Evaluation of Different Concepts for Pressed and Sintered ...

Evaluation of Different Concepts for

Pressed and Sintered Connecting Rods

Mattias Rehn

Mechanical Engineering, master's level

2019

Luleå University of Technology

Department of Engineering Sciences and Mathematics

Abstract

Connecting rod are found in most combustion engines and transmits thrust from the

piston to the crankshaft. The connecting rod needs to withstand forces from the piston

and inertia forces which results in axial tension, compression stresses and bending.

Today the most common manufacturing techniques in automotive industry are drop-

forging, die-casting and the Powder Metallurgy technique used is powder-forging.

In this Master Thesis different connecting rod designs for a single press PM manufac-

turing process were created and evaluated as a part of Hoganas AB’s Total Powder

Metal Car project, TPMC. This paper will serve as a basis for future connecting rod

projects at Hoganas AB when choosing a suitable connecting rod design.

The main objective of this Master Thesis is to evaluate different designs in regards to

the following:

• Buckling strength

• Fatigue life

• Manufacturing rating

The study shows that there is evidence that a single pressed connecting rod is possible.

No absolute answer of which design is the best is given in this paper since in depends

on different parameters and application. For each parameter examined there are results

presented and arguments for and against each design which can aid designers in future

work.

Suggestions of improvement on both the method and on the designs are presented in

respect to the results. The improvements may potentially increase the fatigue life,

buckling strength and improve manufacturability.

i

Preface

This master thesis were made at Hoganas AB in the beginning of 2019 and I would like

to thank them for giving me the opportunity to make my master thesis there.

I would like to first thank my supervisor at Hoganas AB, Michael Andersson for all the

help, support and guidance throughout the project. Also a special thanks to Thomas

Schmidtseifer for all the help and counseling regarding the manufacturing part of this

thesis.

Further I would like to thank my examiner Jesper Sundqvist from Lulea University of

Technology for all the help.

Many thanks to all the other master thesis students at Hoganas AB for their help and

all the laughters during this thesis.

ii

Contents

1 Introduction 3

1.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Delimitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Theory 5

2.1 Product Development Process . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Concept Generation . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.2 Screening and Scoring . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Powder Metallurgy, PM . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 Connecting Rod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.1 Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3.2 Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.3 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.4 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4 Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Methodology 22

3.1 Concept generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22


3.4 Manufacturing ranking . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4 Results 26

4.1 Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.2 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.3 Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30


5 Discussion 33

5.1 Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.2 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5.2.1 Concept 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

5.2.2 Concept 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

iii

5.2.3 Concept 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.2.4 Concept 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.2.5 Concept 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.2.6 Concept 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36



5.4.1 Concept 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.4.2 Concept 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.4.3 Concept 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.4.4 Concept 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.4.5 Concept 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.4.6 Concept 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.4.7 Justification of the ranking . . . . . . . . . . . . . . . . . . . . . 38

6 Conclusions 40

7 Future work 41

A Derivation 43

B Data for FEA 46

C Stress data from FEA 47

D Concepts 55

E Critical points in Haigh-diagram 58

iv

Nomenclature

Ap Area of piston [m2]

a Connecting rod length, c-c small and big eye [m]

ax Acceleration on the connecting rod in x-direction [m/s2]

ay Acceleration on the connecting rod in y-direction [m/s2]

b Distance from center of gravity to pin end [m]

c Distance from center of gravity to crank end [m]

Fp Piston force [N ]

Fx Force in x-direction on the pin end [N ]

Fy Force in y-direction on the pin end [N ]

I Moment of inertia on connecting rod [kg ·m2]

mc Mass of connecting rod [kg]

mp Mass of piston [kg]

n Safety factor [−]

P Pressure on piston [Pa]

R Stress ratio [−]

r Crank length [m]

Tx Force in x-direction on the crank end [N ]

Ty Force in y-direction on the crank end [N ]

xg Distance to center of gravity in x-direction [m]

1

xg Velocity of center of gravity in x-direction [m/s]

y Distance from origin to pin end [m]

y Velocity in y-direction [m]

y Acceleration in y-direction [m/s2]

yg Distance to center of gravity in y-direction [m]

yg Velocity of center of gravity in y-direction [m/s]

ω Angular velocity around crank end [rad/s]

σa Alternating stress [MPa]

σm Mean stress [MPa]

σmax Maximum stress [MPa]

σmin Minimum stress [MPa]

θ Crank angle [−]

ϕ Angle between connecting rod centerline and piston centerline [−]

ϕ Angular velocity around pin end [rad/s]

ϕ Angular acceleration around pin end [rad/s2]

2

1 Introduction

This Master Thesis is an evaluation study on the design of connecting rods for Powder

Metallurgy (PM) manufacturing and it was done at Hoganas AB as a part of their Total

Powder Metal Car project, TPMC. This study will serve as a basis in future projects at

Hoganas AB when choosing which design that will be best suitable for a specific case.

Connecting rods are used in most combustion engines to transmit the thrust from the

piston to the crankshaft. The connecting rods are subjected to cyclic loading and needs

to be strong enough to not break during the cycles, but also be light to minimize the

inertia forces. The loads vary from compressive loads due to the combustion and tensile

loads due to inertia.

The most common production techniques for connecting rods are drop-, powder-forging

and die-casting. For manufacturing high volumes of connecting rods, forged steel were

the best way of producing them for a long time, but since the powder metal processes

were introduced, these two techniques are the most competitive manufacturing pro-

cesses. This because of the cost efficiency of PM connecting rods resulting in almost

net shape which reduces the used material with equal strength and quality.[1]

The technique used today for manufacturing PM connecting rods for the automotive

industry are powder forging and it is made by pressing, sintering, reheating and forging

to obtain full density[2]. The technique is well established but to lower the production

time and cost Hoganas AB wants to manufacture a connecting rod through the standard

PM process with single compaction and sintering combined with sinter hardening and

obtain similar performance.

3

1.1 Objective

The objective of this thesis is to create a basis for future connecting rod projects by

creating five or more concepts of different design using an existing connecting rod from

a VW 1.4 TSI four-cylinder-in-line engine as a reference. The different concepts will

be evaluated using Finite Element Analysis and then benchmarked against each other

and the original to determine which design is best from a strength and manufacturing

perspective. The scope is to focus at the transition from the small and big eye to the

stem and also at the stem. The different parameters for comparison are:

• Buckling strength

• Fatigue life

• Manufacturing rating

1.2 Delimitations

Since a specific connecting rod is chosen as a reference, there are limitations in the

overall size of the concepts to fit in the existing engine. The weight and its distribution

is also important so the weight must be±10g of the original and the center of gravitation

should remain as close as possible to the original.

4

2 Theory

This section explains the product development process, powder metallurgy process, the

different challenges when designing a connecting rod and how to solve them.

2.1 Product Development Process

Ulrich and Eppinger’s [3] product development process was used in this paper to struc-

ture the development of the designs. Since this study will not lead to a finished product

only the concept generation, screening and scoring parts of the process were used.

