the load carrying unit of articulated haulers - analysis...

The load carrying unit of articulated haulers -

Analysis of the welded connections

Växjö June 2009

Thesis no: TD 068/2009

Nermin Dzanic

Martin Lindholm

Metin Uçar

School of Technology and Design

School of Technology and Design, TD

II

Organisation/ Organization Författare/Author(s)

School of Technology and Design Nermin Dzanic, Martin Lindholm and Metin Uçar

Dokumenttyp/Type of document Handledare/tutor Examinator/examiner

Master Thesis Torbjörn Ekevid Anders Karlsson

Titel och undertitel/Title and subtitle

The load carrying unit of articulated haulers - Analysis of the welded connections

Sammanfattning (på svenska)

Detta examensarbete handlar om finita element analys av svetsade förband i korgen på Volvo dumpern A40E. Det genomfördes i samarbete med Volvo CE i Braås. Uppgiften var att ge företaget en lämplig lösning för att minska mängden svetsskarvar på den främre delen av lastenheten. För att uppnå detta har en rad analyser genomförts med hjälp av CATIA och ANSYS på både de befintliga och de justerade (potentiella ersättare) svetsade förbanden. Analyserna visar att utmatningshållfastheten av svetsade förband huvudsakligen beror på inbränningsdjupet. Med andra ord, förstärka svetsförband genom större inbränning är mer fördelaktigt än att använda mer svets på utsidan. Slutsatsen blev att både produktionstid och kostnad kan minskas genom justering av de svetsade förbanden. Eftersom svetsförband på lastenheten är sammankopplade bör mer omfattande studier som inkluderar alla svetsar genomföras för att uppskatta effekterna av liknande justeringar.

Nyckelord

Svetsade förband, svets, notch metoden, dumper, utmattning, Catia, Ansys, Volvo CE, Finita element metoden,

FEM, huvudspänning, 3-D modell, sub-model, mesh, simulering, analys, A40E

Abstract (in English)

The work presented in this master thesis is about the finite element analysis of the welded connections in load carrying unit of the articulated hauler, Volvo A40E. It was performed in cooperation with Volvo CE in Braås. The task was to provide the company with an appropriate solution to reduce the amount of weld used on the front part of the load carrying unit. To accomplish this, a series of analyses utilising CATIA and ANSYS was performed on both existing and adjusted (potential replacement) welded connections. The analyses brought to light the fact that the fatigue resistance of welded connections significantly depends on the penetration depth. In other words, reinforcing the welded connections by deeper penetration is more beneficial than providing support from outside through thicker weld. It was concluded that applying adjusted welds lessens both the production time and cost. Nevertheless, since the welds on the load carrying unit are correlated; more extensive studies covering all welds should be carried out to estimate the impacts of similar replacements.

Key Words

Welded connections, weld, notch method, articulated hauler, fatigue, Catia, Ansys, Volvo CE, Finite element

method, FEM, principal stress, 3-D model, sub-model, mesh, simulation, analysis, A40E

Utgivningsår/Year of issue Språk/Language Antal sidor/Number of pages

2009 English 75

Internet/WWW

III

Abstract

The work presented in this master thesis is about the finite element analysis of the welded

connections in load carrying unit of the articulated hauler, Volvo A40E. It was performed

in cooperation with Volvo CE in Braås.

The task was to provide the company with an appropriate solution to reduce the amount

of weld used on the front part of the load carrying unit. To accomplish this, a series of

analyses utilising CATIA and ANSYS was performed on both existing and adjusted

welded connections

The analyses indicate the fact that the fatigue resistance of welded connections

significantly depends on the penetration depth. In other words, reinforcing the welded

connections by deeper penetration is more beneficial than providing support from outside

through thicker weld.

It was concluded that applying adjusted welds lessens both the production time and cost.

Nevertheless, since the welds on the load carrying unit influence each other; more

extensive studies covering all welds should be carried out to estimate the impacts of

similar replacements.

IV

Preface

The work presented in this master thesis concerns finite element analyses of the welded

connections in load carrying unit of the articulated hauler, Volvo A40E. It was performed

in cooperation with Volvo CE, at the Department of Mechanical Engineering at The

School of Technology and Design, Växjö University, between April and June 2009.

We would like to express our sincere thanks to our supervisor Prof. Torbjörn Ekevid,

Volvo CE and Växjö University, for initiating and excellently supervising the work. We

would also like to thank the engineers and managers at Volvo CE for assisting us

throughout the work.

Finally, thanks to Volvo CE for making possible to perform such an extensive work.

Växjö, June 2009

V

Table of contents

Abstract ............................................................................................................................ III

Preface .............................................................................................................................. IV

Table of contents ............................................................................................................... V

List of figures ................................................................................................................ VIII

List of tables..................................................................................................................... IX

1. Introduction ............................................................................................................ 1

1.1. Background .......................................................................................................................... 1

1.2. Problem formulation ........................................................................................................... 1

1.3. Purpose and aim .................................................................................................................. 2

1.4. The outlines of the thesis ..................................................................................................... 2

1.5. Hypothesis ............................................................................................................................ 3

1.6. Limitations ........................................................................................................................... 3

1.7. Company presentation ........................................................................................................ 3

1.7.1. Volvo group ................................................................................................................. 3

1.7.2. Volvo CE Braås ............................................................................................................ 4

1.7.3. Volvo CE Braås history ................................................................................................ 4

1.8. Articulated haulers A40E ................................................................................................... 5

2. The welding process ............................................................................................... 6

2.1. Welding ................................................................................................................................ 6

2.2. Robot welding ...................................................................................................................... 7

2.3. Robot arc welding ................................................................................................................ 8

2.4. Weld dimensioning ............................................................................................................ 10

3. Fatigue calculations ............................................................................................. 12

3.1. Stress components ............................................................................................................. 12

VI

3.2. Principal stress - eigenvalue approach ............................................................................ 13

3.3. Fatigue ................................................................................................................................ 14

3.4. Fatigue damage .................................................................................................................. 17

3.5. Effective notch stress ......................................................................................................... 18

4. Finite element method ......................................................................................... 20

4.1. One-dimensional analysis ................................................................................................. 21

4.2. Three-dimensional stress analysis .................................................................................... 24

5. Software ................................................................................................................ 27

5.1. ANSYS ................................................................................................................................ 27

5.2. CATIA ................................................................................................................................ 28

6. Method .................................................................................................................. 29

6.1. Preparing the 3-D models ................................................................................................. 30

6.2. Setting up the model for analysis in ANSYS ................................................................... 33

7. Results ................................................................................................................... 38

7.1. Existing welds .................................................................................................................... 41

7.2. Adjusted welds ................................................................................................................... 44

8. Analysis of the results .......................................................................................... 47

9. Discussion and conclusions ................................................................................. 50

10. Further studies ..................................................................................................... 51

11. References ............................................................................................................. 52

11.1. Books ......................................................................................................................... 52

11.2. Articles and theses .................................................................................................... 53

11.3. Electronic sources ..................................................................................................... 53

11.4. Company related sources ......................................................................................... 54

11.5. Pictures ...................................................................................................................... 55

VII

12. Bibliography ......................................................................................................... 56

Appendices Number of pages Appendix A ..................................................................................................................................... 1

Appendix B ..................................................................................................................................... 1

Appendix C ..................................................................................................................................... 2

Appendix D ..................................................................................................................................... 3

Appendix E ..................................................................................................................................... 4

Appendix F ...................................................................................................................................... 1

Appendix G ..................................................................................................................................... 1

Appendix H ..................................................................................................................................... 6

VIII

List of figures

Figure 1: Articulated Hauler A40 ........................................................................................ 5

Figure 2: Fully automate mechanized programmable tools ................................................. 8

Figure 3: Welding torch ....................................................................................................... 9

Figure 4: Wire feeder ........................................................................................................... 9

Figure 5: Weld, a- and s-measure ...................................................................................... 10

Figure 6: Weld, a- and i-measure ....................................................................................... 10

Figure 7: Weld affected area .............................................................................................. 11

Figure 8: Stress element for three-dimensional and two-dimensional (planar) case, ........ 12

Figure 9: Normal stress 𝜎𝜎𝜎𝜎 and shear stress 𝜏𝜏𝜎𝜎 ............................................................... 13

Figure 10: Example of S-N curve ...................................................................................... 15

Figure 11: Stress notations ................................................................................................. 16

Figure 12: Applying the radius of 1 mm on the weld root and weld toe ........................... 19

Figure 13: Continuous domain (left) and group of sub-domains (right) ........................... 21

Figure 14: An axially loaded member ............................................................................... 22

Figure 15: A portion of the member with the length of dx and its axial forces ................. 22

Figure 16 : A tetrahedral element in space defined by x, y, and z coordinates. ................ 24

Figure 17: Flowchart of the structural analysis by ANSYS .............................................. 28

Figure 18: Existing (left) and adjusted (right) welds ......................................................... 29

