1_gillan michael mid module report
TRANSCRIPT
Optimisation of a Connecting Rod of an Internal
Combustion Engine
AUTHOR
Michael Gillan
A THESIS SUBMITTED FOR THE DEGREE OF BACHELOR OF ENGINEERING
(HONOURS) IN MECHANICAL ENGINEERING, AT THE SCHOOL OF
ENGINEERING, GALWAY-MAYO INSTITUTE OF TECHNOLOGY, IRELAND
SUPERVISOR
Laurentiu Dimache
DEPARTMENT OF MECHANICAL & INDUSTRIAL ENGINEERING,
GALWAY-MAYO INSTITUTE OF TECHNOLOGY, IRELAND
SUBMITTED TO THE GALWAY-MAYO INSTITUTE OF TECHNOLOGY
Date: 2/05/2014
ii
DECLARATION OF ORIGINALITY
May, 2014
The substance of this thesis is the original work of the author and due reference and
acknowledgement has been made, when necessary, to the work of others. No part of this
thesis has been accepted for any degree and is not concurrently submitted for any other
award. I declare that this thesis is my original work except where otherwise stated.
_________________________
Michael Gillan
iii
Dedication
I would like to dedicate this thesis to my two children Matthew and Charlotte
Gillan
iv
Abstract
An optimisation study was performed on a forged steel connecting rod to reduce the
weight, manufacturing and material costs. A static analysis was performed to analyse the
stress concentration from the tensile and compressive forces using Ansys 14.5 finite
element analysis.
The main analysis considered buckling, fatigue and static analysis. The connecting rod was
modelled and analysed to find the highest points of stress which was at the top of the shank
at the fillet. The area to be considered for the weight reduction was the shank as this was
the most critical part of the connecting rod, this reduced the weight of the connecting rod
by 9.38 percent.
Various size fillets were applied at the top of the shank to find the most suitable fillet to
reduce stress. The 10mm fillet was the most optimum as it reduced the stress the most, and
the factor of safety was increased by more than fifty percent. CES Materials was used to
find a material with the best properties of fatigue, density, cost, tensile and compressive
strength.
The material with the best properties was the low alloy steel. The connecting rod was
analysed using different materials within Ansys and the low alloy steel reduced the stress
in tension at all locations of the connecting rod, but the 15mm fillet produced better results
at the lower part of the shank. Overall the low alloy steel reduced the stress the most and
would be the most suitable material.
The manufacturing was also considered, using CES Materials to compare manufacturing
methods of cost, surface finish and setup cost. Forging and powder metallurgy were the
two best methods but powder metallurgy produced a better surface finish and including
fracture splitting this would be the cheapest option.
v
Acknowledgements
I would like to thank Mr Laurentiu Dimache for his guidance and support given throughout
the year.
I would also like to thank Co supervisor Dr Gerard Mac Michael for his guidance from the
presentation.
I would also like to thank all the lecturers within GMIT for their guidance and support
throughout the year.
I would also like to thank family and friends for their support throughout the past year.
vi
Glossary
IC…………………………………....Internal Combustion Engine
RPM………………………………....Revolutions per Minute
FEA……………………………….....Finite Element Analysis
FI………………………………….....Failure Index
ABDC………………………………..After bottom dead Centre
ATDC………………………………..After Top Dead Centre
BBDC………………………………..Before Top Dead Centre
BDC……………………………...….Bottom Dead Centre
TDC……………………………...….Top Dead Centre
FI…………………………………….Failure Index
FEA………………………………….Finite Element Analysis
FOS………………………………….Factor of Safety
vii
Symbols
Symbol Unit Description
˚C Degrees Celsius Temperature
K Kelvin Temperature
N Newton Force
Kg Kilogram Mass
M Metre Length
S Second Time
Pa Pascal Pressure
Ω Rad/Second Angular Velocity
Ρ Density Mass per Volume
Phi Degree
R Radius Degree
L Length Metre
W Kg Mass
E GPa Youngs Modulus
ε Poissons Ratio Ratio
Se MPa Endurance strength
Se’ MPa Endurance strength
Ka Percent Surface finish
Kb Percent Size factor
Kc Percent Reliability
Kd Percent Temperature
Ke Percent Stress concentration
viii
Table of Contents
1. Introduction .................................................................................................................... 1
2. Literature review ............................................................................................................ 3
2.1 Introduction ............................................................................................................. 3
2.2 Types of Engines .................................................................................................... 4
2.2.1 Steam Engine ................................................................................................... 4
2.2.2 Two Stroke Engine .......................................................................................... 5
2.2.3 Four Stroke Engine .......................................................................................... 7
2.2.4 Diesel Engine ................................................................................................... 8
3.1 The Connecting Rod ............................................................................................... 9
3.1.1 Introduction ..................................................................................................... 9
3.1.2 Materials ........................................................................................................ 10
3.1.3 Structure ........................................................................................................ 12
3.1.4 Fatigue ........................................................................................................... 13
3.1.5 Buckling ........................................................................................................ 16
3.2 Manufacturing ....................................................................................................... 17
3.2.1 Sandcasting .................................................................................................... 17
3.2.2 Wrought Forged ............................................................................................. 18
3.2.3 Powder metallurgy ......................................................................................... 19
3.2.4 Fracture splitting ............................................................................................ 19
4. Materials & Methods .................................................................................................... 20
4.1 Design process ...................................................................................................... 22
4.2 Force Calculations ................................................................................................ 26
4.3 Inertia Forces ........................................................................................................ 29
4.4 Reduction of Shank ............................................................................................... 31
4.5 Friction .................................................................................................................. 32
4.6 Fatigue .................................................................................................................. 34
ix
4.8 Finite Element Analysis ........................................................................................ 37
4.9 Material Selection ................................................................................................. 40
4.10 Manufacturing ....................................................................................................... 43
5. Results .......................................................................................................................... 45
5.1 Stress Results Tension .......................................................................................... 46
5.2 Stress Results Compression .................................................................................. 50
5.3 Factor of Safety ..................................................................................................... 56
5.4 Comparison of Materials ...................................................................................... 58
5.6 Fatigue .................................................................................................................. 59
6. Discussion .................................................................................................................... 60
7. Conclusion .................................................................................................................... 62
8. Gantt chart .................................................................................................................... 63
9. References .................................................................................................................... 64
10. Appendix A .............................................................................................................. 67
11. Appendix B ............................................................................................................... 70
12. Appendix C ............................................................................................................... 73
13. Appendix D .............................................................................................................. 77
13.1 Verification Results Tension ................................................................................ 78
13.2 Verification Results Compression ........................................................................ 79
13.3 Graphs ................................................................................................................... 80
13.4 Ansys Plots of Various Materials ......................................................................... 82
14. Appendix F ............................................................................................................... 86
x
TABLE OF FIGURES
FIGURE 2-1: DIAGRAM OF A STEAM ENGINE (STEAM ENGINE TERMINOLOGY AND OPERATING PRINCIPLES MAY
2011) ......................................................................................................................................................... 4
FIGURE 2-2: DIAGRAM OF A TWO STROKE ENGINE PROCESS (TWO STROKE ENGINE EXHAUST NOVEMBER 2013) .. 5
FIGURE 2-3: EXPANSION CHAMBER OF A TWO STROKE ENGINE (TWO STROKE ENGINE EXHAUST NOVEMBER 2013)
.................................................................................................................................................................. 6
FIGURE 2-4: DIAGRAM OF A FOUR STROKE ENGINE (TWELVE BUDGET OUTPUT FOUR STROKE DIAGRAM, 2013) . 7
FIGURE 3-1: DIAGRAM OF A CONNECTING ROD (LUKE SCHREIER, 1999) ............................................................ 9
FIGURE 3-2 I-BEAM CONNECTING ROD (R&R RACING PRODUCTS CURRENT CATALOGUE) ............................... 12
FIGURE 3-3 H-BEAM CONNECTING (ROD R&R RACING PRODUCTS CURRENT CATALOGUE) ............................. 12
FIGURE 3-4: LOCATION OF STRESSES (PRAVARDHAN S ET AL, 2005) ............................................................... 13
FIGURE 3-5: VON MISES STRESS DISPLACEMENT OF ROD UNDER TENSILE LOADING USING FAILURE INDEX FEA
(PRAVARDHAN S. ET AL 2005) ................................................................................................................ 14
FIGURE 3-6: VON MISES STRESS DISPLACEMENT OF ROD UNDER TENSILE LOADING USING FAILURE INDEX FEA,
FE MODEL WITH SPRINGS TO THE RIGHT (SHENOY. ET AL 2005) .............................................................. 15
FIGURE 3-7: EFFECTS OF BUCKLING TO A CONNECTING ROD (MOON KYU LEE A, HYUNGYIL LEE A,*, TAE SOO
LEE A, HOON JANG, 2010) ....................................................................................................................... 16
FIGURE 4-1 ENGINE ASSEMBLY ....................................................................................................................... 20
FIGURE 4-2: FLOW CHART FOR REDESIGN PROCESS OF THE CONNECTING ROD ............................................... 21
FIGURE 4-3: RENDERED MODEL OF THE CRANKSHAFT, CONNECTING RODS AND PISTONS ................................. 23
FIGURE 4-4 CONNECTING ROD ASSEMBLY AND MODEL OF CONNECTING ROD FROM CREO PARAMETRIC ......... 24
FIGURE 4-5: DIAGRAM OF CRANKSHAFT, CONNECTING ROD AND PISTON ......................................................... 26
FIGURE 4-6: FREE BODY DIAGRAM OF CRANKSHAFT (R) .................................................................................. 27
FIGURE 4-7: FREE BODY DIAGRAM OF CONNECTING ROD ................................................................................. 28
FIGURE 4-8: VELOCITY AND ACCELERATION GRAPHS (NORTON, R.L., 2003) ................................................ 29
FIGURE 4-9: DIMENSIONS OF THE CRANK PIN ................................................................................................... 33
FIGURE 4-10: SECTION A-A FATIGUE .............................................................................................................. 34
FIGURE 4-11: PRESSURE DISTRIBUTION OVER THE SURFACE OF A PIN (WEBSTER ET AL, 1983). ........................ 37
