group research project

University of Wales: Trinity St. David Swansea

MEng Motorcycle Engineering

GROUP RESEARCH PROJECT By Jack Saunders

23/05/2016 Group Research Project P126806

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Figure 1: NEDC Velocity (m/s) Graph .................................................................................... 12

Figure 2: NEDC Selected Gear Graph ..................................................................................... 12

Figure 3: NEDC Force Due to Acceleration Graph ................................................................. 13

Figure 4: NEDC Vehicle Acceleration Graph ......................................................................... 13

Figure 5: NEDC Aerodynamic Drag Force ............................................................................. 14

Figure 6: NEDC Force Due to Acceleration with Energy Recovery Graph ............................ 14

Figure 7: NEDC Drive Force Graph ........................................................................................ 15

Figure 8: NEDC Rolling Resistance Force Graph ................................................................... 15

Figure 9: NEDC Wheel Torque Graph .................................................................................... 16

Figure 10: NEDC Drive Force with Energy Recovery Graph ................................................. 16

Figure 11: NEDC Wheel Speed (RPM) Graph ........................................................................ 17

Figure 12: NEDC Prop Shaft Torque Graph............................................................................ 17

Figure 13: NEDC Engine Torque (Nm) Graph ........................................................................ 18

Figure 14: NEDC Engine Speed (RPM) Graph ....................................................................... 18

Figure 15: NEDC Dynometer Torque (Nm) Graphs ............................................................... 19

Figure 16: NEDC Engine Angular Acceleration (Rad/s²) Graph ............................................ 19

Figure 17: NEDC Energy Generated with Energy Recovery (J/s) Graph ............................... 20

Figure 18: NEDC Energy Generated (J/s) Graph .................................................................... 20

Figure 19: NEDC Engine Speed from Data (RPM) Graph ...................................................... 21

Figure 20: NEDC Fuel Mass (g/s) Graph ................................................................................ 21

Figure 21: NEDC Fuel Mass with Stop/Start (g/s) Graph ....................................................... 22

Figure 22: NEDC Engine Speed from Data with Stop/Start (RPM) Graph ............................ 22

Figure 23: NEDC NOx (PPM) Graph ...................................................................................... 23

Figure 24: NEDC Hydrocarbons (PPM) Graph ....................................................................... 23

Figure 25: NEDC NOx (Kg/s) Graph ...................................................................................... 24

Figure 26: NEDC NOx with Stop/Start (PPM) Graph ............................................................ 24

Figure 27: NEDC NOx with Stop/Start (Kg/s) Graph ............................................................. 25

Figure 28: Drive Force IF Statement ....................................................................................... 26

Figure 29: Engine Speed IF Statement .................................................................................... 27

Figure 30: Idle IF Statement .................................................................................................... 28

Figure 31: Engine Torque IF Statement................................................................................... 28

Figure 32: RPM lookup ........................................................................................................... 29

Figure 33: Index Drive Cycle NEDC....................................................................................... 29

Figure 34: RPM Match ............................................................................................................ 29

Figure 35: Index Match Result NEDC..................................................................................... 29

Figure 36: WLTP Gear Selected Graph ................................................................................... 31

Figure 37: WLTP Vehicle Velocity (m/s) Graph .................................................................... 31

Figure 38: WLTP Force due to Acceleration (N) .................................................................... 32

Figure 39: WLTP Vehicle Acceleration (m/s²) Graph ............................................................. 32

Figure 40: WLTP Aerodynamic Drag Force (N) Graph .......................................................... 33

Figure 41: WLTP Force due to Acceleration with Energy Recovery (N) Graph .................... 33

Figure 42: WLTP Drive Force (N) Graph ............................................................................... 34

Figure 43: WLTP Rolling Resistance Force (N) Graph .......................................................... 34

Figure 44: WLTP Wheel Torque (Nm) Graph ........................................................................ 35

Figure 45: WLTP Drive Force with Energy Recovery (N) Graph .......................................... 35

Figure 46: WLTP Wheel Speed (RPM) Graph ........................................................................ 36


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Figure 47: WLTP Propshaft Torque (Nm) Graph.................................................................... 36

Figure 48: WLTP Engine Torque (Nm) Graph ........................................................................ 37

Figure 49: WLTP Engine Speed (RPM) Graph ....................................................................... 37

Figure 50: WLTP Dynometer Torque (Nm) Graph ................................................................. 38

Figure 51: WLTP Engine Angular Acceleration (Rad/s²) Graph ............................................ 38

Figure 52: WLTP Energy Generated per Second (J/s) Graph ................................................. 39

Figure 53: WLTP Energy Generated per Second (J/s) Graph ................................................. 39

Figure 54: WLTP Engine Speed with Stop/Start (RPM) Graph .............................................. 40

Figure 55: WLTP Engine Speed from Data (RPM) Graph ...................................................... 40

Figure 56: WLTP Fuel Mass with Stop/Start (g/s) Graph ....................................................... 41

Figure 57: WLTP Fuel Mass (g/s) Graph ................................................................................ 41

Figure 58: WLTP Hydrocarbons with Stop/Start (PPM) Graph .............................................. 42

Figure 59: WLTP Hydrocarbons (PPM) Graph ....................................................................... 42

Figure 60: WLTP NOx with Stop/Start (PPM) Graph ............................................................ 43

Figure 61: WLTP NOx (PPM) Graph ...................................................................................... 43

Figure 62: WLTP NOx with Stop/Start (Kg/s) Graph ............................................................. 44

Figure 63: WLTP NOx (Kg/s) Graph ...................................................................................... 44

Figure 64: Drive Force IF Statement ....................................................................................... 45

Figure 65: Engine Speed IF Statement .................................................................................... 46

Figure 66: Idle Speed Correction ............................................................................................. 47

Figure 67: Engine Torque IF Statements ................................................................................. 47

Figure 68: Drive Cycle Lookup WLTP ................................................................................... 48

Figure 69: Drive Cycle Index WLTP....................................................................................... 48

Figure 70: Drive Cycle Match WLTP ..................................................................................... 48

Figure 71: Index Match WLTP ................................................................................................ 48

Figure 72: Total Fuel Required ................................................................................................ 48

Figure 73: NEDC Fuel Mass with and without Stop/Start Graph ........................................... 50

Figure 74: NEDC RPM with and without Stop/Start Graph .................................................... 50

Figure 75: NEDC NOx with and without Stop/Start (kg/s) Graph .......................................... 51

Figure 76: NEDC Hydrocarbons with and without Stop/Start (PPM) Graph .......................... 51

Figure 77: NEDC vs. WLTP Velocity (m/s) Graph ................................................................ 52

Figure 78: NEDC Vs. WLTP - MPG ....................................................................................... 53

Figure 79: NOx Production NEDC Vs. WLTP ....................................................................... 54

Figure 80: Piston Displacements with Varying Offsets (m) Graph ......................................... 56

Figure 81: Connecting Rod Angle with Varying Offsets Graph ............................................. 56

Figure 82: Piston Acceleration Graph...................................................................................... 57

Figure 83: Piston Velocity (m/Degree) Graph ......................................................................... 57

Figure 84: Cylinder Pressure (Bar) Graph ............................................................................... 58

Figure 85: Inertia Force (N) with varying Offsets Graph ........................................................ 58

Figure 86: Net Force (N) with varying offsets Graph.............................................................. 59

Figure 87: Gas Force (N) Graph .............................................................................................. 59

Figure 88: Work Done (J/s) with varying Offsets Graph ........................................................ 60

Figure 89: Side Friction Force (N) with varying Offsets Graph .............................................. 60

Figure 90: FMEP Piston Skirt 0->12mm Crankshaft Offset Graph ........................................ 63

Figure 91: Actual Bank Angle due to Offset ........................................................................... 66

Figure 92: Bank 1 Connecting Rod Length ............................................................................. 66


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Figure 93: Bank 2 Connecting Rod Equation .......................................................................... 66

Figure 94: V-Twin MCrankspan* X Bank 1 Equation ............................................................ 67

Figure 95: V-Twin MCrankspan* X Bank 2 Equation ............................................................ 67

Figure 96: V-Twin Offset Centre of Mass Angle - Bank 1 ..................................................... 67

Figure 97: V-Twin Offset Centre of Mass Angle - Bank 2 ..................................................... 67

Figure 98: V-Twin MBalance*Y - Bank 1 .............................................................................. 68

Figure 99: V-Twin MBalance*Y - Bank 2 .............................................................................. 68

Figure 100: Offset centre of mass angle - V Twin - Balance Shaft - Bank 1 .......................... 68

Figure 101: Offset Centre of Mass Angle - Bank 2 ................................................................. 68

Figure 102: Single Cylinder Crankshaft MCrank*X (Kgm) Graph ........................................ 69

Figure 103: Single Cylinder Balance Shaft - MBalance*Y (Kgm) Graph .............................. 70

Figure 104: Single Cylinder Balance Shaft Offset Centre of Mass (Degrees) Graph ............. 71

Figure 105: Single Cylinder Crankshaft Offset Centre of Mass Angle (Degrees) Graph ....... 71

Figure 106: Connecting Rod Length (m) - 60 Degree Bank Angle ......................................... 72




Figure 110: Connecting Rod Length (m) - 110 Degree Bank Angle ....................................... 74

Figure 111: V-Twin MCrankspan*X Centre of Mass ............................................................. 75

Figure 112: Cylinder Volume (m) Graph ................................................................................ 78

Figure 113: Cylinder Pressure (Bar) Graph ............................................................................. 78

Figure 114: Mass Fraction Burned Graph ............................................................................... 79

Figure 115: Difference in pressure, non-combustion to combustion at each degree of crank

angle Graph .............................................................................................................................. 79

Figure 116: Air Mass Per Revolution (Kg) Graph................................................................... 80

Figure 117: Air Mass (Kg/Hr) Graph ...................................................................................... 80

Figure 118: Fuel Mass Per Cycle (Kg) Graph ......................................................................... 81

Figure 119: Air Mass Per Cycle (Kg) Graph ........................................................................... 81

Figure 120: Work Done by Pressure Per Degree (J/Degree) ................................................... 82

Figure 121: QTotal - Total Energy Released (J) Graph ........................................................... 82

Figure 122: Change in Energy Release per Degree (J/Degree) Graph .................................... 83

Figure 123: Difference in pressure combustion to non-combustion at each degree Equation 83

Figure 124: MFB Equation ...................................................................................................... 83

Figure 125: Air Mass per Revolution Equation ....................................................................... 83

Figure 126: Air Mass per Cycle Equation ............................................................................... 83

Figure 127: Fuel Mass per Cycle Equation.............................................................................. 84

Figure 128: QTotal Equation ................................................................................................... 84

Figure 129: IMEP Standard->10 Degree Advanced ................................................................ 85

Figure 130: NEDC Model #2 ................................................................................................... 88

Figure 131: NEDC Model #1 ................................................................................................... 88

Figure 132: NEDC #4 .............................................................................................................. 89

Figure 133: NEDC #3 .............................................................................................................. 89