Figure 19: The gaps between the plates ............................................................................. 30

Figure 20: Closing the gaps by extending the plates ......................................................... 31

Figure 21: Connected plates, welds, notches, and radii ..................................................... 32

Figure 22: Weld specifications .......................................................................................... 32

Figure 23: Sliced basket for z direction ............................................................................. 33

Figure 24: Sliced load for z direction ................................................................................ 34

Figure 25: Sliced load and basket for z direction .............................................................. 35

Figure 26: Boundary conditions: flexible and cylindrical supports ................................... 36

Figure 27: The sub-model for z direction .......................................................................... 37

Figure 28: The highest maximum principal stress concentration areas ............................. 38

IX

Figure 29: The hotspot for acceleration in z ...................................................................... 41

Figure 30: The hotspot for acceleration in y ...................................................................... 42

Figure 31: The hotspot for acceleration in x ...................................................................... 43

Figure 32: The hotspot for acceleration in z ...................................................................... 44

Figure 33: The hotspot for acceleration in y ...................................................................... 45

Figure 34: The hotspot for acceleration in x ...................................................................... 46

Figure 35: An example of existing welds indicating the penetration depth ...................... 48

Figure 36: An example of adjusted welds indicating the penetration depth ...................... 48

List of tables

Table 1: The absolute values of maximum and minimum principal stress ....................... 41

Table 2: The damages ........................................................................................................ 48

Table 3: The comparison of existing and adjusted welds .................................................. 50

Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar Page 1 of 56

1. Introduction

This early section of the thesis work intends to provide a sound base for readers. The rationale

behind this study, the formulation of the problem, purpose and aim, and a brief description of

the company where the study was performed are presented.

1.1. Background

The heavy vehicle industry has been a rapidly growing industry for decades. This growth has

been achieved by continuous improvements in terms of products and services provided by

companies. Volvo Construction Equipment (CE) is one of the major companies in this field

and has made extensive contributions to this growth. Regardless of being the market leader,

Volvo CE continually makes investment in development activities in order to assure that its

products have the edge over its rivals. In addition to this, it aims to make sure of contentment

of its customers in all aspects, and reduce the expenditures of development, production,

maintenance etc.

This thesis work is a part of these development activities. It comprehensively covers

production and related phases suchlike development. The major effort will be put on a number

of particular welded connections, which are located on the front part of the load carrying unit.

1.2. Problem formulation

Volvo CE in Braås develops and manufactures heavy off road vehicles used to transport large

volumes of material in terrain difficult to enter. One of their main products is Volvo

articulated hauler A40E. Since the products constantly need to be improved due to both high

competitions in the market and customer contentment, the company requests help for

conducting analyses on the both existing and adjusted (potential replacement) welded

connections of the load carrying unit, i.e. basket. The outcomes of these analyses aim at

guiding the company to choose the best type of welded connections. The task is to provide

the company with an appropriate solution to reduce the amount of weld used to connect the

metal sheets that form the basket.


1.3. Purpose and aim

The main purpose of this thesis work is to separately analyse existing and adjusted welded

connections and then compare the outcome of both cases. This comparison is intended for

guiding the design team to determine how appropriate and beneficial the adjusted welded

connections will be. The primary objective is to strive for a proper solution and thus minimise

the amount of weld used to connect basket components, and in that sense decrease cost and

time required to produce a basket in a way that is applicable in production. Furthermore, the

design of a weld should be taken into consideration to retain or even improve the fatigue

properties. The results of this work might provide Volvo CE engineers innovative ideas to

apply and/or further examine this matter.

1.4. The outlines of the thesis

The primary aim of this study is to make practical and effective use of the theoretical

knowledge of the thesis team in a skilful manner for the intention of surmounting a real-life

problem. Particularly, to comprehend the industrial implementations of the Finite Element

Method, FEM, on solid mechanics problems using advanced modelling and Finite Element

Analysis, FEA, software suchlike CATIA and ANSYS, respectively, is of importance.

Furthermore, observing the possible impacts of altering partly or entirely design and

production activities on the life-cycle phases and total cost of the product in question, and

certainly on the company’s objectives, is of interest.

The potential forecasted results are as following: significant reduction in the amount of

welding material required for production of the basket, and consequently enabling the

company to reduce production costs and time required for production activities.


1.5. Hypothesis

The thesis team anticipates that the problem with applied welding, more specifically overuse

of material used for welding, occurs due to the lack of analysis of load types occurring on the

basket, which leads to an excessively high estimation of requisite weld and consequently

welding material to put the basket together.

1.6. Limitations

In order to prevent the thesis to exceed the extent that it will be greater than a master thesis

covering 15 ECTS, a number of limitations were set up. Only welded connections in the front

part of the basket of the articulated hauler A40E will be examined. Likewise, no changing will

be made to the overall design of the basket. In addition to these limitations, the welding

method will not be altered from the method that Volvo CE utilises in the basket today.

1.7. Company presentation

1.7.1. Volvo group

Volvo was officially founded on 14 April 1927 when the first series-manufactured car was

produced in Gothenburg, Sweden, by Assar Gabrielsson and Gustaf Larson. Since then

company expanded into other business areas, today known as the Volvo Group. Other areas

beside Volvo cars are Volvo Trucks, Buses, Construction Equipment, Penta, Aero and

Financial Services. Already from the beginning focus was on safety, which is even today one

of the most important mark in company’s product development. Through the years,

competitors have come and gone, but Volvo Group has developed from a local industrial

company to one of the largest manufacturers. The company have more than 100 000

employees (2007) and production facilities in 19 countries with different kind of operations in

180 countries. Most employees are working in France, Japan, USA, Brazil, South Korea and

Sweden. During 2007 company’s net sales was 285 billion SEK. The Volvo Group vision is

“to be valued as the world’s leading supplier of commercial transport solutions” (Volvo

Group, 2009), (Steen, et al, 2008)


1.7.2. Volvo CE Braås

Volvo CE in Braås develops and manufactures heavy off road vehicles used to transport large

volumes of material in terrain difficult to enter. The headquarters of Volvo articulated hauler

is in Braås, Sweden where assembly and manufacturing of different components are done.

The production factory in Braås has about 900 employees (2008).

The E series of Volvo articulated haulers was introduced to the market in 2007 proving their

excellence everywhere, with Volvos mission statement “We use our expertise to create

transport-related hardware and software products of superior quality, safety and

environmental care for demanding customers in selected industries” (Volvo 2009a). E series

consisting of four models (A25E, A30E, A35E and A40E) all produced in Braås. 50

articulated haulers were produced per week during 2005, and an increase in volume of 86%

was achieved during period 2001-2007. With 34% of market share Volvo CE Braås holds

market leading position (Steen et al, 2008).

1.7.3. Volvo CE Braås history

Everything started at the end of the 1950’s when the engineering company Livab in Braås

(since 1974 articulated hauler entity) began experimenting in combining driven hauler trailers

and tractors. With some problems in tractors manoeuvrability, principally with tractor’s front

wheels easily sliding in snow, the company started to develop tractor without front wheels,

with articulated steering and drive on the wheels of the load unit.

In 1966, the company presented DR631, the first and unique series-manufactured articulated

hauler with all-wheel drive that could be used in tough and difficult conditions. Since

introduction this type of machine revolutionized mass transport operation, and in the 1980’s

this type of machine had market share of over 50%. By constantly developing and introducing

larger load capacities, six-wheel drive and other innovations Volvo articulated hauler became

world market leader. Today one of Volvo CE’s star products is the articulated hauler. (Volvo

Group, 2009).


1.8. Articulated haulers A40E

Volvo has been leading the development of articulated haulers since they first introduced the

concept of haulers in the sixties. Articulated haulers are constructed to transport rocks and

ground material in extreme conditions; this is done by means of the rotating hitch and the

frame steering, which makes the tractor and the trailer able to move independently.

The A40E is roughly 11 meters long and have a width and height of approximately 3.5

meters. An A40E has a load capacity of 39000 kg, and volume capacity of 24.0 m3 heaped.

Rising of the body takes 12 seconds when it is fully loaded and 10 seconds to lower the body.

This is done with two powerful double-acting, single-stage hoist cylinders. The specifications

of Articulated Haulers A40E in detail are presented in appendix A. (Volvo Group, 2009)

Figure 1: Articulated Hauler A40E (Volvo Group, 2009)


2. The welding process

2.1. Welding

Welding is a joining process that connects two work-pieces, with or without added material.

The process is performed by a local heating of the parent material to its fusion temperature,

either by local yielding or atomic diffusion (Weman, 2002).

One of the first welding processes was forge welding, which has been used for centuries.

