not lost. All the power that is channeled to the shaft is transformed
to another. There is an inverse relationship, therefore, between the torque and the drivetrain
speed.
It is important to distinguish between a vehicle’s horsepower and torque. The speed at
which the vehicle runs is the horsepower while the torque determines the pace at which the
vehicle accelerates. The gear set can increase torque while decreasing the speed by the same
amount. The two parameters relate as,
HorsePower=Torque∗RPM
5252
It can be concluded that an increase in the horsepower of a vehicle in motion at higher wheel
revolutions per minute implies a decreased torque. To increase the torque of a drivetrain, the
gears, belts and chains are decreased. The gear set operates such that while increasing the torque,
16

it decreases the speed of the vehicles in equal measure. Gears with tighter joints pose less
slipping risk. It is important to determine the number of teeth in a gear as the teeth interlock to
form simple machines that produce torque. The gears are used in direction change, change in
speed of rotation as well as determining the rotational motion to a different axis while keeping
the rotation of the axes synchronized. There are different types of gears namely:
(i) Spur gears
(ii) Helical gears
(iii) Herringbone gears
(iv) Rack and pinion gears
(v) Straight and spiral gears
(vi) Worm gears
(vii) Idler gears
(viii) Clutch gears
(ix) Pulley and belts
(x) Compound gear train
(xi) Cam and pistons
The gear ratio is considered a multiplier on speed and a divider on torque. The gear ratio is given
as,
Gear ratio= Number of teeth at the input gear
number of teeth at theoutput gear
For instance, a vehicle can have a gear ratio of 3:1 to gear up or 1:3 to gear down in terms of
increasing and decreasing the velocity of the vehicle. Some power is lost due to the effects of
friction. For higher velocity ratios as a result of gear ratios are desired on smooth terrains while
the drivetrains have higher mechanical advantage are preferred in the inclined surfaces that are
bumpy.
AIMS & OUTCOMES
(i) To determine the motion of the piston with respect to the crankshaft position
(ii) To determine the setting of the gear ratios
17

ANALYSIS
(i) Data was obtained based on the vehicle system payload parameters above.
RESULTS
Table 3 Vehicle payload system parameters
Vehicle Mass 1700 kg Frontal area 3.8 m2
Proportion of mass on
front axle 55% Drag Coefficient 0.42
Height of centre of mass 780 mm Tyre Rolling Radius 394 mm
Maximum Power 55 kW @ 4200 rpm Rolling Resistance KRR 0.025
Maximum Torque 160 Nm @ 2000 rpm Coefficient of friction 0.7
Air Density 1.225 kg/m3 Acceleration due to gravity 9.81 m/s2
Transmission Efficiency 92% Wheelbase 2769 mm
DISCUSSION
(i) Produce estimated power and torque curves for the engine
80 82 84 86 88 90 92 94 96 98 100
Speed
20
21
22
23
24
25
26
27
28
Torque
Speed on Torque Generation
PowerTrain
Figure 9 Estimated power and torque curves for the engine
(ii) Produce a road load curve
18

0 20 40 60 80 100 120
Time(sec)
0
1
2
3
4
5
6
7
Power(Watts)
Road Run Tests
Power
Figure 10 The road run test
0 20 40 60 80 100 120
Time(sec)
0
2000
4000
6000
8000
10000
12000
Revolutions per minute(RPM)
RPM against Time
Figure 11 Plot of te RPM against the time [Matlab r2018b]
19

(iii) Estimate the maximum possible top speed of the vehicle
0 20 40 60 80 100 120
Time(sec)
0
20
40
60
80
100
120
Speed(km/h)
Speed
Figure 12 The maximum possible top speed of the vehicle
(iv) Estimate the maximum gradient which the vehicle can climb
When the vehicle is at an uphill, that the ride starts from the bottom of the slope
with speed u, then the slope makes angle A to the horizontal. It is, therefore, obtained
as,
1
2 M u2+ Pt =1
2 M v2+ Mgvsin A+W f t
(v) The overall maximum and minimum gear ratios
2:1 –minimum gear ratio
5:2 – maximum gear ratio
(vi) Determine the gearbox ratios for the first and top gear.
5:2
(vii) Choose the ratios between the 1st and top gear. To determine the total number of gear
ratios required.
4:1
20