Figure 134: NEDC 6 ................................................................................................................ 90

Figure 135: NEDC #5 .............................................................................................................. 90

Figure 136: WLTP #2 .............................................................................................................. 91

Figure 137:WLTP #1 ............................................................................................................... 91


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Figure 138: WLTP #4 .............................................................................................................. 92

Figure 139: WLTP #3 .............................................................................................................. 92

Figure 140: WLTP #6 .............................................................................................................. 93

Figure 141: WLTP #5 .............................................................................................................. 93

Figure 142: Torque Interpolations ........................................................................................... 94

Figure 143: Fuel Mass Interpolations ...................................................................................... 94

Figure 144: Hydrocarbons Interpolation .................................................................................. 95

Figure 145: NOx Interpolations ............................................................................................... 95

Figure 146: Drive Cycle Results .............................................................................................. 96

Figure 147: Piston FMEP ........................................................................................................ 97

Figure 148: Ignition Advance Results ..................................................................................... 97

Figure 149: Crankshaft Balancing #2 ...................................................................................... 98

Figure 150: Crankshaft Balancing ........................................................................................... 98


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Equation 1: NEDC Acceleration Equation .............................................................................. 26

Equation 2: NEDC Force of Vehicle Equation ........................................................................ 26

Equation 3: NEDC Aerodynamic Drag Force Equation .......................................................... 26

Equation 4: Rolling Resistance Force Equation ...................................................................... 26

Equation 5: Drive Force Equation ........................................................................................... 26

Equation 6: Rolling Tyre Radius ............................................................................................. 27

Equation 7: Wheel Torque Formula ........................................................................................ 27

Equation 8: Prop Shaft Torque Formula .................................................................................. 27

Equation 9: Wheel Speed (RPM) Formula .............................................................................. 27

Equation 10: Engine Speed (RPM) Equation .......................................................................... 27

Equation 11: Engine Torque Formula...................................................................................... 28

Equation 12: Engine Angular Acceleration Formula ............................................................... 28

Equation 13: Energy Required per Second Formula ............................................................... 28

Equation 14: Fuel Required ..................................................................................................... 29

Equation 15: Fuel Required (L) Formula................................................................................. 30

Equation 16: Fuel Required for 100Km Equation ................................................................... 30

Equation 17: MPG ................................................................................................................... 30

Equation 18: NOx Kmol/S Produced (Kmol/s) ....................................................................... 30

Equation 19: NOx Kg per Second Equation ............................................................................ 30

Equation 20: Acceleration of Vehicle ...................................................................................... 45

Equation 21: Force of Vehicle ................................................................................................. 45

Equation 22: Aerodynamic Drag Force ................................................................................... 45

Equation 23: Rolling Resistance Force .................................................................................... 45

Equation 24: Drive Force ......................................................................................................... 45

Equation 25: Rolling Tyre Radius ........................................................................................... 46

Equation 26: Wheel Torque ..................................................................................................... 46

Equation 27: Prop Shaft Torque .............................................................................................. 46

Equation 28: Wheel Speed (RPM) ........................................................................................... 46

Equation 29: Engine Speed (RPM) .......................................................................................... 46

Equation 30: Engine Torque .................................................................................................... 47

Equation 31: Engine Angular Acceleration ............................................................................. 47

Equation 32: Energy Required per Second .............................................................................. 47

Equation 33: Fuel Required in Litres ....................................................................................... 49

Equation 34: Fuel Required in Litres ....................................................................................... 49

Equation 35: MPG ................................................................................................................... 49

Equation 36: NOx Kmol per Second ....................................................................................... 49

Equation 37: NOx Kg Per Second ........................................................................................... 49

Equation 38: Connecting Rod Angle with Offset Equation..................................................... 61

Equation 39: Piston Displacement Equation............................................................................ 61

Equation 40: Piston Velocity Equation .................................................................................... 61

Equation 41: Piston Acceleration Equation ............................................................................. 61

Equation 42: Gas Force Equation ............................................................................................ 61

Equation 43: Inertia Force Equation ........................................................................................ 61

Equation 44: Net Force Equation ............................................................................................. 61

Equation 45: Connecting Rod Force Equation ........................................................................ 62

Equation 46: Side Force Equation ........................................................................................... 62


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Equation 47: Side Friction Force Equation .............................................................................. 62

Equation 48: Work Done per Degree Equation ....................................................................... 62

Equation 49: FMEP (Bar) Equation ......................................................................................... 62

Equation 50: MRot Equation ................................................................................................... 65

Equation 51: MRec Equation ................................................................................................... 65

Equation 52: MCrankspan*X Equation ................................................................................... 65

Equation 53: Offset Centre of Mass Equation ......................................................................... 65

Equation 54: MBalance*Y Equation ....................................................................................... 66

Equation 55: Balance Shaft Offset Centre of Mass Angle ...................................................... 66

Equation 56: Work Done by Pressure per Degree Equation .................................................... 84

Equation 57: Rate of Change of Energy Released Equation ................................................... 84


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Nomenclature

NEDC New European Drive Cycle

WLTP World Harmonized Light Vehicle Test Procedure

GDI Gasoline Direct Injection

CO Carbon Monoxide

NOx Oxides of Nitrogen

HC Hydrocarbons

PM Particulate Matter

PPM Particulates per Million

Km Kilometre

MPG Miles per Gallon

UDC Urban Drive Cycle

EUDC Extra Urban Drive Cycle

RPM Revolutions per Minute

FMEP Friction Mean Effective Pressure

IMEP Indicated Mean Effective Pressure

BMEP Brake Mean Effective Pressure

MRot Rotating Mass

MRec Reciprocating Mass

L Litres/Connecting Rod Length

B1_L Bank 1 Connecting Rod Length

B2_L Bank 2 Connecting Rod Length

TDC Top Dead Centre

A Frontal Area

R Crank Throw

N Newtons

ᵨ Air Density

µ Drag/Friction Coefficient

φ Phi


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Table of Contents 1.0 Introduction ................................................................................................................... 10

2.0 Drive Cycles.................................................................................................................. 10

2.1 Introduction ............................................................................................................... 10

2.2 Collaboration with Team ........................................................................................... 10

2.3 Real World Application ............................................................................................ 11

2.4 Methodology ............................................................................................................. 12

2.4.1 NEDC – New European Drive Cycle - Graphs ............................................. 12

2.4.2 NEDC – New European Drive Cycle Equations ........................................... 26

2.4.3 WLTP – World Harmonized Light Vehicle Test Procedure Graphs ......... 31

2.4.4 WLTP – World Harmonized Light Vehicle Test Procedure Equations ..... 45

2.5 Analysis of Results .................................................................................................... 50

2.6 Potential Further Work .............................................................................................. 54

3.0 Friction Modelling – Crankshaft Offset ........................................................................ 54

3.1 Introduction ............................................................................................................... 54



3.4 Methodology ............................................................................................................. 56

3.4.1 Friction Modelling Methodology – Graphs ................................................... 56

3.4.2 Friction Modelling Methodology – Equations ............................................... 61



4.0 Crankshaft Balancing .................................................................................................... 64

4.1 Introduction ............................................................................................................... 64



4.4 Methodology ............................................................................................................. 65

4.4.1 Single Cylinder Crankshaft Balancing .......................................................... 65

4.4.2 Single Cylinder Balance Shaft Balancing ...................................................... 66

4.4.3 V-Twin Crankshaft Balancing ........................................................................ 66

4.4.4 V-Twin Balance Shaft Balancing .................................................................... 68

4.5 Results ...................................................................................................................... 69


5.0 Ignition Advancement ................................................................................................... 77

5.1 Introduction ............................................................................................................... 77


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5.4 Methodology ............................................................................................................. 78

5.4.1 Ignition Advancement Methodology – Graphs ............................................. 78

5.4.2 Ignition Advancement Methodology – Equations ......................................... 83



6.0 Final Conclusion ........................................................................................................... 86

7.0 References ..................................................................................................................... 87

8.0 Appendices .................................................................................................................... 88

8.1 Appendix A – NEDC Model ..................................................................................... 88

8.2 Appendix B – WLTP Model ..................................................................................... 91

8.3 Torque Interpolations ................................................................................................ 94

8.4 Fuel Mass Interpolations ........................................................................................... 94

8.5 Hydrocarbons Interpolation....................................................................................... 95

8.6 NOx Interpolation ..................................................................................................... 95

8.7 Drive Cycle Results ................................................................................................... 96

8.8 Piston FMEP Data ..................................................................................................... 97

8.9 Ignition Advance ....................................................................................................... 97

8.10 Crankshaft Balancing ................................................................................................ 98


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1.0 Introduction

The following report is a supplement to the overall group project for the MEng Motorcycle

Engineering Degree. The report will cover the personal research and work completed by the

writer and will detail the various subject matters that have been worked on.

Each chapter of the report will have a personal introduction to the section, how the subject

links to other team members, the real world applications of the subject, the methodology used

to understand and develop the models, an analysis of the results of the various models, a

conclusion of the model to sum up the findings and the potential direction the project could

take from that point onwards.

The entire model uses data from a Ford 1.0L 3-Cylinder GDI engine, complete with cylinder

pressures, fuel maps and emissions test results; also supplied were two engines to allow for

component measurements to allow for accurate development of the models.

All mathematical modelling has been completed in Microsoft Excel, utilising the various

tools available within the program.

2.0 Drive Cycles

2.1 Introduction

The drive cycle section of the project is looking at the testing methods used by OEM vehicle

manufacturers and 1st tier suppliers to pass emissions regulations. This section will look at

both the NEDC (New European Drive Cycle) and the WLTP (World Harmonized Light

Vehicle Test Procedure) to understand how the test is used and the differences between them.

A model is developed using both systems to allow for the user to modify inputs to model to

understand how a vehicle or engine in development will behave within the tests and if the

vehicle will pass them.

2.2 Collaboration with Team

The research team have each developed a personal drive cycle model with different inputs

and applications to completely cover all aspects of developing the Ford 1.0L 3-Cylinder GDI

engine to pass the test or for a variant of the engine that is designed under the same principles

to pass.

The writer has developed a model that uses varying inputs that automatically update when the

number of cylinders has changed. When the number of cylinders are changed through the use

of a drop down box, the torques, fuel mass, aerodynamic and component measurements are

updated.


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2.3 Real World Application

The NEDC emissions regulation test is currently used to decide if a vehicle is

environmentally clean enough to be used on the road. The NEDC test changes regularly to

become stricter and stricter on the fuel used. The current NEDC test used for the category of

the 3-Cylinder 1.0L GDI engine is the Euro 6 regulation.

The Euro 6 regulation tests for the same emissions as previous, however it is stricter than the

predecessors. The current regulations from Euro 6 are:

CO - 1.0 g/km

HC - 0.10 g/km

NOx - 0.06 g/km

PM - 0.005 g/km (Direct Injection only)

PM - 6.0x10 ^11/km (Direct Injection only)

(AA, 2015)

The model designed for this report takes interpolations from measured torques, fuel mass and

exhaust emissions to determine if the engine modelled would pass all the current regulations

and provides an estimated MPG (Miles per Gallon) for the vehicle.