FIGURE 4-12: PRESSURE APPLIED TO AREA 2 .................................................................................................... 38
FIGURE 4-13: BOUNDARY CONDITIONS ............................................................................................................ 38
FIGURE 4-14: MESH REFINEMENT .................................................................................................................... 39
FIGURE 4-15: YOUNGS MODULUS /DENSITY VS PRICE ..................................................................................... 41
FIGURE 4-16: COMPRESSIVE STRENGTH VS FATIGUE STRENGTH ...................................................................... 41
FIGURE 4-17: TENSILE STRENGTH VS FATIGUE STRENGTH ............................................................................... 42
FIGURE 4-18: ECONOMIC BATCH SIZE VS RELATIVE EQUIPMENT COST ............................................................. 43
FIGURE 4-19: ROUGHNESS VS RELATIVE COST INDEX ....................................................................................... 44
FIGURE 4-20: TOOLING COST ........................................................................................................................... 44
xi
FIGURE 5-1: STRESS LOCATIONS ...................................................................................................................... 45
FIGURE 5-2: VON MISES STRESS 5MM FILLET (TENSION) ................................................................................ 46
FIGURE 5-3: VON MISES STRESS 7MM FILLET (TENSION) ................................................................................. 47
FIGURE 5-4: VON MISES STRESS 10MM FILLET (TENSION) ............................................................................... 48
FIGURE 5-5: VON MISES STRESS 15MM FILLET (TENSION) ............................................................................... 49
FIGURE 5-6: STRESS LOCATION POINTS ............................................................................................................ 50
FIGURE 5-7: VON MISES STRESS 5MM FILLET (COMPRESSION) ........................................................................ 50
FIGURE 5-8: VON MISES STRESS 7 MM FILLET COMPRESSION ........................................................................... 51
FIGURE 5-9: VON MISES STRESS 10 MM FILLET COMPRESSION ......................................................................... 52
FIGURE 5-10: VON MISES STRESS 15 MM FILLET COMPRESSION ....................................................................... 53
FIGURE 5-11: RESULTS OF 5, 7, 10 AND 15 MM FILLETS, COMPRESSION AND TENSION ..................................... 54
FIGURE 5-12: DISPLACEMENT WITH COMPRESSIVE LOAD ................................................................................. 55
FIGURE 5-13: DISPLACEMENT WITH LOAD IN TENSION ..................................................................................... 55
FIGURE 5-14: FACTOR OF SAFETY COMPRESSION ............................................................................................. 56
FIGURE 5-15: FACTOR OF SAFETY TENSION ..................................................................................................... 57
FIGURE 5-16: COMPARISON OF MATERIALS ...................................................................................................... 58
FIGURE 5-17: ORIGINAL CONROD AND OPTIMISED CONROD ............................................................................. 59
FIGURE 10-1: CONNECTING ROD ASSEMBLY (FRONT VIEW AND SIDE VIEW). .................................................... 67
FIGURE 10-2: CONNECTING ROD AND CAP DISASSEMBLY ................................................................................ 67
FIGURE 10-3: CONNECTING ROD CAP FRONT AND SIDE VIEW ........................................................................... 68
FIGURE 10-4: PISTON AND GUDGEON PIN ......................................................................................................... 68
FIGURE 10-5: CRANKSHAFT ............................................................................................................................. 69
FIGURE 10-6: VOLUME OF ORIGINAL CONNECTING ROD AND OPTIMISED CONROD ........................................... 69
FIGURE 11-1: ORIGINAL CROSS SECTIONAL AREA OF SHANK (MD SOLIDS)...................................................... 70
FIGURE 11-2: MOMENT OF INERTIA Y-AXIS (ORIGINAL CONNECTING ROD) ...................................................... 70
FIGURE 11-3: MOMENT OF INERTIA Z-AXIS (ORIGINAL CONNECTING ROD) ...................................................... 71
FIGURE 11-4: MODIFIED CROSS SECTIONAL AREA (MD SOLIDS) ...................................................................... 71
FIGURE 11-5: MOMENT OF INERTIA AND AREA Y-Y AXIS (MODIFIED CONROD) ............................................... 72
FIGURE 11-6: AREA VS CRITICAL LOAD ........................................................................................................... 72
FIGURE 13-1: STRESS CONCENTRATION Q ........................................................................................................ 80
FIGURE 13-2: STRESS CONCENTRATION KT ...................................................................................................... 80
FIGURE 13-3: SURFACE FACTOR KA ................................................................................................................. 81
FIGURE 13-4: RELIABILITY FACTOR ................................................................................................................. 81
FIGURE 13-5: VON MISES STRESS LOW ALLOY STEEL COMPRESSION AND TENSILE .......................................... 82
FIGURE 13-6: VON MISES STRESS MEDIUM CARBON STEEL COMPRESSION AND TENSION ................................ 83
FIGURE 13-7: VON MISES STRESS HIGH CARBON STEEL COMPRESSION AND TENSION ..................................... 84
FIGURE 13-8: VON MISES STRESS TITANIUM STEEL COMPRESSION AND TENSION ........................................... 85
xii
Table of Tables
TABLE 3-1: LIST OF MATERIALS USED FOR GENERAL AUTOMOTIVE USE (MICHAEL F 1988) ............................. 10
TABLE 3-2: MATERIALS USED FOR HIGH PERFORMANCE CONNECTING RODS (MICHAEL F 1988) ...................... 11
TABLE 3-3: TITANIUM ALLOY COMPARED TO PF-11C50/60 STEELS (J.W. QIU A ET AL, 2012) ........................ 11
TABLE 4-1: TECHNICAL INFORMATION OF THE ENGINE (KAWASAKI ZX 7R 96-03 SERVICE MANUAL) ................ 25
TABLE 4-2 MATERIAL PROPERTIES OF THE ORIGINAL CONNECTING ROD .......................................................... 25
TABLE 4-3: MATERIAL PROPERTIES OF EACH MATERIAL .................................................................................. 34
TABLE 4-4: CONSTRAINTS APPLIED CES MATERIALS ...................................................................................... 40
TABLE 4-5: LIMITS APPLIED IN CES MATERIALS ............................................................................................. 43
TABLE 5-1: LOCATION OF STRESS, FOS AND DISPLACEMENT (5 MM FILLET) ................................................... 46
TABLE 5-2: LOCATION OF STRESS, FOS AND DISPLACEMENT (7 MM FILLET).................................................... 47
TABLE 5-3: LOCATION OF STRESS, FOS AND DISPLACEMENT (10 MM FILLET).................................................. 48
TABLE 5-4: LOCATION OF STRESS, FOS AND DISPLACEMENT (15MM FILLET) .................................................. 49
TABLE 5-5: LOCATION OF STRESS, FOS AND DISPLACEMENT (5MM FILLET) .................................................... 50
TABLE 5-6: LOCATION OF STRESS, FOS AND DISPLACEMENT (7 MM FILLET).................................................... 51
TABLE 5-7: LOCATION OF STRESS, FOS AND DISPLACEMENT (10 MM FILLET).................................................. 52
TABLE 5-8: LOCATION OF STRESS, FOS AND DISPLACEMENT (15 MM FILLET).................................................. 53
TABLE 5-9: STATIC FACTOR OF SAFETY 7 AND 10MM FILLET .......................................................................... 57
TABLE 5-10: FATIGUE CYCLES AND COST VS MATERIAL .................................................................................. 59
TABLE 13-1: REACTION FORCES COMPRESSION ................................................................................................ 77
TABLE 13-2: REACTION FORCES TENSION ........................................................................................................ 77
TABLE 13-3: PERCENTAGE ERROR (TENSION) .................................................................................................. 78
TABLE 13-4: PERCENTAGE ERROR (COMPRESSION) .......................................................................................... 79
1
1. Introduction
The connecting rod has to withstand dynamic forces from the axial motion of the piston
and the rotational motion of the crankshaft. The connecting rod of an internal combustion
engine is considered a crucial part of the engine. Literature suggests many different
methods of optimization of a connecting rod. (Lee a et al, 2010) states that buckling is to
be considered when reducing the size of the shank, but (Shenoy et al, 2005) states fatigue
strength is a critical factor compared to the static and buckling resistance. (Shenoy et al,
2005) used quasi dynamics to analyse crack growth of the material while in motion.
(Mirehei et al, 2008) states that stress concentration factors can be used to calculate the life
span of the connecting rod. (Shenoy, 2004) states the minimum factor of safety should be
three. Due to the development of Finite element analysis it has become easier and cheaper
to develop stronger and lighter connecting rods.
The material properties needs to be suitable for the tensile and compressive forces applied,
materials widely used in vehicles today use various types such as medium carbon steel,
alloy steel and in some circumstances titanium which is mainly used in competition use.
(Qui J.W et al, 2012) states the relative density of the material has an impact to the
mechanical properties. A relative new material C70 steel can be used in the fracture split
process at room temperature. This method has a thirty percent cost reduction of the
manufacturing process.
(Michael F, 1988) states that near net shape from powder metallurgy results in less
machining as compared to forging. The forging process removes any abnormalities within
the steel due the blows exerted on the steel.
Research Objective
The objective of this project is to analyse the connecting rod using FEA software to predict
cause of failure, reduce weight and choose the best material and manufacturing process.
2
Aims
The aim of the project is to analyse the connecting rod and to reduce stress concentration
using FEA. This will involve researching literature to see what methods were successful
and not so successful.
Project overview
Chapter 2 and 3 reviews research from literature to see what has been done, and will be
used to define the best approach to the project. Also in this chapter will be a discussion of
different materials and manufacturing methods.
Chapter 4 shows the analysis to the project and how the analysis was approached.
Chapter 5 shows the results and finds the most suitable fillet and material to increase the
fatigue life and factor of safety.
Chapter 6 will discuss the results and which method worked best.
Chapter 7 will discuss the overall project and discuss success and failures throughout the
project.
3
2. Literature review
This chapter will be discussing the history of the combustion engine and looking at
different methods used in reducing the weight of a connecting rod from analysing journals.
This chapter is going to review connecting rod failure and analyse the root causes of the
problem.
2.1 Introduction
The development of the Zx7r engine is advancing in technology every year due to
competing in main championships such as Moto GP and World Superbikes. Competing
with rival teams, the bikes have to be able to produce power to be able to win races and to
avoid engine failure. Main causes of engine failure is from the connecting rod, due to
excessive forces its put under from higher compression ratios and tighter tolerances to
produce more power.
The invention of the internal combustion four stroke engines was patented by Nikolaus
August Otto in 1867 the engine was named the Otto cycle (Heywood John B, 1988).
The diesel engine was developed by Rudolph Diesel in 1892 (Heywood John B, 1988).the
diesel engine has more torque and was more powerful than the petroleum engine and
therefore was ideal for heavy type work.
There are many types of IC engines being used today, mainly used for automotive
purposes such as motorcycles, cars, trucks and aviation. The advancement in technology is
developing engines which are smaller more powerful and fuel efficient, and due to tighter
manufacturing tolerances, stronger and lighter materials are being used and they are
becoming more reliable.
There are many different engines requiring different fuels such as Gasoline, Diesel,
Biofuels, steam and aviation. The next chapter will be explaining the background and the
different categories of engines.
4
2.2 Types of Engines
There are many types of engines which are being developed further to improve fuel
efficiency, CO 2 emissions, reliability and reduce vibration. Below is a list of the different
types of engines.