2.1.1 Concept Generation

The concept generation process starts with a problem formulation and the target speci-

fication. It ends up with a number of concepts to solve the initial problem. Even though

the concept generation is a creative process there is need for a structured method to

explore all of the design room and not miss a solution. The process can be divided in

to the following steps:

• Clarify the problem

• Search information externally and internally

• Work systematically

• Reflect in the results

2.1.2 Screening and Scoring

The concept selection process is used to evaluate the concept with the respect to the

given specification. The concepts are compared in regards of relative strengths and

weaknesses to be able to select the concepts to further develop. Both the screening and

scoring is done with a selection matrix.

The screening uses a reference concept to evaluate the other ones against with the use

of selection criteria while the scoring can uses different reference points. The screening

is a rough comparison method while the scoring uses a finer rating scale with weighted

5

criteria. After each of the processes there is often a possibility to combine and improve-

ment the concepts, sometimes new concept is created and the process starts again.

These iterative processes are a good way to improve and find the optimal concept.[3]

2.2 Powder Metallurgy, PM

The densifying starts with the metal powder being filled in a die cavity by gravity

and compacted under high pressure from top and bottom at the same time achieving

relative homogeneous density as seen in Figure 2.1. The particles are compacted so

close that their irregularities interlock and cold welding occurs between them.

Figure 2.1: Basic press cycle with three stages: filling, densifying and ejection. [4]

There are several parameters to have in mind when designing the compaction tool e.g.

every portion of the cavity must be filled the right amount of powder, the tool should

have as few punches as possible and the densification should happen at the same time

in all of the cavity. The powder flows very little sideways during densification which

has to be considered to achieve homogeneous density. The density is higher at the ends

close to the punches and lower at the centre due to friction between powder and the

die wall which also needs to be considered when designing the product.

6

The next step in the PM process is the sintering and there are five things to consider

during the process which are:

• Temperature and time

• Geometrical structure of the powder particles

• Composition of the powder mix

• Density of the powder compact

• Composition of the atmosphere in the sintering furnace

The temperature of the furnace controls the time the specimen needs to be in the

furnace. With higher temperature the time needed to achieve the bonding between the

particles decreases. With high temperature the production efficiency increases but the

need for maintenance of the furnace increases which results in a larger cost. For PM

the most common sintering conditions are 15-60 minutes at 1120-1150◦C.

The structure of the particles impact the time needed in the furnace. Finer particles

can be sintered faster than coarse particles. On the other hand fine powders are harder

to compact and shrink more during the sintering process.

The composition of the powder is selected to satisfy the physical properties needed and

to control the dimension changes during the sintering process. When having a mixture

of two or more metal powders the alloying and bonding process takes place at the same

time. At the common sintering temperatures the alloying process is slow and it is not

achievable to get full homogenization, except between iron and carbon.

With higher density the total contact area between the particles is also larger which

makes the alloying and binding processes more efficient during the sintering.

The atmosphere in the sintering furnace fulfills different functions which can be con-

tradictory. It protects the specimens from oxidation and prevents carburization in

carbon-free material or vice versa, if it contains carbon. [4]

7

Sinter hardening is one way to acquire a PM component with low alloyed steel with

high performance. By controlling the cooling rate, especially through rapid cooling,

in the furnace it is possible to control the final microstructure of the part. This leads

to control over the mechanical performance of the part and eliminated the need for a

secondary hardening treatment. This makes the process cost efficient.[5]

Geometrically most simple parts are rarely made with PM because it can not compete

with other methods but the fact that the frequency decreases with complexity is because

the tools and process gets more expensive.

The ability to maintain the dimensional accuracy on the sintered part depends on the

final processing step and the direction of the dimensions. The tolerances are better kept

perpendicular to the press direction than the in press direction. If the final step for

example involves hardening, the tolerances decrease but with sizing or coining narrow

tolerances can be achieved. Sized and coined parts are being subjected to both plastic

and elastic deformation. When there is dimensional changes during the sintering process

sizing can be used to increase the tolerances. A relatively moderate force is needed since

only small plastic deformation is necessary. Coining is used when not only dimensional

tolerances is required but also an increase in density. The force used is higher than the

one used in sizing. The strain-hardening of the part leads to an increase in hardness

and tensile strength but the elongation is decreased.

With the PM process it is possible to produce complicated parts with high accuracy and

near net shape with few process steps in large series for a relative low cost. The shapes

achievable using the PM process are often difficult or impossible to produce with other

methods of manufacturing. Many cases where other methods are used today could be

adapted to PM without compromising the part and in some cases improve the part.

8

The parts can be divided into different degree of complexity, in Figure 2.2 it can be seen

how frequent they are and examples of products with different complexity. The degree

of complexity is determined by a number of parameters. For example the number of

punches needed which is determined by the height differences in the part. The number

and the shape of holes, radii and tapering effect the degree of complexity. Even helical

gears can be made and they have a high degree of complexity, this is due to the shape

but also the complex press cycle needed.

Figure 2.2: Degree of complexity of PM -parts related to their frequency. Top right:

Degree 2. Bottom right: Degree 5.[4]

9

2.3 Connecting Rod

A connecting rod can be divided into three parts, the pin end that connects to the

piston, the crank end that connects to the crankshaft and the shaft as can be seen

in Figure 2.3. The connecting rod transmits the thrust from the piston to the crank,

making reciprocating motion to rotary motion. With a four-stroke engine the complete

cycle is 720◦ where the connecting rod needs to withstand buckling, axial tension and

compression stresses from the piston. The high compression loads are due to combustion

and high tensile loads due to inertia.

Figure 2.3: Different parts of a connecting rod.

10

2.3.1 Forces

The forces acting on the connecting rod and piston can be seen in the free body diagram

in Figure 2.4 and it was used to derive the forces, velocities and accelerations acting on

it.

Figure 2.4: Free body diagram of the piston and connecting rod.

11

By using trigonometric relationships the angular velocity around the pin end seen in

Equation (2.1) was derived and by deriving it the angular acceleration seen in Equation

(2.2) was obtained.

ϕ =rω cos θ

a cosϕ(2.1)

ϕ =1

cosϕ

(−rω2 cos θ

a+ ϕ2 sinϕ

)(2.2)

The forces on the piston in the y-direction can be seen in Equation (2.3) and the

expression for Fp in Equation (2.4).

Fy = −mpy − Fp (2.3)

Fp = PAp (2.4)

The acceleration in x- and y-direction on the connecting rod can be seen in Equation

(2.5) and (2.6) respectively.

ax = bϕ cosϕ− bϕ2 sinϕ (2.5)

ay = y + bϕ sinϕ+ bϕ2 cosϕ (2.6)

In Equation (2.7) the relationship between the forces on the connecting rod in the

y-direction can be seen.

Ty = mcay − Fy (2.7)

12

With the help of forces in x-direction and moment around the center of gravity a matrix

for Fx and Tx can be derived and it can be seen in Equation (2.8).

[1 1

−b cosϕ c cosϕ

][Fx

Tx

]=

[mcax

Iϕ− cTy sinϕ+ bFy sinϕ

](2.8)

To translate the forces, velocities and accelerations to the connecting rods own coordi-

nate system Equation (2.9) were used.

