engd3016 design analysis engine connecting rod

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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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




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


[12] http://en.wikipedia.org/wiki/Fatigue_%28material%29

24/02/2008




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,


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

http://books.google.com/books?hl=en&id=VAY2wzNMm1EC&dq=temperature+effect+fatigue&printsec=frontcover&source=web&ots=pxGCEPbo74&sig=j1o8vHmvmltfz0x9ApLHji3TbUw#PPP1,M1



engd3016 design analysis engine connecting rod

Documents