Steam engine
Two Stroke engine
Four stroke engine
2.2.1 Steam Engine
A steam engine produces mechanical work by means of expanding gasses Figure 2-1
shows the diagram for a steam engine. This type of engine is similar to a combustion
engine, the difference is there are two steam inlet ports top and bottom of the cylinder,
when the piston is at full stroke steam is released via a valve which exerts a pressure on
the piston and retracts the piston. Once the piston is in the retract position, a steam inlet
valve opens and exerts a pressure to the back of the piston extending its stroke.
Combustion engines were developed from the theory of the steam engine (Heywood John
B, 1988) and were improved to run on a fuel. Steam engines are cleaner to the environment
compared to the combustion engine, but the steam engine has to be heated up, taking
considerable amount of time before the engine can be in use.
Figure 2-1: Diagram of a steam engine (Steam engine terminology and operating principles May 2011)
5
2.2.2 Two Stroke Engine
IC engines can vary depending on the requirement; two stroke engines seen in Figure 2-2
don’t require the use of intake or exhaust valves, there is a reed valve which is a one way
valve which allows fuel/air mixture to enter the crankcase under high velocity, the
crankshaft rotates and circulates the fuel/air mixture into the cylinder ports where the
piston compresses the fuel and ignites from the spark plug electrode. This cycle is a two
cycle process, hence the reason they’re called a two stroke engine. These engines are
mainly used in small applications such as generators, power washers, motorcycles etc.
Main problems with the two stroke engine are they need to be rebuilt on a regular basis due
to the high rpm they reach.
Figure 2-2: Diagram of a two stroke engine process (two stroke engine exhaust November 2013)
6
2.2.2.1 Cylinder ports two stroke engine
The cylinder contains ports which allow fuel/air mixture to enter and exit through different
ports. The inlet ports are situated to the rear of the cylinder where fuel/air mixture is
induced into the cylinder under vacuum, the crankshaft rotates and the piston displaces to
the top of the cylinder where the inlet ports are covered and allowing the piston to
compress and ignite the fuel. When the fuel/air mixture ignites, the piston is forced down,
rotating the crankshaft and uncovering the exhaust port and pushing the burnt gases into
the exhaust.
Some two stroke engines have a power valve which changes the height of the exhaust port
at different rpm; this allows the power from the engine to be more consistent through the
rpm.
The exhaust on a two stroke engine has to be designed so there is a certain amount of back
pressure, the shape of the exhaust is cone shaped as shown in Figure 2-3. As the piston
retracts the fuel is sucked into the cylinder and some excess fuel/air mixture is sent into the
exhaust, this is where the back pressure or echo of the sound waves which push the fuel/air
mixture back into the cylinder for the compression stroke.
Figure 2-3: Expansion chamber of a two stroke engine (two stroke engine exhaust November 2013)
7
2.2.2.2 Lubrication of the two stroke engine
The fuel can either be mixed or can be fed into the engine via a pump, the oil to fuel ratio
depends on the size of the engine e.g. piston size and stroke, as the oil reduces friction, and
lubricates between the piston and cylinder wall, and also lubricates the main crankshaft
bearings and small end bearings.
2.2.3 Four Stroke Engine
The four stroke engine has a four stroke cycle; the crankshaft rotates 720 degrees for every
cycle, below in Figure 2-4 is the diagram of a four stroke engine for the four cycles. On the
intake stroke the piston moves down and the inlet valve opens and draws the fuel/air
mixture into the cylinder. The piston moves up and compresses the fuel/air mixture and is
ignited from the spark plug electrode, the explosion from the compressed fuel/air mixture
pushes the piston down, from the kinetic energy developed the crankshaft rotates, the
exhaust valves open and the piston pushes the exhaust gasses out of the cylinder.
These types of engines are very reliable and are able to cover high mileage. With
advancement in technology the engines are getting more compact and more economical.
The four stroke engine is more complicated compared to a two stroke engine as four stroke
engines require camshafts, timing chain, and inlet and exhaust valves. These types of
engines cannot reach high rpm compared to the two stroke engine because of the dynamic
forces from the timing chain, inlet, exhaust valves and the valve springs.
Figure 2-4: Diagram of a four stroke engine (Twelve Budget Output Four Stroke Diagram, 2013)
8
2.2.4 Diesel Engine
The diesel engine was named after Rudolph Diesel, which he invented in 1892 (Heywood
John B, 1988). The diesel engine is widely used around the world, mainly for automotive
use; their main uses are for cars, trucks generators and ships. The diesel engine has many
advantages compared to the petroleum engine, there more economical and can produce
more torque due to higher compression ratios.
The diesel engine is a four stroke engine, the properties of diesel require a higher
compression force to be ignited, as diesel is not as flammable as petrol, glow plugs are
used instead of spark plugs in a diesel engine as it’s the compression cycle that ignites the
fuel once the engine is started.
9
3.1 The Connecting Rod
This chapter is going to review the different methods used to evaluate the stresses of a
connecting rod and improve the design using different materials and looking at the
structure of the connecting rod to evaluate the best type of structure.
3.1.1 Introduction
The connecting rod shown in Figure 3-1, and the piston are the main parts of an engine
which are under extreme conditions from the dynamic forces of acceleration and
deceleration, therefore the connecting rod is a major factor in the reliability of an engine
(Moon Ky Lee a et al, 2010).
Different manufacturing methods are used in producing a connecting rod, depending on the
application and forces it is put under, this will be reviewed in chapter 3.2.
The connecting rod has to be able to withstand fatigue due to the forces produced to the
rod from tension, compression, bending and inertia forces of the rod.
Failure can be caused by lubrication failure, when the two metals from the connecting rod
and crankshaft pin meet and cause excess metal to overlap causing redistribution of the oil.
This can be the root cause of engine failure. Also other types of failure are due to buckling
which will be reviewed in chapter 3.1.5.
Figure 3-1: Diagram of a connecting rod (Luke Schreier, 1999)
10
3.1.2 Materials
Selection of materials plays an important role, there are many factors needed to be
considered for the connecting rod to be strong enough to withstand forces such as inertial
forces and rigid enough to withstand the forces from buckling or exceeding its yield/
compressive strength. The connecting rod used is from a 750 cc motorcycle engine and the
material used is 708M20 steel which is the main material used for connecting rods in
motorcycle engines.
There are many types of engines used worldwide and there are materials used for
connecting rods which apply to different situations depending on the application needed
Table 3-1 displays lists of materials which are used in general engines (Michael f 1988).
Table 3-1: list of materials used for general automotive use (Michael f 1988)
Nodular cast iron,
Hsla steel 4140 (o.Q T-315)
AL 539.0 casting alloy,
Duralcan AL-SiC (p)
Composite, Ti-6-4,
Most connecting rods are made from iron in the automotive industry as this is the cheapest
method for producing connecting rods. These are mainly used for cars and trucks, to keep
the cost of materials and manufacturing to a minimum.
For high performance engines the connecting rod is required to be light yet strong, Table
3-2 is an example of materials used for this purpose. For high performance engines, cost
may not be an issue so the selection of the strongest material is more important, such as for
competition use. In some cases the material may need to be strong and light but yet the
costs may need to be monitored.
Wrought processing and powder metallurgy are the main processes for competitive mass
production, near net shape from powder metallurgy results in less machining of the rod and
tighter tolerances can be achieved and results in no waste (Michael F, 1988).
11
Table 3-2: materials used for high performance connecting rods (Michael f 1988)
Magnesium alloys
Titanium alloys
Beryllium alloys
Aluminium alloys
Connecting rods made from titanium or titanium alloys are mainly used in the high
performance industry due to the material properties. Titanium is used for high performance
engines due to their strength to weight ratio, which allows the engine to achieve maximum
rpm at a faster rate and reduces inertia stresses and vibration to the engine.
A new titanium PM material was formed by (Qiu J.W et al, 2012) who states that this new
material has higher strength properties compared to PF-11C50/60 steels. Due to the
properties of this titanium, it can be used for the purpose of high performance connecting
rods. (Qiu J.W et al, 2012) states that the relative density of the material has an impact to
the mechanical properties
Using a titanium material Ti–1.5Fe–2.25Mo (wt.%), which is used in powder metallurgy,
is compared to PF-11C50/60 steels shown in Table 3-3
Table 3-3: Titanium alloy compared to PF-11C50/60 steels (J.W. Qiu a et al, 2012)
12
3.1.3 Structure
The structure of a connecting rod plays a major role into the strength when in motion.
There are many types of connecting rods which represent different shapes for different
applications. I-beam type connecting rods seen in Figure 3-2 can achieve higher rpm
because the mass of the rod is low and the inertia forces are reduced, but are limited to the
amount of compression from the cylinder as the connecting rod can only withstand a
certain cylinder pressure due to the structure of the rod. Figure 3-3 shows an H beam
connecting rod, these types of connecting rods are usually used in engines requiring high
compression due to the stiffness of the design but are limited to maximum rpm due to the
weight as the inertia forces are increased.
Figure 3-2 I-Beam Connecting Rod (R&R Racing Products Current Catalogue)
Figure 3-3 H-Beam Connecting (Rod R&R Racing Products Current Catalogue)
13
3.1.4 Fatigue
Literature review suggests static cyclic loads in compression and tensile loading to obtain
resultant loading. Fatigue strength under cyclic load is the most critical factor compared to
the constraints of static strength and buckling resistance. Optimum load of maximum
compressive and tensile loads applied to the constraints (Shenoy et al, 2005).
The structural factors were the buckling effects, bending, stresses and the stiffness of the
connecting rod. Maximum tensile loads increase at the crank end and the compressive
forces increase at the small end pin connecting to the piston. The forces to the small end
have different forces to the big end while in rotation.
(Shenoy et al, 2005) used Quasi-dynamics to analyse crack growth of the material while in
motion, Figure 3-4 shows the connecting rod main stress areas. From their results the main
areas of high stress were at points 3, 4, 9, 10 and 11. High stress was also concentrated at
location 11 at the oil hole, this is a stress concentration area, modifications to this area
could be considered in the design. Increasing the radius to the edges of the rod to reduce
stress concentration and increasing the section modulus to reduce bending stresses. The
possibility of reducing material at the shank region of the connecting rod is also a
possibility.
Figure 3-4: Location of stresses (Pravardhan S et al, 2005)
14
Figure 3-5 shows the results from FEA specifying displacement for failure index which is
the inverse of factor of safety; this is used to calculate the severity of the stress before the
analysis is undertaken (Shenoy et al, 2005). Equation 3.1 shows the calculation for FI.
Equation 3.1
Seen in Figure 3-5, the constraints were used without the use of the connecting pin from
the crankshaft, the flanges at point 1 are compressing and have the highest stress
concentration factor. According to (Shenoy et al 2005) they described that when the pin is
in place for the analysis the stress concentration area reduced considerably.
Figure 3-5: Von Mises stress displacement of rod under tensile loading using Failure Index FEA (Pravardhan
S. et al 2005)
Figure 3-6 includes the pin on FEA, springs were put in place and this increased the
rigidity of the connecting rod. As shown in Figure 3-6 the stress concentration is reduced.