During the late 1880’s and 1890’s and until today many modern welding methods were

developed such as manual metal arc welding, MMA, metal inert/active gas welding,

MIG/MAG, including continuous wire as electrode and inert/active gas to protect the weld,

submerged arc welding, flux-cored welding (electrode including powder fill material), electro

slag welding, tungsten inert gas welding, TIG, and more modern laser and electron beam

welding. As research and development of welding methods continue, the welding robots,

mechanized programmable tools that are completely automate are becoming more and more

common (Avesta welding, 2005).

Different methods and energy sources are used for welding, such as gas welding, electrical arc

welding, pressure welding consisting of friction, ultrasound, high frequency, resistance

welding etc. Some other types of welding methods are laser welding and electron beam

welding (Weman, 2002). Welding can be performed in many different environments, and is

today most common in industrial processes. It can be very dangerous if not required

precautions are taken. Some of damages that might appear are poisonous, burns, fires,

electrical shocks, overexposure to ultraviolet light, eye damage, skin damages, heat radiations

and other type of damages.

Preventive measures at the working place to observe are as followings; working place shall be

ventilated, work piece shall have effective lagging, person that perform welding shall not take

uncomfortable working posture nor use heavy equipment, etc. (Esab, 2009).


2.2. Robot welding

In industry, welding is the most efficient and economical way to join materials. To further

decrease cost and increase efficiency, fully automate mechanized programmable tools so

called robots were introduced, see figure 2. Robot welding is mainly used in the processes

where repetitive tasks on similar pieces are common, where the welds in more than one axis

are involved and where pieces difficult to access are present. Automating procedure would be

difficult or impossible to implement if welded joints are too wide or in different position, or

they need adjustment to fit together.

In recent decades, automating a welding process has been rapidly improved, in comparison to

manual welding by increasing the speed and quality. Once a welding robot is programmed

correctly top-notch welds are easily repeatable, hence it performs precisely the same weld

each time on the work pieces with same specifications and dimensions. A fully equipped and

optimized robot can work continuously for 24 hours a day 365 days a year without need for

any breaks. One of the big advantages is safer workplace, reducing the risk of damages by

moving operator away from unhealthy and hazardous environment. Some other important

benefits worth mentioning are greater cycle speed, precision, productivity and increase in

return on investment. (Robots, 2009 and Robot-welding, 2009)

There are two popular types of industrial welding robots; articulating and rectilinear.

Rectilinear robots are moving linearly using any of three axes x, y, and z, with wrist allowing

rotational movements. Working zone of a rectilinear robot is box shaped. On the other hand

articulated robots use arms and rotating joints, with moves similar to those of a human arm,

using rotating wrist integrated at the end. Working zone of an articulating robot is irregularly

shaped. These robot types like others need on a regular basis recalibration or reprogramming

to work properly. In order to set up a robot welding facility numerous of factors are taken into

consideration. Some of these being reliability, number of axes, maintenance, seam tracking

systems, controls, weld monitors, arc weld equipment, part transfer, fixtures etc. (Weld-

engineer, 2009)


Figure 2: Fully automate mechanized programmable tools (Robot-Welding, 2009)

2.3. Robot arc welding

One of the most popular automated welding processes is the gas metal arc welding (GMAW),

more known by its subtypes as metal inert gas (MIG) and metal active gas (MAG).

Comparing to the manual, automatic arc welding involves high duty cycles and requires

equipment to operate in those conditions. Equipment components must have necessary

controls and features to interface with main control system. Also special power source is

required to perform an arc weld, where it must deliver controllable voltage and current

normally between 10 to 35 V and 5 to 500 A. Automating arc processes utilizes more

complex power source, the welding machine communicates electronically with power source

to control the welding power program for the most optimal performance.

All arc welding processes,, regardless of being automatic or manual, use torch see figure 3 to

transmit current to the electrode, where the torch also works as a shield to the weld area from

surrounding atmosphere. In robot arc welding automatic torch cleaner is used to remove the

spatter. Torch nozzle placed close to the arc gradually picks up the spatter. One of the

available systems is to spray an antispatter agent into the nozzle of the gun. There are

different types of welding torches, and choice depends on welding process, process variation,

current, electrode size and shield medium. Torches can also differ in the way they are cooled,

where water and air cooling are the most common.


Figure 3: Welding torch, (Robot-Welding, 2009)

For adding filler material during robot welding so called wire feeders are used, see figure 4.

They provide continuous electrode wire into the arc. Normally the wire feeder is mounted on

the robot arm. A control interface is needed between robot controller, the power supply and

wire feeder.

Figure 4: Wire feeder, (Alabama Laser, 2009)

To guarantee that the tip and the tool frame are accurately known with respect to each other,

the calibration process of tool centre point (TCP) is important. In robot arc welding, end of

arm sensing is used to detect the position of the seam on the work piece with respect to the

robot tool frame. Profile data analysis gives the qualified position of the seam to the sensor

reference frame. "If the sensor reference frame pose is known with respect to the end-frame of

the robot, and the tool frame pose is known with respect to the end-frame, then the sensor data

may be used to accurately position the tool centre point (TCP) with respect to the work

piece". (Robot welding, 2009)


2.4. Weld dimensioning

Figure 5 and 6 below show some general weld notation.

Figure 5: Weld, a- and s-measure (Volvo weld standard booklet, October, 2008)

Figure 6: Weld, a- and i-measure (Volvo weld standard booklet, October, 2008)

In fillet welds a-measure stands for the height of the largest isosceles triangle, between the

weld face and the fusion faces. s-measure represents the distance between the surfaces of the

part to the bottom of the penetration, and is also known as weld depth. It is the minimum

transmitting part of the weld, and cannot be greater than the thickness of the thinnest part. i-

measure stands for the minimum penetration in the gap from the surface of the parent metal.

Figure 7 shows how the work pieces change during welding process, (Volvo weld standard

booklet, October 2008).


Figure 7: Weld affected area (Volvo weld standard booklet, October, 2008)


3. Fatigue calculations

3.1. Stress components

Figure 8: Stress element for three-dimensional and two-dimensional (planar) case, (Marghitu, 2001, p.121)

For the general three-dimensional stress element three positive normal stresses σx, σy and σz,

and six (acting in the positive direction of the reference axis) shear stresses τxy, τyx, τyz, τzy, τzx

and τxz are represented in figure 8. For the static equilibrium to be fulfilled following equation

is required.

,yxxy ττ = ,zyyz ττ = xzzx ττ = (3.1)

For the general two-dimensional stress element, figure 8 illustrates normal stresses σx and σy

as a positive oriented, while τyx is positive and τxy negative oriented.


3.2. Principal stress - eigenvalue approach

A traction vector t is related to a surface vector with outer normal vector n such that

nSt T= (3.2)

where

=

=

z

y

x

zzzyzx

yzyyyx

xzxyxx

nnn

and nSσσσσσσσσσ

(3.3)

When the traction vector t is divided into a component parallel to n and a component in a

perpendicular direction, the normal stress, σn, and the shear stress, τn, are obtained. That is:

σnntn TTnjijiiin ornntn ==== σσσ (3.4)

and

σnmtm TTnjijiiin ornmtm ==== τστ (3.5)

Figure 9: Normal stress 𝜎𝜎𝜎𝜎 and shear stress 𝜏𝜏𝜎𝜎 , (Ottosen & Ristinmaa, 2005, p. 55)

Eq. (3.4) and (3.5) gives a physical understanding of the eigenvalue problem of the stress

tension. When solving this problem the stress invariants are obtained. If the coordinate system

is chosen by a special method, a particular simple form of the stress tension is obtained.


This happens when the traction vector t is collinear with the unit vector n (see figure 9), i.e.

the direction of n should be chosen so that:

ii nt λ= (3.6)

where λ is some factor, which with Eq. (3.4) hint that λ= σn. In this situations are ni and mi

orthogonal which leads to that the shear stress τn=0. Combining Cauchy’s formula, see Eq.

(3.7), and Eq. (3.6) results in Eq. (3.8).

𝑡𝑡𝑖𝑖 = 𝜎𝜎𝑖𝑖𝑖𝑖 𝜎𝜎𝑖𝑖 𝑜𝑜𝑜𝑜 𝑡𝑡 = 𝜎𝜎𝜎𝜎 (3.7)

0)(0)( =−=− nIσ λλδσ orn jijij (3.8)

With this and the characteristic equation:

0)det( =− Iσ λ (3.9)

the three principal stresses can be obtained, i.e. σ1=λ1, σ2=λ2 and σ3=λ3. The corresponding

principal direction can be provided by Eq. (3.8).

When the coordinate system is selected collinear whit the principal directions n1, n2 and

n3,the stress tensor will take the form provided by Eq. (3.10).

[ ]321

3

2

1

000000

' nnnAAAσ =

== TT where

σσ

σσ (3.10)

The theory of this chapter was gathered from (Ottosen & Ristinmaa, 2005, p. 53-56).

3.3. Fatigue

When a material/component is exposed to repeated load cycles, it may break down even

though the stress limit has not been reached. Mattson (2005, p. 3) states that metal fatigue is a

process which gradually cases damages to a material component subjected to repeated

loading.


