ENGD3016 – Solid Mechanics, A. Lees
Design Analysis –
Engine Connecting Rod Warwick Shipway, Mechanical Engineering,
Year 3
17.02.2008
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
2
CONTENTS
1. Introduction.......................................
2. Procedure..........................................
3. Definitions & Parameters...........................
3.1 F.E.A. Assumptions .............................
4. Calculations.......................................
4.1 Compressive Force............................
4.2 Tensile Force................................
4.3 Tensile & Compressive Stress.................
4.4 Smith Topper Watson Formula..................
5. Results............................................
5.1 2D Analysis..................................
5.2 3D Analysis..................................
5.3 Re-Designing the Connecting Rod..............
5.4 Re-Design of the Fillet......................
5.5 High Performance Connecting Rods.............
6. Discussions........................................
6.1 2D Analysis..................................
6.2 3D Analysis..................................
6.2.1 3D Modelling..........................
6.2.2 Rounding all Edges....................
6.2.3 Re-Design of the Fillet...............
6.2.4 High Performance Con Rod..............
6.3 Further Analysis.............................
6.3.1 A Note on Materials...................
7. Conclusions........................................
8. References.........................................
9. Bibliography.......................................
3
3
4
4
5
5
5
7
7
8
8
12
21
23
24
27
28
28
31
31
31
32
33
33
34
35
36
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
3
ENGD3016 – Solid Mechanics, A. Lees
Design Analysis –
Engine Connecting Rod Warwick Shipway, Mechanical Engineering,
Year 3
17.02.2008
1. Introduction From a set of schematic drawings of a 4-cylinder supercharged
Volkswagen engine a design analysis is performed to determine the
stresses and hence operational safety factor of the connecting rod,
using CAD packages.
This report will investigate loading and constraint conditions,
accurate modelling of the con rod, design optimisation to reduce
stress and implications on changing the geometry. It will also query
the stated forces, and the validity of the assumptions made on the
model conditions and magnitude of the forces in tension.
2. Procedure The connecting rod will be created using Pro-Engineer and AutoCad,
and a 2D and 3D model will be imported into Algor for finite element
analysis (F.E.A.). Engine data from the Volkswagen technical
specification provided in section 3 is used to calculate loads in
compression and tension. These loads will be used for F.E.A. on the
connecting rod.
The data will also be used for manual calculations (as opposed to
computational calculations) to confirm that the stresses produced in
the F.E.A. are of similar results.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
4
3. Definitions & Parameters The data accompanying the technical drawings is shown below, to be
used for load calculations.
Engine Type Petrol (supercharged)
Maximum Engine Speed 6500 rpm
Maximum cylinder Pressure 90 bar
Connecting Rod Length 122 mm
Small End Inner Diameter 23 mm
Small End Width 24 mm
Big End Diameter 45 mm
Big End Width 24 mm
Gudgeon Pin Material Steel
Gudgeon Pin Inner Diameter 12 mm
Gudgeon Pin Outer Diameter 20 mm
Gudgeon Pin Length 58 mm
Rod Centre/Piston Centre Offset 0.75 mm (assume 0.0 mm)
Piston Mass (incl. rings) 331g
Cylinder Bore 75 mm
Stroke 72 mm
Bolt Diameter M8×1
Bolt Torque 30 Nm
Bearing Shell Material White Metal
Bearing Shell Thickness 1.5 mm
Little End bearing Shell Phosphor Bronze
Connecting Rod Material Forged Steel
Fatigue Limit for Forged Steel 240 N/mm2
Young‟s Modulus for Steel 207300 N/mm2
Table 1. Technical Specification for connecting rod.
3.1 – Calculation Assumptions The connecting rod rotates about the centre axis of the gudgeon pin
and it is known that the point of maximum pressure for compression is
at combustion. At TDC the spark ignites the fuel, which in turn
impacts on the piston head, causing the piston and connecting rod
downwards. This can also be expressed with geometrical mathematics
(kinematically) as shown below: -
Figure 1 – con rod geometry
Using figure 1 the displacement of the connecting rod is
Where
Taking the second derivative of this
For any arbitrary crank speed, ω.
coscos lrx
l
rrx
2coscos
222
sinsin 1
l
r
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
5
Note: this is an approximation ignoring any minor differences.
This predicts that when θ = 0 degrees (i.e. TDC, cos θ = 1) it will
be the point of highest acceleration. Therefore, the calculations for
acceleration for the tensile force must be at TDC.
Equally the explanation is valid for compressive forces, as the
diagram can be flipped to produce compressive, or cos θ = 180 degrees
= -1. The vector magnitude is negative as the vector magnitude
(force) is in the opposite direction (i.e. compression).
4. Calculations 4.1 – Compressive Force, FC The compressive force occurs at TDC as explained in section 3.1 and
as such is caused by the ignition of the fuel. It is stated in Table
1 the maximum pressure of the cylinder is 90 bar, and so by
calculating the x-sectional area of the cylinder the applied force
can be found: -
Where
1 bar = 1×10-5 Pa
Therefore
4.2 – Tensile Force, FT The tensile force is due to the rotation of the big end from the
pistons downward stroke to its upward stroke (either from air/fuel
compression or exhaust exiting). The cylinder pressure cannot be used
to calculate the force at BDC (maximum cylinder volume and so minimum
cylinder pressure). Also of course there is no ignition force.