The oil to lubricate the shell bearing was ignored as this didn’t affect the rigidity of the
connecting rod.
1
.
15
Figure 3-6: Von Mises stress displacement of rod under tensile loading using Failure Index FEA, FE model
with springs to the right (Shenoy. et al 2005)
(Mirehei et al, 2008) studied the fatigue life of a universal tractor using Ansys to find the
life span of a connecting rod, he also stated that stress concentration factors can be used to
calculate the life span of the rod. (Shenoy, 2004) states that the mesh type to be used
within Ansys is the tetrahedral mesh as he states this is a high quality mesh and produces
more accurate results compared to the TET4 mesh. According to (Rahman et al, 2007,
2008b) he states that the TET 4 mesh is too stiff and is not as accurate.
(Mirehei et al, 2008) studied the fatigue life of a universal tractor and worked out the life
span of the connecting rod and he also states that the stress concentration factor can be
used to calculate the life span. (Shenoy, 2004) states that the minimum value for the factor
of safety should be three for a high fatigue life.
16
3.1.5 Buckling
Buckling of the connecting rod is to be considered when reducing the size of the shank
compared to the yield strength and fatigue (Lee a et al, 2010). They also state that the
buckling sensitivity is higher than that of yield strength and fatigue. There are different
types of buckling, side buckling where the connecting rod bends on the same direction as
the connecting pin shown in Figure 3-7b. Front and rear buckling is the bending of the rod
from the front and rear of the rod, due to excessive force produced on the rod shown in
Figure 3-7a. (Lee a et al, 2010) refers to the Euler formula to determine the critical
buckling of the connecting rod. This only applies to long slender beams and certain
boundary conditions, because of the geometry of the connecting rod this formula cannot be
used. Buckling is stated to be an important factor to the redesign of the connecting rod
when reducing the size. To determine the maximum buckling load the Gordon Rankine
formula equation can be used to determine the maximum force that can be applied to the
connecting rod.
Figure 3-7: Effects of buckling to a connecting rod (Moon Kyu Lee a, Hyungyil Lee a,*, Tae Soo Lee a,
Hoon Jang, 2010)
17
3.2 Manufacturing
The manufacturing of connecting rods has a major impact to the strength, fatigue, cost and
the production rate. There are several ways to manufacture connecting rods, but some of
the processes are restricted in the mass production as being too slow or too expensive.
Different methods of manufacturing connecting rods can be seen below;
Sandcasting
Wrought Forged
Powder Metallurgy
Fracture Splitting.
These processes will be further explained and evaluated to find a process which produces a
strong connecting rod and has a high number of fatigue cycles and also considering the
cost of the process.
3.2.1 Sandcasting
Sand casting is a process where moulds are made from sand, an object resembling the
shape of the mould is placed in a box and sand is then added and compacted to form the
shape of the connecting rod. Molten steel is then poured into the mould and left to cool.
The connecting rod is then heat treated and straightened to tolerance accuracy. This
process produces 90% of the connecting rod; other machining processes have to be done to
produce the radii and surface finish. (Visser Danielle, 2008) states this process is
economically competitive compared to forging due to the extended tool life.
The advantages of sandcasting are
Processes 90% of the connecting rod
Reduced machining
Waste of material reduced
Disadvantages
Poor surface finish
Requires machine operations
Not suitable for mass production
Slow process
18
3.2.2 Wrought Forged
Wrought forging process involves a number of dies where plain carbon steel is heated and
placed on top of the die where several blows are applied to form the shape, the metal billet
is then placed on several more moulds until the desired shape is produced. Excess metal is
removed before being heat treated and straightened. The final finishing processes involve
milling, broaching, boring, honing and grinding to obtain the required dimensions. From
this process between twenty five and thirty percent of excess metal is removed from the
rough stock.
The advantages of wrought forging are
Produces directional grain
Voids are removed from the internal structure increasing strength
Increases density, strength and hardness
Disadvantages
Involves several processes
Time consuming
Waste material
Machining necessary to correct tolerances
19
3.2.3 Powder metallurgy
Powder metallurgy involves mixing different metallic powders which are then placed in a
die where a press compresses the powder into a near net shape of the connecting rod, it is
then put through several heat cycles to sinter and bond the powder.
The advantages of this process are
Near net shape finish
Accurate tolerances
No waste
Disadvantages
Density of structure reduced compared to forging
Expensive tooling for small production
Production of powder metallurgy very high
3.2.4 Fracture splitting
This method is a fairly new technology which enables the connecting rod to be forged as a
complete unit, the rod is then hardened and a force is applied to fracture the connecting rod
at the cap end. This enables the connecting rod and cap to align perfectly. This reduces the
machining processes such as sawing and increases productivity. A C-70 steel was
developed which could be fracture split, this was developed in Europe in the early 2000s
(Visser Danielle, 2008). This method can be done at room temperature and cuts the energy
costs for production.
20
4. Materials & Methods
This chapter will be discussing the methods undertaken and evaluate any problems which
arised during the analysis. The connecting rod is known for engine failure, this chapter will
be investigating different methods to find the cause. This chapter will also be investigating
different means of reducing stress concentration by using different size fillets and using
different materials.
The connecting rod was analysed to find out the root cause of failure, there are many types
of failure such as fatigue, material defects and buckling. This chapter will investigate each
of these cases to find the cause of
failure and also to reduce weight.
Figure 4-1 displays the engine
assembly before it was disassembled.
The internal parts of the engine were
disassembled, measured and
modelled and were analysed using
finite element analysis.
The method for the redesign process
can be seen in Figure 4-2 this method
will be used until optimisation of the
connecting rod is achieved.
Figure 4-1 Engine Assembly
21
Figure 4-2: Flow Chart for Redesign Process of the Connecting Rod
22
4.1 Design process
The objective function is to reduce weight of the connecting rod by means of reducing the
area of the shank and also where least stress occurs, sections can be reduced in size but
careful consideration has to be made to the reliability, fatigue life and also if the
connecting rod can withstand the forces. Reduction of cost is also a factor to consider, such
as the manufacturing cost. The shape has a major factor from manufacturing and any
changes in the shape will be considered.
Choice of materials is a constraint to the strength of the connecting rod and this will limit
the material properties of the connecting rod. There are many materials which have good
strength to weight ratio but this comes at a cost.
There are many design variables to be considered in the connecting rod, evaluation of the
stresses within Ansys will determine areas which can be reduced.
The redesign process will involve modelling the connecting rod, importing the model to
Ansys and analyse the main stress concentration areas and reduce any areas which are
significantly below the yield stress. This process will be repeated until a limit is reached
until such that the number of cycles of fatigue increases.
23
The engine was disassembled and the internal parts, piston, connecting rod assembly and
crankshaft were measured and modelled within Creo which can be seen in appendix A.
The 3-D model was then animated for the purpose of the presentation to explain how the
engine works. Figure 4-3 displays the rendered engine assembly.
Several problems were encountered from the model of the connecting rod when importing
into Ansys as an IGES file. The model is supposed to be a volume within Ansys, but due to
the complexity of the model this didn’t happen. Due to this problem the model of the
connecting rod was simplified until it could be imported as a solid. The reason for this
happening is the procedure of modelling within Creo has to be done in a precise way to
avoid complications within Ansys.
Figure 4-3: Rendered model of the crankshaft, connecting rods and pistons
24
Figure 4-4 Connecting rod assembly and model of connecting rod from Creo Parametric
Figure 4-4 shows the assembly of the connecting rod and cap and the modelled connecting
rod. The volume of the connecting rod can be seen in Figure 10-6, Appendix A.
Table 4-1 shows the technical information of the motorcycle engine and information is
given for the material properties of the connecting rod and piston. The mass of the
connecting rod was compared to the model and was calculated using equation 4-1.
Equation 4-1
Where ρ = 7.85 * 103
kg/m3
V = 35.47*10
-6 m
3
Mass = 0.278 kg
25
The mass of the actual connecting rod is 0.205 kg. There is a twenty six percent difference
between the model and the actual connecting rod. The difference in the masses could be
due to several reasons; the connecting rod was measured using Vernier calliper and a micro
meter, a more accurate way of measuring is to use a coordinate measurement machine.
Table 4-1: Technical information of the engine (Kawasaki ZX 7R 96-03 Service Manual)
Engine Type 4-Stroke, DOHC, 4 cylinder
Bore and Stroke 73.0×44.7mm
Displacement 748 cm3
Compression Ratio 11.5
Maximum Power 90 kW @ 11800 rpm
Maximum Torque 78 NM @ 9300 rpm
Piston Diameter 72.952mm
Cylinder Diameter 73mm
Table 4-2 Material properties of the original connecting rod
Material 708M20
Young’s Modulus 206 GPa
Poisson Ratio 0.27
Tensile Strength 880 MPa
Density 7.85 kg/m3
Yield Strength 680 MPa
Elongation 16 %
Fatigue Limit 800 MPa
Mass of Gudgeon Pin 0.035 kg
Mass of piston 0.125 kg
Mass of Connecting Rod 0.14 kg
Mass of Cap 0.065 kg
Table 4-2 displays the material properties of the connecting rod and piston assembly.
These properties will be used within Ansys for the material properties and the results can
be compared to the yield strength and compressive stress to that in the table to see if failure
will occur.
26
4.2 Force Calculations
Figure 4-5 represents a free body diagram of the crankshaft, connecting rod and piston.
From this diagram it can be broken up into different segments to analyse the forces given
the torque from Table 4-1.
Figure 4-5: Diagram of crankshaft, connecting rod and piston
R=Crankshaft radius
L=length of the connecting rod
W=mass of the piston
R= displacement
= angle of rotation
= angle phi
R = 0.0225m
L = 0.1m
R = √(0.0025)2 + (0.1)2
R = 0.1025m
= Tan-1
0.0225/0.1025
= 12.38°
= 90 – 12.38
= 77.62 °
r
R L W
r
27
The torque given from the manufacturer of 78Nm from Table 4-1 is produced from the
crankshaft, given this free body diagrams can be used to find the force applied to the
piston. Assuming no losses within the engine due to friction, this will be discussed in
chapter 4.3.
Figure 4-6: Free body diagram of crankshaft (R)
28
To find the reaction forces using sum of the forces and moments.
∑ Fx = 0 = -49 + R2cos(77.62) = 0
R2 = 228.55 N
∑ M = 0 = 78 + R2sin(77.62)(0.0225) = 0
R2 = 3550.29N
R2 = 78Nm/0.0225sin77.62
R2 = 3550.29 N
∑ Fy = 0 = -R1 + 3550.29 = 0
R1= -3550.29N
Figure 4-7: Free body diagram of connecting rod
C1 = R2
C2 = -3467.73 N
The total force acting on the connecting rod in compression is 3467.73 N which is due to
the ignition forces from the piston. Dividing this force over the projected area of the
gudgeon pin will give the pressure applied to the connecting rod.