After a number of cycles a small crack may occur in the material, this crack may then

propagate until it reaches a point where the structure will not be able to carry the load and a

failure due to fatigue will arise. Zahavi and Torbilo (1996, p. 183) declare that it is primary

the surface layer conditions that are responsive for a fatigue failure. The reason is the fact that

the most loads will be in this location, besides the surface layers are also exposed to

environmental effects. Furthermore, Gustafsson and Saarinen (2007, p. 2-5) claim that the

crack will arise in areas with high stress concentrations: these areas can be a change in the

geometry, a weld, etc. There are five major causes that may lead to a crack in a weld or in the

Heat Affected Zone, HAZ, which are undercuts, incomplete penetration, lack of fusion,

porosity and start & stop of weld.

Dahlberg and Ekberg (2002, p. 190) point out that August Wöhler carried out a search on this

matter in the middle of the 19th century. He constructed a machine where a rotated load could

carefully be controlled on various materials; subsequently he plotted the stress attribute as a

function of the number of cycles. Worth mentioning is that when this curve is plotted in a log-

log scale, a curve with straight lines will arise. The resulting plot is a, so called, S-N curve or

Wöhler curve. In this curve(s), it is clear that the higher stress yields lower number of cycles

before failure due to fatigue. During his experiments he also concluded that it is better to use

the stress range, i.e. )( minmax σσ − , in fatigue calculations, rather than maximum stress.

Figure 10: Example of S-N curve (msm, 2009)


The endurance limit, or Sn, shown in figure 10 is the limit when the material can withstand

"unlimited" number of cycles; this limit is usually between 106 and 107 cycles. However not

all materials have this clear endurance limit as shown above, e.g. aluminium (Juvinalland

Marshek, 2000, p 304-309).

In most real life situations are the stresses not completely reversed, they are instead a mixture

of reversed and static stress. See figure 11 below.

Figure 11: Stress notations (Maintenance world, 2009)

where

σmax:: maximum stress

σmin: minimum stress

σa = (σmax-σmin)/2

σm = (σmax+σmin)/2

Δσ = (σmax+σmin)

R= σmin/σmax

When σm = 0 are the stresses completely reversed, and can therefore withstand the number of

cycles that correspond to Sn. Another case might be, as in figure 11, that σm>0, which means

that the specimen is exposed to tensile mean stress and results into the requirement that the

fluctuating stress must be less than Sn for "infinite life".


3.4. Fatigue damage

The stress amplitude is in the most practical cases not constant, instead they vary during a

products life time. These variations are in numerous textbooks referred to as spectrum

loading. This fact makes the direct utilization of an S-N curve, which are designed for

constant stress amplitude, unsuitable in most occasions. Instead another theory is introduced

for this kind of loading, fatigue damage. This idea take care of the total number of cycles and

the number of cycles at a certain stress amplitude, i.e. the damage at each stress amplitude are

summarize to obtain the fatigue damage for a potential failure.

Cumulative damage

As mentioned earlier, an S-N curve shows how many cycles (Ni) that are needed for a failure

due to fatigue for certain stress amplitude (Si). A smaller amount of cycles (ni), i.e. ni<Ni, will

then cause less damage, damage fraction, (di). For a failure due to fatigue to occur the sum of

all damage fractions must be greater or equal to one, see Eq. (3.11).

1... 1321 ≥++++ −idddd (3.11)

One theory for predicting the damages are the Palmgren-Miner theory that was introduced in

1924, and then further developed in 1945. This theory suggests that the damage fraction is

linear proportional to the actual number of cycles and the number of cycles needed for

generating a fatigue failure at a specific stress level, see Eq. (3.12).

∑= Nn

d i (3.12)

Combining Eq. (3.11) and (3.12) gives that failure will occur when:

∑ ≥ 1i

i

Nn

(3.13)

The theory of this chapter was gathered from Collins (1993, p 255-259).


With:

m

CNσ∆

= (3.14)

Leads to:

)log(log1)log( NCm

−=∆σ (3.15)

This after some manipulation and simplification gives following formula for the value of the

damage for the construction to withstand fatigue loading:

∑ ∑ <

∆∆

≈= 1m

allow

i

Nn

dσσ (3.16)

3.5. Effective notch stress

In welded joints, the fatigue crack initiation is expected at the notch, i.e. either the weld root

or the weld toe. The total stress at the notch is effective notch stress, ENS, which is attained

by considering linear-elastic material behaviour. An effective contour is employed instead of

the real weld contour so that the non-linear material behaviour at the notch root, and statistical

nature and scatter of weld shape parameters can be taken into account.

The ENS method is applied to welded joints which might fail from the weld root or weld toe.

The effective notch stresses can be obtained by finite element or boundary models, and

compared with a common S-N curve for carrying out fatigue assessment. To acquire accurate

results for structural steels, an effective notch root radius of r = 1 mm is recommended. The

method can also be implemented to aluminium structures.

There are some certain restrictions of the method. For instance, the stress components should

not be parallel to the weld or to the root gap, and the wall thickness should not be smaller than

5 mm (t > 5 mm). In addition, the method is not capable of handling low fatigue cycle.

Therefore, there should be more than 105 cycles (N>105).


The tip of the introduced effective notch radius touches the root of the real notch. An

example, applying 1 mm of notch radius on the weld root and weld toe, is illustrated in figure

12.

Figure 12: Applying the radius of 1 mm on the weld root and weld toe (Hobbacher, 1996, p. 29)

The method can handle advanced weld geometries and unusual welded joints. Therefore, it is

a powerful method. The theory of this chapter was gathered from (Hobbacher, 1996, p. 28-

29).


4. Finite element method

Engineering studies on physical phenomena cope with formulating physical processes,

establishing mathematical models and performing numerical analyses of mathematical

models. The mathematical formulation of physical phenomena brings forward mathematical

statements suchlike differential equations, which are of importance due to the fact that by

means of these equations physical processes and models can be comprehended. In traditional

variational methods, derivation of approximation functions is carried out with respect to the

entire region. Significant drawbacks for engineering applications can occur on account of the

fact that considering entire region may lead to inaccurate results. Therefore, a new method,

the FEM that offers approximation to the exact solution, has been developed to assist

engineers whilst seeking solutions to problems.

The FEM, unlike traditional variational methods, implements a methodical approach that

considers sub-domains instead of entire domain. The increase of computer power in recent

decades has made possible to carry out complex computations with ease, and hence greatly

contributed to the enlargement of the method. The entire method is characterised by three

basic steps:

1. A continuous geometrically complex domain is represented as a group of sub-

domains, so-called finite elements. Each element is considered as an independent

domain, and has a simple geometrical shape.

2. By utilising the concept of continuous functions that can be represented by a linear set

of algebraic polynomials, approximation functions are derived over each element.

3. In the final stage, governing equations are fulfilled over each element and then an

appropriate method is employed to establish relations among elements. Thereupon, all

sub-domains are located in the global domain, and mathematical relations among

coefficient suchlike nodal values are established.

The difference between continuous domain and sub-domains is illustrated in figure 13.


Figure 13: Continuous domain (left) and group of sub-domains (right)

The theory of this chapter was gathered from (Reddy, 1993, p. 3-16) and (Martinussen, 2007,

p. 17-18).

4.1. One-dimensional analysis

The equations regulating the motion of structural elements (i.e. bars, beams, and plates) could

be constituted by considering the energy principle. In addition to this, Newton’s second law

and an element of the member with its forces could be considered to establish the governing

equations. Nevertheless, the energy principle is more appropriate for finite element modelling.

Here, the principle of virtual displacements, which is an application of Newton’s second law

and the energy principle, is employed to exemplify the procedure of the FEM for solid

mechanics applications.

First, one can consider an axially loaded bar with the length of L and the cross-sectional area

of A. The material properties of bar are independent of its position, which means that the

material of the body is homogeneous. The cross-section of the bar could be either constant or

vary along length dimension of the bar. In such case, the axial stress in the member of the bar

would be uniform. Here, the only stress component, which is nonzero, is 𝜎𝜎𝑥𝑥 = 𝜎𝜎𝑥𝑥(𝑥𝑥, 𝑡𝑡).


dx

f

x

Figure 14: An axially loaded member, (Reddy, 1993, p.124)

dx

Figure 15: A portion of the member with the length of dx and its axial forces, (Reddy, 1993, p.124)

Considering dynamic equilibrium, it is concluded that

𝜕𝜕𝜎𝜎𝑥𝑥𝜕𝜕𝑥𝑥

+ 𝑓𝑓𝑥𝑥 = 𝜌𝜌𝜕𝜕2𝑢𝑢𝜕𝜕𝑡𝑡2 (4.1)

where the cross-sectional properties of the member are not present. In order to establish the

governing equations for case at hand, all the forces along the x axis should be summed

according to Newton’s second law:

�𝐹𝐹𝑥𝑥 = 𝑚𝑚𝑚𝑚 (4.2)

which leads to

𝐴𝐴𝜎𝜎𝑥𝑥 (𝜎𝜎𝑥𝑥 + 𝑑𝑑𝜎𝜎𝑥𝑥)(𝐴𝐴 + 𝑑𝑑𝐴𝐴)


−𝜎𝜎𝑥𝑥𝐴𝐴 + (𝜎𝜎𝑥𝑥 + 𝑑𝑑𝜎𝜎𝑥𝑥)(𝐴𝐴 + 𝑑𝑑𝐴𝐴) + 𝑓𝑓𝑑𝑑𝑥𝑥 = 𝜌𝜌[𝐴𝐴 + (𝐴𝐴 + 𝑑𝑑𝐴𝐴)]𝑑𝑑𝑥𝑥2𝜕𝜕2𝑢𝑢𝜕𝜕𝑡𝑡2 (4.3)

If the terms of Eq. (4.3) are divided by dx, and taking the limit of dx→0, the algebraic

expression in Eq. (4.4) is obtained.