DISCUSSION
In the modern applications, the gears, pulleys, and cams are used as they rotate about
fixed axes. They are used in machinery to generate the motion and to transmit forces and energy
from one form to another. One common example is the four stroke engine that uses the otto
cycle. For a rigid body motion, it is possible that the body rotates about the center of the mass
and has a different approach. For the vehicle motion, there is rectilinear or curvilinear translation
which ensures that the vehicle moves at the same velocity and acceleration.
r B=r A +r B
A
The values are seen to change with respect to distance and orientation of the crankshaft
during motion. It is, therefore, possible to determine several kinematic quantities such at the
acceleration and the motion of a point in the rotation body. For the acceleration, the point is on
the curved path such that,
a= d
dt ( ^v )= d
dt ( ^ω∗ ^v )
^ω d
dt ( ^r ) + d
dt ( ^ω )∗ ^r
21

Figure 13 [Wang]
It is possible to do the absolute motion analysis with relation with the powertrain using
the crankshaft. The general plane motion is set to undergo the simultaneous translation and
rotation. It is also important to consider the rolling motion without having a slip.
CONCLUDING REMARKS
One of the key factors to consider is the load conditions. There are several ways to
determine the maximum gradient based on the weight of the vehicle, the weight of the payload,
the max gross weight of vehicle, the speed of vehicle at the start of the gradient, and the road
conditions whether good, dry, wet, or paved. Theoretically the stall speed of these vehicles is
Zero as they are 4x4 Petrol/Electric Hybrids. When the 4x4 Lock is activated each wheel is
driven independently by the electric motors only. The petrol engine engages directly through a
transaxle which means that it can only engage above a certain minimum speed as there is no
gearbox - and that minimum speed is 70kph. he basic calculation is that the energy the EV has at
22

the bottom of the hill, plus whatever it can generate in it's power plant, turns into gravitational
PE and kinetic energy (with heat, sound, work against friction) as it climbs the hill.
Motors are used to convert the electrical energy to mechanical energy which can be used
to propel the gears. They are also used in driving robots. The toothed wheels are fixed to an axle
where a drive gear and a driven gear are connected to the input and output axle. The gear train is
provided when a number of gears are connected together. The choice of gears is based on the
vendor catalogs or the standard formulae. There are two specific standards used namely the
AGMA and the ASME.
REFERENCES
Gerhard Antony, Precision gearhead torque rating for automation and robots, Motion System
Design, June 2003.
Buckingham (1963) Buckingham Earle, Analytical mechanics of gears, Dover Publications Inc.
1963
Crowder (2005) Crowder, Richard M. Electric Drives and Their Controls, Oxford Science
Publications ISBN 0 19 856565 8, 1995
Feinstein (2007) Feinstein Alan, Bayside Motion Group, Power Transmission Design, 2007
Maskinelement Handbok (2003) Department of Machine Design, Maskinelement Handbok,
Department of Machine Design, KTH, Stockholm, Sweden 2003.
Roos, Wikander (2004) Roos Fredrik, Wikander Jan, Towards a Design and Optimization
Methodology for Automotive Mechatronics, FISITA World Congress, Barcelona, May 2004.
Svensk Standard SS 1863, Kugg och snäckväxlar – Cylindriska kugghjul med raka kuggar –
Geometriska data., Spur gears- geometrical data, Utgåva 4, SIS- Swedish Institute of Standards,
1978.
Svensk Standard SS 1871, Kugg och snäckväxlar – Cylindriska kugghjul med raka eller sneda
kuggar – Beräkning av bärförmåga. Spur and helical gears – Calculation of load capacity. Utgåva
3, SIS- Swedish Institute of Standards, 1978.
Vedmar Lars, Maskinelement, Lunds Tekniska Högskola, 2002
23