Pressure= F/A
Projected area = 15.588*18
A = 280.59 mm2
P = 12.35 MPa
29
4.3 Inertia Forces
Figure 4-8: Velocity and acceleration graphs (NORTON, R.L., 2003)
Figure 4-8 represents the velocity and acceleration forces produced from the dynamic
forces of the connecting rod and the piston, graph developed from Engine software. Using
equation 4-2 which was setup from the free body diagram in Figure 4-5, the displacement
can be calculated. Software used from Design of Machines which uses a software package
called Engine which calculates the inertia forces given in equations 4-2, 4-3, and 4-4.
√ (
)
Equation 4-2
Equation 4-3 is the second derivation of equation 4-2 which is the velocity, from this
equation it can be derived to find the acceleration shown in equation 4-4.
√ (
)
Equation 4-3
30
( )(( ) ( ) )
Equation 4-4
As force is equal to mass times acceleration the forces exerted from the piston to the
connecting rod in tensile force can be calculated using equation 4-5. Using all these
equations the results can be graphed shown in Figure 4-8.
Equation 4-5
Mass piston and gudgeon pin = 0.16 kg
a = 13103.8 m/s2
F = 2096.61 N
To find the pressure acting on the connecting rod due to the acceleration force we use
equation 4-6.
Equation 4-6
F = 2096.61N
Projected area = 15.58*18 = 70.15
A = 280.59 mm2
P = 7.47 MPa
31
4.4 Reduction of Shank
The Gordon Rankine formula can be used to find the maximum load produced on the
connecting rod before buckling occurs, using equation 4-7. The details of the cross section
and moment of inertia can be seen in appendix B Figure 11-1.
Equation 4-7
Where,
σc= Compressive Strength
A = Area
α = 1/7500 (For a pinned-pinned support)
L = Length of the shank
K = Axis of Gyration
√
(
)
Equation 4-8
Pr = 43755.19 N
The maximum buckling load the shank will be able to withstand from buckling is 43755.19
N from equation 4-8. To find the factor of safety by dividing Cr over the max load applied
from the compressive force equation 4-9 gives.
Equation 4-9
n = 12.62
The next step is to reduce the cross sectional area using equation 4-7. Inputting the
equation into Excel and reducing the factor of safety to three, the minimum area can be
calculated, the graph shown in Appendix B Figure 11-6 was used to show area vs critical
load in. This method was used to calculate the minimum area needed.
√
(
)
Pr = 11276.33 N
Equation 4-10
n = 3.25
Using equation 4-10 and dividing Cr by the max compressive load the factor of safety is
reduced to 3.25. The new cross sectional area and the moment of inertia can be seen in
Appendix B Figure 11-4.
32
4.5 Friction
Friction was considered to see how much of an effect this had between the lubrication
point of the crank pin and the connecting rod. To determine the shear viscous stress of the
fluid, assuming there is a linear velocity within the distribution of the fluid. Figure 4-9
represents the dimensions of the conrod. Using equation 4-11 to find the velocity with
respect to the oil clearance.
Equation 4-11
Oil clearance = mm
Equation 4-12
= Angle of rotation of the connecting rod
Rpm = 5900
Velocity = 44.33 m/s
Equation 4-13
ϓ = 1.847×106
1/s
To determine the shear forces using 4-14
Equation 4-14
F = 22.09 N
33
To find the moment caused from the shear viscous force from the oil, calculating the
moment produced using equation 4-15.
Moment = Force × Distance Equation 4-15
Moment = 22.09×0.017
Moment = 0.375 Nm
Because the friction from the shear viscous forces of the oil is so small, friction will be
neglected in this study.
Figure 4-9: Dimensions of the crank pin
34
4.6 Fatigue
A fatigue analysis will show how the connecting rod will last with stress amplitudes
applied over time. To find the factor of safety and the infinite number of cycles for the
original connecting rod at the weakest section shown in Figure 4-10, section A-A. Using
material properties of 708M20 steel from Table 4-3.
Table 4-3: Material properties of each material
Material Density kg/m3
Youngs Modulus (GPa)
Yield Strength (MPa)
Tensile Strength (MPa)
Cost (euro/kg)
Titanium Alloy 4600 115 975 1100 20.9
Medium Carbon Steel
7850 208 602.5 805 0.47
Low Alloy Steel
7850 211 950 1155 0.50
708M20 Steel 7850 206 680 880 0.72
High Carbon Steel
7850 207.5 780 1095 0.47
Figure 4-10: Section A-A Fatigue
The endurance strength takes into account all the factors which will reduce the life of the
material such as the material properties, surface finish, fillets and the section size
difference from one section to the other.
Se = Endurance strength
Se = ka,kb,kc,kd,ke se’
Se’= [0.566-9.68*10-5
*880]880 = 414.31 MPa
35
Ka = Surface finish (Appendix D, Figure 13-3)
Kb = Size factor
Kc = Reliability (Appendix D, Figure 13-4)
Kd = Temperature
Ke = Stress concentration (Appendix D, Figure 13-2)
Ka = 0.35 (Forged)
Kb = 1 (Axial loading)
Kc = 0.814 (Reliability of 99%)
Kd = 1 (Temp <350 degrees)
Ke = 1/Kf
Kf = 1+q(Kt-1)
q = 1 (Appendix D, Figure 13-1)
Kt = d/w = 18/24.5 = 0.7346
h/w = 12.25/24.5 = 0.5
Kt = 0.22
Kf = 1+0.9(0.22-1)
Kf = 0.298
Se = (0.35)(1)(0.814)(1)(0.298)(414.31)
Se = 35.17 MPa
σm = Mean stress
σa = Stress amplitude
Equation 4-16
Equation 4-17
Using equation 4-16 and 4-17 to find the mean and amplitude stress.
σm = 9.91 MPa
σa = 2.44 MPa
To find the factor of safety for fatigue using equation 4-18.
36
Sut = 880 MPa
Se = 35.17 MPa
Equation 4-18
n = 12.40
To find the infinite number of cycles using equation 4-19
-
Equation 4-19
(
)
Sut = 880 MPa
Se = 35.17 MPa
N = 1.67×106
cycles
The calculations for the number of cycles for fatigue for each material can be seen in
appendix C.
37
4.8 Finite Element Analysis
A finite element analysis was carried out to analyse the stresses on the connecting rod.
Given the forces calculated from chapter 4.2, these were applied to the connecting rod
surfaces as a pressure. Because the pressure over the area of the pin is not evenly
distributed, the pressure was reduced over hundred and twenty degrees, seen in Figure
4-11. The connecting rod was modelled using Creo and imported into Ansys 14.5 as an
IGES file. The academic version of Ansys software used is limited to thirty two thousand
nodes, to reduce the number of nodes symmetry was used. Due to the model being
symmetric, the model was split into a quarter of its original size which reduces the number
of nodes and decreases the amount of time to solve. Material properties were then specified
and inputted. The element type was then selected, the element type is Tet 10 which is used
for a 3-D structural analysis. Figure 4-12 displays the pressure applied at area 2 of 12.35
MPa.
Figure 4-11: Pressure distribution over the surface of a pin (Webster et al, 1983).
38
Figure 4-12: Pressure applied to area 2
The boundary conditions were applied to area 3 in all degrees of freedom shown in Figure
4-13. Areas 36, 117 and 95 were constrained in the x-direction. Areas 8, 32, 2,102 and 10
were constrained in the z-direction. A pressure of 7.47 MPa was applied to area 2 for the
tensile analysis.
Figure 4-13: Boundary conditions
39
Figure 4-14 displays the mesh on the connecting rod. The mesh was refined at the highest
stress points at the upper and lower point of the shank. Refining the mesh at these points
gives a more accurate answer.
Figure 4-14: Mesh refinement
40
4.9 Material Selection
CES Materials was used to find the best material regarding cost, strength and density.
Applying constraints in CES Materials to reduce the selection of materials listed below. An
important factor to be considered in the selection of material is it has to withstand high
compressive buckling forces and tensile forces.
Fatigue is an important factor as the material has to withstand a high number of cycles.
Below is the objectives and constraints to decide what factors will be used to find the
appropriate material within CES Materials.
Objective
To select an appropriate material
Constraints
To be as light as possible
Cheap as possible
Strong enough to carry peak load without failure from fatigue
Table 4-4: Constraints applied CES Materials
Physical attribute Minimum Maximum
Fracture toughness 15 MPa √
Service temperature 200 degrees
Using equation 4-20 to find the strength to weight ratio and also inputting the price on the
x-axis, this will determine the cost of material with respect to the strength to weight ratio
seen in Figure 4-15.
Equation 4-20
P = density
E = Youngs Modulus
41
Figure 4-15: Youngs Modulus /Density Vs price
Medium carbon, high carbon and low alloy steel have the highest strength to weight ratio
and are also the lowest cost. Titanium has a much higher cost compared to the materials
previously mentioned.
Figure 4-16: Compressive strength Vs fatigue strength
Figure 4-16 displays the compressive strength vs fatigue strength. The compressive
strength of the low alloy steel has a wide range of strength but also has a high fatigue life.
Titanium alloys also has a high fatigue life and the range of compressive strength is
reduced compared to the low alloy steel.
42
Figure 4-17: Tensile strength Vs fatigue strength
Figure 4-17 displays the tensile forces vs fatigue strength. Again the low alloy steel looks
to be the best material for fatigue life and tensile strength.
From analysing all the graphs from CES Materials low alloy steel has the best material
properties and is cost effective.
43
4.10 Manufacturing
Manufacturing has a big impact on the material properties such as the density, where
forging produces a connecting rod of high density due to the blows applied during
manufacturing. Using CES Materials to find the best methods to manufacture the
connecting rod, limits were applied which can be seen below in Table 4-5.
Table 4-5: Limits applied in CES Materials
Figure 4-18 displays the economic batch size compared to the relative equipment cost.
Forging has a high equipment cost compared to powder and sintering which has a medium
equipment cost, powder and sintering can produce higher batch sizes compared to forging.
Figure 4-18: Economic batch size vs relative equipment cost
Physical attribute Minimum Maximum
Mass Range 0.4 kg 0.6 kg
Section thickness 2.5mm 30mm
Tolerance <0.25 mm
Bore tolerance <0.02 mm
Surface Finish <5 µm
Batch size 10000 units
44
Figure 4-19: Roughness vs relative cost index
Figure 4-19 displays surface roughness vs relative cost index per unit. Pressing and
sintering produces the best surface finish compared to the other processes. Sand casting
and forging would require further machining processes to achieve a good surface finish.
Figure 4-20: Tooling cost
Figure 4-20 displays the tooling cost for each process, sand casting produces the lowest
cost and forging and press sintering are around the same.
45
5. Results
This section will review the results and specify the optimum connecting rod. The model of
the connecting rod was converted to an IGES file and exported into Ansys. Problems were
encountered with the complicated geometry of the model, the connecting rod model was
simplified to allow for analysis within Ansys.