𝜕𝜕𝜕𝜕𝑥𝑥

(𝜎𝜎𝑥𝑥𝐴𝐴) + 𝑓𝑓 = 𝜌𝜌𝐴𝐴𝜕𝜕2𝑢𝑢𝜕𝜕𝑡𝑡2 (4.4)

where the body for per unit length is denoted by f.

The typical stress-strain relation is given as

𝜀𝜀𝑥𝑥 =𝜎𝜎𝑥𝑥𝐸𝐸

(4.5)

where E denotes the modulus of elasticity. The normal strain in the direction of x is defined

by 𝜀𝜀𝑥𝑥 .

𝜎𝜎𝑥𝑥 = 𝐸𝐸𝜀𝜀𝑥𝑥 = 𝐸𝐸𝜕𝜕𝑢𝑢𝜕𝜕𝑥𝑥

(4.6)

Substituting the terms in Eq. (4.6) into Eq. (4.4) results in

𝜌𝜌𝐴𝐴𝜕𝜕2𝑢𝑢𝜕𝜕𝑡𝑡2 −

𝜕𝜕𝜕𝜕𝑥𝑥 �

𝐸𝐸𝐴𝐴𝜕𝜕𝑢𝑢𝜕𝜕𝑥𝑥�

= 𝑓𝑓(𝑥𝑥, 𝑡𝑡) (4.7)

One can rearrange this algebraic equation into Eq. (4.8) for static problems

−𝑑𝑑𝑑𝑑𝑥𝑥 �

𝐸𝐸𝐴𝐴𝜕𝜕𝑢𝑢𝜕𝜕𝑥𝑥�

= 𝑓𝑓(𝑥𝑥) (4.8)

which could be employed for determining the displacement u(x). Reddy (1993, p. 125) states

that Eq. (4.8) is derived under the assumption that all material points on the line x=constant

move by the same distance u(x). Thus, it can b e concluded that the stress concentration is

uniform at any cross-section.

The theory of this chapter was gathered from (Reddy, 1993, p. 123-125)


4.2. Three-dimensional stress analysis

The general finite element procedure can be applied to three-dimensional stress analysis

problems. In fact, three-dimensional problems clearly represent all the practical cases.

Therefore, it is of importance to study this matter.

Triangle is employed as the continuum element for two-dimensional problems. However, in

three-dimensional problems, tetrahedron with four nodes is employed. Since tetrahedron

elements are utilised to represent three-dimensional problems, the total number of equations

required to solve problems can be large. Thereof, one can make use of magnitude of the

problems to overcome this difficulty. Figure 16 below illustrates a tetrahedral element i, j, m,

p.

Figure 16 : A tetrahedral element in space defined by x, y, and z coordinates (Zienkiewicz & Taylor, 2000, p. 128).

The displacement of any point on tetrahedral element can be defined by displacement

components u, v, and w.

𝐮𝐮 = �𝑢𝑢𝑣𝑣𝑤𝑤� (4.10)

In the light of the facts that a linear variation of a quantity can be defined by four nodal

values, and displacement values at the nodes can be equated, one can obtain four equations in

the form of,


𝑢𝑢𝑖𝑖 = 𝛼𝛼1 + 𝛼𝛼2𝑥𝑥𝑖𝑖 + 𝛼𝛼3𝑦𝑦𝑖𝑖 + 𝛼𝛼4𝑧𝑧𝑖𝑖 , 𝑒𝑒𝑡𝑡𝑒𝑒. (4.11)

The values of 𝛼𝛼1,𝛼𝛼2,𝛼𝛼3 and 𝛼𝛼4 can then be evaluated in terms of nodal displacements

𝑢𝑢𝑖𝑖 ,𝑢𝑢𝑖𝑖 ,𝑢𝑢𝑚𝑚 and 𝑢𝑢𝑝𝑝 .

𝑢𝑢 =1

6𝑉𝑉�(𝑚𝑚𝑖𝑖 + 𝑏𝑏𝑖𝑖𝑥𝑥 + 𝑒𝑒𝑖𝑖𝑦𝑦 + 𝑑𝑑𝑖𝑖𝑧𝑧)𝑢𝑢𝑖𝑖 + �𝑚𝑚𝑖𝑖 + 𝑏𝑏𝑖𝑖 𝑥𝑥 + 𝑒𝑒𝑖𝑖 𝑦𝑦 + 𝑑𝑑𝑖𝑖 𝑧𝑧�𝑢𝑢𝑖𝑖 +�

�(𝑚𝑚𝑚𝑚 + 𝑏𝑏𝑚𝑚𝑥𝑥 + 𝑒𝑒𝑚𝑚𝑦𝑦 + 𝑑𝑑𝑚𝑚𝑧𝑧)𝑢𝑢𝑚𝑚 + �𝑚𝑚𝑝𝑝 + 𝑏𝑏𝑝𝑝𝑥𝑥 + 𝑒𝑒𝑝𝑝𝑦𝑦 + 𝑑𝑑𝑝𝑝𝑧𝑧�𝑢𝑢𝑝𝑝� (4.12)

The volume 𝑉𝑉 of tetrahedron can now be acquired by rearranging Eq. (4.12), as stated below:

6𝑉𝑉 = 𝑑𝑑𝑒𝑒𝑡𝑡 ��

1 𝑥𝑥𝑖𝑖1 𝑥𝑥𝑖𝑖

𝑦𝑦𝑖𝑖 𝑧𝑧𝑖𝑖𝑦𝑦𝑖𝑖 𝑧𝑧𝑖𝑖

1 𝑥𝑥𝑚𝑚1 𝑥𝑥𝑝𝑝

𝑦𝑦𝑚𝑚 𝑧𝑧𝑚𝑚𝑦𝑦𝑝𝑝 𝑧𝑧𝑝𝑝

�� (4.13)

The displacement components, 𝑚𝑚𝑖𝑖 ,𝑚𝑚𝑖𝑖 ,𝑚𝑚𝑚𝑚 and 𝑚𝑚𝑝𝑝 , constituting the displacement vector 𝑚𝑚𝑒𝑒 , can

be determined with expanding relevant determinants into their cofactors. As each of the

components consists of 3 components, there are thus 12 displacement components defining

the element displacement.

𝑚𝑚𝑒𝑒 = �

𝑚𝑚𝑖𝑖𝑚𝑚𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚𝑝𝑝

� where 𝑚𝑚𝑖𝑖 = �𝑢𝑢𝑖𝑖𝑣𝑣𝑖𝑖𝑤𝑤𝑖𝑖� etc. (4.14)

Consequently, the displacements of an arbitrary point and the shape functions can be

expressed as in Eq. (4.15) and Eq. (4.16), respectively:

𝒖𝒖 = �𝑰𝑰𝑁𝑁𝑖𝑖 , 𝑰𝑰𝑁𝑁𝑖𝑖 , 𝑰𝑰𝑁𝑁𝑚𝑚 , 𝑰𝑰𝑁𝑁𝑝𝑝�𝒂𝒂𝑒𝑒 = 𝑵𝑵𝒂𝒂𝑒𝑒 (4.15)

𝑁𝑁𝑖𝑖 =𝑚𝑚𝑖𝑖 + 𝑏𝑏𝑖𝑖𝑥𝑥 + 𝑒𝑒𝑖𝑖𝑦𝑦 + 𝑑𝑑𝑖𝑖𝑧𝑧

6𝑉𝑉 (4.16)

where I is a 3x3 identity matrix.