The NEDC is made up of two parts, the first being the UDC (Urban Driving Cycle) that

covers town driving and is supposed to represent typical European cities by not exceeding

50km/h and keeping to a low engine load; this takes up the first 780 seconds of the test. This

section is repeated four times. (Diesel Net, 2013)

The second part of the NEDC test is the EUDC (Extra Urban Driving Cycle) and covers

higher speed driving modes with a maximum speed of 120km/h. A lower speed test has been

devised for vehicles with a lower power output, with a maximum test speed of 90km/h. This

test takes up the final 400 seconds. (Diesel Net, 2013)

As seen in the following sections, the NEDC test is not necessarily representative of a

vehicle being used on the public roads as it accelerates from one speed to another and holds it

perfectly for periods of time. In a real situation, over the same time period, the vehicle would

be accelerating and decelerating at much different points and gear changes may not be at the

perfect engine speed for fuel economy and reduced emissions.

To counter this, the EU along with other countries such as Japan and India are in the process

of developing the WLTP test that as seen in the graphs below, appears more like a realistic

situation, showing more aggressive accelerations and decelerations. This test also produces

greater emissions results and typically uses more fuel. While this test is closer to the real

situations, it is still possible for the OEM manufacturers to develop engine mapping strategies

to suit the emissions test. (United Nations Economic Comission for Europe, 2016)


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2.4 Methodology

2.4.1 NEDC – New European Drive Cycle - Graphs

Figure 1: NEDC Velocity (m/s) Graph

Figure 2: NEDC Selected Gear Graph


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Figure 4: NEDC Vehicle Acceleration Graph

Figure 3: NEDC Force Due to Acceleration Graph


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Figure 6: NEDC Force Due to Acceleration with Energy Recovery Graph

Figure 5: NEDC Aerodynamic Drag Force


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Figure 8: NEDC Rolling Resistance Force Graph

Figure 7: NEDC Drive Force Graph


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Figure 10: NEDC Drive Force with Energy Recovery Graph

Figure 9: NEDC Wheel Torque Graph


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Figure 12: NEDC Prop Shaft Torque Graph

Figure 11: NEDC Wheel Speed (RPM) Graph


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Figure 14: NEDC Engine Speed (RPM) Graph

Figure 13: NEDC Engine Torque (Nm) Graph


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Figure 16: NEDC Engine Angular Acceleration (Rad/s²) Graph

Figure 15: NEDC Dynometer Torque (Nm) Graphs


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Figure 18: NEDC Energy Generated (J/s) Graph

Figure 17: NEDC Energy Generated with Energy Recovery (J/s) Graph


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Figure 20: NEDC Fuel Mass (g/s) Graph

Figure 19: NEDC Engine Speed from Data (RPM) Graph


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Figure 22: NEDC Engine Speed from Data with Stop/Start (RPM) Graph

Figure 21: NEDC Fuel Mass with Stop/Start (g/s) Graph


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Figure 24: NEDC Hydrocarbons (PPM) Graph

Figure 23: NEDC NOx (PPM) Graph


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Figure 26: NEDC NOx with Stop/Start (PPM) Graph

Figure 25: NEDC NOx (Kg/s) Graph


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Figure 27: NEDC NOx with Stop/Start (Kg/s) Graph


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2.4.2 NEDC – New European Drive Cycle Equations

The development of the drive cycle model designed within Microsoft Excel requires a

number of equations to be used along with combining pre-measured data.

The velocity trace was taken from a previous drive cycle model developed by Ben Howells of

UWTSD along with the selected gears throughout the drive cycle model.

𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 = 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 2 − 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 1

Equation 1: NEDC Acceleration Equation

The above formula shows the equation for calculating the acceleration of the vehicle.

𝐹𝑜𝑟𝑐𝑒 𝑜𝑓 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 = 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 × 𝑀𝑎𝑠𝑠 𝑜𝑓 𝑉𝑒ℎ𝑖𝑐𝑙𝑒

Equation 2: NEDC Force of Vehicle Equation

The above equation shows how the force of the vehicle accelerating is calculated, taking into

account the mass of the vehicle. The same equation is used when taking into account an

energy recovery system; this involves just adding the mass of the energy recovery

components to the mass of the vehicle, prior to multiplying it by the acceleration.

𝐴𝑒𝑟𝑜𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝐷𝑟𝑎𝑔 𝐹𝑜𝑟𝑐𝑒 =1

2× ᵨ × 𝐴 × µ × 𝑉2

Equation 3: NEDC Aerodynamic Drag Force Equation

The above formula is used to calculate the aerodynamic drag force acting against the vehicle.

The aerodynamic drag force will negatively affect the performance of the vehicle within the

emissions test, therefore the lower the drag force, the greater the improvement in the test.

𝑅𝑜𝑙𝑙𝑖𝑛𝑔 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐹𝑜𝑟𝑐𝑒 = µ ×𝑀𝑎𝑠𝑠 𝑜𝑓 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 × 𝐺𝑟𝑎𝑣𝑖𝑡𝑦

Equation 4: Rolling Resistance Force Equation

𝐷𝑟𝑖𝑣𝑒 𝐹𝑜𝑟𝑐𝑒 = 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 𝐹𝑜𝑟𝑐𝑒 + 𝐴𝑒𝑟𝑜𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝐷𝑟𝑎𝑔 𝐹𝑜𝑟𝑐𝑒

+ 𝑅𝑜𝑙𝑙𝑖𝑛𝑔 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐹𝑜𝑟𝑐𝑒

Equation 5: Drive Force Equation

The above formula, combines all the forces that the vehicle must overcome in order to move,

therefore when the drive force calculates a negative value that must be corrected in Excel.

The above formula shows that if the vehicle is not moving, where column ‘D’ is the velocity,

the drive force will be equal to 0.

Figure 28: Drive Force IF

Statement


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The same set of equations are used when energy recovery is taken into account, however the

drive force equation will use the vehicle force equation that included the mass of the energy

recovery system.

𝑅𝑜𝑙𝑙𝑖𝑛𝑔 𝑡𝑦𝑟𝑒 𝑟𝑎𝑑𝑖𝑢𝑠 =

((𝑅𝑖𝑚 𝑆𝑖𝑧𝑒 + (2 × 𝑇𝑦𝑟𝑒 𝑃𝑟𝑜𝑓𝑖𝑙𝑒)) × 𝑇𝑦𝑟𝑒 𝑊𝑖𝑑𝑡ℎ)2

1000

Equation 6: Rolling Tyre Radius

The above formula is used to calculate the actual radius of the tyre that is in movement

during the drive cycle. The rim size should be multiplied by 25.4 to convert from inches to

millimetres where necessary.

𝑊ℎ𝑒𝑒𝑙 𝑇𝑜𝑟𝑞𝑢𝑒 = 𝐷𝑟𝑖𝑣𝑒 𝐹𝑜𝑟𝑐𝑒 × 𝑅𝑜𝑙𝑙𝑖𝑛𝑔 𝑇𝑦𝑟𝑒 𝑅𝑎𝑑𝑖𝑢𝑠

Equation 7: Wheel Torque Formula

The above formula is used to calculate the torque at the wheel during the drive cycle. The

equation may be modified to replace the drive force with drive force inclusive of the energy

recovery system.

𝑃𝑟𝑜𝑝 𝑆ℎ𝑎𝑓𝑡 𝑇𝑜𝑟𝑞𝑢𝑒 = 𝑊ℎ𝑒𝑒𝑙 𝑇𝑜𝑟𝑞𝑢𝑒

(𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝑅𝑎𝑡𝑖𝑜 × 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦)

Equation 8: Prop Shaft Torque Formula

The above formula is used to calculate the Prop Shaft torque using the calculated wheel

torque with or without the energy recovery system. The resultant prop shaft torque can vary

greatly depending upon the vehicles differential ratio or differential efficiency.

𝑊ℎ𝑒𝑒𝑙 𝑆𝑝𝑒𝑒𝑑 (𝑅𝑃𝑀) =(60 × 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦)

(2 × 𝜋 × 𝑅𝑜𝑙𝑙𝑖𝑛𝑔 𝑇𝑦𝑟𝑒 𝑅𝑎𝑑𝑖𝑢𝑠)

Equation 9: Wheel Speed (RPM) Formula

The above formula is used to calculate the vehicles wheel speed using the rolling tyre radius,

Pi and the vehicles velocity in m/s.

𝐸𝑛𝑔𝑖𝑛𝑒 𝑆𝑝𝑒𝑒𝑑 (𝑅𝑃𝑀) = 𝑊ℎ𝑒𝑒𝑙 𝑆𝑝𝑒𝑒𝑑 × 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝑅𝑎𝑡𝑖𝑜 × 𝐺𝑒𝑎𝑟 𝑅𝑎𝑡𝑖𝑜

Equation 10: Engine Speed (RPM) Equation

The above formula is used to calculate the engine speed based upon the wheel speed,

differential ratio and the gear ratio.

Figure 29: Engine Speed IF Statement


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The above IF statement allows the user to automatically calculate the engine speed via the

gear inputs. The statement looks at column ‘G’ which contains the currently selected gear and

chooses which of the six equations it should use depending upon them. Using the above IF

statements means that the user could change the gear ratios and the rest of the model would

automatically update itself to correspond with the new inputs.

Using the above IF statement, the minimum RPM value throughout the model will be 800,

therefore keeping it to the idle speed of the engine. The engine speed values prior to this IF

statement can be used to simulate the effects of having a Stop/Start system.

𝐸𝑛𝑔𝑖𝑛𝑒 𝑇𝑜𝑟𝑞𝑢𝑒 = 𝑃𝑟𝑜𝑝 𝑆ℎ𝑎𝑓𝑡 𝑇𝑜𝑟𝑞𝑢𝑒

𝐺𝑒𝑎𝑟 𝑅𝑎𝑡𝑖𝑜 × 𝐺𝑒𝑎𝑟 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦

Equation 11: Engine Torque Formula

The above equation is used to determine the engine torque based upon the calculated prop

shaft torque, gear ratio and gear efficiency.

The above IF statement allows the user to automatically calculate the engine torque via the


chooses which of the seven equations it should use depending upon that results. Using the

above IF statement means that the user could change the gear ratios and the rest of the model

would automatically update itself to correspond with the new inputs.

𝐸𝑛𝑔𝑖𝑛𝑒 𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = (2 × 𝜋 × (𝑅𝑃𝑀 2 − 𝑅𝑃𝑀 1))

60

Equation 12: Engine Angular Acceleration Formula

The above formula is required to calculate the rate of angular acceleration of the engine using

the engine speeds.

𝐸𝑛𝑒𝑟𝑔𝑦 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑝𝑒𝑟 𝑆𝑒𝑐𝑜𝑛𝑑 = 𝐷𝑟𝑖𝑣𝑒 𝐹𝑜𝑟𝑐𝑒 × 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦

Equation 13: Energy Required per Second Formula

The above formula is used to calculate the energy required to move the vehicle every second.