So, the tensile force is due to the force of the component
accelerating upwards towards TDC, and so Newton‟s 2nd Law can be
used, that is
Where
Where
b = stroke length/2 = 72/2 = 36mm
l = connecting rod length centre to centre = 122mm
ω = 6500 rpm × (2π/60) = 680.678 rad/s
Therefore
The mass of the part in question is calculated by summation of the
little end components, i.e. the piston and rings, the gudgeon pin,
the bearing shell and the top of the connecting rod.
A
FessureinderMaximumCyl CPr
NAMaxCylPFC 3976244189
222
44184
75
4mm
dA
maFT
l
baOfSmallEndAcca n 12
222 /464.21601122.0
036.01678.680036.01 sm
l
bba
(i)
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
6
The gudgeon pin and bearing shell can be calculated by knowing the
volume and material density.
ρsteel = 7800kg/m3
ρcopper = 8900kg/m3
The mass of the top of the connecting rod can be predicted by use of
the CAD model as shown, assuming a 22mm length is adequate to the
little end.
Then the inside and an approximation of the outside diameter of the
little end is used: -
Figure 3. The con rod small end volume.
Therefore
)(10166159.1058.04
)012.0020.0(
4
).( 352222
mlaInternalDiaExternalDi
Vgudgeon
)(1043159.2024.04
)020.0023.0(
4
).( 362222
mlaInternalDiaExternalDi
Vbearing
)(09096.010166159.17800 5 kgmVm gudgeon
)(0216.01043159.28900 6 kgmbearing
)(546.00728.00297.00216.009096.0331.0 kgmMassesComponents
Figure 2. Approximation of the volume of the little end.
)(10802.3022.0)0047.00047.02(
)...0047.00067.02()02.0014.0(
36 m
VRodWeb
)(0297.0780010802.3 6 kgmRodWeb
)(103305.9024.0
...4
)023.0032.0(
36
22
m
VLittleEnd
)(0728.07800103305.9 6 kgmLittleEnd
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
7
Using this mass in Newton‟s 2nd Law gives a tensile force of
4.3 – Tensile & compressive Stress By use of equations (i) and (ii) the compressive and tensile stress
can be calculated from the simple stress equation. The stress
calculations dictate that the smallest x-sectional area will produce
the highest stresses, but the x-sectional area of the connecting rod
can only be calculated with quite large assumptions, due to the
complex curves and radii along this point. The picture in figure 2
shows this, and indeed is used to calculate a more accurate result.
Simple calculations show the x-sectional area to be
A = (0.014×0.02)–(2×0.0067×0.0047)–(2×0.0047×0.0047)
= 1.728×10-4 m3
This is neglecting the fillet cut out section.
4.4 – Smith Topper Watson Formula In cyclic loading it is known that a material will fail
catastrophically and unexpectedly (neglecting S-N curve predictions)
due to fatigue rather than from crack propagation at yield; and a
connecting rod is a typical example of cyclic loading. Therefore the
Smith Topper Watson formula is employed to calculate the equivalent
stress, σe.
The formula states
The fatigue limit is found experimentally to be 240N/mm2 for forged
steel, using the S-N curve in figure 4. Using this fatigue limit a
working safety factor can be calculated by finding the equivalent
stress, σe.
Figure 4 – S-N curve.
Using the smallest x-sectional area found in figure 2 the stress for
tension and compression can be found as
(ii) )(4.11794464.21601546.0 NmaFT
2
CT
Te
(iii)
)/(230)(08.23010728.1
39762 2
4mmNMpaC
)/(68)(25.6810728.1
4.11794 2
4mmNMpaT
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
8
Using these results in equation (iii) produces an equivalent stress
of
With a stated fatigue limit of 240 MPa the safety factor can be
calculated as: -
These results produced here will be compared to the equivalent
stresses produced from finite element analysis, and the con rod will
then be optimised to try and lower the equivalent stresses.
5. Results 5.1 - 2D analysis The model is drawn in AutoCad, as shown below in figure 5, and
imported as a 2D model in Algor, with a thickness selected as 20mm
(an average value from the technical drawings).
This is imported into Algor and constrained in all directions and
rotations. For compressive stress the inside of the big and little
end is constrained and loads applied respectively.
The resultant compressive stresses are shown in figure 6.
)(899.1002
08.23025.6825.68
2MPaCT
Te
38.2988.100
240
)(
)(
MPaessWorkingStr
MPaessFatigueStrorSafetyFact
Figure 5. The imported model is meshed and compressive stresses
are applied.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
9
The largest minimum principle stress is shown as sections 1 and 2,
and are given as: -
σ1 = 210 N/mm2
σ2 = 215 N/mm2
The corresponding tensile stress is shown below, with maximum stress
concentrations highlighted at points 3 and 4.