[cosϕ sinϕ

− sinϕ cosϕ

][x

y

]=

[x′

y′

](2.9)

For the full derivation see Appendix A.

The data for the engines pressure cycle for different angular velocity ranging from 1000-

6000 rpm were given and can be seen in Figure 2.5. The data is based on simulations

made by CVUT in Prague.

Figure 2.5: The engines pressure cycle.

13

The mass and geometrical data used can be seen in Table 2.1, the connecting rod length

is the center-center distance of the holes. To acquire the data Hoganas AB had made

reverse engineering on the original connecting rod and measured it with a ZEISS CMM

(Coordinate Measurement Machine).

Table 2.1: Mass and geometrical data.

Piston radius Piston mass Connecting rod mass Connecting rod length Crankshaft length

37,25 mm 0,34 kg 0,34 kg 140,04 mm 40 mm

2.3.2 Buckling

Buckling is important to have in mind when designing a connecting rod due to the

high compression and inertia loads acting on it during a cycle, evermore due to the

force acting on the rod from an angle. The critical load is the value of the axial force

when the conditions go from stable to unstable and failure can occur. The critical

loads corresponds to different order of buckling modes. The higher modes are often of

no interest because the part will break when the load reaches the lowest critical value.

Other than the critical load a factor called Buckling Load Factor, BLF, can be obtained

which is a safety factor against buckling. [6]

2.3.3 Fatigue

Failure caused by fatigue occurs when an object is subjected to a dynamic load repeti-

tively for a large number of cycles. The failure will happen at a lower stress level than if

the force was to be applied statically and the failure starts with a small crack in a point

of high stress, such as in sharp corners or different transition areas. The crack gets

larger until the remaining material cannot withstand the loads and a fracture occurs.

This applies to a connecting rod since the load is dynamic and cyclic and when failure

happens in a connecting rod the engine will most likely brake as well. Therefore when

designing the connecting rod against failure, an infinite life is desired. [6]

With testing of the material it is possible to determine the failure load. The material

is subjected to different stress levels and the amount of cycles to failure is determined.

When enough data is collected it is possible to plot a S-N diagram which shows the

endurance limit.

14

The number of cycles to failure, N, is on the x-axis and the stress level is on the y-

axis as seen in Figure 2.6. If the load is below a certain stress level which a fatigue

failure will never occur and infinite life is obtained. S-N curves with a horizontal part

of the endurance limit as the one in Figure 2.6 is often presented but they are often a

simplification since there is always a slight decline. In this project this simplification is

valid since there is great knowledge about the material used. [6]

Figure 2.6: An example of a S-N curve.

The different parameters that determine the fatigue life which needs to be considered

during a design process are: [1]

• Manufacturing parameters

• Material properties

• Service conditions

• Loads

• The geometry of the part

15

A Haigh-diagram, similar to the S-N diagram, can be made from testing and is used

when there is compression, tensile, bending and torsion in the specimen, curves with

different probability of fracture can be made. Therefore a Haigh-diagram is better to

use when evaluating fatigue in connecting rods. An example of a Haigh-diagram can

be seen in Figure 2.7 and in the diagram the stress amplitude is plotted against the

mean stress.

Figure 2.7: An example of a Haigh-diagram.[7]

The alternating stress σa and mean stress σm are calculated using the maximum and

minimum stress as seen in Equation (2.10) and (2.11), then used with a Haigh-diagram

to determine if failure will happen. [8]

σa =σmax − σmin

2(2.10)

σm =σmax + σmin

2(2.11)

16

When the operating point, P, is obtained and inserted in the Haigh-diagram the prob-

ability of failure can be determined. There will be failure if the point is above the

line and if the point is under the line a safety factor against failure can be determined

according to Equation (2.12).[8]

n =AB

AP(2.12)

Equation (2.12) is used when σm is constant but σa can vary. In Figure 2.8 it can

be seen where point A, B and P are placed. This method of calculating the safety

factor were chosen because it is the most conservative method and therefore will not

overestimated the fatigue strength.[8]

Figure 2.8: A Haigh-diagram with operating point P, point A and B for determining

safety factor.

17

2.3.4 Material

It is crucial to have a combination of cost effective and high performance material to

have a working connecting rod. Since PM materials have pores in them the connecting

rods needs to have martensite structure to improve the strength. The material used to

achieve this is chromium based alloy combined with sinter hardening which gives good

qualities against fatigue and is cost effective e.g. AstaloyTMCrA + 2%Ni + 0.6%C and

Astaloy CrM + 0.45%C.[11]

Astaloy CrA and Astaloy CrM are both water atomised iron powders. Astaloy CrA

contains 1.8% chromium which offers high strength, stable dimensions and good com-

pressibility at a low cost. With the addition of copper or, as in this case, nickel it

enables sinter hardening. The Astaloy CrM contains 3% chromium and 0.5% molyb-

denum which gives it great hardenability. After sintering high strength and hardness

can be achieved. It can be sintered in high temperature and is suitable for sinter

hardening.[4]

The material parameters used for the calculations can be seen in Table 2.2.

Table 2.2: Material data for the concepts.

Density, ρ Young’s Modulus, E Poisson’s ratio, ν

7.15 g/cm2 150 GPa 0.28

18

The Haigh-diagram for Astaloy CrA + 2%Ni + 0.6%C can be seen in Figure 2.9 which

will be used for the fatigue calculations for the concepts. The diagram was constructed

based on data from measurements made by Hoganas AB.

Figure 2.9: A Haigh-diagram for Astaloy CrA + 2%Ni + 0.6%C with 50% probability

of fracture.

19

The material in the original connecting rod is C70. It is a crackable forging steel with

alloy elements which enables hardening of forged parts when controlled cooling is used

after forging. The material parameters can be seen in Table 2.3[2]

Table 2.3: Material data for the original connecting rod.

Density, ρ Young’s Modulus, E Poisson’s ratio, ν

7.85 g/cm2 206 GPa 0.3

For the original connecting rod a Haigh-diagram for its material C70 was made using

data from Lipp and Kaufmann (2011) at R = -2.5 and the help of FKM-guidelines[10],

which can be seen in figure 2.10.

Figure 2.10: A Haigh-diagram for C70 at R = -2.5.

20

2.4 Finite Element Analysis

Since the connecting rod has a complex geometry with e.g. different cross section areas

the use of FEA is necessary. It is used to investigate the stresses and displacement to

see if there are any critical areas which need to be redesigned. The obtained stresses

are used to determine the fatigue life and where such failure will happen. The critical

buckling load will also be calculated using FEA.

According to Shenoy and Fatemi (2006) static axial loads are mostly used when design-

ing connecting rods. However they compare with using quasi-dynamic analysis. Since

there are time varying inertia loads the results are different from the two analysis types

and the static giving less realistic values as seen in Figure 2.11. The time varying loads

is introducing bending stresses and axial loads which is varying along the length of the

connecting rod.

The stress range used in a static analysis is the difference between the maximum stress,

which is the maximum tensile force, and the minimum stress, which is the maximum

compressive force. Rather than using the load range at the maximum power output as

in a dynamic analyse. This could result in a connecting rod with a very conservative

design. Another factor discussed is that with a static analysis the model gets over

constrained and this being another factor for the less realistic values.