The results from the above formula can be useful in calculating the MPG the engine is

capable of through the calorific value of the fuel; however this is not the most accurate

method.

Figure 30: Idle IF

Statement

Figure 31: Engine Torque IF Statement


29 | P a g e

The energy required can also be calculated to take into account the mass of the energy

recovery system by using the drive force inclusive of the energy recovery system.

By using a curve expert curve fitting tool it is possible to create interpolations of the torque,

fuel, HC and NOx from the Ford Fox data. The interpolations predict the values from 0 RPM

to 6500RPM to provide the in between values that can be matched to the drive cycle.

The full results of the interpolations will be included in the Appendix.

The above formula is used to lookup the exact matching RPM in the torque, fuel mass, HC

and NOx sheets as the value calculated previously. The result can be changed depending on if

stop/start technology has been taken into account.

The above formula is used to identify the row number within Microsoft Excel that the RPM

result will be located in.

The above formula is used to look up the column number that the torque, fuel mass, HC and

NOx will be located in based upon the interpolated results.

The above formula is used to pull the interpolated data out, depending upon the results of the

row number and column number formulas.

The resultant interpolated values will differ, dependant on if it is Torque, Fuel Mass, HC or

NOx that is being extrapolated from that data.

Total Fuel Required to complete drive cycle= The sum of all the fuel mass from 0 to 1180 seconds

Equation 14: Fuel Required

Figure 32: RPM lookup

Figure 34: RPM Match

Figure 33: Index Drive Cycle NEDC

Figure 35: Index Match Result NEDC


30 | P a g e

The above equation is used to calculate total amount of fuel to get through the NEDC test in

kg.

Total Fuel Required (Litres) =𝐹𝑢𝑒𝑙 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 (𝑘𝑔)

0.75

Equation 15: Fuel Required (L) Formula

The above equation is used to convert the fuel required from Kg to L.

𝐹𝑢𝑒𝑙 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑓𝑜𝑟 100𝐾𝑚 = (𝐹𝑢𝑒𝑙 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 (𝐿)

11) × 100

Equation 16: Fuel Required for 100Km Equation

The above equation is used to convert the fuel required from the standard complete drive

cycle to the volume of fuel required to complete a 100Km journey.

𝑀𝑃𝐺 =625

𝐹𝑢𝑒𝑙 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑓𝑜𝑟 100𝐾𝑚4.5

Equation 17: MPG

The above formula is used to convert the fuel required to complete a 100Km journey into the

Distance possible in miles per gallon of fuel available.

𝑁𝑂𝑥 𝐾𝑚𝑜𝑙 𝑝𝑒𝑟 𝑆𝑒𝑐𝑜𝑛𝑑 𝑃𝑟𝑜𝑑𝑢𝑐𝑒𝑑 = (𝑁𝑂𝑥 𝑃𝑃𝑀

106) × 64

Equation 18: NOx Kmol/S Produced (Kmol/s)

𝑁𝑂𝑥 𝐾𝑔 𝑝𝑒𝑟 𝑆𝑒𝑐𝑜𝑛𝑑 = 𝐹𝑢𝑒𝑙 𝑀𝑎𝑠𝑠 𝑝𝑒𝑟 𝑆𝑒𝑐𝑜𝑛𝑑

1000114

× (𝑁𝑂𝑥 𝑃𝑃𝑀

106) × 30

Equation 19: NOx Kg per Second Equation

The above equations are used to get the NOx production into Kg/s. When the NOx

production is converted to Kg/s it is possible to take the sum of these results and see the total

NOx produced across the drive cycle along with the NOx per Km.


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2.4.3 WLTP – World Harmonized Light Vehicle Test Procedure Graphs

Figure 37: WLTP Vehicle Velocity (m/s) Graph

Figure 36: WLTP Gear Selected Graph


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Figure 39: WLTP Vehicle Acceleration (m/s²) Graph

Figure 38: WLTP Force due to Acceleration (N)


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Figure 41: WLTP Force due to Acceleration with Energy Recovery (N) Graph

Figure 40: WLTP Aerodynamic Drag Force (N) Graph


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Figure 43: WLTP Rolling Resistance Force (N) Graph

Figure 42: WLTP Drive Force (N) Graph


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Figure 45: WLTP Drive Force with Energy Recovery (N) Graph

Figure 44: WLTP Wheel Torque (Nm) Graph


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Figure 47: WLTP Propshaft Torque (Nm) Graph

Figure 46: WLTP Wheel Speed (RPM) Graph


37 | P a g e

Figure 49: WLTP Engine Speed (RPM) Graph

Figure 48: WLTP Engine Torque (Nm) Graph


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Figure 51: WLTP Engine Angular Acceleration (Rad/s²) Graph

Figure 50: WLTP Dynometer Torque (Nm) Graph


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Figure 53: WLTP Energy Generated per Second (J/s) Graph

Figure 52: WLTP Energy Generated per Second (J/s) Graph


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Figure 55: WLTP Engine Speed from Data (RPM) Graph

Figure 54: WLTP Engine Speed with Stop/Start (RPM) Graph


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Figure 57: WLTP Fuel Mass (g/s) Graph

Figure 56: WLTP Fuel Mass with Stop/Start (g/s) Graph


42 | P a g e

Figure 59: WLTP Hydrocarbons (PPM) Graph

Figure 58: WLTP Hydrocarbons with Stop/Start (PPM) Graph


43 | P a g e

Figure 61: WLTP NOx (PPM) Graph

Figure 60: WLTP NOx with Stop/Start (PPM) Graph


44 | P a g e

Figure 63: WLTP NOx (Kg/s) Graph

Figure 62: WLTP NOx with Stop/Start (Kg/s) Graph


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2.4.4 WLTP – World Harmonized Light Vehicle Test Procedure

Equations

The development of the drive cycle model designed within Microsoft Excel requires a

number of equations to be used along with combining pre-measured data.

The velocity trace was taken from a previous drive cycle model developed by Ben Howells of

UWTSD along with the selected gears throughout the drive cycle model.

𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 = 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 2 − 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 1

Equation 20: Acceleration of Vehicle

The above formula shows the equation for calculating the acceleration of the vehicle.

𝐹𝑜𝑟𝑐𝑒 𝑜𝑓 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 = 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 × 𝑀𝑎𝑠𝑠 𝑜𝑓 𝑉𝑒ℎ𝑖𝑐𝑙𝑒

Equation 21: Force of Vehicle

The above equation shows how the force of the vehicle accelerating is calculated, taking into

account the mass of the vehicle. The same equation is used when taking into account an

energy recovery system; this involves just adding the mass of the energy recovery

components to the mass of the vehicle, prior to multiplying it by the acceleration.

𝐴𝑒𝑟𝑜𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝐷𝑟𝑎𝑔 𝐹𝑜𝑟𝑐𝑒 =1

2× ᵨ × 𝐴 × µ × 𝑉2

Equation 22: Aerodynamic Drag Force

The above formula is used to calculate the aerodynamic drag force acting against the vehicle.

The aerodynamic drag force will negatively affect the performance of the vehicle within the

emissions test, therefore the lower the drag force, the greater the improvement in the test.

𝑅𝑜𝑙𝑙𝑖𝑛𝑔 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐹𝑜𝑟𝑐𝑒 = µ ×𝑀𝑎𝑠𝑠 𝑜𝑓 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 × 𝐺𝑟𝑎𝑣𝑖𝑡𝑦

Equation 23: Rolling Resistance Force

𝐷𝑟𝑖𝑣𝑒 𝐹𝑜𝑟𝑐𝑒 = 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 𝐹𝑜𝑟𝑐𝑒 + 𝐴𝑒𝑟𝑜𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝐷𝑟𝑎𝑔 𝐹𝑜𝑟𝑐𝑒

+ 𝑅𝑜𝑙𝑙𝑖𝑛𝑔 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐹𝑜𝑟𝑐𝑒

Equation 24: Drive Force

The above formula, combines all the forces that the vehicle must overcome in order to move,

therefore when the drive force calculates a negative value that must be corrected in Excel.

The above formula shows that if the vehicle is not moving, where column ‘D’ is the velocity,

the drive force will be equal to 0.

Figure 64: Drive Force IF

Statement


46 | P a g e

The same set of equations are used when energy recovery is taken into account, however the

drive force equation will use the vehicle force equation that included the mass of the energy

recovery system.

𝑅𝑜𝑙𝑙𝑖𝑛𝑔 𝑡𝑦𝑟𝑒 𝑟𝑎𝑑𝑖𝑢𝑠 =

((𝑅𝑖𝑚 𝑆𝑖𝑧𝑒 + (2 × 𝑇𝑦𝑟𝑒 𝑃𝑟𝑜𝑓𝑖𝑙𝑒)) × 𝑇𝑦𝑟𝑒 𝑊𝑖𝑑𝑡ℎ)2

1000

Equation 25: Rolling Tyre Radius

The above formula is used to calculate the actual radius of the tyre that is in movement

during the drive cycle. The rim size should be multiplied by 25.4 to convert from inches to

millimetres where necessary.

𝑊ℎ𝑒𝑒𝑙 𝑇𝑜𝑟𝑞𝑢𝑒 = 𝐷𝑟𝑖𝑣𝑒 𝐹𝑜𝑟𝑐𝑒 × 𝑅𝑜𝑙𝑙𝑖𝑛𝑔 𝑇𝑦𝑟𝑒 𝑅𝑎𝑑𝑖𝑢𝑠

Equation 26: Wheel Torque

The above formula is used to calculate the torque at the wheel during the drive cycle. The

equation may be modified to replace the drive force with drive force inclusive of the energy

recovery system.

𝑃𝑟𝑜𝑝 𝑆ℎ𝑎𝑓𝑡 𝑇𝑜𝑟𝑞𝑢𝑒 = 𝑊ℎ𝑒𝑒𝑙 𝑇𝑜𝑟𝑞𝑢𝑒

(𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝑅𝑎𝑡𝑖𝑜 × 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦)

Equation 27: Prop Shaft Torque

The above formula is used to calculate the Prop Shaft torque using the calculated wheel

torque with or without the energy recovery system. The resultant prop shaft torque can vary

greatly depending upon the vehicles differential ratio or differential efficiency.

𝑊ℎ𝑒𝑒𝑙 𝑆𝑝𝑒𝑒𝑑 (𝑅𝑃𝑀) =(60 × 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦)

(2 × 𝜋 × 𝑅𝑜𝑙𝑙𝑖𝑛𝑔 𝑇𝑦𝑟𝑒 𝑅𝑎𝑑𝑖𝑢𝑠)

Equation 28: Wheel Speed (RPM)

The above formula is used to calculate the vehicles wheel speed using the rolling tyre radius,

Pi and the vehicles velocity in m/s.