The total strain of a point in three-dimensional analysis can be determined in matrix form by 6

components,

𝜀𝜀 =

⎩⎪⎨

⎪⎧𝜀𝜀𝑥𝑥𝜀𝜀𝑦𝑦𝜀𝜀𝑧𝑧𝛾𝛾𝑥𝑥𝛾𝛾𝑦𝑦𝛾𝛾𝑧𝑧⎭⎪⎬

⎪⎫

(4.17)

By taking account of Eq. (4.12) and Eq. (15), one can attain the relation below,

𝜀𝜀 = 𝑆𝑆𝑁𝑁𝑚𝑚𝑒𝑒 = 𝐵𝐵𝑚𝑚𝑒𝑒 = �𝐵𝐵𝑖𝑖 ,𝐵𝐵𝑖𝑖 ,𝐵𝐵𝑚𝑚 ,𝐵𝐵𝑝𝑝�𝑚𝑚𝑒𝑒 (4.18)

where 𝑆𝑆 is a linear operator. The strain displacement matrix 𝐵𝐵 has 4 components 𝐵𝐵𝑖𝑖 ,𝐵𝐵𝑖𝑖 ,𝐵𝐵𝑚𝑚 ,

and 𝐵𝐵𝑝𝑝 .

The relation between stresses 𝝈𝝈 and strains 𝜀𝜀 can be established by the elasticity matrix 𝐷𝐷 in

the form of,

𝝈𝝈 =

⎩⎪⎨

⎪⎧𝜎𝜎𝑥𝑥𝜎𝜎𝑦𝑦𝜎𝜎𝑧𝑧𝜏𝜏𝑥𝑥𝑦𝑦𝜏𝜏𝑦𝑦𝑧𝑧𝜏𝜏𝑧𝑧𝑥𝑥 ⎭

⎪⎬

⎪⎫

= 𝐷𝐷 (𝜀𝜀 − 𝜀𝜀0) + 𝜎𝜎0 (4.19)

in which, 𝜀𝜀0 and 𝜎𝜎0 stand for initial strains and initial residual stresses, respectively. Here, the

elasticity matrix can be written in the matrix form considering modulus of elasticity 𝐸𝐸 and

Poisson’s ratio 𝑣𝑣, which are material properties. The theory of this chapter was gathered from

(Zienkiewicz & Taylor, 2000, p. 127-132).


5. Software

5.1. ANSYS

ANSYS is a comprehensive general-purpose finite element modelling software utilised to

numerically solve various problems of mechanical engineering. ANSYS is capable of

performing static, dynamic, structural (linear and nonlinear), heat transfer, fluid flow,

electromagnetism, and acoustic analyses (Moaveni, 1999).

There exist two different methods to use ANSYS. These are Graphical User Interface, GUI,

and command files. Occasionally, both methods can be cooperatively used. The GUI method

is more conventional and assists users to perform analyses by means of windows and toolbars,

whereas the second method is advantageous in terms of easy model modifications and

minimal file space requirements (Nakasone, Yoshimoto, & Stolarski, 2006).

As in the FEA, the analysis is in general done in three consecutive stages, pre-processing,

solution, and post-processing. In the course of first stage, the problem is defined, material and

geometric properties are assigned, and, if required, mesh is generated. Loads (point or

pressure) and constraints (translational and rotational) are specified, and then set of equations

are solved in the second stage. In the final, further processing, stage, nodal displacements, and

element forces and moments can be viewed (Nakasone, Yoshimoto, & Stolarski, 2006).

Figure 17 demonstrates the flow of activities of structural analysis by ANSYS.


Figure 17: Flowchart of the structural analysis by ANSYS (Nakasone, Yoshimoto, & Stolarski, 2006, p.54)

5.2. CATIA

CATIA is a shortening for Computer-Aided Three-dimensional Interactive Application. It is a

3-D modelling software that is used in various industries, (e.g. automotive and industrial

equipment, architecture and construction) all over the world.

CATIA is the flagship of the company Dassault Systèmes, which have been a pioneer in this

area since the company started in 1981. In order to be able to distribute the software

worldwide, they started a partnership with IBM same year as the company where founded.

When CATIA first where developed the founders used technology that was intended for

animated 3D movies, and applied this technology to CAD systems for manufacturing

industries. This first version have since then been improved over the years. Dassault Systèmes

have in total over 100’000 customers in 80 countries. (3DS 2009a and 3DS 2009b)

END

Graphical display of results

Solution

Input boundary conditions

FE discretization of area

Input material constants

Create area

START


6. Method

As pointed out above, the purpose of this study is to examine existing weld connections, and

propose adjusted connections which are smaller in size and have deeper penetration, and then

make comparison between them. The part examined is the front part of the load carrying unit.

To fulfil this purpose, first of all the 3-D model of the load carrying unit was built up. A set of

analysis in ANSYS was then performed to obtain required stress results of the existing welds.

Once the results were obtained, numerous adjustments on the welds (according to the data

from production department at the company, see Table 3 in chapter 8) were done so that the

corresponding analyses could be carried out.

Since the load carrying unit is symmetric, it is enough to study only one half of the body. In

figure 18, the right half demonstrates the a- and s-measures of existing and adjusted welds.

The welds of interest are numbered in figure 18. The other welds are included, because they

are in contact with the welds studied.

Figure 18: Existing (left) and adjusted (right) welds


6.1. Preparing the 3-D models

The 3-D model of the load carrying unit of the articulated hauler at hand consists of a set of

sheet metal plates with different geometry. These metal plates were located in the correct

position in the global xyz coordinate system. Nevertheless, most of the plates were not in

contact. In order to set up the model for analyses, a solid model of the load carrying unit were

required. Here, it should be noted that since the actual dimensions of the load carrying unit are

fairly big, sample 3-D models below are employed to simplify the setup method of the model.

Figure 19 provides a sample 3-D model to demonstrate the gaps between the plates.

Figure 19: The gaps between the plates (Volvo CE Calculation Models Booklet, 2007)

Through the use of 3-D modelling software CATIA, the gaps between plates were closed by

means of extending them. The holes in the plates, which are utilised to assist positioning of

the plates during production, were also filled. Figure 20 exemplifies how a 3-D model can

look like after the gaps are filled.


Figure 20: Closing the gaps by extending the plates (Volvo CE Calculation Models Booklet, 2007)

In reality, the plates are connected by welds with different shapes and sizes. These welds were

also included in the 3-D model. Afterwards, in order to accurately simulate the stress

distribution in welds, the notch method was introduced. This method is principally based on

removing material between welded plates. To ease the stress concentrations in the weld,

radiuses are applied on the weld toes and roots. Figure 21 illustrates a 3-D model representing

connected plates, welds, notches, and radii. The dimensions of material to be removed depend

on the weld specifications suchlike a-, s-, and i-measures. Weld specifications and radii are

illustrated in figure 22.


Figure 21: Connected plates, welds, notches, and radii (Volvo CE Calculation Models Booklet, 2007)

Figure 22: Weld specifications (Volvo CE Calculation Models Booklet, 2007)

As stated earlier, the illustrated examples above provide means for comprehending the

preparation steps of the load carrying unit. The 3-D model of this study is presented in

appendix B.


Since the existing and adjusted welds were examined and compared throughout this study,

two corresponding 3-D models of the load carrying unit were prepared. In the 3-D model for

adjusted welds, only the welds and notches of interest were modified.

6.2. Setting up the model for analysis in ANSYS

After completing the steps above, the 3-D models were ready for analyses in ANSYS. There

are several steps forming the FEA. Firstly, the mesh was generated to confirm that the global

model of the load carrying unit was correctly built, see appendix C. Next, three global

analysis models were created in order to perform computations in x, y, and z directions,

separately. The reason for creating three individual analysis models is to consider only one

load case at a time. Because, if all load cases are considered together, there might be

interference between different load cases, which might lead to inappropriate results.

Each model was sliced into smaller pieces so that local models, so-called sub-models, could

be built. Sliced basket for z direction is presented in figure 23 whereas corresponding x and y

can be found in appendix D.

Figure 23: Sliced basket for z direction


There are numerous ways of applying load on the basket in ANSYS. Some of them are as

following: applying pressure on a certain area, using densities to imitate load or combination

of these two. In this study, the density approach is utilised because it is simpler to accomplish

in ANSYS.

In order to establish load cases for each model, corresponding densities were calculated. The

3-D model representing the load was created with the aim of calculating the density. Load

model was then sliced into smaller pieces, local load models, using the same pattern as for the

load carrying unit. By slicing the load, weight of each piece could be calculated. The weight

of the load pieces with the same density were added to the corresponding local models of the

load carrying unit with the density of structural steel, see appendix E. Figure 24 demonstrates

sliced load for z direction whereas appendix D shows for x and y directions.

Figure 24: Sliced load for z direction


With the resulting weights and volumes for each piece of the load carrying unit,

corresponding densities were calculated. The resulting densities were then introduced in

ANSYS assuring that maximum assumed loads were applied on each sliced part of the load

carrying unit. The sliced load carrying unit and load together for z direction are presented in

figure 25. The other directions can be found in appendix D.