Using points 1 and 2 the minimum principle stress is observed in
tension (using figure 7), and referencing points 3 and 4 the maximum
principle stress is observed in compression (using figure 6). The
stress in these areas is shown to be: -
Tension
σ1 = 5.9 N/mm2 σ2 = 58.2 N/mm
2
σ3 = 298.7 N/mm2 σ4 = 160.8 N/mm
2
Compression
σ1 = 210 N/mm2 σ2 = 215 N/mm
2
σ3 = 0.57 N/mm2 σ4 = 14.2 N/mm
2
These substitute into the Smith Topper Watson formula using equation
(iii) as:
Figure 6. The compressive load produces stresses as above.
1 2
3
4
Figure 7. The tensile force is shown to have the largest stress
in circled areas 3 and 4.
)(16.892
2152.582.58 2
)2(
Nmmncompressioe
)(2.252
2109.59.5
2
2
)1(
NmmCT
Tncompressioe
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
10
However, of note the precision of this design is shown in figure 8,
with the highest error being 35%.
These locations are used to re-design the con rod, with AutoCad, with
emphasis on locations 1, 2, 3 and 4.
Using the equation σ = F/A for constant force it is of course deduced
that only increasing the area of the 2D model will decrease the
stresses at these locations (other than changing the thickness and/or
material).
The results are shown below.
)(4.2112
57.07.2987.298 2
)3(
Nmmtensione
)(6.1182
2.148.1608.160 2
)4(
Nmmtensione
Figure 8. The precision error is 35% around the little end.
Figure 9. A simple re-design, increasing the area in the
high stress locations.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
11
The maximum and minimum principle stresses are found using the same
base parameters of loads and constraints, to allow accurate
comparisons.
The corresponding stresses are:-
In compression
σ5 = 90 MPa σ6 = 22 MPa
in tension
σ5 = 0.69 MPa σ6 = 132 MPa
Using equation (iii) this corresponds to an equivalent stress: -
σe5 = 35.1 MPa σe6 = 93.58 MPa
The precision of both compressive and tensile analysis is shown in
figure 11.
Figure 10. The compressive stress is shown on the left, with the
highest areas in blue. The tensile stress is shown on the right with
highest stresses shown as red.
5
6
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
12
5.2 - 3D analysis In compression the force applied is at combustion as explained in
section 3, and so the force is interpreted to act upon the lower half
of the small end, as this is the interface between the gudgeon pin
and piston head. Equally in compression the constraints are due to
the connecting rod pushing down on the crankshaft, and so the top
part of the con rod is constrained in all directions, both rotational
and linear.
Figure 11. The compressive precision is shown on the left, and has a
maximum error of 27%. The tensile precision on the right may produce
inaccuracies of up to 35%.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
13
Figure 12. The first 3D stress analysis.
Figure 13. High precision error around
the stress concentrations.
Figure 14. The model has been drawn more accurately along the
high stress concentration areas.
The constraint and loads are as point
nodes, with 32 nodes of 1242.5N each.
It produces a maximum stress with high
concentrations around the small end
(point node application), but the
precision error around this area is 25%,
as shown in figure 13, on the right
So this area has been re-designed more
accurately to the drawing, using a
radius of 10mm around the big end and
6mm around the little end.
The corresponding stress analysis has
been done, using 36 nodes of 1104.4N
each.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
14
Figure 15. The corresponding stress is 430N/mm2. The precision error in
this area is 3.5%.
But this still produces a high precision error, and it is assumed the
point nodes are the source. The forces along the edges of the model
are taken off and the load magnitude is corrected appropriately. This
is shown in Figure 15.
The stress calculations explained in section 3 and 4 dictate that the
smallest x-sectional area will produce the highest stresses. This
area is shown in figure 16 below:
But, in figure 15 the high stress concentrations are a product of the
load and constraint conditions, as explained, and so more accurate
modelling is still required.
To attempt to produce more accurate results the gudgeon pin and
bearing shell is modelled. Concurrently the node constraints are
applied to surfaces, rather than points, to attempt a more
homogeneous application of force on the connecting rod.
The connecting rod with gudgeon pin and bearing shell is assembled,
with constraints and loads applied to the surface.
Figure 16. The high stress areas should propagate here as defined through
calculations, but accuracy errors produce concentrations.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
15
The material for the con rod is defined as forged steel, with a
specific modulus of elasticity (E) of 207,300 N/mm2, as defined in
Table 1. Steel (4130) is selected and E is changed to stated. The
material for the gudgeon pin is defined as steel and so 4130 steel is
selected. The material for the bearing shell is defined as Phosphor
Bronze. The mechanical properties are researched on Efunda and are
identified as below: -
UNS C51100 Composition
Category Copper Alloy Element Weight%
Type Phosphor Bronze Cu 95.6
Designations US: LINS C51100 Sn 4.2
P 0.2
Mechanical Properties (at 25 oC)
Density (*1000 kg/m3) 8.8-8.94
Poisson‟s Ratio 0.34
Elastic Modulus (GPa) 117
Tensile Strength (Gpa) 317-710
Yield Strength (Gpa) 345-552
Elongation % 48
This is very similar to standard copper defined in Aglor‟s
material selection, and so the default material specification is
used.
Once the materials are defined and the analysis is run the stress
produced from applying loads and constraints to the surfaces are as
below: -
Figure 17. The gudgeon pin and bearing shell is modelled, and the
forces are applied to the outside surface of the gudgeon pin.