𝐸𝑛𝑔𝑖𝑛𝑒 𝑆𝑝𝑒𝑒𝑑 (𝑅𝑃𝑀) = 𝑊ℎ𝑒𝑒𝑙 𝑆𝑝𝑒𝑒𝑑 × 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡𝑖𝑎𝑙 𝑅𝑎𝑡𝑖𝑜 × 𝐺𝑒𝑎𝑟 𝑅𝑎𝑡𝑖𝑜

Equation 29: Engine Speed (RPM)

The above formula is used to calculate the engine speed based upon the wheel speed,

differential ratio and the gear ratio.

Figure 65: Engine Speed IF Statement


47 | P a g e

The above IF statement allows the user to automatically calculate the engine speed via the


chooses which of the six equations it should use depending upon them. Using the above IF

statements means that the user could change the gear ratios and the rest of the model would

automatically update itself to correspond with the new inputs.

Using the above IF statement, the minimum RPM value throughout the model will be 800,

therefore keeping it to the idle speed of the engine. The engine speed values prior to this IF

statement can be used to simulate the effects of having a Stop/Start system.

𝐸𝑛𝑔𝑖𝑛𝑒 𝑇𝑜𝑟𝑞𝑢𝑒 = 𝑃𝑟𝑜𝑝 𝑆ℎ𝑎𝑓𝑡 𝑇𝑜𝑟𝑞𝑢𝑒

𝐺𝑒𝑎𝑟 𝑅𝑎𝑡𝑖𝑜 × 𝐺𝑒𝑎𝑟 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦

Equation 30: Engine Torque

The above equation is used to determine the engine torque based upon the calculated prop

shaft torque, gear ratio and gear efficiency.

The above IF statement allows the user to automatically calculate the engine torque via the


chooses which of the seven equations it should use depending upon that results. Using the

above IF statement means that the user could change the gear ratios and the rest of the model

would automatically update itself to correspond with the new inputs.

𝐸𝑛𝑔𝑖𝑛𝑒 𝐴𝑛𝑔𝑢𝑙𝑎𝑟 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = (2 × 𝜋 × (𝑅𝑃𝑀 2 − 𝑅𝑃𝑀 1))

60

Equation 31: Engine Angular Acceleration

The above formula is required to calculate the rate of angular acceleration of the engine using

the engine speeds.

𝐸𝑛𝑒𝑟𝑔𝑦 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑝𝑒𝑟 𝑆𝑒𝑐𝑜𝑛𝑑 = 𝐷𝑟𝑖𝑣𝑒 𝐹𝑜𝑟𝑐𝑒 × 𝑉𝑒ℎ𝑖𝑐𝑙𝑒 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦

Equation 32: Energy Required per Second

The above formula is used to calculate the energy required to move the vehicle every second.

The results from the above formula can be useful in calculating the MPG the engine is

capable of through the calorific value of the fuel; however this is not the most accurate

method.

Figure 66: Idle Speed

Correction

Figure 67: Engine Torque IF Statements


48 | P a g e

The energy required can also be calculated to take into account the mass of the energy

recovery system by using the drive force inclusive of the energy recovery system.

By using a curve expert curve fitting tool it is possible to create interpolations of the torque,

fuel, HC and NOx from the Ford Fox data. The interpolations predict the values from 0 RPM

to 6500RPM to provide the in between values that can be matched to the drive cycle.

The full results of the interpolations will be included in the Appendix.

The above formula is used to lookup the exact matching RPM in the torque, fuel mass, HC

and NOx sheets as the value calculated previously. The result can be changed depending on if

stop/start technology has been taken into account.

The above formula is used to identify the row number within Microsoft Excel that the RPM

result will be located in.

The above formula is used to look up the column number that the torque, fuel mass, HC and

NOx will be located in based upon the interpolated results.

The above formula is used to pull the interpolated data out, depending upon the results of the

row number and column number formulas.

The resultant interpolated values will differ, dependant on if it is Torque, Fuel Mass, HC or

NOx that is being extrapolated from that data.

Total Fuel Required to complete drive cycle= The sum of all the fuel mass from 0 to 1180 seconds

Figure 72: Total Fuel Required

Figure 68: Drive Cycle Lookup WLTP

Figure 70: Drive Cycle Match WLTP

Figure 69: Drive Cycle Index WLTP

Figure 71: Index Match WLTP


49 | P a g e

The above equation is used to calculate total amount of fuel to get through the NEDC test in

kg.

Total Fuel Required (Litres) =𝐹𝑢𝑒𝑙 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 (𝑘𝑔)

0.75

Equation 33: Fuel Required in Litres

The above equation is used to convert the fuel required from Kg to L.

𝐹𝑢𝑒𝑙 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑓𝑜𝑟 100𝐾𝑚 = (𝐹𝑢𝑒𝑙 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 (𝐿)

11) × 100

Equation 34: Fuel Required in Litres

The above equation is used to convert the fuel required from the standard complete drive

cycle to the volume of fuel required to complete a 100Km journey.

𝑀𝑃𝐺 =625

𝐹𝑢𝑒𝑙 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑓𝑜𝑟 100𝐾𝑚4.5

Equation 35: MPG

The above formula is used to convert the fuel required to complete a 100Km journey into the

Distance possible in miles per gallon of fuel available.

𝑁𝑂𝑥 𝐾𝑚𝑜𝑙 𝑝𝑒𝑟 𝑆𝑒𝑐𝑜𝑛𝑑 𝑃𝑟𝑜𝑑𝑢𝑐𝑒𝑑 = (𝑁𝑂𝑥 𝑃𝑃𝑀

106) × 64

Equation 36: NOx Kmol per Second

𝑁𝑂𝑥 𝐾𝑔 𝑝𝑒𝑟 𝑆𝑒𝑐𝑜𝑛𝑑 = 𝐹𝑢𝑒𝑙 𝑀𝑎𝑠𝑠 𝑝𝑒𝑟 𝑆𝑒𝑐𝑜𝑛𝑑

1000114

× (𝑁𝑂𝑥 𝑃𝑃𝑀

106) × 30

Equation 37: NOx Kg Per Second

The above equations are used to get the NOx production into Kg/s. When the NOx

production is converted to Kg/s it is possible to take the sum of these results and see the total

NOx produced across the drive cycle along with the NOx per Km.


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2.5 Analysis of Results

Figure 73: NEDC Fuel Mass with and without Stop/Start Graph

Figure 74: NEDC RPM with and without Stop/Start Graph


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Figure 76: NEDC Hydrocarbons with and without Stop/Start (PPM) Graph

Figure 75: NEDC NOx with and without Stop/Start (kg/s) Graph


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Having completed the drive cycle model in Microsoft Excel, the comparisons can be made

between the economic performance of the Ford Fox engine with and without stop/start

technology as seen in figure 74 above. The graph shows that where normally the engine

would continue to idle at certain stages and therefore using fuel and creating more HC and

NOx, the stop/start technology switches the engine off for small periods.

The small periods with the stop/start active allow the engine to save fuel and therefore appear

to perform to a higher standard within the NEDC test. Figure 73 above demonstrates this

further by showing where the fuel mass in g/s drops to zero when the engine switches off.

Figure 76 above shows the difference between having stop/start and not with respect to the

hydrocarbons being produced. The graph clearly shows that for some sections the stop/start

technology causes a drop in hydrocarbons across the test; the graph also shows however some

huge spikes in hydrocarbons at the start with stop/start technology.

While the huge spikes can potentially be legitimate, there is a chance that this could be down

to an error in the interpolation table.

Figure 75 shows that the stop/start technology allows the NOx production to decrease at the

correct moments, dropping to zero when the vehicle would normally be idling; however

based on the results stop/start actually has only a tiny impact on the NOx production within

the drive cycle and should be reduced using more effective methods.

Figure 77: NEDC vs. WLTP Velocity (m/s) Graph


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Figure 77 shows the difference between the NEDC test and the WLTP test. The NEDC test

that is widely claimed to be misrepresentative of real world driving is shown to have sections

on the velocity graph where it accelerates at a very flat rate and then holds speeds for periods

of time.

The new WLTP test is shown to be more representative to real world driving as it shows the

spikes in velocity throughout the entire test. The only time the velocity of the vehicle is flat is

when the vehicle has actually come to a stop; these patterns can be seen throughout all of the

WLTP drive cycle graphs.

The above graph shows a common trend between the increase in number of cylinders and the

reduction in fuel economy, along with an increase in fuel economy as the test moves from

NEDC to WLTP.

The results show that moving from an NEDC to WLTP test wouldn’t just provide more

accurate emissions results, but it may actually prove to be positive for OEM vehicle

manufacturers as they will be able to officially advertise a greater fuel economy.

Figure 78: NEDC Vs. WLTP - MPG


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2.6 Potential Further Work

The potential for further work within the field of drive cycles is positively endless.

The main priority would be improving the options for the variations, meaning that

instead of just changing the cylinders and having pre-arranged inputs for each of those

cylinders, each of them could have a variation within themselves.

For example, instead of just changing the cylinders and having the vehicle mass,

aerodynamics and tyre profiles change all at once, each of them could be

interchangeable and editable therefore providing greater options for analysing how to

get the most out of the drive cycle.

3.0 Friction Modelling – Crankshaft Offset

3.1 Introduction The friction modelling with crankshaft offsets section looks into the benefits of offsetting the

crankshaft to reduce friction on the power stroke. This section of the project will look at how

the model developed and will analyse the results of the friction modelling to ascertain which

crankshaft offset is most appropriate for the Ford 3-Cylinder 1.0L GDI engine.

Figure 79: NOx Production NEDC Vs. WLTP


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The friction modelling with crankshaft offsets is something that the entire team is looking

into due it being such an important aspect of modern engine design. Each team member will

be looking at what the best crankshaft offset is and analysing it themselves. This section is

something that all team members are taking part in, however it is also the section that ties the

team together the least as it depends and supplements no other team member.


The real world applications of crankshaft offsets is something that is very prominent in

modern day engine design. Due to the need to pass rigorous emissions and fuel economy

tests, any possible opportunity to improve the efficiency of the engine should be taken.

The crankshaft is offset to the left by a small margin, therefore reducing the connecting rod

angle on the power stroke and therefore reducing the frictional force applied to the sidewall

from the piston skirt.

Offsetting the crankshaft in this way will increase the frictional force on the compression and

exhaust strokes, however due to the lower pressure on these particular strokes, it is typically

the case of being beneficial regardless of frictional losses on the other strokes.

The Ford Fox 3 Cylinder 1.0L GDI Turbo charged engine is currently using a crankshaft that

is offset by 8mm. The author has modelled the frictional forces starting with no offset and

increasing to 12mm to see if there are any improvements to be made to the frictional force on

the sidewall and therefore reduce the FMEP losses.