Figure 25: Sliced load and basket for z direction

In the following step, various constraints were applied. Load carrying unit was located on the

frame with flexible supports. The front part of the basket was supported by four springs with

stiffness of 190 kN/mm each, while only one spring with stiffness of 2,6 MN/mm supporting

the rear part, see figure 26.


Figure 26: Boundary conditions: flexible and cylindrical supports

In order to attain different load cases, acceleration of 1,3 g, 1,8 g, and 2,8 g were uniformly

applied on the whole body for x, y, and z directions, respectively. These are experimental

values and were provided by the development department at the company. After that the

analysis was performed to obtain results for maximum and minimum principal stresses. To

acquire more accurate results in the area of interest, denser mesh were required. Since the size

of load carrying unit is fairly big, generating a fine mesh is not possible due to the fact that

today’s computers are not powerful enough. To overcome this dilemma, sub-models were

utilised to ease generating denser mesh. Each sub-model was isolated with the impacts from

global model maintained. There are three sub-models for established load cases. The sub-

model for z direction is presented in figure 27. For other two sub-models, see appendix F.

Cylindrical

support (peg)

Flexible

support in y

direction,

k=190

Flexible supports in z

direction, k=190 kN/mm

Flexible support in z

direction, k=2,6 MN/mm


Figure 27: The sub-model for z direction

The denser mesh had the element size of 0,8 mm for weld toe and root whereas the element

size for the rest of the sub-model was 30 mm. The analysis was then performed to locate

stress concentration areas, so-called hotspots. Once these hotspots were located, the mesh was

refined in order to perform further inspections for more accurate values in these areas. Here,

element size was 0,25 mm, see appendix G

Since there were two cases, existing and adjusted welds, to be analysed and their results were

to be compared, the procedure presented in this chapter was performed for each individual

case.


7. Results

A careful examination of maximum absolute values of principal stresses of both the existing

and adjusted welded connections indicates that there is a similarity between the areas

subjected to high stress concentration.

The areas of highest stress concentrations are pointed out in figure 28. In the case of existing

welded connections, the highest stress concentration areas were on the weld roots. One of

them was in Area 1 when acceleration of 1,8 g was applied in y direction. The other two were

captured in Area 2 when acceleration of 1,3 g and 2,8 g were applied in x and z direction,

respectively.

Carrying out the same analyses for the adjusted welded connections reveals that the pattern of

high stress concentration areas was the same, see figure 28. The weld roots in Area 1 and

Area 2 were the most affected areas in the case of acceleration in y and z direction. However,

for the acceleration in x direction, the most affected area was on the weld toe in Area 2.

Figure 28: The highest maximum principal stress concentration areas

Area 1

The hotspots

B and E

Area 2

The hotspots A,

C, D, and F


As pointed out in chapter 6.2, first the stress concentration areas were located and then the

mesh was refined in these areas to obtain more accurate results. In this chapter all results

obtained during simulations are presented. Further discussion about the results can be found

in chapter 8.

Table 1 shows the maximum and minimum principal stress values for each point of interest

and the damage values calculated for these points. The damage was calculated by the

following formula.

∑ ++=

∆∆

= zyx

m

allow

ddddσσ (7.1)

where m is 3 for welds representing the slope of Wöhler curve. The maximum allowable

stress is 368 MPa for welds and represented by allowσ .


Existing welded connections Adjusted welded connections

The principal stress values

in the acceleration of Z direction (MPa)


in the acceleration of Z direction (MPa)

A

Minimum Maximum

D

Minimum Maximum

Z-direction 138 18 Z-direction 109 23

Y-direction 8 133 Y-direction 1 120

X-direction 156 5 X-direction 152 10

Damage d = 0,176 Damage d = 0,131


in the acceleration of Y direction (MPa)


in the acceleration of Y direction (MPa)

B

Minimum Maximum

E

Minimum Maximum






in the acceleration of X direction (MPa)


in the acceleration of X direction (MPa)

C

Minimum Maximum

F

Minimum Maximum





Table 1: The absolute values of maximum and minimum principal stress


7.1. Existing welds

The hotspot A

The maximum absolute value of the principal stress for acceleration in z direction was 138

MPa (see figure 29), whereas the following results for x and y directions in the same point

were 156 MPa and 133 MPa, respectively. See appendix H for other figures.

Figure 29: The hotspot for acceleration in z


The hotspot B

The maximum absolute value of the principal stress for acceleration in y direction was 191

MPa (see figure 30), whereas the following results for x and z directions in the same point


Figure 30: The hotspot for acceleration in y


The hotspot C

The maximum absolute value of the principal stress for acceleration in x direction was 210

MPa (see figure 31), whereas the following results for y and z directions in the same point


Figure 31: The hotspot for acceleration in x


7.2. Adjusted welds

The hotspot D

The maximum absolute value of the principal stress for acceleration in z direction was 109

MPa (see figure 32), whereas the following results for x and y directions in the same point


Figure 32: The hotspot for acceleration in z


The hotspot E

The maximum absolute value of the principal stress for acceleration in y direction was 160

MPa (see figure 33), whereas the following results for x and z directions in the same point


Figure 33: The hotspot for acceleration in y


The hotspot F

The maximum absolute value of the principal stress for acceleration in x direction was 213

MPa (see figure 34), whereas the following results for y and z directions in the same point


Figure 34: The hotspot for acceleration in x


8. Analysis of the results

Once the hotspot for acceleration in a particular direction, for instance x direction, was

captured, the same point was examined in the other two directions to determine the principal

stress values that are to be employed in damage calculations. The underlying reason behind

taking into account the same point in the other two directions is to assure that the impact of

the individual load cases on the same point is considered. The same procedure was repeated

for all directions.

The maximum absolute values of principal stresses obtained by the procedure explained

above were utilised for damage calculations. Consequently, the three damage values for each

case were obtained, see table 2.

Existing Adjusted

z 0,176 0,131

y 0,166 0,093

x 0,256 0,273

Table 2: The damages

For the welded connections at hand, the damage values should be lower than one for the

structure to withstand the fatigue loading. As seen in table 2, the damage values satisfy this

criterion. The damage values for adjusted welded connections are even smaller compared to

the existing ones. It should be noted that the damage in the direction of x for adjusted welded

connections is bigger than existing one. This is because even though highest stress

concentration area, Area 2 as pointed out in figure 28 was the same for both cases; the weld

toe was affected for the adjusted welded connections while the weld root was affected in

existing case.

These results suggest that the penetration depth plays a crucial role in making welded

structures stronger against fatigue loading. It can be concluded that supporting welded

connections from inside, i.e. penetration, rather than outside leads to better fatigue resistance.

Figure 35 and 36 illustrate the difference between penetration depths of existing and adjusted

welds.


Weld

Notch

Radius

s6 = 6mm

a5 = 5mms6a5 means 1 mm of

penetration (i1)

Penetration i1

Figure 35: An example of existing welds indicating the penetration depth

Weld

Radius

s5 = 5mm

a3 = 3mm

s5a3 means 2 mm of penetration (i2)

i2NotchPenetration

Figure 36: An example of adjusted welds indicating the penetration depth


As the damage results indicate, it is possible to replace the existing welds with the adjusted

ones with respect to fatigue. Table 3 represents a comparison between the existing and

adjusted welds in terms of time. By implementing the improved welds, in total 1,09 minutes

of operational time for welding can be saved per unit.

Existing Welds Adjusted Welds

Weld

position

Length

(m)

Weld

specification

Welding time

(min.)

Weld

specification

Welding time

(min.)

Time Saved

(min)

1 0,5 s6a5 0,9 s5a3 0,67 0,23

2 0,5 s6a5 0,9 s5a3 0,67 0,23

3 1,25 s6a5 2,3 s6a3 1,67 0,63

Total 1,09

Table 3: The comparison of existing and adjusted welds

The welding operation of the front part costs 1242 SEK per hour. With reduction of 1,09

minutes, approximately the cost of 23 SEK per unit can be saved.


9. Discussion and conclusions

This thesis work was initially limited to analyse the welds in the front part of the load carrying

unit. Nevertheless, as the work progressed, it was discovered that carrying out required

analyses for every weld would exceed the time set for the work, approximately ten weeks.

Therefore, the focus was put upon only three particular welds instead. Since the analysis

procedure applied can be implemented on other welds, the created 3-D models, and the

analysis routine developed in ANYS can be used as a base and modified for analysing the

other welds in the load carrying unit.

As it was predicted earlier, the overuse of welding material occurs due to the excessive

estimation of the forces that the load carrying unit are subjected to. This conclusion can easily

be drawn, if the outcome of the analyses of existing and adjusted welds is compared. In detail,

there were mainly two areas where the highest fatigue damage occurs. However, detailed

inspections of these areas indicate that the damage potential is much smaller than the

requirement, d<1. This was the case for both the existing and adjusted welds. Besides,

evaluating the fatigue damages of both cases reveals that implementing adjusted welds would

not cause any problem with respect to fatigue, see table 2.