[1]
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
16
This produces a maximum von mises stress of 293N/mm2, and 260N/mm2
along the smallest x-sectional area. This is more appropriate to the
predicted stress locations, but stress concentrations still arise
along the gudgeon pin area (i.e. applied loads). Most of the stress
however is not located in the middle of the beam shape, but along the
outer surfaces.
The accuracy of the stress analysis shows the precision error to be
about 26% along the complex curves, but along the maximum stress
locations it is accurate.
This is therefore an accurate model, and a better simulation of the
real components, with no major precision errors except for the
complex curved areas, and it is therefore assumed that there are
stress concentrations in this area.
But, the nature of Algor dictates that when a component (gudgeon pin
and bearing shell) is mated to another component (connecting rod
small end) it „welds‟ it together along all surfaces. This is
adequate for the bottom part of the gudgeon pin as it is in the
direction of the force. But, for the top part it would create a small gap, due to manufacturing and assembly tolerances, i.e. you cannot
fit a 20mm tube into a 20mm hole.
So, only the lower half of the gudgeon pin is modelled, so as not to
give more strength to the little end.
Figure 18. The main stress ares are along the bottom of
the gudgeon pin, and along the centre of the connecting
rod.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
17
As the model is now a more accurate simulation it is appropriate to
more accurately investigate the compressive and tensile forces,
produced from the ignition and exhaust stages of the Otto cycle.
The forces however are applied to the inside surface of the gudgeon
pin, to more accurately simulate the compressive force from the
piston head.
The stress produced from half a gudgeon pin is found. But the
precision shown in figure 20 is inaccurate by up to 35%.
Although the simulation is more accurate, the error is higher, and so
it is more appropriate to further investigate the whole gudgeon pin,
but apply the loads on the inside surface, to simulate the continuum
mechanical force through the piston head. The whole gudgeon pin is
therefore analysed as before, and in compression the minimum
principle stress is investigated.
The analysis provides stresses as shown in figure 21, and the bottom
picture shows the locations of the highest stress regions.
Figure 20. The precision error for a
modelled half gudgeon pin.
Figure 19. The constraints to
the big end and forces along
the inside of the gudgeon pin
on the little end.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
18
The pink doted areas are the areas of investigation for compressive
stresses, using minimum principle stress. They are assigned to
subscript 1 and 2 as shown here. The negative values (dark blue) have
larger values of stress than the orange coloured areas, note the
legend on the right of figure 22. The stress is not negative though,
rather the direction has changed.
The corresponding minimum stresses here are
σ1 = 286.6N/mm2
σ2 = 265.5N/mm2
The stresses produced on the other side of the con-rod are the same,
as the model is symmetrical and the constraints and loads are central
about the y-axis.
Figure 21. The highest minimum stress locations are shown as pink
dots 1 and 2.
2
1
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
19
The corresponding tensile stresses at this point are found in a
similar manner as the 2D analysis, with the loads applied on the
inside of the top part of the gudgeon pin. The load application and
consequent stress is shown in figure 22.
The largest tensile stresses occur in the areas 3 and 4, with
stresses as
σ3 = 88.1 N/mm2
σ4 = 108.8 N/mm2
The corresponding compressive (minimum) stresses in these locations
are σ3 = 1.5 N/mm2
σ4 = 6.5 N/mm2
The compressive precision in these locations are acceptable, except
for node 1, which specifically has a 19% precision error, as shown in
figure 23.
4
3
Figure 22. The tensile surface force application and consequent high
stress locations.
Figure 23. The precision error is adequate except for the interface
of the gudgeon pin, bearing shell and con rod.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
20
To summarise the compressive force produces: -
Min stress 1 = 286.6 MPa
2 = 265.5 MPa
Max stress 3 = 9.3 MPa
4 = 5.1 MPa
The tensile force produces: -
Min stress 1 = 1.5 MPa
2 = 6.5 MPa
Max stress 3 = 88.1 MPa
4 = 108.8 MPa
This produces an equivalent stress of
Taking the largest equivalent stress as the first place to fail from
fatigue the safety factor is equated to be 3.05.
Using the software a displaced model can be superimposed on top of
the original model to help visualise any design considerations.
Figure 24 shows the original connecting rod in tensional
displacement.
)(7.142
6.2865.15.1)1( MPancompressioe
)(7.292
5.2655.65.6)2( MPancompressioe
)(5.652
3.91.881.88)1( MPatensione
)(7.782
1.58.1088.108)2( MPatensione
Figure 24. The displaced model in tension.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
21
However it is not visually representative as the bottom half of the
gudgeon pin is „welded‟ onto the little end.
If the displaced model is used for half a gudgeon pin a more accurate
representation is shown: -
5.3 – Re-Designing the Connecting Rod As with the 2D analysis the major contributing factor to the
equivalent stress and working factor of the component is the tensile
force. As such this is closely examined for optimisation purposes.
But, the first re-design
involved rounding all the edges
to see if it affects the con
rod. This would decrease the
frictional inertia of the con
rod through the oil, but it is
not known whether it will
affect the stress
concentrations.
Figure 26. The first re-design
involved rounding all the edges to
see the (if any) effects on stress.
Figure 25. The model in tensile and compressive displacement.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
22
The resultant stresses in compression (figure 27) and tension (figure
28) is shown below.