Figure 2.11: The difference in von Mises stress amplitude in different locations between

static and quasi-dynamic analysis.[12]

21

3 Methodology

This section explains the work process from ideas to finished concepts with the use of

Ulrich and Eppinger’s (2016) product development process.

3.1 Concept generation

The concept generation started with a study of different designs already used for con-

necting rods, both from external sources and also from earlier projects carried out by

Hoganas AB. This resulted in 13 different designs where some were totally different

and some more similar to each other. All the concepts where designed to be able to

manufacture with PM.

3.2 Modeling

The first model created was a base with the right dimensions of the big and small end

which should not be altered between the different concepts. There were no drawing

or CAD-model for the original connecting rod but Hoganas AB had made reverse

engineering of the original for an earlier project where the dimensions were measured.

These measurements were acquired and used in PTC Creo, a CAD software, to create

the base seen in figure 3.1.

Figure 3.1: The base used for the different concepts.

22

As seen in Figure 3.2 representation of the original connecting rod was also done to be

able to benchmark against.

Figure 3.2: The model of the original connecting rod.

The concepts were modeled but after concept screening it resulted in nine concepts

making it to the FEA stage. In the concept screening the concepts were evaluated

against the delimitations and if they did not meet the specification they were eliminated.

During the FEA the iterative process began with the concepts being altered to obtain

the optimal shape and minimize the stress in different areas.


The analyse method chosen was a static analysis even though some studies showed

an increase in stress levels compared to a dynamic one. This was done to reduce

computational time and since the objective was to compare different concepts this

simplification will effect all the concepts in the same way. A rigid link was put in both

the small and the big hole to be able to constrain them. This could be done since the

deformation in the ends is not to be examined. The small end was constrained in X

and Z translation. The big end was constrained in all translation direction and X and

Y rotation. The force was applied in the small end, the accelerations, angular velocity

and angular acceleration were applied at the center of gravity as seen in Figure 3.3.

23

Figure 3.3: One of the concepts with the forces and constraints applied.

The mesh was created by using PTC Creo’s built-in system where it iterates, making

higher order mesh for each run until the stresses converge. Then using mesh control to

be able to control the size of the elements in critical areas.

To make the scoring process the nine remaining concepts were analysed once to see if

they met the specification in regards to stress levels. Three concepts did not make it

past the scoring due to high stress concentrations and the need for large alterations

resulting in overweight or not manufacturable solutions.

The different load cases which were tested were:

• Maximum Compressive Force

• Maximum Tensile Force

• Maximum Angular Velocity

• Maximum Angular Acceleration

• Maximum Acceleration in x-direction

The maximum acceleration in y-direction was neglected due to its small impact on the

connecting rod and in Appendix B the table with the input data can be seen.

24

The results were evaluated for the normal stress in y-direction and critical areas where

risk of failure was determined for the different concepts. The areas and the stress data

can be seen in Appendix C which were then used for the fatigue evaluation. The number

of critical areas varies depending on concept.

For the buckling analysis a single compressive load of 1 kN was applied at the small

end with the same constraints. This results in the value on the Buckling Load Factor

being the amount of force in kN the connecting rod can withstand before any buckling

will occur.

3.4 Manufacturing ranking

For the manufacturing ranking the parameters that will have impact are the number

of punches, punch levels, if there is a tapered geometry, how long the tapering is and

number of radii. For the ranking the radii at the small and the big hole were neglected

since it is the same for all concepts. The rating were made somewhat subjectively.

The number of rods manufactured per hour will be determined theoretically by evalu-

ating how difficult the filling of the cavity is. It is also assumed that the press is in line

with the sintering furnace so the press can feed the furnace directly with components.

25

4 Results

In this section the final concepts, results of the stress analysis and manufacturing rating

are presented.

4.1 Concepts

In Figure 4.1 the first concept named Plus is seen and the design can be described as

an inverted I-beam with thicker sections were the I-beam has thinner sections and vice

versa.

Figure 4.1: Concept 1: Plus.

The second concept named Tapered + I can be seen in Figure 4.2 and it is a concept

which can be described as tapered I-beam. The stem is tapered with a cavity to lower

the weight without compromising the height or thickness.

Figure 4.2: Concept 2: Tapered + I.

26

The next concept named I-Beam + Tapered can be seen in figure 4.3 and it closely

resembles the original but redesigned to be PM friendly. The cavity has a tapered part

to minimize the number and size of radii.

Figure 4.3: Concept 4: I-Beam + Tapered.

In Figure 4.4 the concept named Hole can be seen. The stem is completely flat and

therefore very PM friendly. It has holes to reduce the weight without introducing any

radii or tapered sections.

Figure 4.4: Concept 5: Hole.

27

Tapered Round can be seen in Figure 4.5 and to try to counteract the problem with the

tapered design where one end of the stem becomes thin, this concept has the thinnest

part in the middle. The roundness in the tapered area is to avoid sharp transitions to

minimize stress concentrations.

Figure 4.5: Concept 7: Tapered Round.

The last concept named Tapered can be seen in Figure 4.6. The stem of this concept

is tapered which eliminates any use of radii but the stem get thin at the big eye.

Figure 4.6: Concept 14: Tapered.

The rejected concepts can be seen in Appendix D.

28

4.2 Fatigue

The values of the stress amplitude and the mean stress can be seen in Table 4.1 and

the points plotted in the Haigh-diagram are found in Appendix E.

Table 4.1: Stress amplitude and mean stress in different locations on the connecting

rods. The results are given in MPa.

1 2 3 4 5 6

Original

σa 221,760 221,785 171,320 198,705 196,740 -

σm -183,640 -172,515 -158,980 -171,795 -126,560 -

Concept 1 (Plus)

σa 146.895 152.840 170.760 146.790 153.373 163.035

σm -190.805 -161.560 -141.240 -198.910 -160.826 -131.665

Concept 2 (Tapered + I)

σa 241,545 210,855 197,250 178,850 180,005 -

σm -194,955 -197,045 -169,650 -134,450 -148,695 -

Concept 4 (I-Beam + Tapered)

σa 150,420 164,706 154,544 193,590 147,238 151,110

σm -138,080 -167,293 -157,155 -96,110 -144,961 -106,390

Concept 5 (Hole)

σa 226,955 207,788 201,150 186,620 211,615 221,385

σm -148,245 -202,511 -154,550 -156,080 -196,185 -142,815

Concept 7 (Tapered Round)

σa 168,160 203,565 189 139,045 - -

σm -142,040 -152,235 -85,60 -114,455 - -

Concept 14 (Tapered)

σa 204,550 205,265 138,250 177,615 - -

σm -146,050 -137,235 -108,950 -80,385 - -

29

All the concepts had their stress in the safe zone in the Haigh-diagram and their cal-

culated safety factor can be seen in Table 4.2.

Table 4.2: Safety factor in the different critical areas, lowest safety factor are bold.