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3.4 Methodology

3.4.1 Friction Modelling Methodology – Graphs

Figure 81: Connecting Rod Angle with Varying Offsets Graph

Figure 80: Piston Displacements with Varying Offsets (m) Graph


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Figure 83: Piston Velocity (m/Degree) Graph

Figure 82: Piston Acceleration Graph


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Figure 85: Inertia Force (N) with varying Offsets Graph

Figure 84: Cylinder Pressure (Bar) Graph


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Figure 87: Gas Force (N) Graph

Figure 86: Net Force (N) with varying offsets Graph


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Figure 89: Side Friction Force (N) with varying Offsets Graph

Figure 88: Work Done (J/s) with varying Offsets Graph


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3.4.2 Friction Modelling Methodology – Equations

𝐶𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑛𝑔 𝑅𝑜𝑑 𝐴𝑛𝑔𝑙𝑒

= sin−1((𝑅

𝐿) × sin(𝐶𝑟𝑎𝑛𝑘 𝐴𝑛𝑔𝑙𝑒) − (

(𝐶𝑟𝑎𝑛𝑘 𝑜𝑓𝑓𝑠𝑒𝑡 − 𝑃𝑖𝑛 𝑂𝑓𝑓𝑠𝑒𝑡)

𝐿))

Equation 38: Connecting Rod Angle with Offset Equation

The above equation shows the method for calculating the connecting rod angle with an offset.

The crankshaft offset and the gudgeon pin offset are both taken into account along with the

crank throw and the connecting rod length.

𝑃𝑖𝑠𝑡𝑜𝑛 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = ((𝑅 + 𝐿) × (cos(𝜑)) − (𝑅 × cos(𝐶𝑟𝑎𝑛𝑘 𝐴𝑛𝑔𝑙𝑒)) + (𝐿 × cos(𝜑))

Equation 39: Piston Displacement Equation

The above equation shows the method for calculating piston displacement with crankshaft

offsets.

𝑃𝑖𝑠𝑡𝑜𝑛 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝑃𝑖𝑠𝑡𝑜𝑛 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 2 − 𝑃𝑖𝑠𝑡𝑜𝑛 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 1

Equation 40: Piston Velocity Equation

The above equation shows the method for calculating the velocity of the piston in m/degree

taking into account the piston displacements that have been calculating with crankshaft offset

connecting rod angles.

𝑃𝑖𝑠𝑡𝑜𝑛 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = (𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 2 − 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 1) × (6 × 𝐸𝑛𝑔𝑖𝑛𝑒 𝑆𝑝𝑒𝑒𝑑)2

Equation 41: Piston Acceleration Equation

The above equation shows the method for calculating the acceleration of the piston in m/s²,

making use of the piston velocity calculated using crankshaft offsets.

𝐺𝑎𝑠 𝐹𝑜𝑟𝑐𝑒 = 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 (𝑃𝑎) × 𝑃𝑖𝑠𝑡𝑜𝑛 𝐴𝑟𝑒𝑎

Equation 42: Gas Force Equation

The above equation shows the method for calculating the gas force in N as a result of the

pressure and piston area.

𝐼𝑛𝑒𝑟𝑡𝑖𝑎 𝐹𝑜𝑟𝑐𝑒 = 𝑃𝑖𝑠𝑡𝑜𝑛 𝐴𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 × 𝑃𝑖𝑠𝑡𝑜𝑛 𝑀𝑎𝑠𝑠

Equation 43: Inertia Force Equation

The above equation shows the method for calculating the inertia force as a result of the

previously calculated piston acceleration and the piston assembly mass.

𝑁𝑒𝑡 𝐹𝑜𝑟𝑐𝑒 = 𝐺𝑎𝑠 𝐹𝑜𝑟𝑐𝑒 − 𝐼𝑛𝑒𝑟𝑡𝑖𝑎 𝐹𝑜𝑟𝑐𝑒

Equation 44: Net Force Equation

The above equation shows the method for calculating the resultant net force as a result of the

gas force and inertia force.


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𝐶𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑛𝑔 𝑅𝑜𝑑 𝐹𝑜𝑟𝑐𝑒 = 𝑁𝑒𝑡 𝐹𝑜𝑟𝑐𝑒

cos𝜑

Equation 45: Connecting Rod Force Equation

The above equation shows the method for calculating the connecting rod force as a result of

the net force and the offset crankshafts new connecting rod angle.

𝑆𝑖𝑑𝑒 𝐹𝑜𝑟𝑐𝑒 = 𝑁𝑒𝑡 𝐹𝑜𝑟𝑐𝑒 × tan𝜑

Equation 46: Side Force Equation

The above equation shows the method for calculating the side force as a result of the net

force and the new connecting rod angle from the offset crankshaft.

𝑆𝑖𝑑𝑒 𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝐹𝑜𝑟𝑐𝑒 = 𝑆𝑖𝑑𝑒 𝐹𝑜𝑟𝑐𝑒 × 𝜇

Equation 47: Side Friction Force Equation

The above equation shows the method for calculating the side friction force as a result of the

side force acting against the cylinder wall with a coefficient of friction.

𝑊𝑜𝑟𝑘 𝐷𝑜𝑛𝑒 𝑝𝑒𝑟 𝐷𝑒𝑔𝑟𝑒𝑒 = 𝑃𝑖𝑠𝑡𝑜𝑛 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 × 𝑆𝑖𝑑𝑒 𝐹𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝐹𝑜𝑟𝑐𝑒

Equation 48: Work Done per Degree Equation

The above equation shows the method for calculating the work done per degree in Joules

using the piston velocity and the previously calculated side friction force.

𝐹𝑀𝐸𝑃 (𝐵𝑎𝑟) =𝑆𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑤𝑜𝑟𝑘 𝑑𝑜𝑛𝑒

𝐶𝑦𝑙𝑖𝑛𝑑𝑒𝑟 𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡105

Equation 49: FMEP (Bar) Equation

The above equation shows the method for calculating the FMEP in Bar for the piston pushed

again the sidewall due to the side friction force.


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With the friction model completed, the final results can be plotted in the graph shown

in figure 90 above. The results show that at the lower engine speeds the crankshaft

offset has a very small effect, however as the engine speeds pick up and the gas

pressure begins to reach its peak the crankshaft offset has a greater benefit.

The greater benefit at the 2000->4000 RPM range is due to that being the region in

which the engine is running at its peak gas pressure and the crankshaft offset is used

to reduce side friction force in the power stroke when the gas pressure will be having

its greatest effect.

The graph also shows that from 6000 RPM onwards the offset that is most beneficial

becomes the worst and having no offset is best. The author feels that this is due to the

gas pressure dropping and therefore having not much of a benefit in reducing the

frictional force on the power stroke whereas the engine speed increase is going to

cause a greater side friction force on the compression and exhaust strokes.

The author believes that the maximum crankshaft offset of 12mm is the best and if the

engine is redesigned this should be taken into account in the process.

Figure 90: FMEP Piston Skirt 0->12mm Crankshaft Offset Graph


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In order to further understand how the crankshaft offsets can benefit the design of an

engine, more offsets could help to understand how the frictional side forces can be

reduced.

The FMEP of the piston rings could also be analysed to understand how much

potential there is for reducing the FMEP of the piston rings by offsetting the

crankshaft and not having them pressed again the side wall on the power stroke.

4.0 Crankshaft Balancing

4.1 Introduction

This section of the report will cover the balancing of both the single cylinder and v-twin

crankshafts with crankshaft offsets; it will cover how this section ties into the rest of the team

in the group projects and how this applies to real world applications.

This section will also cover the equations used to complete this model and will look at the

results of the balancing in the form of graphs.


As the entire team is looking at crankshaft offsets, the author decided that looking at how to

balance a crankshaft with an offset would be beneficial to the group project. As the other

team members are completing drive cycle models with different sized engines, the balancing

work has been completed on a single cylinder and a v-twin engine.


Crankshafts with offsets are now a part of modern day engine design and therefore it is

important that they are balanced correctly so as to not cause unnecessary vibrations within the

engine. If the crankshaft is not correctly balanced, the vibrations can cause unnecessary wear

to components in the engine, especially bearings.


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4.4 Methodology

The following two equations are relevant to all four sections of the crankshaft balancing.

𝑀𝑅𝑜𝑡 =2

3× 𝐶𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑛𝑔 𝑅𝑜𝑑 𝑀𝑎𝑠𝑠

Equation 50: MRot Equation

The above equation demonstrates how to calculate the rotating mass within the engine.

𝑀𝑅𝑒𝑐 = (1

3× 𝐶𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑛𝑔 𝑅𝑜𝑑 𝑀𝑎𝑠𝑠) + 𝑃𝑖𝑠𝑡𝑜𝑛 𝑀𝑎𝑠𝑠

Equation 51: MRec Equation

The above equation demonstrates how to calculate the reciprocating mass within the engine.

4.4.1 Single Cylinder Crankshaft Balancing

𝑀𝐶𝑟𝑎𝑛𝑘𝑠𝑝𝑎𝑛 × 𝑥

= 𝑅 × (√(((𝑀𝑅𝑜𝑡 + (𝑀𝑟𝑒𝑐

2))2) + (((

𝑀𝑅𝑒𝑐

2) × (

(𝐶𝑟𝑎𝑛𝑘 𝑂𝑓𝑓𝑠𝑒𝑡 − 𝑃𝑖𝑛 𝑂𝑓𝑓𝑠𝑒𝑡)

𝐿))2) )

Equation 52: MCrankspan*X Equation

The above equation shows the method for calculating the mass moment of the crank span

taking into account crankshaft and gudgeon pin offsets. Therefore dividing the mass moment

by the required X value will return the mass required and vice versa.

𝑂𝑓𝑓𝑠𝑒𝑡 𝐶𝑒𝑛𝑡𝑟𝑒 𝑜𝑓 𝑀𝑎𝑠𝑠 𝐴𝑛𝑔𝑙𝑒

= tan−1

(

(

(

𝑀𝑅𝑒𝑐2 )

(𝑀𝑅𝑜𝑡 + (𝑀𝑟𝑒𝑐2 ))

)

× ((𝐶𝑟𝑎𝑛𝑘 𝑂𝑓𝑓𝑠𝑒𝑡 − 𝑃𝑖𝑛 𝑂𝑓𝑓𝑠𝑒𝑡)

𝐿)

)

Equation 53: Offset Centre of Mass Equation

The above equation demonstrates the method for calculating the angle the centre of mass is

offset from the centre. This is due to the crankshaft being physically offset and therefore

requiring the centre of mass to be offset as well.


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4.4.2 Single Cylinder Balance Shaft Balancing

𝑀𝐵𝑎𝑙𝑎𝑛𝑐𝑒 × 𝑌 = (𝑀𝑅𝑒𝑐

2) × 𝑅 × √((1 + ((

(𝐶𝑟𝑎𝑛𝑘 𝑂𝑓𝑓𝑠𝑒𝑡 − 𝑃𝑖𝑛 𝑜𝑓𝑓𝑠𝑒𝑡)

𝐿)2))))

Equation 54: MBalance*Y Equation

The above equation demonstrates how to calculate the mass moment for the single cylinder

balance shaft. The resultant value can then be divided by the required Y value to receive the

required mass and vice versa.