The largest con rod minimum stress is shown below:
Location 5, σC5 = 287.4 Mpa
Due to the symmetrical design the stress is the same on the other
side.In tension the largest stress is located at point 6.
The stresses in locations 5 and 6 are found to be as follows:-
Location 6, σT6 = 100.9 Mpa
Location 5 in tension, σT5 = 80 MPa
Location 6 in compression, σC6 = 0.36 MPa
This equates to an equivalent stress of
σe5 = 121.3 MPa
σe6 = 71.5 MPa
5
Figure 27. The resultant stresses from figure 26.
6
Figure 28. The tensile largest maximum principle stress is located at
point 6.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
23
The precision error is acceptable apart from location 6, which
specifically has a 30.1% error, so as such the equivalent stress at
this point could be up to 92.9 MPa, which is still les than the
equivalent stress in location 5.
5.4 – Re-Design of the Fillet The stress found previously in figure 27 shows the largest
concentrations is at the shaft area, specifically around the side
face. The cause of this is suggested to be due to the fillet radii,
and as such this part is re-designed, as shown in figure 30.
This area is re-designed by changing the width from 16mm to 10mm.
Figure 29. The tensile precision (left) and compressive precision (right).
Figure 30. The fillet area is modified.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
24
This produces compressive and tensile stresses in locations 5 and 6
of magnitude: -
σC5 = 208.5 MPa σT5 = 59.6 MPa
σC6 = 2.7 MPa σT6 = 104.3 MPa
Obviously the stresses in location 6 are approximately the same, as
nothing has changed in this area.
This gives way to an equivalent stress of
σe5 = 89.4 MPa
σe6 = 74.7 MPa
5.5 – High Performance Connecting Rods Aftermarket connecting rods are used when the performance of a
vehicle has been enhanced, and it is known or suggested that the
standard OEM connecting rods will fail. The aftermarket con rods
shown below are a typical example of design for this purpose, and as
such the design is used in an attempt to decrease the stress.
When the geometrical shape of the con rods from Revolution (figure
31) are analysed it seems that the majority of them have a smooth
shape along the little end. This is the focus for the re-design.
Figure 31. Some high performance con rod designs from Revolution.
[2]
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
25
Interestingly the majority of the con rods here are made of
aluminium, of Ultra Lite 7075-T6 grade. This is a very specific
material, which has been heat treated to T6 grade, and is an
aerospace derived alloy. Specifically the aerospace derivation comes
from Boeing wing spars and some of their other structural designs.
The surface has been impinged to provide better fatigue life.
Considering this specific material it is not applicable to use the
Algor material selection for T6 Aluminium alloy. Equally it is not
possible to find the mechanical properties of this material from
external sources without contacting the manufacturer.
Using figure 31 above the con rod can
be re-designed as shown on the right.
This is academic however and patent
and copyright implications would need
to be considered for any production.
The compressive minimum stress has the highest region over location
7, and is approximately 140 MPa.
Using the same load and constraint conditions for accurate
comparisons the tensile maximum stress has the highest region over
location 8.
Figure 32. The con rod re-design
using high performance rod geometry.
7
Figure 33. The compressive minimum stress for a high performance con
rod.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
26
The corresponding stresses are: -
σC7 = 140 MPa σT7 = 9.7 MPa
σC8 = 8.2 MPa σT8 = 94.5 MPa
This gives way to an equivalent stress of
σe7 = 26.9 MPa
σe8 = 69.7 MPa
The precision is accurate, except in the locations shown in figure
35, where the compressive error is 33% and tensile error is 40%.
These are localised however.
Figure 35. The precision error in compression (left) and in
tension (right).
8
Figure 34. The tensile maximum stress for a high performance con rod.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
27
6. Discussions Using the Smith Topper Watson formula it is obvious that the tensile
stresses are of more concern to the fatigue limit of the component,
so optimisation has been concentrated in this area, for both the 2D
and 3D analysis.
The calculations for the tensile force uses an approximation of the
mass of the little end. But the specific mass used in the
calculations is an approximation, with the length of the crank shaft
to the little end being 22mm. From figure 36 it can be shown that the
two masses are of equivalence:
mba = mMr
and is used for engine balance equations (note the similarity between
bending moments, using the centre of gravity). As such it could be
suggested that the mass of the little end to the centre of gravity
should be used as the mass in Newton‟s 2nd Law. This is not of
concern for the optimisation, but is to calculate the fatigue life
and safety factor.
But, there are other ways to calculate the tensile force, one such is
given as [4]
Where, Y = Inertia Constant = 1 + R/L
R = Crank Throw
L = Rod Length
W = Weight of the piston, pin and small end
ω = Angular Velocity of the Crankshaft
Of course the stress needs to be multiplied by the x-sectional area
to provide the force. But, questions arise, like what x-sectional
g
WRYessTensileStr
12
2
Figure 36. The mass of the con rod can be considered as two
masses at the little and big end. [3]
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
28
area, and what weight of the small end (i.e. the small end diameters
on width only). These need to be accurately calculated to allow
decent computational analysis for optimisation purposes.
An S-N curve is used to predict the fatigue limit of the material.
But a lifespan of 5000 hours is specified and if the S-N curve was
available it would be appropriate to check the specific fatigue
limit. It would be assumed that the 6500rpm red line was in use for
its 5000 hour life.