1 2 3 4 5 6

Original 1,81 1,79 2,30 2,00 1,96 -

Concept 1 (Plus) 2,49 2,36 2,10 2,51 2,36 2,19

Concept 2 (Tapered + I) 1,52 1,74 1,84 2,0 2,0 -

Concept 4 (I Beam + Tapered) 2,38 2,20 2,33 1,81 2,44 2,33

Concept 5 (Hole) 1,58 1,77 1,79 1,93 1,74 1,62

Concept 7 (Tapered Round) 2,13 1,77 1,84 2,54 - -

Concept 14 (Tapered) 1,75 1,74 2,55 1,96 - -

4.3 Buckling

The results of the buckling load factor from the analysis are presented in Table 4.3. The

result is the amount of compressive force in kN the connecting rod can withstand before

it buckles. Each results correspond to one buckling mode, from a practical standpoint

the first is of interest since it will break before reaching the higher order of modes.

Table 4.3: The Buckling Load Factors for the different concepts and the first factor in

comparison with the original in percent.

1 % 2 3

Original 402,26 1 556,59 825,2

Concept 1 (Plus) 346,37 0,86 466,97 842,56

Concept 2 (Tapered + I) 354,67 0,88 684,24 808,56

Concept 4 (I-Beam + Tapered) 499,29 1,24 654,88 675,78

Concept 5 (Hole) 373,22 0,93 537,64 618,43

Concept 7 (Tapered Round) 325,33 0,81 485,35 809,63

Concept 14 (Tapered) 198,51 0,49 794,91 1059,25

30

In Figure 4.7 the different modes can be seen for concept 14. In which direction the

first mode buckles is depending on the design and the first mode might buckle around

the x-axis rather the z-axis as this concepts does.

Figure 4.7: The three modes for concept 14.

31


In Table 4.4 the result of the ranking can be seen and 1 is the best. The concepts

have been compared to each other to be able to rank them. The ranking is done with

more respect to the problem with densification and density gradients due to radii and

tapered sections and less with the punches and punch levels.

Table 4.4: The manufacturing ranking of the concepts.

1 Concept 5 (Hole)

2 Concept 1 (Plus)

3 Concept 14 (Tapered)

4 Concept 7 (Tapered Round)

5 Concept 4 (I Beam + Tapered)

6 Concept 2 (Tapered + I)

The number of rods which can be manufactured per hour can be seen in Table 4.5.

Table 4.5: Number of rods per hour theoretical manufactured for each concept.

Rods/h

Concept 1 (Plus) 480

Concept 2 (Tapered + I) 480

Concept 4 (I-Beam + Tapered) 480

Concept 5 (Hole) 480

Concept 7 (Tapered Round) 600

Concept 14 (Tapered) 600

32

5 Discussion

In this section the results of the fatigue, buckling and manufacturing ranking will be

discussed. The choice of FEA-method will also be addressed.

5.1 Buckling

All the concepts, except for number 4, perform worse than the original. This is expected

since the I-beam shape of the original is known to counteract buckling well. Concept 14

performs the worst against buckling of all the concepts and will only withstand half of

the force before buckling compared to the original, but it will not buckle under normal

loading conditions for this engine since maximum force is 38.5 kN. This result is also

expected due to its narrow geometry on the stem and because the thickness varies.

This buckling result is a good indicator that a simpler geometry, that will be more PM

friendly, could be a good option for a connecting rod.

If this would be a study to determine the best design for this exact engine, the buckling

analysis could be done with a real extreme value for the loads and a safety factor would

be the result. The method used in this study for the buckling analysis is beneficial in a

comparison study where the results will act as guidelines for choosing design regardless

of which engine. This is since it gives a buckling load factor which easier can be used

for another load cycle without needing to re-simulate the designs.

5.2 Fatigue

When comparing the safety factors the lowest ones are the most interesting to compare

but another factor to consider is the range of the safety factors for each concept and to

have in mind the number of critical areas. Even if a concept has a low safety factor in

one area, the fact that there are less critical areas could be beneficial in an improvement

standpoint. There are two ways to calculate the safety factor for this case, the one used

with the stress amplitude varies and one where both the stress amplitude and mean

stress varies proportionally. To know which one to choose in this case, a more in depth

study would be needed so the decision were made that both were investigated. The one

presented in this paper were the more conservative and therefore used since it will not

overestimate the fatigue life. Since the model of the original is only a representation

33

and not an exact copy the fatigue results and its safety factor should not be interpreted

as the real value, only as an approximation to compare the concepts with. One other

factor to have in mind is that the Haigh-diagram for the concepts are constructed with

a 50% probability of fracture.

There are problems with the design of the transitions on the connecting rod when

designing a PM friendly one. This is due to the fact that to counteract the stress

concentrations, smooth transitions is desirable, large radii are good but with PM small

radii are more beneficial for manufacturing. With large radii there can be problem in

the densification and resulting in less density in the middle, which can lead to failure.

Because of this, large radii which can be seen in a forged connecting rod is possible with

PM but might be worse than small radii since it may lead to less control of the density.

All of this effects the fatigue results and is needed to have in mind when evaluating the

concepts for improvements in this regard.

5.2.1 Concept 1

This concept has the highest safety factor of all the concepts and even higher than the

original. The most problematic areas are in the transition from the big end to the stem

which were expected since the radii are the smallest there and on the stem close to the

small end. Even though there were six problematic areas recognized, the safety factors

are high enough to say that the number of areas is not something negative in this case.

To improve the concept the first thing would be to look into the radii and see if there

were any that could be redesigned against fatigue better without compromising the

manufacturing. Another thing could be to look into the width of the stem part that

protrudes in z-direction and see if that would improve the concept.

5.2.2 Concept 2

Concept 2 has the lowest safety factor but only in one area. Otherwise it performs

similar to the other concepts. The area is the outside of the stem, at the transition

to the large end where its design is the most narrow. It was expected to have a lower

safety factor here since the radius is smaller than the other one without the tapered

stem but the fact that it is lower here than in the cavity was not expected.

34

With another radius on the stem in the transition to the big end the problem with the

high stress in this area could be solved. It would be wise to also investigate if there

could be anything done in the cavity at the big end to make the design even better

resulting in a design which would perform better against fatigue.

It is positive that the transition at the small end performs well against fatigue and it

seems that little to no redesign is needed.

5.2.3 Concept 4

This concept is placed in the middle in regards to the safety factor and the area with

the lowest safety factor being in the stem where the tapering ends and the flat section

begins. There were six areas recognized as problematic but the safety factor of all but

the lowest is above the original. This concept performs well against fatigue. Most of

the concepts problem areas are at or around the cavity at the big end as expected

since the shape at the small end is relatively uniform. The radii to the small end were

investigated but with such high safety factor it should not be a problem.

The biggest issue is the transition from the tapered section to the flat section and it

could be wise to investigate if it can be made better in regard to fatigue. Even though

there were six identified problematic areas, it would not be a problem from a fatigue

standpoint for five of them.

5.2.4 Concept 5

The biggest problem with this concept from a fatigue standpoint is in the holes which

makes this concept one of the worst. The lowest safety factors are found in the lower

hole and overall there are six investigated areas where the lowest ones are connected

to the holes. In the transition to the small end there seems to be a high enough safety

factor not to have a fatigue problem.