𝑂𝑓𝑓𝑠𝑒𝑡 𝐶𝑒𝑛𝑡𝑟𝑒 𝑜𝑓 𝑀𝑎𝑠𝑠 𝐴𝑛𝑔𝑙𝑒 = tan−1 ((𝐶𝑟𝑎𝑛𝑘 𝑂𝑓𝑓𝑠𝑒𝑡 − 𝑃𝑖𝑛 𝑂𝑓𝑓𝑠𝑒𝑡)

𝐿)

Equation 55: Balance Shaft Offset Centre of Mass Angle

The above equation shows the method for calculating the angle the centre of mass is offset

from the centre. This is due to the crankshaft being physically offset and therefore requiring

the centre of mass of the balance shaft to be offset as well.

4.4.3 V-Twin Crankshaft Balancing

𝐴𝑐𝑡𝑢𝑎𝑙 𝑂𝑓𝑓𝑠𝑒𝑡 𝐷𝑢𝑒 𝑡𝑜 𝐵𝑎𝑛𝑘 𝐴𝑛𝑔𝑙𝑒 = 𝐶𝑟𝑎𝑛𝑘 𝑂𝑓𝑓𝑠𝑒𝑡 × cos (𝐵𝑎𝑛𝑘 𝐴𝑛𝑔𝑙𝑒

2)

Figure 91: Actual Bank Angle due to Offset

The equation above shows how with a Vee style engine, the crankshaft offset is not

necessarily what would be expected and changes depending upon the angle at which the

banks are.

𝐵𝑎𝑛𝑘 1 𝐶𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑛𝑔 𝑅𝑜𝑑 𝐿𝑒𝑛𝑔𝑡ℎ = 𝐿 − (𝐶𝑟𝑎𝑛𝑘 𝑂𝑓𝑓𝑠𝑒𝑡 × sin (𝐵𝑎𝑛𝑘 𝐴𝑛𝑔𝑙𝑒

2))

Figure 92: Bank 1 Connecting Rod Length

The above equation shows how the connecting rod for bank 1 changes in length due to being

offset on a vee twin style engine. As the crankshaft is offset to the left, the left hand bank is

the one that has a shortened connecting rod.

𝐵𝑎𝑛𝑘 2 𝐶𝑜𝑛𝑛𝑒𝑐𝑡𝑖𝑛𝑔 𝑅𝑜𝑑 𝐿𝑒𝑛𝑔𝑡ℎ = 𝐿 + (𝐶𝑟𝑎𝑛𝑘 𝑂𝑓𝑓𝑠𝑒𝑡 × sin (𝐵𝑎𝑛𝑘 𝐴𝑛𝑔𝑙𝑒

2))

Figure 93: Bank 2 Connecting Rod Equation


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The above equation demonstrates the method for changing the connecting rod length for bank

2 with an offset crankshaft on a vee style engine. The connecting rod on bank 2 is extended

due to the crankshaft being offset to the left.

𝑉 − 𝑇𝑤𝑖𝑛 𝑀𝐶𝑟𝑎𝑛𝑘𝑠𝑝𝑎𝑛 × 𝑥 − 𝐵𝑎𝑛𝑘 1

= 𝑅

× (√(((2 × 𝑀𝑅𝑜𝑡 + (𝑀𝑅𝑒𝑐))2) + (((𝑀𝑅𝑒𝑐) × ((𝐴𝑐𝑡𝑢𝑎𝑙 𝑂𝑓𝑓𝑠𝑒𝑡 − 𝑃𝑖𝑛 𝑂𝑓𝑓𝑠𝑒𝑡)

𝐵1_𝐿))2) )

Figure 94: V-Twin MCrankspan* X Bank 1 Equation

The above equation shows the method used for calculating the mass moment of the crankspan

with respect to Bank 1. The mass moment can then be divided by the chosen X value to attain

the required mass for the crankspan.

𝑉 − 𝑇𝑤𝑖𝑛 𝑀𝐶𝑟𝑎𝑛𝑘𝑠𝑝𝑎𝑛 × 𝑥 − 𝐵𝑎𝑛𝑘 2

= 𝑅

× (√(((2 × 𝑀𝑅𝑜𝑡 + (𝑀𝑅𝑒𝑐))2) + (((𝑀𝑅𝑒𝑐) × ((𝐴𝑐𝑡𝑢𝑎𝑙 𝑂𝑓𝑓𝑠𝑒𝑡 − 𝑃𝑖𝑛 𝑂𝑓𝑓𝑠𝑒𝑡)

𝐵2_𝐿))2) )

Figure 95: V-Twin MCrankspan* X Bank 2 Equation

The above equation shows the method used for calculating the mass moment of the crankspan

with respect to Bank 2. The mass moment can then be divided by the chosen X value to attain

the required mass for the crankspan.

𝑂𝑓𝑓𝑠𝑒𝑡 𝐶𝑒𝑛𝑡𝑟𝑒 𝑜𝑓 𝑀𝑎𝑠𝑠 𝐴𝑛𝑔𝑙𝑒 − 𝐵𝑎𝑛𝑘 1

= tan−1(((𝑀𝑅𝑒𝑐)

(2 × 𝑀𝑅𝑜𝑡 + (𝑀𝑟𝑒𝑐))) × (

(𝐴𝑐𝑡𝑢𝑎𝑙 𝑂𝑓𝑓𝑠𝑒𝑡 − 𝑃𝑖𝑛 𝑂𝑓𝑓𝑠𝑒𝑡)

𝐵1_𝐿))

Figure 96: V-Twin Offset Centre of Mass Angle - Bank 1

The above equation shows the method for calculating the angle that the mass moment is

offset at with respect to the new connecting rod length on bank 1.

O𝑓𝑓𝑠𝑒𝑡 𝐶𝑒𝑛𝑡𝑟𝑒 𝑜𝑓 𝑀𝑎𝑠𝑠 𝐴𝑛𝑔𝑙𝑒 − 𝐵𝑎𝑛𝑘 2 = tan−1 (((𝑀𝑅𝑒𝑐)

(2×𝑀𝑅𝑜𝑡+(𝑀𝑟𝑒𝑐))) ×

((𝐴𝑐𝑡𝑢𝑎𝑙 𝑂𝑓𝑓𝑠𝑒𝑡−𝑃𝑖𝑛 𝑂𝑓𝑓𝑠𝑒𝑡)

𝐵2_𝐿))

Figure 97: V-Twin Offset Centre of Mass Angle - Bank 2

The above equation shows the method for calculating the angle that the mass moment is

offset at with respect to the new connecting rod length on bank 2.


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4.4.4 V-Twin Balance Shaft Balancing

𝑀𝐵𝑎𝑙𝑎𝑛𝑐𝑒 × 𝑌 − 𝐵𝑎𝑛𝑘 1

= (𝑀𝑟𝑒𝑐) × 𝑅 × √((1 + (((𝐴𝑐𝑡𝑢𝑎𝑙 𝑂𝑓𝑓𝑠𝑒𝑡 − 𝑃𝑖𝑛 𝑜𝑓𝑓𝑠𝑒𝑡)

𝐵𝐿_1)2))))

Figure 98: V-Twin MBalance*Y - Bank 1

The above equation shows the method for calculating the mass moment of the balance shaft

with respect to the new connecting rod length on bank 1. The mass moment can then be

divided by the chosen Y value to calculate the required balance shaft mass.

𝑀𝐵𝑎𝑙𝑎𝑛𝑐𝑒 × 𝑌 − 𝐵𝑎𝑛𝑘 2

= (𝑀𝑟𝑒𝑐) × 𝑅 × √((1 + (((𝐴𝑐𝑡𝑢𝑎𝑙 𝑂𝑓𝑓𝑠𝑒𝑡 − 𝑃𝑖𝑛 𝑜𝑓𝑓𝑠𝑒𝑡)

𝐵𝐿_2)2))))

Figure 99: V-Twin MBalance*Y - Bank 2

The above equation shows the method for calculating the mass moment of the balance shaft

with respect to the new connecting rod length on bank 2. The mass moment can then be

divided by the chosen Y value to calculate the required mass of the balance shaft.

𝑂𝑓𝑓𝑠𝑒𝑡 𝐶𝑒𝑛𝑡𝑟𝑒 𝑜𝑓 𝑀𝑎𝑠𝑠 𝐴𝑛𝑔𝑙𝑒 − 𝐵𝑎𝑛𝑘 1 = tan−1 ((𝐴𝑐𝑡𝑢𝑎𝑙 𝑂𝑓𝑓𝑠𝑒𝑡 − 𝑃𝑖𝑛 𝑂𝑓𝑓𝑠𝑒𝑡)

𝐵𝐿_1)

Figure 100: Offset centre of mass angle - V Twin - Balance Shaft - Bank 1

The equation above shows the offset centre of mass angle for bank 1 with respect to the new

connecting rod length for bank 1.

𝑂𝑓𝑓𝑠𝑒𝑡 𝐶𝑒𝑛𝑡𝑟𝑒 𝑜𝑓 𝑀𝑎𝑠𝑠 𝐴𝑛𝑔𝑙𝑒 − 𝐵𝑎𝑛𝑘 2 = tan−1 ((𝐴𝑐𝑡𝑢𝑎𝑙 𝑂𝑓𝑓𝑠𝑒𝑡 − 𝑃𝑖𝑛 𝑂𝑓𝑓𝑠𝑒𝑡)

𝐵𝐿_2)

Figure 101: Offset Centre of Mass Angle - Bank 2

The equation above shows the offset centre of mass angle for bank 2 with respect to the new

connecting rod length for bank 2.


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4.5 Results

Figure 102: Single Cylinder Crankshaft MCrank*X (Kgm) Graph


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Figure 103: Single Cylinder Balance Shaft - MBalance*Y (Kgm) Graph


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Figure 105: Single Cylinder Crankshaft Offset Centre of Mass Angle (Degrees) Graph

Figure 104: Single Cylinder Balance Shaft Offset Centre of Mass (Degrees) Graph


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Figure 107: Connecting Rod Length (m) - 45 Degree Bank Angle



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Figures 106-110 show how the connecting rod length vastly changes with the v-twin

depending on how big the bank angle is. If the engine were to be redesigned with a crankshaft

offset and as a v-twin engine, the design would have to be carefully considered to include

these details.



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The above graph shows how the mass moment is significantly different between the two

banks as the offset increases. As both banks are connecting to the same crankshaft, a decision

would have to be made to decide if it would be best to cater closer to the needs of one bank or

go for a middle ground so as to not cause significant problems with either.

Figure 111: V-Twin MCrankspan*X Centre of Mass


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The potential for expanding the work into crankshaft balancing is very big. The first thing the

author feels would be important would be to see the frictional benefits or losses of having two

different sized connecting rods within a v-twin engine due to the crankshaft being offset.

Completing this study would allow the author to more accurately understand the benefits of

offsetting the crankshaft on a v-configuration engine.

The second point of expansion for this work would be to look closer into which of the two

banks should be catered to, if none at all. With the v-twin engine having different connecting

rod lengths due to the offset, the mass moments and offset angles are different from one bank

to another. Optimizing one bank over another may prove more beneficial in terms of

efficiency, however it may also prove more beneficial to go for a middle ground to keep the

efficiency on both banks the same.