6.1 – 2D Analysis The results from the first 2D analysis show the largest equivalent
stress is 211.4 MPa, due to a high tensile stress in the inside of
the little end. The comparisons between this FEA result and the
calculated equivalent stress of 100 MPa is not very accurate. The
theoretical forces are used in the FA analysis, and the area is quite
accurately calculated, but this area is not considered in the 2D
analysis. A thickness of 20mm is used for analysis. This is the only
comparative difference between the two results, and so it is
speculated that the mesh and the accuracy of the model being 2-
dimensional are the major contributions to the errors.
The precision error is at maximum 35% and is located around the
little end, at the application of the loads. This is expected.
However, locations 1, 3 and 4 are all in this region, and so accurate
stress results cannot be conclusive.
The compressive stress concentrations found in the 2D analysis shown
in figure 6 is located on one side of the shaft. This is due to the
meshing rather than any design parameters. The stress located in this
area should be about the central point, or at least equal on the
other edge, due to a symmetrical design.
The design optimisation of the 2D model shows a substantial drop in
equivalent stress. Comparatively the working safety factor for the
re-designed con rod is 3.8, which is much higher than the initial
value of 1.13.
But, both the compressive and tensile equivalent stresses have
discrepancies in the precision error and consequently FEA results are
not accurate compared to that of theory. The precision over the whole
con rod is accurate, except for small areas. This however is where
the high stresses are localised. As such the values cannot be
conclusive.
Also the re-design involved increasing the outer diameter of the
little end and increasing the width of the con rod shaft. This would
have other implications on the engine as a whole, as increasing the
mass of the rod will increase inertia, and therefore decrease power
and efficiency of the engine. By increasing the outer diameter it
would also have implications on the design of the piston to still be
able to fit over the top of the end.
The design implications are considered more thoroughly in the 3D
discussion.
6.2 - 3D Analysis The first 3D analysis provided a safety factor of 240/78.7 = 3.05,
and is higher than the theoretical value obtained of approximately
2.4. But, by comparing the theoretical equivalent stress of 100 MPa
it is of an acceptable level (FEA results having a maximum of 79
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
29
MPa). This suggests that the F.E.A. results are accurate to
predictions, and as such there are no large discrepancies.
The accuracy of the elements at the small end (location 1) is
unacceptable however, having a 19% error. If the worst case scenario
is taken and the stress there is 19% higher than predicated it
produces a compressive stress of 386.9 MPa, and an equivalent stress
of 17.1 MPa. This is still much lower than the most likely fatigue
failure location, and so is ignored for optimisation purposes.
It is important to note that the error at the gudgeon pin is due to
the constraint type (surface) and meshing density, and as such the
stress is not representable to a real connecting rod.
Also to more accurately predict the forces and resulting stresses
other parameters need to be considered. K. Luebbersmeyer states that
it is “...advisable to pay attention to the careful design of the
side forces of big end con rod eyes in all cases of crank end
guidance” [5]
This statement is referring to how the big end is mated to the
crankshaft, and the location and angle of the cut (split). The force
is still applicable though, and in this report it is not considered
to be or analysed.
Indeed computational analysis has shown that the split is subject to
high load with figure 37 being an example: -
The displaced model suggests that the angular split is of importance. Interestingly there are high stress concentrations at what is
presumably the application of constraints and forces. They are not
referred to, but the stress colour coding is not known (i.e. we
cannot assume that red is the highest stress areas), nor is the model
accuracy in these areas.
It is stated that “to determine the resulting forces the mass of the
con rod is divided into rotating and reciprocating portions, with the
big end being rotational” [7]. This is used for design implications
on vibration reduction, and smooth running of the engine, but these
forces are not considered in this report.
Figure 37. The stress analysis using an angular split. [6]
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
30
Also there is a „side force‟ applied to the cylinder (and therefore
an equal and opposite for applied to the piston and con rod small end
as per Newton‟s 3rd law. This side force is of importance, and is
considered when analysing dynamic excitation, in which the connecting
rod is one of the major components in this excitation. But this
design consideration is not applied to the re-designing analysis in
this report. However, other implications can supersede the con rod
dynamic excitation, and some other measures can be introduced to
counter-act the excitation, for example well designed engine mounting
positions.
Figure 38. Side force during operation [8]
The cyclic loading is not maximum at each stroke. Figure 39 shows
this
Figure 39 – The cyclic stress that the con rod experiences.
The dynamical velocity and acceleration of the connecting rod is not
constant over its 3600 (4-stroke) cycle. The point of combustion will
produce more force than the point of intake, and therefore with
constant area the stress will be higher. Stage 1 and 2 will produce
the highest stress as the dynamical V and α will decrease due to
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
31
friction. This is valid when considering the fatigue limit, or
precisely the specific limit when considering the 5000 hour life
specification. If one cycle is considered to be 360o then the
compressive stresses (either maximum or at stage 3) will occur twice.
This is the same for tension as well. The outcome of this is that the
con rod will experience these stresses 4 times per cycle. This
however is purely considerate if the specific fatigue yield is
considered and not the fatigue limit of forged steel, as this is the
stress at which the steel can experience and continue to operate
indefinitely.