The shape of the lower hole should be investigated to try to obtain a better shape to

increase the safety factor and also the width of the top hole to see if that will effect the

safety factor.

35

5.2.5 Concept 7

This was one of the better against fatigue with a relative high safety factor and there

were also only four problematic areas found where two of them seem to be not a problem.

There is no problem at the transitions, either to the big or small end, but at the thinnest

part of the stem.

This concept performed well against fatigue and the only problematic area to investigate

further is the shape and thickness of the stem. The stem might perform better with a

thicker stem or a different radius on the roundness of it.

5.2.6 Concept 14

With the tapered design of this concept there is no high stresses at the small end

therefore all problematic areas are at the big end. The lowest safety factor is in the

middle of all the concepts but the fact that there are only four areas identified and two

of them are close together this design relatively good against fatigue.

To be able to make this design better the stem width could be investigated as well as

the big transition radii going from the big end to the stem. At area 3 there is a stress

concentration which will not be a problem for the fatigue but could be investigated for

a better design.


The choice of a static FEA-method serves its purpose in this study since it is a qual-

itative study which compares the different concepts. If the values on the stress would

have been the most important value, a dynamic method would be preferable since it

will yield more realistic results. With the constraints used on the small and the big

hole on the models, where they are not allowed to deform, is another factor that will

effect the stress if the goal is to get more realistic values. Since those ends were not

to be examined in this paper it was a valid simplification to save computational time.

Therefore the stress values in this paper should not be taken as absolute, rather as a

comparative study.

36


Here follows an explanation about the difference in the concepts and why they got

their ranking. This ranking is somewhat subjective and might not reflect how all

manufacturers perceive manufacturing difficulties. It was made with the help of Thomas

Schmidtseifer[13] who is an expert in PM manufaturing. This is due to for example

the individual equipment available at part makers since if they only have a two level

machine they will not like a three level part, therefore ranking it lower. Therefore

this ranking is done with more respect to the problem with densification and density

gradients and less with the punches due to the different equipment available. The small

and the big end will not be discussed since it is not in the scope for this paper. They

are the same for all the concepts.

5.4.1 Concept 1

This concept requires five punches on three punch levels to manufacture and can be

described as an inverted I-beam, where the stem sections are thin where the I-beam is

thicker and vice versa. This will benefit in the manufacturing process since there will be

no problem with density gradients due to tapering. The main problem in manufacturing

for this concept will be the radii in the transitions to the stem. This is due to in PM

it is beneficial to have as small radii as possible because of larger radii give density

gradient which compromise the strength of the connecting rod.

5.4.2 Concept 2

This concept requires three punches on three punch levels to manufacture and is a type

of I-beam with a tapered stem. This design will have problems with density gradients

both due to the tapered stem but also due to the radii in the cavity of the stem. The

inner radii are needed to be able to avoid stress concentration but it results in a more

difficult design to manufacture.

5.4.3 Concept 4

This concept reassembles the original the most with a version of an I-beam and it

requires four punches on three levels. The beneficial with this compared to the original

is the tapering in the cavity which eliminates an inner radius but it adds another difficult

37

section to manufacture. On the other hand the other inner radii can be relatively small

which benefits the design in less for risk density gradients.

5.4.4 Concept 5

This concept requires three punches on two punch levels. The use of rods for the holes

removes the need to use an extra punch which is needed when making a cavity or

similar designs. With the hole design it is possible to lower the weight without making

a more complex design. This results in a flat, no tapered section, minimum use of radii

and therefore a relatively easy design to manufacture. The shape of the lower hole in

this design is the most difficult to manufacture since it is a rather complex geometry

compared to a normal hole.

5.4.5 Concept 7

The geometry of this concept is tapered but with a round shape instead of a straight

curve. It needs again three punches on two punch levels to manufacture and it eliminates

the need of radii on the stem. The main manufacturing problem with this design is

to obtain the round tapering with minimum density gradients to not compromise the

strength.

5.4.6 Concept 14

This concept has a tapered stem with no cavity or radii, it needs two punches on two

punch levels to manufacture, which is the lowest of all the concepts. With no need

for radii the only problem with this is the thickness and length of the tapered section,

which will give problem in the densification of the powder.

5.4.7 Justification of the ranking

Concept 5 ranks the best due to the need for only three punches, zero tapered sections

and radii, the holes are made with rods which are there from the beginning. Concept

1 comes before concepts 7 and 14 even though it needs five punches and the other two

only need three and two punches respectively. This is because it does not have any

tapered section, it has more radii but that does not impact densification of the powder

and the manufacturing as much as a tapering does. The number of punches for concept

38

7 (three punches) and 14 (two punches) is different and the tapering on 14 gives bigger

density variations. Therefore concept 7 ranks higher.

The two concepts ranking in the bottom are 2 and 4. They both need three and

four punches respectively and have tapered sections. Concept 4 has a more complex

geometry than 2 which makes the manufacturing more difficult but gives less density

variations. Therefore it ranks higher.

The amount of rods per hour is not included in the ranking since it is based on an

optimal manufacturing process with no problem in the process.[13]

39

6 Conclusions

For this master thesis the objective was to evaluate different design for pressed and

sintered connecting rods, the conclusions from this study are as follow:

• Buckling will not be an issue for the concepts since from the buckling analysis

the conclusion can be drawn that none of the concepts will buckle under the

engine cycle given for this specific case. Even though there are differences in the

Buckling Load Factor and the majority of the concept performs worse than the

original connecting rod, the worst one still has a safety factor of 5.

• From the fatigue results there is evidence that a single press and sintered

connecting rod is possible.

• The concepts with long tapered sections, concept 4, 7 and 14, have their highest

stress concentration on their sides due to their stem being thinner and compression

occurs in the material in that area.

• The concepts with radii and short tapering experience their stress concentrations

in the transition areas.

• The biggest issue in the manufacturing of connecting rods is to control the density

since the need of large radii and tapered section or just one of them. There are

clear differences and difficulties in the manufacturing of the concepts which will be

beneficial for different manufactures depending on their equipment as mentioned

in the discussion part.

The conclusions above do not mention any concept as the best one since this study is

a evaluation to be used as a basis for future connecting rod studies. This is because

material, application and manufacturer may affect which design is the best one. The

study will help and minimize the time spent to make the decision on which design to

move forward with.

40

7 Future work

In order to improve this study the following things can be done:

• Use a different FEA-method and investigate how the stresses behave e.g. use a

dynamic analysis instead of a static one.

• Evaluate the stresses in the big and small end in order to have a complete stress

analysis.

• Investigate the problematic areas mentioned in the discussion to further improve

the concepts.

• Make a more detailed manufacturing comparison with a rating rather than ranking

where every manufacturing parameter is more closely evaluated.

41

References

[1] Afzal, Adila. 2004. Fatigue Behaviour and Life Predictions of Forged Steel and Powder Metal

Connecting Rods, The university of Toledo.

[2] Dale, James R. 2005. Connecting Rod Evaluation, Metal Powder Industries Federation.

[3] Ulrich, Karl T and Eppinger, Steven D. 2016. Product Design and Development. 6th edition.

New York, NY: McGraw-Hill Education.