The final point of expansion that the author feels should be done is looking into more

configurations of crankshafts and how crankshaft offsets affects them. For example, 3

cylinder, V-4, Straight 6 etc.


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5.0 Ignition Advancement

5.1 Introduction

In terms of improving the efficiency of an engine, advancing the ignition could be one of the

ways it can be done. This section will cover how advancing the ignition on the Ford Fox 3-

Cylinder 1.0L GDI Turbo engine could prove beneficial to the engine, along with looking at

how this collaborates with other members of the team, the real world applications of ignition

advancement and the methodology behind setting up the model.


The author has chosen to take on the subject of ignition advancement, feeling that it is an

important subject in modern day engine design. Modelling what happens to the engines IMEP

as the ignition advances means a risk of detonation. The Ford engine being studied within this

group project is currently running a delayed spark to prevent detonation due to high cylinder

pressure around TDC, therefore advancing the ignition will sure to cause it.

Team member Manfredi Sammartini is looking into the benefits of injecting very tiny

amounts of water into the combustion chamber before the spark to reduce the combustion

temperature and therefore allow for an advanced ignition without risk of detonation.


Due to many vehicles moving to turbo charged engines in their production vehicles, cylinder

pressures have been increasing. The increase in cylinder pressure essentially means that the

only way to prevent detonation is to retard the ignition and burn after TDC. While this

method does prevent detonation, it also means a loss in performance and efficiency within the

engine as pressure has already begun to drop.

Examining how the advancement of ignition could aid in improving efficiency and

performance, could push vehicle manufacturers and engine designers to look into the benefits

of ignition advancement and how they can avoid detonation to make use of those benefits.


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5.4 Methodology

5.4.1 Ignition Advancement Methodology – Graphs

Figure 112: Cylinder Volume (m) Graph

Figure 113: Cylinder Pressure (Bar) Graph


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Figure 115: Difference in pressure, non-combustion to combustion at each degree of crank angle Graph

Figure 114: Mass Fraction Burned Graph


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Figure 117: Air Mass (Kg/Hr) Graph

Figure 116: Air Mass Per Revolution (Kg) Graph


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Figure 119: Air Mass Per Cycle (Kg) Graph

Figure 118: Fuel Mass Per Cycle (Kg) Graph


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Figure 121: QTotal - Total Energy Released (J) Graph

Figure 120: Work Done by Pressure Per Degree (J/Degree)


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5.4.2 Ignition Advancement Methodology – Equations

∆𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 = 𝑃1 − (𝑃1 × (𝑉𝑜𝑙𝑢𝑚𝑒 1

𝑉𝑜𝑙𝑢𝑚𝑒 2)𝑛)

Figure 123: Difference in pressure combustion to non-combustion at each degree Equation

The above equation shows how the ΔPressure is calculated using the start pressure, the

volumes and the polytropic index.

𝑀𝐹𝐵 =∑ 𝑉𝑜𝑙𝑢𝑚𝑒 × ∆𝑃𝑆𝑜𝑐→𝜃

∑ 𝑉𝑜𝑙𝑢𝑚𝑒 × ∆𝑃𝑆𝑜𝑐→𝐸𝑂𝐶

Figure 124: MFB Equation

The above equation shows how the mass fraction burned is calculated using the volumes and

ΔP.

𝐴𝑖𝑟 𝑀𝑎𝑠𝑠 𝑝𝑒𝑟 𝑅𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛 =𝐴𝑖𝑟 𝑀𝑎𝑠𝑠 (𝑘𝑔𝑝ℎ𝑟)

(60 × 𝐸𝑛𝑔𝑖𝑛𝑒 𝑆𝑝𝑒𝑒𝑑 (𝑅𝑃𝑀)

Figure 125: Air Mass per Revolution Equation

The above equation shows how the air mass per revolution is calculated using the air mass in

kg/hr and the engine speed in RPM.

𝐴𝑖𝑟 𝑀𝑎𝑠𝑠 𝑝𝑒𝑟 𝐶𝑦𝑐𝑙𝑒 = 𝐴𝑖𝑟 𝑀𝑎𝑠𝑠 𝑝𝑒𝑟 𝑅𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛

1.5

Figure 126: Air Mass per Cycle Equation

The above calculation shows how the air mass per cycle is calculated using the air mass per

revolution.

Figure 122: Change in Energy Release per Degree (J/Degree) Graph


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𝐹𝑢𝑒𝑙 𝑀𝑎𝑠𝑠 𝑝𝑒𝑟 𝐶𝑦𝑐𝑙𝑒 =𝐴𝑖𝑟 𝑀𝑎𝑠𝑠 𝑝𝑒𝑟 𝐶𝑦𝑐𝑙𝑒

𝐴𝑖𝑟: 𝐹𝑢𝑒𝑙 𝑅𝑎𝑡𝑖𝑜

Figure 127: Fuel Mass per Cycle Equation

The above equation demonstrations how the fuel mass per cycle is calculated using the air

mass per cycle and the Air: Fuel ratio.

𝑄𝑇𝑜𝑡𝑎𝑙 = 𝐹𝑢𝑒𝑙 𝑀𝑎𝑠𝑠 𝑝𝑒𝑟 𝐶𝑦𝑐𝑙𝑒 × 𝐶𝑎𝑙𝑜𝑟𝑖𝑓𝑖𝑐 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐹𝑢𝑒𝑙

Figure 128: QTotal Equation

The above equation demonstrates how to calculate the total energy released at each RPM.

𝑊𝑜𝑟𝑘 𝐷𝑜𝑛𝑒 𝑏𝑦 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑝𝑒𝑟 ° = 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 (𝑃𝑎) × (𝑉𝑜𝑙𝑢𝑚𝑒 2 − 𝑉𝑜𝑙𝑢𝑚𝑒 1)

Equation 56: Work Done by Pressure per Degree Equation

The above equation demonstrates how to calculate the work done per degree of crank angle

by the pressure within the cylinder, using the pressure in pascal and the two corresponding

volumes.

∆𝑄 = (𝑀𝐹𝐵2 −𝑀𝐹𝐵1) × 𝑄𝑇𝑜𝑡𝑎𝑙

Equation 57: Rate of Change of Energy Released Equation

The above equation demonstrates how to calculate the energy released per degree using the

mass fraction burned and the total energy released at each RPM.

In order to then advance the ignition by 1° at a time, the values were recalculated by bring the

start and end of combustion 1° earlier but still using the same volumes, therefore simulating

the effect of burning 1° earlier.

This method was used from no advanced ignition up to 10° to see the benefits.


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Figure 129 above shows how advancing the ignition timing can improve the IMEP

drastically. The graph shows that the IMEP increases with each degree of advancement until

around 9-10 degrees of advanced timing when it seems to offer no improvement by

advancing beyond that point. The advancement of the ignition timing shows a potential 6 Bar

improvement in IMEP.

The negatives would be that this level of advancement in ignition would surely cause

detonation problems and therefore would require the water injection system being developed

by Manfredi Sammartini in order keep the detonation under control and therefore benefit

from the IMEP improvements.


In order to improve the ignition advancement model, it would be recommended by the author

to begin modelling detonation and see a direct correlation between advancing the ignition and

detonation occurring.

The ignition advancement model could also be linked to the friction modelling previously

mentioned in this report, and seeing how the different pressures from advanced ignition could

affect the resultant FMEP with and without crankshaft offsets, therefore producing a resultant

BMEP.

Figure 129: IMEP Standard->10 Degree Advanced


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6.0 Final Conclusion

The final conclusion that the author makes is that the research and modelling completed aids

towards the development of the group project and therefore allows the group project to

continue developing in the future.

The author does however feel that there could be some areas that need improving such as

adding detonation to the ignition advancement model and expanding the crankshaft balancing

to include three cylinders or more. These subject however can be expanded on in due time as

the project continues to develop.


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7.0 References

AA. (2015, October 1). Euro Car Emissions Standards | AA. Retrieved from Breakdown

Cover, Insurance, Route Planning | AA:

https://www.theaa.com/motoring_advice/fuels-and-environment/euro-emissions-

standards.html

Carley, L. (2011, February). How Piston Rings Affect Horsepower - Engine Builder

Magazine. Retrieved from Engine Builder Magazine:

http://www.enginebuildermag.com/2011/02/how-piston-rings-affect-horsepower/

Diesel Net. (2013, July). Emission Test Cycles: ECE 15 + EUDC / NEDC. Retrieved from

DieselNet: Diesel Emissions Online:

https://www.dieselnet.com/standards/cycles/ece_eudc.php

Heywood, J. B. (1988). Internal Combustion Engine Fundamentals. Singapore: McGraw-Hill

International Editions.

Kane, J. (2012). Crankshaft Design, Materials, Loads and Manufacturing, by EPI, Inc.

Retrieved from EPI, Inc. Home page.: http://www.epi-

eng.com/piston_engine_technology/crankshaft_design_issues.htm

Manning, J. (2012). Chapter 13 - Connecting Rod. In J. Manning, Internal Combustion

Engine Design (p. 333). Shoreham-by-Sea: Ricardo UK Limited.

Manning, J. (2012). Internal Combustion Engine Design. Shoreham-by-Sea: Ricardo UK

Limited.

McDonald, M. (2015, April 20). Lectures and Notes. Swansea, West Glamorgan, United

Kingdom.

Microsoft. (2013). Microsoft Excel 2013.

Taylor, C. F. (1985). The Internal Combustion Engine in Theory and Practice, Volume 2:

Combustion, Fuels, Materials, Design Revised Edition. In General Problems in Detail

Design (pp. 430,431). Massachussets: M.I.T.

United Nations Economic Comission for Europe. (2016). World Harmonized Light Vehicle

Test Procedure (WLTP) - Transport - Vehicle Regulations - UNECE Wiki. Retrieved

from Dashboard - UNECE Wiki:

https://www2.unece.org/wiki/pages/viewpage.action?pageId=2523179


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8.0 Appendices

8.1 Appendix A – NEDC Model

Figure 131: NEDC Model #1

Figure 130: NEDC Model #2


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Figure 133: NEDC #3

Figure 132: NEDC #4


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Figure 135: NEDC #5

Figure 134: NEDC 6


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8.2 Appendix B – WLTP Model

Figure 137:WLTP #1

Figure 136: WLTP #2


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Figure 139: WLTP #3

Figure 138: WLTP #4


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Figure 141: WLTP #5

Figure 140: WLTP #6


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8.3 Torque Interpolations

8.4 Fuel Mass Interpolations

Figure 142: Torque Interpolations

Figure 143: Fuel Mass Interpolations


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8.5 Hydrocarbons Interpolation

8.6 NOx Interpolation

Figure 144: Hydrocarbons Interpolation

Figure 145: NOx Interpolations


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8.7 Drive Cycle Results

Figure 146: Drive Cycle Results


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8.8 Piston FMEP Data

8.9 Ignition Advance

Figure 147: Piston FMEP

Figure 148: Ignition Advance Results


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8.10 Crankshaft Balancing

Figure 150: Crankshaft Balancing

Figure 149: Crankshaft Balancing #2

group research project

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