Figure 5-1 shows the points at which failure would likely occur and this will be used to
show the stress at these locations. From Ansys the stress at points A-A, B-B, C-C and D-D
will be shown for each analysis.
Figure 5-1: Stress locations
46
5.1 Stress Results Tension
5mm Fillet
Table 5-1 displays the stress at each location given in Figure 5-1 for a 5mm fillet. The
highest stress concentration occurs at section B-B. The Von Mises stress can be seen in
Figure 5-2 where the max stress can be seen at the fillet at the top of the shank. The factor
of safety was also done to find the weakest point of the connecting rod.
Table 5-1: Location of stress, FOS and displacement (5 mm fillet)
Figure 5-2: Von Mises stress 5mm fillet (Tension)
Section Stress (MPa) Factor of Safety Max displacement mm
A-A 106.80 6.37 B-B 172.69 3.94 0.039771 mm C-C 94.11 7.23 D-D 44.89 15.15
47
7mm Fillet
Figure 5-3 shows the Von Mises stress with a 7mm fillet. Table 5-2 displays the stress at
the four locations of the connecting rod.
Table 5-2: Location of stress, FOS and displacement (7 mm fillet)
Section Stress (MPa) Factor of Safety Displacement mm
A-A 124.67 5.45
B-B 160.3 4.24 0.028761mm
C-C 146.73 4.63
D-D 146.73 4.63
Figure 5-3: Von Mises stress 7mm fillet (Tension)
48
10mm Fillet
Figure 5-4 displays the maximum Von Mises stress using a 10mm fillet. Table 5-3 displays
the stress at the four locations.
Table 5-3: Location of stress, FOS and displacement (10 mm fillet)
Figure 5-4: Von Mises stress 10mm fillet (Tension)
Section Stress (MPa) Factor of Safety Displacement mm
A-A 107.36 6.34
B-B 142.47 4.77 0.031588mm
C-C 85.831 7.92
D-D 44.89 15.15
49
15mm Fillet
Figure 5-5 displays the Von Mises stress using a 15mm fillet. Table 5-4 displays the stress
at the four locations.
Table 5-4: Location of stress, FOS and displacement (15mm fillet)
Figure 5-5: Von Mises stress 15mm fillet (Tension)
Section Stress (MPa) Factor of Safety Displacement mm
A-A 107.82 6.31
B-B 173.20 3.93 0.039737mm
C-C 95.41 7.13
D-D 44.95 15.13
50
5.2 Stress Results Compression
The results for the load applied in compression using 5, 7, 10 and 15 mm fillets are shown
in this chapter.
Figure 5-6: Stress location points
Table 5-5 displays the stress at the four sections of the connecting rod, (Figure 5-6)
displays the results at each point.
Table 5-5: Location of stress, FOS and displacement (5mm fillet)
Figure 5-7 displays the Von Mises stress, the highest stress concentration is located at the
top of the shank.
Figure 5-7: Von Mises stress 5mm fillet (Compression)
Section Stress (MPa) Factor of Safety Displacement mm
A-A -23.89 28.46
B-B -196.84 3.45 0.031829 mm
C-C -120.11 5.66
D-D 0.37113 -
51
7mm Fillet
Table 5-6 displays the Von Mises stress at each location of the connecting rod.
Table 5-6: Location of stress, FOS and displacement (7 mm fillet)
Section Stress (MPa) Factor of Safety Displacement mm
A-A -23.250 29.24
B-B -146.8 4.63 0.033712 mm
C-C -116.14 5.85
D-D 0.2246 3090
Figure 5-8 shows the Von Mises stress, where maximum stress occurs at the lower shank.
Figure 5-8: Von Mises stress 7 mm fillet compression
52
10mm Fillet
Table 5-7 displays the stress using a 10 mm fillet, Figure 5-9 displays the Von Mises stress
where max stress occurs at the top of the shank.
Table 5-7: Location of stress, FOS and displacement (10 mm fillet)
Figure 5-9: Von Mises stress 10 mm fillet compression
Section Stress (MPa) Factor of Safety Displacement mm
A-A 12.65 53.71
B-B -106.87 6.36 0.031588 mm
C-C -120.73 5.63
D-D 0.363 -
53
15mm Fillet
Table 5-8 displays the stress using a 15 mm fillet, Figure 5-10 displays the Von Mises
stress where max stress occurs at the top of the shank.
Table 5-8: Location of stress, FOS and displacement (15 mm fillet)
Figure 5-10: Von Mises stress 15 mm fillet compression
Section Stress (MPa) Factor of Safety Displacement mm
A-A -36.88 18.44
B-B -90.08 7.55 0.031759 mm
C-C -115.32 5.89
D-D 0.38 -
54
Graphing the results using various size fillets from compression and tensile forces, it can
be shown which fillet is the best option for reducing stress concentration. Figure 5-11
shows the stress at different locations of the connecting rod. The ten millimetre fillet
reduces the stress concentration in tensile forces, but the 15mm fillet reduces the stress in
compressive forces. The stress from the 10mm fillet isn’t much higher than the 15mm fillet
in compression, the 10mm fillet would probably be the best option for the design due to a
big reduction in the tensile stress. Section A-A would be the weakest section of the
connecting rod resulting in the 10mm fillet being the most optimum fillet.
Figure 5-11: Results of 5, 7, 10 and 15 mm fillets, compression and tension
-250
-200
-150
-100
-50
0
50
100
150
200
A-A B-B C-C D-D
Stre
ss M
Pa
Section
Stress Comparison of 5, 7, 10, 15mm Fillet
Tensile 10mm Red CSA
Compression 10mm RedCSACompression 5mm RedCSATension 5mm Red CSA
Compression 15mm RedCSATension 15mm Red CSA
55
Figure 5-12 shows the displacement with a compressive force applied using different size
fillets, the 7mm fillet seems to be considerably higher compared to the rest of them, there
may have been a wrong input within Ansys as this result doesn’t match closely with the
rest of the results.
Figure 5-12: Displacement with compressive load
Figure 5-13 shows the difference in displacement between the fillets with an axial force in
tension, the lowest displacement is the 7mm fillet.
Figure 5-13: Displacement with load in tension
0.031829
0.033712
0.031588 0.031759
0.0305
0.031
0.0315
0.032
0.0325
0.033
0.0335
0.034
Dis
pla
cem
en
t m
m
Size of fillet
Displacement Compression
5mm fillet
7mm fillet
10mm fillet
15mm fillet
0.039771
0.028761
0.031588
0.039737
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
Dis
pla
cem
en
t m
m
Size of fillet
Displacement Tension
5mm fillet
7mm fillet
10mm fillet
15mm fillet
56
5.3 Factor of Safety
Figure 5-14 shows the factor of safety with the connecting rod in tension, the 10mm fillet
produces the highest at section A-A, but comparing to the rest of the fillets it is much
higher, an error could of have occurred in the analysis. The 5 and 7mm fillet produce very
similar results and the 15mm fillet has a steady factor of safety at all the sections.
Figure 5-14: Factor of safety compression
Figure 5-15 shows the factor of safety with the connecting rod in tension, the 10mm fillet
produces the highest factor of safety over the complete section of the conrod and increases
at section D-D due to the larger section.
0
10
20
30
40
50
60
A-A B-B C-C
Fact
or
of
Safe
ty
Location Point
FOS 5, 7, 10 and 15mm Fillet Compression
5mm fillet
7mm fillet
10mm fillet
15mm fillet
57
Figure 5-15: Factor of safety Tension
Table 5-9 represents the static factor of safety for the 7 and 10mm fillet, the 7mm fillet was
the original connecting rod and increasing the fillet to 10mm at section B-B this has
reduced the stress considerably and increased the factor of safety by a factor of two.
Table 5-9: Static Factor of safety 7 and 10mm Fillet
The results show that the 10mm fillet increases the factor of safety and would be the most
suitable fillet to use from this analysis.
0
5
10
15
20
25
30
A-A B-B C-C D-D
Fact
or
of
Safe
ty
Location Point
FOS 5,7,10 and 15mm Fillet Tension
5 mm fillet
7mm fillet
10mm fillet
15mm fillet
Fillet Size Factor of Safety
7mm (Original Conrod Compression) 4.63
7mm (Tension) 4.24
10mm (Compression) 6.36
10mm (Tension) 10.27
58
5.4 Comparison of Materials
Figure 5-16 represents the different materials used for the analysis of the connecting rod.
All the tests were taken from Ansys and graphed. Comparing the different materials shown
in Figure 5-16 shows that the most suitable material is low alloy steel which coincides with
the results from the material selection in chapter 4-9. High carbon steel closely matches
low alloy steel with a compressive force applied but the low alloy steel produces much less
stress in tension.
The plots from Ansys for the various materials can be seen in Appendix D chapter 13.3.
Figure 5-16: Comparison of materials
-250
-200
-150
-100
-50
0
50
100
150
200
A-A B-B C-C D-D
Stre
ss M
Pa
Section
Comparsion of Materials
Low alloy steel Stress(Tensile)
Low alloy steel Stress(Compression)
High carbon Stress(Tensile)
High carbon Stress(compression)
Medium carbon Stress(compression)
Medium carbon stress(Tensile)
Titanium Stress(Compression)
Titanium Stress (Tensile)
708M20 Stress(Compression)
708M20 Stress (Tensile)
59
5.6 Fatigue
Fatigue is the most important factor when considering the life of a connecting rod. Table
5-10 displays the number of cycles for an infinite life. Medium carbon steel produces the
highest number of cycles which is a small increase compared to the fatigue life of 708M20
steel. Titanium has a good fatigue life but the cost of the material is much higher compared
to the other materials. The cost of low alloy steel is higher than carbon steel but the results
from low alloy steel produce a connecting rod with a higher factor of safety and a good
fatigue life.
Table 5-10: Fatigue cycles and cost vs material
Material No. Cycles Cost (Euro/Kg)
708M20 Steel 1.67×106
Cycles 0.72
High Carbon Steel 1.67×106
Cycles 0.47
Titanium 1.67×106
Cycles 20.9
Medium Carbon Steel 1.68×106
Cycles 0.47
Low Alloy Steel 1.66×106
Cycles 0.5015
Figure 5-17: Original conrod and optimised conrod
Shown in Figure 5-17 displays
the original and the optimised
conrod. The shank on the
optimised conrod is considerably
smaller compared to the original
and the weight has been reduced
by 9.38 percent. The volume and
percentage difference can be seen
in Appendix A, Figure 10-6.
60
6. Discussion
The factor of safety for buckling was reduced to three and the results show that the
connecting rod was still able to withstand the compressive forces applied which (Lee a et
al, 2010) recommended in the literature.