[4] Hoganas AB. 2013. Hoganas Handbook for Sintered Components 1-3.

[5] Chasoglou, Dimitris and Bergman, Ola. 2017. Sinter hardening material solutions for high

performance applications.

[6] Gere, James M. 2004. Mechanics of Materials. 6th edition. London: Thomson Learning.

[7] Ekberg, Anders. High Cycle Fatigue (HCF) part II, Chalmers

http://www.am.chalmers.se/~anek/teaching/fatfract/98-6.pdf (2019-16-05)

[8] Lundh, Hans. 2016. Grundlaggande hallfasthetslara. Lund: Studentlitteratur AB.

[9] Lipp, Klaus and Kaufmann, Heinz. 2011. Schmiede- und Sinterschmiedewerkstoffe fur PKW-

Pleuel. Springer Automotive Media C Vol. 72, nr. 5: 416–421. DOI: 10.1365/s35146-011-0096-1

[10] Forschungskuratorium Maschinenbau. 2003. Analytical strength assessment of components in

mechanical engineering : FKM-guideline. 5th edition. Frankfurt: VDMA Verl.

[11] Andersson, Michael and Larsson, Caroline. 2016. Cost Effective PM Connecting Rod Concept.

[12] Shenoy, P S and Fatemi, A. 2006. Dynamic analysis of loads and stresses in connect-

ing rods. Proc. IMechE Journal of Mechanical Engineers Vol. 220, part C: 615-624. DOI:

10.1243/09544062JMES105

[13] Thomas Schmidtseifer Manager Market Development & Customer Projects Hoganas AB,

e-mail February-June 2019

42

A Derivation

With the help of Figure 2.4 and trigonometric relations the equations were derived.

The distance, velocity and acceleration of the connecting rod can be seen in Equation

(A.1)-(A.5).

y = a cosϕ+ r cos θ (A.1)

y = −aϕ sinϕ− rθ sin θ (A.2)

θ = ω (A.3)

⇒ y = −aϕ sinϕ− rω sin θ (A.4)

y = −aϕ sinϕ− aϕ2 cosϕ− rω2 cos θ (A.5)

The velocity and acceleration of the connecting rods angle of obliquity were derived in

Equation (A.6)-(A.10).

sinϕ

r=

sin θ

a(A.6)

ϕ cosϕ

r=ω cos θ

a(A.7)

⇒ ϕ =rω cos θ

a cosϕ(A.8)

ϕ cosϕ− ϕ2 sinϕ

r=−ω2 cos θ

a(A.9)

⇒ ϕ =1

cosϕ

(−rω2 cos θ

a+ ϕ2 sinϕ

)(A.10)

43

Distance, velocity and acceleration of centre of gravity is expressed in Equation (A.11)-

(A.16).

xg = b sinϕ (A.11)

xg = bϕ cosϕ (A.12)

xg = ax = bϕ cosϕ− bϕ2 sinϕ (A.13)

yg = y = b cosϕ (A.14)

yg = y + bϕ sinϕ (A.15)

yg = ay = y + bϕ sinϕ+ bϕ2 cosϕ (A.16)

Force in the y-direction in the piston can be calculated using Equation (A.17)-(A.19).

mpy + Fp + Fy = 0 (A.17)

⇒ Fy = −mpy − Fp (A.18)

Fp = PAp (A.19)

Force in the y-direction in the connecting rod can be calculated using Equation (A.20)

and (A.21).

Fy + Ty −mcay = 0 (A.20)

⇒ Ty = mcay − Fy (A.21)

44

Force in the x-direction in the connecting rod can be calculated using Equation (A.22)

and (A.23).

Fx + Tx −mcax = 0 (A.22)

⇒ mcax = Fx + Tx (A.23)

The moment around centre of gravity is seen in Equation (A.24).

Iϕ = c(Ty sinϕ+ Tx cosϕ)− b(Fy sinϕ+ Fx cosϕ) (A.24)

Solving for Fx+Tx in Equation (A.24) and combining it with Equation (A.23) in matrix

form gives:

[1 1

−b cosϕ c cosϕ

][Fx

Tx

]=

[mcax

Iϕ− cTy sinϕ+ bFy sinϕ

](A.25)

To translate the forces and accelerations to the connecting rods own coordinate system

equation (A.26) were used.

[cosϕ sinϕ

− sinϕ cosϕ

][x

y

]=

[x′

y′

](A.26)

45

B Data for FEA

Max comp. force Max tensile force Max ang. vel. Max ang. acc. Max ax

N = 3500, θ = 27◦ N = 6000, θ = 342◦ N = 6000, θ = 0◦ N = 6000, θ = 175◦ N = 6000, θ = 19◦

Concept 1

(Plus)

Force (N) -38515 5464 -9849.2 -7010.54 -33483

Ang. vel (rad/s) 94.0764 171.3582 179.4483 -178.8459 170.4340

Ang. acc (rad/s2) -3.3323e4 -1.1027e5 -1.1291e5 1.1317e5 -1.0437e5

ax (m/s2) -3.789e3 -0.8409e4 -1.0359e4 1.0755e4 -1.1309e4

ay (m/s2) -4.5459e3 -1.7677e4 -1.7394e4 1.3819e4 -1.4854e4

Concept 2

(Tapered H)

Force -38516 5467 -9849.1 -7010.54 -33485

Ang. vel 94.0764 171.3582 179.4734 -178.8459 170.434

Ang. acc -3.3323e4 -1.1027e5 -1.1291e5 1.1317e5 -1.0437e5

ax -3.7034e3 -0.8125e4 -1.0069e4 1.0464e4 -1.1046e4

ay -4.5686e3 -1.7753e4 -1.7476e4 1.3737e4 -1.4929e4

Concept 4

(H-Beam + Tapered)

Force -38515 5465 -9970.9 -7010.6 -33482

Ang. vel 94.0764 171.3582 179.4734 -178.8459 170.4340

Ang. acc -3.3323e4 -1.1027e5 -1.1277e5 1.1317e5 -1.0437e5

ax -3.6847e3 -0.8063e4 -1.0094e4 1.0401e4 -1.0982e4

ay -4.5736e3 -1.7769e4 -1.7419e4 1.3719e4 -1.4945e4

Concept 5

(Hole 1)

Force -38515 5464 -9970.9 -7010.54 -33482

Ang. vel 94.0764 171.3582 179.4734 -178.8459 170.4340

Ang. acc -3.3323e4 -1.1027e5 -1.1277e5 1.1317e5 -1.0437e5

ax -3.7324e3 -0.8221e4 -1.0256e4 1.0563e4 -1.1131e4

ay -4.5609e3 -1.7727e4 -1.7373e4 1.3765e4 -1.4904e4

Concept 7

(Tapered Round)

Force -38516 5465 -9970.9 -7010.4 -33483

Ang. vel 94.0764 171.3582 179.4734 -178.8459 170.4340

Ang. acc -3.3323e4 -1.1027e5 -1.1291e5 1.1317e5 -1.0437e5

ax -3.7747e3 -0.8361e4 -1.0399e4 1.0706e4 -1.1264e4

ay -4.5497e3 -1.7690e4 -1.7332e4 1.3805e4 -1.4867e4

Concept 14

(Tapered)