6.2.1 - 3D Modelling The 3D analysis was re-designed a few times to get an accurate base
result. This is because of the accuracy of the conditions, (where the
force and constraints were applied).
After it was assumed the accuracy was of an acceptable level the
stress was further analysed. The first and consequent Smith Topper
Watson analysis on the 3D model use nodes of the highest stresses for
the con-rod only, as the gudgeon pin experiences more stress, but is
not under investigation here. Also the precision is inaccurate in
this area.
Also using the Smith Topper Watson formula the tensile and
compressive stress needs to be used in location 1 of figure 21. But
the high stress location (1) in is neglected in reality for tensile
stresses, as they are in the model due to the mating of components on
all surfaces. But, for the compressive force this would be a high
stress area due to the locations and direction of the forces.
This is also why the compressive stress (1) and tensile stress (4) is
a negative number, as it is mated to this part and is pulling that
section in the direction of the applied force. This is a simulation
inaccuracy, and is not representable to the actual model. Also it is
impossible to have a negative stress; rather as a vector it
represents the direction.
Of importance location 1 needs to have a high stress area, as the
bearing shell is designed to yield on initial compression so that it
doesn‟t spin around.
6.2.2 – Rounding all Edges The first re-design rounded all the edges off to see any
implications. Actual connecting rods are likely to have this
rounding, to reduce the frictional inertia through the oil. But, it
actually increased the equivalent stress in the centre of the shaft
121 MPa, compared to the original of 78.7 MPa. But, it is unlikely
that the actual manufacturing of the con rod by forging will produce
perfectly sharp edges, and as such a result of 121 MPa is considered
more accurate. The theoretical value lies half way in between these
two computed results, and so cannot be used to associate which stress
is more accurate.
6.2.3 – Re-Design of the Fillet Because the high stress regions are in the „I‟ section of the shaft
this area is re-designed. An increase in fillet radii is designed to
thicken up the „I‟ section.
„I‟ sectional beams are used in all structural engineering
disciplines to give good structural rigidity per unit area, due to
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
32
the second moment of area. It is the same case in con rod design,
with the mass of the rod of great importance.
The results from increasing the fillet radii are considerable though,
with a 26% decrease in stress at the shaft area, compared with the
rounded design.
6.2.4 – High Performance Con Rod By using manufactured high performance connecting rods the equivalent
stress can be compared. The resultant stress was found to be at a
maximum of 69.7 MPa. This is again lower than the original values set
in 2D and 3D, and the re-design could continue to the nth degree, but
other implications would need to be considered, some of which are
described below.
It is known that “the weight and design of the con rod have a direct
influence on the power-to-weight ratio, power output, and smooth
engine operation” [9]. This is due to a large amount of variables
like its contribution to the rotating inertia (con rod, piston, pin
etc.), its heat dissipation, and its fluid inertia.
Specifically it has been stated by Dr Lehmann that the following
areas are of importance to con rod design: -
1. Dimensional stability of the areas that accept the two sheets
2. Oil channels for lubricating the little end.
3. Securing con rod cap.
4. Design of critical zones in accordance with loading.
5. Engineer con rod web to reduce mass.
6. The little end is flattened into a trapezoid shape at the top,
and is associated with loading, and permits close
spacing to the bearing shell to reduce bearing shell
flexure.
Also part 6 is associated with balancing the mass of the con rod post
forging. The design optimisations associated in this report deal
mostly with statement 6 above.
With these statements in mind it can be shown that the re-designed
con rod did indeed decrease the stress, but at a consequence. By
using ProEngineer the mass of the model can be computed as follows.
Firstly the material is defined, either manually or using the library
by going into Edit > Setup > Material. Then by going into Analysis >
Model > Mass Properties, the mass is found. Figure 40 shows print
screens of the operation.
Figure 40. The mass of the connecting rod can be investigated
using ProEngineer.
[10]
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
33
The mass of the original model is found to be 0.000487279 tonne. The
re-designed model has a mass of 0.0006619287 tonne. This is obviously
incorrect, but it can be used as a scalar relationship.
6.3 – Further Analysis As explained there are many implications in changing the con rod
design, more so than the resultant stress, and it is beyond the scope
of this report to take them all into account.
If this report was to be investigated further then it would be
appropriate to model the pistons and the crankshaft, to allow a more
precise simulation of the forces. Also by applying separation nodes
it would ensure the gudgeon pin does not „weld‟ to the con rod. A
finer mesh density would allow more accurate results. The limitations
here are the processing power of the computer and there are no
technical drawings for the other components
Also it would be good practice to use the results for empirical
testing, and indeed no manufacturer would risk their reputation on
just a model. One example is Vandervell Products, who have installed
a special rig on which big end deflections can be measured and
stiffness evaluated. They state that if the eye distorts too much it
can lead to fatigue failure of the rod. [11]
In the initial analysis it is stated that the highest stresses are at
TDC and BDC. But, the spark is retarded to a certain extent to
prevent knocking, so maximum pressure is not achieved at TDC, rather
just after. The spark ignition delay is not however specified in
Table 1, and so cannot be accounted for to a high degree of accuracy
when applying the load and constraints on the model. Equally the rod
and piston centre is offset by 0.75mm, but is assumed to be zero for
analytical purposes.