From literature (Shenoy et al, 2005) states that the maximum tensile force increased at the
crank end and the compressive force increased at the small end pin, connecting to the
piston while in motion. The results from this analysis show that the maximum stress occurs
at the small end pin in compression and tension, this analysis was only considering static.
The results from Figure 5-1 show that the optimum fillet is 10mm at the top part of the
shank. The 15mm fillet was better at section B-B but overall the 10mm fillet reduced the
stress the most at the critical parts.
Figure 5-12 displays the displacement with a compressive load, but the 7mm fillet has a
higher displacement compared to the other fillets. An error could have occurred in the
analysis and maybe another analysis would be recommenced to confirm the results.
Figure 5-13 displays the displacement with a tension force applied, the fillet with the least
displacement was the original fillet of 7mm and the 10mm was next. The 10mm has the
same displacement in tension and compression which would conclude a mistake could
have been made as different forces were applied which should result in different values.
Figure 5-14 displays the factor of safety with a compressive force applied, the 10mm fillet
has a much higher factor of safety at section A-A compared to the rest of the fillets, and
comparing the displacement mentioned earlier this would confirm that an error was made.
Figure 5-15 clearly shows that the 10mm fillet has a higher factor of safety at all the
critical points of the connecting rod with a tension force applied.
Material properties has an impact to the strength, fatigue and weight of the connecting rod,
Figure 5-16 displays the comparison of different materials used for the analysis using
Ansys. The optimum material was the low alloy steel as this produced the least amount of
stress at the critical points. The cost was also a factor, the low alloy steel was not the
cheapest but produced a connecting rod with a good fatigue life which can be seen in Table
5-10 where cost is compared to the number of cycles of fatigue.
61
The manufacturing process is an important process to the finish of the connecting rod. The
strength to weight ratio was a consideration seen in Figure 4-15, the low alloy, medium
carbon and high carbon steel were closely matched for cost and strength to weight ratio.
But after considering the results the low alloy steel seems to produce the best results
overall. The surface finish vs relative cost index was graphed shown in Figure 4-19 which
shows that the powder metallurgy process produces a better quality finish compared to
forging. Applying the process of fracture splitting and powder metallurgy, this would result
in a better quality connecting rod and also reduce the cost of manufacturing compared to
forging which was recommended in literature (Visser Danielle, 2008).
62
7. Conclusion
The aim of the project was to find the cause of failure of a connecting rod and to improve
the design regarding the weight, material selection and manufacturing and to reduce the
cost.
The axial forces were calculated using free body diagrams but the calculations were only
an estimate and more accurate calculations could be calculated from measuring forces from
an engine in motion. The shank was reduced and buckling was considered from the
compressive forces.
Analysing various size fillets at the top of the shank as this showed the highest stress
concentration the 10mm fillet was the optimum fillet, increasing the factor of safety and
reducing stress concentration. The best material was the low alloy steel as this had the best
material properties concerning fatigue, yield strength and cost.
The project was successful in reducing the weight of the connecting rod by 9.38 percent
and increased the factor of safety by changing the material to low alloy steel. An error may
have occurred with the analysis of the 10mm fillet so more work would need to be done to
confirm the results.
For future work to improve the analysis, a dynamic analysis could be considered which
would show the stresses at various points over the three hundred and sixty degrees of
rotation. To reduce the overall volume of the connecting rod using algorithms could be
used to find the optimum shape using software such as Matlab. Bench testing of an engine
could also be considered to compare results from FEA.
63
8. Gantt chart
64
9. References
Weight reduction method of connecting-rod by non-linear FEM analysis: Susumu Numajiri
(Mitsubishi Motors Corporation), Shinya Miura (MMC Computer Research Ltd.)',
1996. JSAE Review, 17 (1), 1//, p. 92.
ALI, S.S.P.A.F., 2013. Connecting Rod Optimization for Weight and Cost
Reduction [Online]. Available from:
http://www.eng.utoledo.edu/mime/faculty_staff/faculty/afatemi/papers/2005SAEShenoyFa
temi2005-01-0987.pdf [Viewed 7/11/2013].
BIN ZHENG, Y.L.A.R.L., 2013. 'Stress and Fatigue of Connecting Rod in Light Vehicle
Engine'. The Open Mechanical Engineering Journal, 2013, 7, 14-17.
DANIEL, G.B. & CAVALCA, K.L., 2011. 'Analysis of the dynamics of a slider–crank
mechanism with hydrodynamic lubrication in the connecting rod–slider joint
clearance'. Mechanism and Machine Theory, 46 (10),10//, pp. 1434-1452.
'Development of high strength connecting rod by forging Toyohisa Manabe, Motohide
Mori, Masaaki Yano, Takashi Kobayashi (Toyota Motor Corporation), Naoki Iwama, Ichi
Nomura (Aichi Steel Works Co. Ltd.)', 1996. JSAE review, 17 (4), 10, p. 442.
FANTINO, B. & BOU-SAÏD, B., 2003. 'Inertia, shear-thinning and thermal effects on
connecting rod bearing behaviour'. In: D. DOWSON, M.P.G.D.A.A.A.L. (ed.) Tribology
Series. Elsevier, pp. 779-787.
H. B. RAMANI, N.K., P. M. KASUNDRA, November- 2012. 'Analysis of Connecting
Rod under Different Loading Condition'. Vol. 1 (Issue 9,).
KHARE, S., SINGH, O.P., BAPANNA DORA, K. & SASUN, C., 2012. 'Spalling
investigation of connecting rod'. Engineering Failure Analysis, 19 (0), 1//, pp. 77-86.
KUBOTA TSUYOSHI, I.S., ISOBE TSUNEO, KOIKE TOSHIKATSU, 2013.
'Development of fracture splitting method for case hardened connecting rods'.
KURATOMI, H., TAKAHASHI, M., HOUKITA, T., HORI, K., MURAKAMI, Y. &
TSUYUKI, S., 1995. 'Development of a lightweight connecting rod made of a low-carbon
martensite steel'. JSAE Review, 16 (4),10//, pp. 406-407.
65
Lee, Moon Kyu, Hyungyil Lee, Tae Soo Lee, and Hoon Jang, 2010 "Buckling sensitivity
of a connecting rod to the shank sectional area reduction." Materials & Design 31, no. 6.
Ahmad Ridzuan, I. (2010). Analysis of connecting rod fracture using finite element
analysis (Doctoral dissertation, Universiti Malaysia Pahang).
Mirehei, A., M. Hedayati Zadeh, A. Jafari, and M. Omid, 2008 "Fatigue analysis of
connecting rod of universal tractor through finite element method (ANSYS)."Journal of
Agricultural Technology 4, no. 2.
NORTON, R.L., 2003. Design of machinery: an introduction to the synthesis and analysis
of mechanics and machines / Robert L. Norton. 3rd/International ed.
QIU, J.W., LIU, Y., LIU, Y.B., LIU, B., WANG, B., RYBA, E. & TANG, H.P., 2012.
'Microstructures and mechanical properties of titanium alloy connecting rod made by
powder forging process'. Materials & Design, 33 (0), 1//, pp. 213-219.
RAM, B., 2013. 'Dynamic Simulation of a Connecting Rod made of Aluminium'. IOSR
Journal of Mechanical and Civil Engineering (IOSR-JMCE), e-ISSN: 2278-1684 Volume
5 (Issue 2 (Jan. - Feb. 2013), PP 01-05).
Shenoy, Pravardhan S., and Ali Fatemi., 2005"Connecting rod optimization for weight and
cost reduction." Journal of Sound and Vibration 243, no. 3.
Weight reduction method of connecting-rod by non-linear FEM analysis: Susumu Numajiri
(Mitsubishi Motors Corporation), Shinya Miura (MMC Computer Research Ltd.)', 1996.
JSAE Review, 17 (1), 1//, p. 92.
CES EduPack (2009), Granta Design Ltd., Cambridge, UK, www.grantadesign.com.
Michael f Ashby (Material Selection in Mechanical Design 1988 Second edition)
(1/11/2013)
Visser, Danielle. A Comparison of Manufacturing Technologies in the Connecting Rod
Industry. Submission to FIERF 06-06, 2008.
WHITTAKER, D., 2001a. 'The competition for automotive connecting rod markets'. Metal
Powder Report, 56 (5), 5//, pp. 32-37.
66
WHITTAKER, D., 2001b. 'The competition for automotive connecting rod markets'. Metal
Powder Report, 56 (5), 5//, pp. 32-37.
R&R Racing Products Current Catalog Retrieved 2 December 2013 from
http://rrconnectingrods.com/catalog.html 2013
Steam engine terminology and operating principles May 2011. Retrieved October 10,
2013, from http://the-nerds.org/Steam-101.html
Thermodynamics Two / Four Stroke Engine 2013.Retrieved 8 October 2013, from
http://www.roymech.co.uk/Related/Thermos/Thermos_4_Stroke.html
Twelve Budget Output Four Stroke Diagram, 2013. Retrieved October 16 2013, from
Two stroke engine exhaust November 2013. Retrieved September 30 2013, from https://
two+stroke+engine&ie=utf-8&oe=utf-8&rls=org.mozilla: en-GB:official&client=firefox-
a&channel=fflb&gws_rd=cr&ei=GmF5UtylDMqf7AbWn4CgCg
WHITTAKER, D., 2001a. 'The competition for automotive connecting rod markets'. Metal
Powder Report, 56 (5), 5//, pp. 32-37.
WHITTAKER, D., 2001b. 'The competition for automotive connecting rod markets'. Metal
Powder Report, 56 (5), 5//, pp. 32-37.
Kawasaki ZX 7R 96-03 Service Manual, 2008, Retrieved 7 November 2013, from
http://www.manualedereparatie.info/download/Kawasaki-Ninja-ZX-7R-Service-
Manual.html
67
10. Appendix A
Figure 10-1: Connecting rod assembly (front view and side view).
Figure 10-2: Connecting rod and cap Disassembly
68
Figure 10-3: Connecting rod cap front and side view
Figure 10-4: Piston and Gudgeon pin
69
Figure 10-5: Crankshaft
Figure 10-6: Volume of original connecting rod and optimised conrod
Percent reduction = 9.38 %
70
11. Appendix B
The cross sectional area for the original connecting rod is shown below. These were
calculated using MD Solids.
Figure 11-1: Original cross sectional area of shank (MD Solids)
Figure 11-2: Moment of inertia y-axis (Original connecting rod)
71
Figure 11-3: Moment of inertia z-axis (Original connecting rod)
The cross sectional area for the modified connecting rod is shown below. These were
calculated using MD Solids.
Figure 11-4: Modified cross sectional area (MD Solids)
72
Figure 11-5: Moment of inertia and area Y-Y axis (Modified conrod)
Figure 11-6: Area Vs Critical load
Gordon Rankine formula used to graph the area of I beam with respect to the critical load
using Excel.