Force -38515 5465 -9970.9 -7010.5 -33482

Ang. vel 94.0764 171.3582 179.4734 -178.8459 170.4340

Ang. acc -3.3323e4 -1.1027e5 -1.1277e5 1.1317e5 -1.0437e5

ax -3.6754e3 -0.8033e4 -1.0063e4 1.0369e4 -1.0953e4

ay -4.5761e3 -1.7777e4 -1.7428e4 1.371e4 -1.4953e4

Original

Force -38515 5451 -9970.9 -7014 -33470

Ang. vel 94.0764 171.3582 179.4734 -178.8459 170.4340

Ang. acc -3.3323e4 -1.1027e5 -1.1291e5 1.1317e5 -1.0437e5

ax -3.7516e3 -0.8285e4 -1.0321e4 1.0628e4 -1.1191e4

ay -4.5559e3 -1.771e4 -1.7354e4 1.3783e4 -1.4887e4

46

C Stress data from FEA

1 2 3 4 5 6

Concept 1

(Plus)

(X: -53,27,

Y: 10,43, Z: 0)

(X: -42,36,

Y: 3,93, Z: 5,4)

(X: -42,36,

Y: 3,93, Z: -5,33)

(X: -90,92,

Y: 8,81, Z: 0)

(X: -118,58,

Y: 8,12, Z: 2,61)

(X: -111,74,

Y: 3,09, Z: 6,47)

Max Comp. -306,6 -314,4 -312 -302,6 -311,3 -294,7

Max Tensile -43,91 -8,72 29,52 -52,12 -7,453 31,37

Max ang. vel. -164,8 -122,6 -92,71 -176 -132,3 -86,85

Max ang. acc. -166,4 -130,5 -92,9 -176 -132,4 -86,68

Max ax -337,7 -310,5 -282 -345,7 -314,2 -267,4

Concept 2

(Tapered + H)

(X: -42,3,

Y: 6,1, Z: 0)

(X: -38,89,

Y: -0,51, Z: 4)

(X: -39,47,

Y: 3,2, Z: 6,5)

(X: -116,38,

Y: 0,35, Z: 4,07 )

(X: -115,94,

Y: 5,89, Z: 8,44)(X: , Y: , Z: )

Max Comp. -409,9 -407,9 -353,7 -313,3 -328,7 -

Max Tensile -42,04 13,81 -30,7 44,4 31,31 -

Max ang. vel. -205,3 -141,8 -152,2 -78,4 -10,1 -

Max ang. acc. 46,59 -22,58 27,6 -56,87 -36,72 -

Max ax -436,5 -362,8 -366,9 -261,5 -299,8 -

Concept 4

(H Beam + Tapered)

(X: -55,15,

Y: 10,18, Z: 4,78)

(X: -31,50,

Y: 3,48, Z: 2,02)

(X: -48,59,

Y: 6,72, Z: 2,07)

(X: -55,11,

Y: 3,17, Z: 2)

(X: -119,65,

Y: 7,05, Z: 6,44)

(X: -53,87,

Y: -10,31, Z: 3,17)

Max Comp. -286,9 -332 -311,7 -289,7 -292,2 -257,5

Max Tensile -13,66 -2,587 -2,611 11,26 2,277 44,72

Max ang. vel. -128,5 -118,2 -126,4 97,48 -96,54 -45,92

Max ang. acc. 12,34 -12,26 -3,265 -19,8 -26,5 -71,71

Max ax -288,5 -312,5 -306,3 -277,3 -272,4 -203,3

Concept 5

(Hole)

(X: -111,91,

Y: -2,5, Z: -3,2)

(X: -111,9,

Y: 2,5, Z: 3,11)

(X: -119,99,

Y: -7,84, Z: -6,42)

(X: -119,98,

Y: 7,86, Z: 6,42)

(X: -32,38,

Y:-8, Z: 3,19)

(X: -32,33,

Y: 8, Z: 3,17)

Max Comp. -375,2 -366,9 -355,7 -342,7 -362,7 -364,2

Max Tensile 78,71 5,277 46,6 30,54 -33,18 78,57

Max ang. vel. -61,23 -164,5 -80,01 -10,33 -180,5 -75,86

Max ang. acc. -112,6 -4,527 -89,73 -23,47 15,43 -98,78

Max ax -273,9 -410,3 -290,9 -325,1 -407,8 -240,9

Concept 7

(Tapered Round)

(X: -78,

Y: 7,14, Z: 3,6)

(X: -82,85,

Y: 9,1, Z: -3,63)

(X: -120,

Y: 5,76, Z: -6,2)

(X: 120,

Y: 5,29, Z: 6,27)(X: , Y: , Z: ) (X: , Y: , Z: )

Max Comp. -308 -324,3 -274,6 -253,5 - -

Max Tensile -2,898 -45 2,64 24,59 - -

Max ang. vel. -130,5 -176,3 103,4 -76,68 - -

Max ang. acc. 26,12 51,33 -5,195 -29,81 - -

Max ax -310,2 -355,8 -241,7 -231 - -

Concept 14

(Tapered)

(X: -49,88,

Y: 5,33, Z: -3,36)

(X: -46,78,

Y: 5,5, Z: -7,05)

(X: -28,7,

Y: 0,24, Z: -6,44)

(X: -47,03,

Y: -5,45, Z: -3,46)(X: , Y: , Z: ) (X: , Y: , Z: )

Max Comp. -303,3 -307,1 -247,2 -258 - -

Max Tensile -59,58 -47,16 29,3 97,23 - -

Max ang. vel. -185,1 -179,1 -67,36 -7,5 - -

Max ang. acc. 58,5 68,03 -39,29 -132,4 -

Max ax -350,6 -342,5 -218,8 -161,1 - -

Original(X: -115,87,

Y: 0,875, Z: -1,42)

(X: -116,38,

Y: 0, Z: 1,45)

(X: -122,14,

Y: 8,78, Z: -3,17)

(X: -91,39,

Y: 8,79, Z: -6,3)

(X: -91,39,

Y: -8,76, Z: -3,24)(X: , Y: , Z: )

Max Comp. -405,4 -394,3 -330,3 -350 -323,3 -

Max Tensile 38,12 49,27 12,34 -27,24 70,18 -

Max ang. vel. -123,7 -89,64 -107,8 -168,7 -55,93 -

Max ang. acc. -50,71 -64,3 -18,52 26,91 -92,89 -

Max ax -365,9 -344,5 -310,8 -370,5 -261,6 -

The following figures shows where on the concepts the stress were measured.

47

Original

48

Concept 1 (Plus)

49

Concept 2 (Tapered + I)

50

Concept 4 (I Beam + Tapered)

51

Concept 5 (Hole)

52

Concept 7 (Tapered Round)

53

Concept 14 (Tapered)

54

D Concepts

Rejected Concepts

55

E Critical points in Haigh-diagram

Original

58

Concept 1

59

Concept 2

60

Concept 4

61

Concept 5

62

Concept 7

63

Concept 14

64

Evaluation of Different Concepts for Pressed and Sintered ...

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