It would be appropriate to analyse the connecting rod at elevated
temperatures, as the inside of the chamber will have a massive
temperature compared to ambient. The F.E.A. software is capable of
increasing the temperature of the elements (nodes), but it is the
cyclic temperature (the operating temperature) that the con rod will
experience. Fatigue yielding is more likely to occur due to cyclic
temperatures rather than elevated. [12]
6.3.1 – A Note on Materials It is worth noting, along with the manufacturing techniques, that
materials can have great implications on the stresses and fatigue
life of the connecting rod. Such an example is the aluminium alloy
used at Revolution. Other materials include titanium and cast irons
being used for particular applications, with the manufacture being
forging and machining.
One case study is the Rover K series. The con rods are drop forgings
(080X47 material) which have been heat treated to give an ultimate
tensile stress of 775 MN/mm2. The little end is induction heated for
assembly [13]. This engine is (or was) used in fundamental Lotus and
Caterham cars, in other words high performance cars.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
34
7. Conclusions In reality this report does not adequately address the problem
enough to optimise the design of the con rod. The assumptions
made and the precision errors were too high to be ignored, and
some of the stresses were too concentrated.
Equally the smallest x-sectional area in the middle of the con-
rod produced no maximum and minimum stresses (it is localised
in the applied constraints and loads, and is ignored), and so
fatigue analysis cannot be introduced in this area. If Von-
Mises stresses were used as an indication then the compressive
stroke (ignition) would cause the middle of the rod to fail
under fatigue.
Although the compressive stress is higher due to ignition of
the fuel providing the only source of energy, by use of the
Smith Topper Watson formula it is shown that the tensile force
has a greater implication on the safety factor.
There are other ways of calculating the stresses (and therefore
the forces), but there are unknowns in the example stated. But
these could be used to more accurately predict the forces,
rather than making assumptions on the mass of the little end.
The two dimensional re-design decreases the equivalent stress
by 55%, and could be decreased further, but it is not
representable to a real con rod.
Increasing the fillet radii decreases the stress by 26%,
producing a safety factor of 2.7.
By using a high performance con rod the stress is reduced
further. But using the software to find the mass it is found
that it has increased.
To summarise the new design decreases the
stress by 42%, but increases the mass
by 26%.
The increase in mass will have implications on the inertia of the
piston assembly, and therefore detrimental to the performance of the
car, but it is not specified to optimise the con rod for performance,
and as such no material losses have been attempted.
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
35
8. References [1] http://www.efunda.com/materials/alloys/alloy_ho
me/show_alloy_found.cfm?ID=UNS_C51100&prop=all&Page_Title=%20Me
tal%20Alloys%20Keyword%20Search%20Results
[2] www.revolution4ever.com
[3] [13] Stone, R., 1999, Introduction to Internal combustion
Engines, 3rd Ed., Macmillan ISBN 0 333 74013 0
[4] [8] [11] Fenton. J., 1986, Gasoline Engine Analysis,
University Press, Cambridge
ISBN 0 85298 6343
[5] Luebbersmeyer, K., The Design & Development of Small Internal
Combustion Engines, IMechE, Conference Publications, Read at
the Isle of Man, 1978
ISBN 0 85295 394 8
[6] [7] [9] Damour, P., 2002, Internal Combustion Engine Handbook,
Germany ISBN 0 7680 11139 6
Edited by Schafer, F., Basshuysen, R
[10] Lehmann, U., 2002, Internal Combustion Engine Handbook, Germany
ISBN 0 7680 11139 6
Edited by Schafer, F., Basshuysen, R
[12] http://en.wikipedia.org/wiki/Fatigue_%28material%29
24/02/2008
Course: Solid Mechanics ENGD3016
Title: Design Analysis – Con. Rod
Student: W. Shipway P04125213
Lecturer: A. Lees
36
9. Bibligraphy
PIASCIK, R. S., GANGLOFF, R. P., SAXENA, A., Elevated Temperature
Effects on fatigue and Fracture ISBN 0-8031-2413-9, Available online
http://books.google.com/books?hl=en&id=VAY2wzNMm1EC&dq=temperature+ef
fect+fatigue&printsec=frontcover&source=web&ots=pxGCEPbo74&sig=j1o8vH
mvmltfz0x9ApLHji3TbUw#PPP1,M1
Stone. R., 1999, Introduction to Internal combustion Engines, 3rd
Ed., Macmillan ISBN 0 333 74013 0
Fenton. J., 1986, Gasoline Engine Analysis, University Press,
Cambridge ISBN 0 85298 6343
Luebbersmeyer, K., The Design & Development of Small Internal
Combustion Engines, IMechE, Conference Publications, Read at the Isle
of Man, 1978
Damour. P., 2002, Internal Combustion Engine Handbook, Germany,
Edited by Schafer, F., Basshuysen, R
Taylor, C., F., 1966, The Internal Combustion Engine in Theory and
Practice, Vol. 1: Thermodynamics, Fluid Flow, Performance, 2nd Ed.,
M.I.T.
Green, A., B., Lucas, G., G., 1969, Internal Combustion Engines,
English University Press
Various Authors, 1991, Computers in Engine Technology, IMechE, London