0
5000
10000
15000
20000
25000
30000
35000
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
Cri
tica
l lo
ad N
Area mm^2
Buckling load
Buckling load
73
12. Appendix C
Fatigue Endurance Strength Medium Carbon steel
Se = Endurance strength
Se = ka,kb,kc,kd,ke se’
Se’= [0.566-9.68*10-5
*805]805 = 392.9
MPa
Ka = Surface finish (Figure 13-3 App D)
Kb = Size factor
Kc = Reliability (Figure 13-4 App D)
Kd = Temperature
Ke = Stress concentration
Ka = 0.35 (Forged)
Kb = 1 (Axial loading)
Kc = 0.814 (Reliability of 99%)
Kd = 1 (Temp <350 degrees)
Ke = 1/Kf
Kf = 1+q(Kt-1)
q = 1
Kt = d/w = 18/24.5 = 0.7346
h/w = 12.25/24.5 = 0.5
Kt = 0.22
Kf = 1+0.9(0.22-1)
Kf = 0.298
Se = (0.35)(1)(0.814)(1)(0.298)(392.9)
Se = 33.36 MPa
σm = Mean stress
σa = Stress amplitude
Equation 12-1
Equation 12-2
Using equation 12-1 and 12-2 to find the
mean and amplitude stress.
σm = 9.91 MPa
σa = 2.44 MPa
To find the factor of safety for fatigue using
equation 12-3.
Sut = 805 MPa
Se = 33.36 MPa
Equation 12-3
n = 11.7
To find the infinite number of cycles using
equation 12-4.
Equation 12-4
(
)
Sut = 805 MPa
Se = 33.36 MPa
N = 1.68×106
cycles
74
Fatigue Endurance Strength Low Alloy steel
Se = Endurance strength
Se = ka,kb,kc,kd,ke se’
Se’= [0.566-9.68*10-5
*1155]1155 = 524.59
MPa
Ka = Surface finish (Figure 13-3 App
D)
Kb = Size factor
Kc = Reliability (Figure 13-4 App
D)
Kd = Temperature
Ke = Stress concentration
Ka = 0.35 (Forged)
Kb = 1 (Axial loading)
Kc = 0.814 (Reliability of 99%)
Kd = 1 (Temp <350 degrees)
Ke = 1/Kf
Kf = 1+q(Kt-1)
q = 1
Kt = d/w = 18/24.5 = 0.7346
h/w = 12.25/24.5 = 0.5
Kt = 0.22
Kf = 1+0.9(0.22-1)
Kf = 0.298
Se = (0.35)(1)(0.814)(1)(0.298)(524.59)
Se = 44.54 MPa
σm = Mean stress
σa = Stress amplitude
Equation 12-5
Equation 12-6
Using equation 12-5 and 12-6 to find the
mean and amplitude stress.
σm = 9.91 MPa
σa = 2.44 MPa
To find the factor of safety for fatigue
using equation 12-7.
Sut = 1155 MPa
Se = 44.54 MPa
Equation 12-7
n = 15.78
To find the infinite number of cycles using
equation 12-8.
Equation 12-8
(
)
N = 1.66×106
cycles
75
Fatigue Endurance Strength High Carbon steel
Se = Endurance strength
Se = ka,kb,kc,kd,ke se’
Se’= [0.566-9.68*10-5
*1095]1095 = 503.70
MPa
Ka = Surface finish (Figure 13-3 App D)
Kb = Size factor
Kc = Reliability (Figure 13-4 App D)
Kd = Temperature
Ke = Stress concentration
Ka = 0.35 (Forged)
Kb = 1 (Axial loading)
Kc = 0.814 (Reliability of 99%)
Kd = 1 (Temp <350 degrees)
Ke = 1/Kf
Kf = 1+q(Kt-1)
q = 1
Kt = d/w = 18/24.5 = 0.7346
h/w = 12.25/24.5 = 0.5
Kt = 0.22
Kf = 1+0.9(0.22-1)
Kf = 0.298
Se = (0.35)(1)(0.814)(1)(0.298)(503.70)
Se = 42.76 MPa
σm = Mean stress
σa = Stress amplitude
Equation 12-9
Equation 12-10
Using equation 12-9 and 12-10 to find the
mean and amplitude stress.
σm = 9.91 MPa
σa = 2.44 MPa
To find the factor of safety for fatigue
using equation 12-11.
Sut = 1095 MPa
Se = 42.76 MPa
Equation 12-11
n = 15.13
To find the infinite number of cycles using
equation 12-12 .
Equation 12-12
(
)
N = 1.67×106
cycles
76
Fatigue Endurance Strength Titanium steel
Se = Endurance strength
Se = ka,kb,kc,kd,ke se’
Se’= [0.566-9.68*10-5
*975]975 = 459.83
MPa
Ka = Surface finish (Figure 13-3 App D)
Kb = Size factor
Kc = Reliability (Figure 13-4 App D)
Kd = Temperature
Ke = Stress concentration
Ka = 0.35 (Forged)
Kb = 1 (Axial loading)
Kc = 0.814 (Reliability of 99%)
Kd = 1 (Temp <350 degrees)
Ke = 1/Kf
Kf = 1+q(Kt-1)
q = 1
Kt = d/w = 18/24.5 = 0.7346
h/w = 12.25/24.5 = 0.5
Kt = 0.22
Kf = 1+0.9(0.22-1)
Kf = 0.298
Se = (0.35)(1)(0.814)(1)(0.298)(459.83)
Se = 39.04 MPa
σm = Mean stress
σa = Stress amplitude
Equation 12-13
Equation 12-14
Using equation 12-13 and 12-14 to find the
mean and amplitude stress.
σm = 9.91 MPa
σa = 2.44 MPa
To find the factor of safety for fatigue using
equation 12-15.
Sut = 975 MPa
Equation 12-15
n = 13.76
To find the infinite number of cycles using
equation 12-16.
Equation 12-16
(
)
N = 1.67×106
cycles
77
13. Appendix D
The results have to be verified to determine no mistakes were made during the analysis,
below are the calculations to determine if the reaction forces are correct.
Table 13-1 and Table 13-2 show the reaction forces from Ansys, the calculations for
verifying the results can be seen below each table.
Table 13-1: Reaction forces compression
THE FOLLOWING X,Y,Z SOLUTIONS ARE IN THE GLOBAL COORDINATE SYSTEM
NODE FX FY FZ
TOTAL VALUES
VALUE 500.18 866.33 -0.34421E-01
Fy = P*A
P=12.35 MPa
A=9*7.794228531
A=70.14805678 mm2
Fy = 866.33 N
Fx = 12.35*9*4.5
Fx = 500.18 N
Table 13-2: Reaction forces tension
THE FOLLOWING X,Y,Z SOLUTIONS ARE IN THE GLOBAL COORDINATE SYSTEM
NODE FX FY FZ
TOTAL VALUES
VALUE 302.54 -524.01 -0.26937E-05
Fy = 7.47*7.794228531*9
Fy = 524.01 N
Fx = 7.47*9*4.5
Fx = 302.54 N
78
13.1 Verification Results Tension
To verify the results at the small end pin in tension with a force of 2096.61N.
σ = 7.51 MPa
Stress at the small end
Stress concentration
Using Figure A-15-12 to find the stress concentration at the pin, below are the calculations.
Kf = 1+q(Kt-1) (Figure 13-2 Appendix D)
q = 0.9 (Figure 13-1 Appendix D)
Kt = d/w = 18/24.5 = 0.7346
h/w = 12.25/24.5 = 0.5
Kt = 2.5
When a clearance exists multiply Kt by 50%
Kt = 2.5*1.5
Kt = 3.75
Kf = 1+0.9(3.75-1)
Kf = 3.475
σ = 3.475*7.51
σ = 26.09 MPa
Table 13-3: Percentage error (Tension)
Fillet size (mm) Section Stress Percentage Difference %
5 A-A 106.80 309.35
7 A-A 124.67 377.84
10 A-A 107.36 311.5
15 A-A 107.82 313.26
79
13.2 Verification Results Compression
To verify the results with a compressive force of 3467.73N
σ = 12.43 MPa
Stress at the small end pin
Stress concentration
Using the Figure A-15-12 to find the stress concentration at the pin below.
Kf = 1+q(Kt-1) (Figure 13-2 appendix)
q = 0.9 (Figure 13-1 Appendix)
Kt = d/w = 18/24.5 = 0.7346
h/w = 12.25/24.5 = 0.5
Kt = 2.5
When a clearance exists multiply Kt by 50%
Kt = 2.5*1.5
Kt = 3.75
Kf = 1+0.9(3.75-1)
Kf = 3.475
σ = 3.475*12.43
σ = 43.19 MPa
Table 13-4 compares the stress results from Ansys to the calculated results. The results are
considerably different, the verification is not possible for this analysis due to the geometry
of the connecting rod.
Table 13-4: Percentage error (compression)
Fillet size (mm) Section Stress Percentage Difference %
5 A-A -23.89 44.68
7 A-A -23.250 46.17
10 A-A -12.65 70.71
15 A-A -36.88 14.61
80
13.3 Graphs
Figure 13-1: Stress concentration q
Figure 13-2: Stress concentration Kt
81
Figure 13-3: Surface factor ka
Figure 13-4: Reliability factor
82
13.4 Ansys Plots of Various Materials
Modified Conrod with 10mm fillet
Low alloy steel
Plots displaying Von misses stress in tension and compression displayed in Figure 13-5
Figure 13-5: Von Mises stress low alloy steel compression and tensile
Tensile
Section Stress (MPa)
A-A 50.056
B-B 65.98
C-C 40.07
D-D 20.98
Compression
Section Stress (MPa)
A-A -17.76
B-B -186.09
C-C -127.56
D-D 0.412
83
Medium Carbon Steel
Plots displaying Von Mises stress in tension and compression displayed in Figure 13-6
Figure 13-6: Von Mises stress medium carbon steel Compression and Tension
Tension
Section Stress (MPa)
A-A 107.36
B-B 142.47
C-C 86.574
D-D 44.89
Compression
Section Stress (MPa)
A-A -17.76
B-B -186.09
C-C -127.56
D-D -0.41
84
High Carbon Steel
Plots displaying Von Mises stress in tension and compression displayed in Figure 13-7
Figure 13-7: Von Mises stress High carbon steel Compression and Tension
Compression
Section Stress (MPa)
A-A -22.39
B-B -182.71
C-C -125.74
D-D 0.370
Tensile
Section Stress (MPa)
A-A 107.76
B-B 142.04
C-C 86.26
D-D 45.17
85
Titanium
Plots displaying Von Mises stress in tension and compression displayed in Figure 13-8
Figure 13-8: Von Mises stress Titanium steel Compression and Tension
Tension
Section Stress (MPa)
A-A 109.74
B-B 103.97
C-C 90.46
D-D 46.165
Compression
Section Stress (MPa)
A-A -8.65
B-B -143.81
C-C -128.47
D-D 0.601
86
14. Appendix F
87
88
89
90
91
92
93
94