APPENDIX
Appendix A
Matlab Implementation
%% Advanced powertrain Engineering
... Setup the Import Options
clear all
close all
clc
format short
opts = spreadsheetImportOptions("NumVariables", 2);
% Specify sheet and range
opts.Sheet = "Sheet1";
opts.DataRange = "A2:B74";
% Specify column names and types
opts.VariableNames = ["Angle", "Travel"];
opts.VariableTypes = ["double", "double"];
% Import the data
tbl = readtable("powertrainData.xlsx", opts, "UseExcel", false);
%% Convert to output type
Angle = tbl.Angle
Travel = tbl.Travel
%% Clear temporary variables
clear opts tbl
%plotting the relationship between the angle and the travel
figure(1)
plot(Angle,Travel,'r-.','LineWidth',2.0)
grid on
xlabel('Angle')
ylabel('Travel Distance')
legend('PowerTrain')
title('Crankshaft Position-->Travel Distance')
opts = spreadsheetImportOptions("NumVariables", 2);
% Specify sheet and range
opts.Sheet = "Sheet1";
opts.DataRange = "A2:B21";
% Specify column names and types
opts.VariableNames = ["VarName1", "VarName2"];
opts.VariableTypes = ["double", "double"];
% Import the data
tbl = readtable("torqueCount.xlsx", opts, "UseExcel", false);
%% Convert to output type
speed = tbl.VarName1;
torque = tbl.VarName2;
24

%% Clear temporary variables
clear opts tbl
%plotting the relationship between the speed and the torque generated
figure(2)
plot(speed,torque,'b-.','LineWidth',2.0)
grid on
xlabel('Speed')
ylabel('Torque')
legend('PowerTrain')
title('Speed on Torque Generation')
%% Analysing the road runs
%% Setup the Import Options
opts = spreadsheetImportOptions("NumVariables", 8);
% Specify sheet and range
opts.Sheet = "Sheet1";
opts.DataRange = "A2:H5551";
% Specify column names and types
opts.VariableNames = ["Time", "afr", "map", "mat", "pw", "rpm", "SpeedMX5_Wheels", "tps"];
opts.VariableTypes = ["double", "double", "double", "double", "double", "double", "double", "double"];
% Import the data
tbl = readtable("roadRun1.xlsx", opts, "UseExcel", false);
%% Convert to output type
Time = tbl.Time;
afr = tbl.afr;
map = tbl.map;
mat = tbl.mat;
pw = tbl.pw;
rpm = tbl.rpm;
SpeedMX5_Wheels = tbl.SpeedMX5_Wheels;
tps = tbl.tps;
%% Clear temporary variables
clear opts tbl
figure(3)
plot(Time,pw,'g-.','LineWidth',2.0);
xlabel('Time(sec)')
ylabel('Power(Watts)')
title('Road Run Tests')
legend('Power')
grid on
figure(4)
plot(Time,SpeedMX5_Wheels,'b-.','LineWidth',2.0);
xlabel('Time(sec)')
ylabel('Speed(km/h)')
grid on
25

legend('Speed')
figure(5)
plot(Time,rpm,'r-.','LineWidth',2.0);
xlabel('Time(sec)')
ylabel('Revolutions per minute(RPM)')
title('RPM against Time')
grid on
opts = spreadsheetImportOptions("NumVariables", 8);
% Specify sheet and range
opts.Sheet = "Sheet1";
opts.DataRange = "A2:H6350";
% Specify column names and types
opts.VariableNames = ["Time", "afr", "map", "mat", "pw", "rpm", "SpeedMX5_Wheels", "tps"];
opts.VariableTypes = ["double", "double", "double", "double", "double", "double", "double", "double"];
% Import the data
tbl = readtable("RoadRun4.xlsx", opts, "UseExcel", false);
%% Convert to output type
Time1 = tbl.Time;
afr1 = tbl.afr;
map1 = tbl.map;
mat1 = tbl.mat;
pw1 = tbl.pw;
rpm1 = tbl.rpm;
SpeedMX5_Wheels1 = tbl.SpeedMX5_Wheels;
tps1 = tbl.tps;
%% Clear temporary variables
clear opts tbl
figure(6)
subplot(3,1,1)
plot(Time1,pw1,'g-.','LineWidth',2.0);
xlabel('Time(sec)')
ylabel('Power(Watts)')
title('Road Run Tests')
legend('Power')
grid on
subplot(3,1,2)
plot(Time1,SpeedMX5_Wheels1,'b-.','LineWidth',2.0);
xlabel('Time(sec)')
ylabel('Speed(km/h)')
grid on
legend('Speed')
subplot(3,1,3)
plot(Time1,rpm1,'r-.','LineWidth',2.0);
xlabel('Time(sec)')
ylabel('Revolutions per minute(RPM)')
title('RPM against Time')
grid on
26

Appendix B
clear all
close all
clc
R = 287; % J / kgK
gamma = 1.4; % Ratio of specific heats
Cv = R / (gamma - 1); % Specific heat at constant volume J/kgK
Cp = Cv + R; % Specific heat at constant pressure J/kgK
CR = 10; % Compression Ratio
Q_23 = 600; % Heat Supplied (J)
M_air = 5.566e-4; % Mass of air (kg)
P_1 = 100e3; % Atmospheric pressure (Pa)
T_1 = 273+40; % Temperature at start of cycle (K)
V_1 = M_air * R * T_1 / P_1;
V_2 = V_1 / CR;
P_2 = P_1 * (CR^gamma);
T_2 = (CR^(gamma-1)) * T_1;
V_3 = V_2;
T_3 = T_2 + (Q_23 / (M_air * Cv));
P_3 = (T_3 / T_2) * P_2;
V_4 = V_1;
T_4 = T_3 / (CR^(gamma-1));
P_4 = P_3 / (CR^gamma);
V = linspace(V_2,V_1,1000);
P_c = P_2 .* ((V_2 ./ V) .^ gamma);
P_e = P_3 .* ((V_3 ./ V) .^ gamma);
F1 = figure;
hold on
L1 = plot(1e6*V,P_c./1e3);
L2 = line([1e6*V_2 1e6*V_2],[P_2/1e3 P_3/1e3]);
L3 = plot(1e6*V,P_e./1e3);
L4 = line([1e6*V_4 1e6*V_4],[P_4/1e3 P_1/1e3]);
set(L1,'color','red')
set(L2,'color','blue')
set(L3,'color','green')
set(L4,'color','black')
%set(findobj('type','line'),'linewidth',2)
27

set(gca,'xlim',[0 1.1e6*V_1])
title('OTTO AIR STANDARD CYCLE')
xlabel('Volume (c.c.)')
ylabel('Pressure (kPa)')
disp(['Pressures (Pa) ', num2str([P_1 P_2 P_3 P_4])])
disp(['Pressures (psi) ', num2str((14.7/100000)*[P_1 P_2 P_3 P_4])])
disp(['Temperatures (K) ',num2str([T_1 T_2 T_3 T_4])])
Appendix C
clear
close all
clc
B = 78.1e-3; % Bore diameter (m)
S = 82e-3; % Stroke (m)
l = 150e-3; % Connecting Rod Length (m)
CR = 10; % Compression Ratio
n = 6000; % Engine Speed (RPM)
% Weibe Parameters
% 50% point 8 degrees
% 10% - 90% points 31 degrees
% Exponent 2
% Terminate at 1
% Read in PV data
load -ascii P_theta_data_2.txt
thetad=P_theta_data_2(:,1); % Crank Angle (degrees)
P=P_theta_data_2(:,2); % Cylinder Pressure (Pa)
thetar = thetad .* (pi/180); % Crank Angle (Radians)
SV = pi * (B^2) * S / 4; % Cylinder swept volume (m^3)
CV = SV / (CR - 1); % Cylinder Clearance volume (m^3)
BE_x = (S/2) * sin(thetar); % Big and lateral offset (m)
BE_y = (S/2) * (1-cos(thetar)); % Big end height (m)
sm = l - sqrt((l^2) - (BE_x.^2)); % Piston Secondary Motion (m)
% Calculate Pistoin Motion 0 = TDC, S = BDC
P_y = BE_y + sm;
% Calculate cylinder volume
Vol_Cyl = CV + ((pi/4) * (B^2) .* P_y);
% MASS FRACTION BURNT CALC
% Cut out compression and expansion process between -90 and +90 degrees
ind_t1 = find(thetar>= -pi/2);
ind_t1 = ind_t1(1);
ind_t3 = find(thetar>= 0);
ind_t3 = ind_t3(1);
ind_t2 = ind_t3-1;
ind_t4 = find(thetar>= pi/2);
ind_t4 = ind_t4(1);
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% Prepare compression curves
MFB_theta_data_c = thetar(ind_t1:ind_t2,1);
MFB_P_data_c = P(ind_t1:ind_t2,1);
MFB_V_data_c = Vol_Cyl(ind_t1:ind_t2,1);
motor_P_c = MFB_P_data_c(1) .* (( MFB_V_data_c(1) ./ MFB_V_data_c).^1.32);
MFB_c = (MFB_P_data_c - motor_P_c);
% Prepare expansion curves
MFB_theta_data_e = thetar(ind_t3:ind_t4,1);
MFB_P_data_e = P(ind_t3:ind_t4,1);
MFB_V_data_e = Vol_Cyl(ind_t3:ind_t4,1);
% Calculate motoring expansion curve
% Starting point, motor_P_c(end), MFB_V_data_c(end)
% Assume curve of form PV^n is constant, find n
P_ratio = motor_P_c(end) / MFB_P_data_e(end);
V_ratio = MFB_V_data_e(end) / MFB_V_data_c(end);
n_exp = log10(P_ratio)/log10(V_ratio);
motor_P_e = motor_P_c(end) .* (( MFB_V_data_e(1) ./ MFB_V_data_e).^1.25);
% Calculate MFB expansion curve fit
% Ending point, MFB_P_data_e(end), MFB_V_data_e(end)
FIT_P_e = MFB_P_data_e(end) .* (( MFB_V_data_e(end) ./ MFB_V_data_e).^1.23);
MFB_e = (MFB_P_data_e - FIT_P_e);
% Stitching together the compression and expansion curves
% Correction
correc = (MFB_theta_data_e(1) - MFB_theta_data_c(end))/(MFB_theta_data_c(end) - MFB_theta_data_c(end-1));
correc = correc * (MFB_c(end) - MFB_c(end-1));
MFB_e = MFB_e + (MFB_c(end) - MFB_e(1)) + correc;
MFB_angle = (180/pi) * [MFB_theta_data_c; MFB_theta_data_e];
MFB_curve = [MFB_c; MFB_e];
MFB_curve = 100 * (MFB_curve / max(MFB_curve));
F1 = figure;
L1 = plot(thetad,P./100000);
F2 = figure;
L2 = plot(Vol_Cyl.*1e6,P./100000);
xlabel('Volume (c.c.)')
ylabel('Pressure (atm)')
title('SI Engine 6000 rpm Bore 78.1mm Stroke 82mm CR 10:1 con-rod length 150mm')
F3 = figure;
L3 = plot(MFB_angle,MFB_curve);
set(gca,'xlim',[-60 60])
set(gca,'ylim',[-10 110])
grid on
title('Mass Fraction Burnt')
xlabel('Crank Angle (\circ)')
ylabel('MASS FRACTION BURNT (%)')
set(L3,'linewidth',1)
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LL1 = line([-8 20],[0 100]);
set(LL1,'color','black')
if 1==0
F4 = figure;
L4 = plot((180/pi)*[MFB_theta_data_c; MFB_theta_data_e],1e-5*[motor_P_c; motor_P_e], ...
(180/pi)*[MFB_theta_data_c; MFB_theta_data_e],1e-5*[MFB_P_data_c;MFB_P_data_e] );
grid on
legend('Motored','Firing')
xlabel('Crank Angle (\circ)')
ylabel('Cylinder Pressure (atm)')
title('Firing and Motoring Cylinder Pressure')
set(L4,'linewidth',2)
F5 = figure;
L5 = plot((180/pi)*[MFB_theta_data_c; MFB_theta_data_e],1e-5*[motor_P_c; FIT_P_e], ...
(180/pi)*[MFB_theta_data_c; MFB_theta_data_e],1e-5*[MFB_P_data_c;MFB_P_data_e] );
grid on
legend('Fitting Curves','Engine Data')
xlabel('Crank Angle (\circ)')
ylabel('Cylinder Pressure (atm)')
title('Curve Fitting for MFB')
set(L5,'linewidth',2)
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