Applying the adjusted welds in production results in 1,09 minutes of time reduction, which

leads to 23 SEK decrease in cost per unit. Though these outcomes may seem insignificant,

their significance of these numbers would be obvious if long term and large production

volumes are considered.


10. Further studies

In this thesis work only one part of the load carrying unit was examined, which is the result of

lack of time to perform a more extensive research. To get a better understanding how the

welds in the basket are subjected to fatigue, more studies should be done covering all of them.

To be able to make the changes on the welds in the load carrying unit, more load cases should

be established, covering most of the situations that may arise in reality. This would assure that

the basket would withstand the employment over its entire lifetime.


11. References

11.1. Books

Zahavi, Eliahu & Torbilo, Vladimir. 1996. Fatigue Design – Life Expectancy of Machine

parts. USA. CRC Press

Dahlberg, Tore & Ekberg, Anders. 2002. Failure Fracture Fatigue – An Introduction.

Lund. Studentlitteratur

Juvinall, Robert C. & Marshek, Kurt M. 2000. Fundamentals of Machine Component

Design. John Wiley & Sons, USA

Moaveni, Saeed .1999. Finite Element Analysis-Theory and Application with ANSYS.

Prentice-Hall

Nakasone, Y., Yoshimoto, S., & Stolarski, T. 2006. Engineering Analysis with ANSYS

Software. Elsevier Butterworth-Heinemann

Reddy, J. N. 1993. An Introduction to the Finite Element Method. McGraw-Hill

Zienkiewicz, O. C., & Taylor, R. L. 2000. The Finite Element Method (5th Edition upp1.,

Vol.I: The Basis). Butterworth-Heinemann

Weman, Klas. 2002. Karlebo-Svetshandbok. Liber.

Engfeldt, Jan. 2005. Avesta Welding Manual.Avesta

Marghitu, Dan B. 2001. Mechanical Engineer's Handbook. Academic Press Series in

Engineering. San Diego, CA: Academic Press. Department of Mechanical Engineering,

Auburn University, Auburn Alabama


Collins, Jack A. 1993. Failure of Materials In Mechanical Design – Analysis, prediction,

prevention. Canada. JohnWiley & Sons, Second Edition

Hobbacher, A. 1996. Fatigue Design of Welded Joints and Components:

Recommendations of IIW Joint Working Group XIII-XV. Woodhead Publishing

Ottosen, Niels Saabye & Ristinmaa, Matti. 2005. The Mechanics of Constitutive

Modelling. (1st Edition). Elsevier. Division of Solid Mechanics. Lund University

11.2. Articles and theses

Steen, J. & Bartsch, S. 2008. Master thesis, School of Management and Economics, Växjö

University -Internal Material Handling At Volvo Construction Equipment Braås.

Mattson, Henrik. 2005. Evaluation of Fatigue Procedures for Welds and Rotating axes.

Luleå

Gustafsson, Johannes & Saarinen, Juha. 2007. Multi-axial fatigue in welded details – An

investigation of existing design approach. Göteborg

Martinussen, M. 2007. Numerical Modelling and Model Reduction of Heat Flow in

Robotic Welding. Norwegian University of Science and Technology – Department of

Engineering Cybernetics. Trondheim. Norway

11.3. Electronic sources

Volvo Group 2009

http://www.volvogroup.com (accessed on 2009.03.07)

Volvo 2009a

http://www.volvo.com/group/global/en-gb/volvo+group/mission_vision/our_mission.htm

(accessed on 2009.03.07)

http://www.volvogroup.com/�

http://www.volvo.com/group/global/en-gb/volvo+group/mission_vision/our_mission.htm�


Volvo 2009b http://www.volvo.com/constructionequipment/global/engb/AboutUs/history/history+track

/1966/introduction.htm (accessed on 2009.03.07)

Volvo 2009c

http://www.volvo.com/constructionequipment/global/engb/products/articulatedhaulers/intr

oduction.htm (accessed on 2009.03.07)

Volvo 2009d

http://volvo.com/dealers/sv-se/Swecon/products/articulatedhaulers/A40E/introduction.htm

(accessed on 2009.03.07)

Esab 2009

www.esab.se (accessed on 09.03.05)

3DS 2009a

http://www.3ds.com/fileadmin/PRODUCTS/CATIA/PDF/CATIAbd.pdf

(Accessed on 09.05.28)

3DS 2009b

http://www.3ds.com/se/plm-glossary/(Accessed on 09.05.28)

Robots 2009

www.robots.com (Accessed on 09.05.24)

Robot-welding 2009

www.robot-welding.com, 2009 (Accessed on 09.05.24)

Weld-engineer 2009

www.weldengineer.com, 2009 (Accessed on 09.05.24)

11.4. Company related sources

Volvo weld standard booklet, October, 2008

http://www.volvo.com/constructionequipment/global/engb/AboutUs/history/history+track/1966/introduction.htm�

http://www.volvo.com/constructionequipment/global/engb/AboutUs/history/history+track/1966/introduction.htm�

http://www.volvo.com/constructionequipment/global/engb/products/articulatedhaulers/introduction.htm�

http://www.volvo.com/constructionequipment/global/engb/products/articulatedhaulers/introduction.htm�

http://volvo.com/dealers/sv-se/Swecon/products/articulatedhaulers/A40E/introduction.htm�

http://www.esab.se/�

http://www.3ds.com/fileadmin/PRODUCTS/CATIA/PDF/CATIAbd.pdf�

http://www.3ds.com/se/plm-glossary/�

http://www.robots.com/�

http://www.robot-welding.com/�

http://www.weldengineer.com/�


11.5. Pictures

Figure 1: http://www.volvogroup.com (accessed on 2009.03.06)

Figure 2 & 3: www.robot-welding.com, 2009 (Accessed on 09.05.24)

Figure 4: www.alspi.com/wirefeed.htm (accessed on 09.05.24)

Figure 5-7: Volvo weld standard booklet, October, 2008

Figure 8: Marghitu, Dan B. 2001. Mechanical Engineer's Handbook. Academic Press

Figure 9: Ottosen, Niels Saabye & Ristinmaa, Matti. 2005. The Mechanics of Constitutive

Modelling. (1st Edition). Elsevier. Division of Solid Mechanics. Lund University

Figure 10: http://www.msm.cam.ac.uk/phasetrans/2006/SI/8.jpg (accessed on 2009.05.29)

Figure 11: http://www.maintenanceworld.com/Articles/material-engineering/Fatigue-

Failures/stress.jpg (accessed on 2009.05.29)

Figure 12: Hobbacher, A. 1996. Fatigue Design of Welded Joints and Components:

Recommendations of IIW Joint Working Group XIII-XV. Woodhead Publishing

Figure 14 & 15: Reddy, J. N. 1993. An Introduction to the Finite Element Method.

McGraw-Hill

Figure 16: Zienkiewicz, O. C., & Taylor, R. L. 200. The Finite Element Method (5th

Edition. Vol.I: The Basis). Butterworth-Heinemann

Figure 17: Nakasone, Y., Yoshimoto, S., & Stolarski, T. 2006. Engineering Analysis with

ANSYS Software. Elsevier Butterworth-Heinemann

http://www.robot-welding.com/�


Figure 19-22: Volvo CE Calculation Models Booklet, 2007

12. Bibliography

Rao, Singiresu S. 1999. The Finite Element Method in Engineering. Butterworth-

Heinemann

Ellyin, Fernand. 1997. Fatigue Damage, Crack Growth and Life Prediction.

Chapman&Hall

Cook, Robert D. 1995. Finite Element Modelling for Stress Analysis. John Wiley&Sons

Martinsson, Johan. 2005. Fatigue Assessment of Complex Welded Steel Structures. Royal

Institute of Technology-Department Aeronautical and Vehicle Engineering

Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar A1

Appendix A

Figure A.1: Volvo articulated hauler A40E specifications (Volvo, 2009d)

Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar B1

Appendix B

Figure B.1: The 3-D model of the load carrying unit

Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar C1

Appendix C

Figure C.1: Generated mesh for load case z

Figure C.2: Generated mesh for load case y

Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar C2

Figure C.3: Generated mesh for load case x

Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar D1

Appendix D Sliced basket

Figure D.1: Sliced basket in x direction

Figure D.2: Sliced basket in y direction


Sliced load

Figure D.3: Sliced load for x direction

Figure D.4: Sliced load for y direction


Sliced basket and load

Figure D.5: Sliced basket and load for x direction

Figure D.6: Sliced basket and load for y direction

Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar E1

Appendix E Since the left and right parts of the basket are symmetric, only one half was used during

analysis and calculations. Therefore the max basket load and the volume were divided by two.

Max basket load: m=39000/2=19500 kg

Basket volume: V=18,85/2=9,425 m3

Load density: 33 /2069

425,919500 mkg

mkg

volumemass

==

=ϕ

Load case 1: Z-direction

Sliced load parts: L [kg] Load density: φ=2069 kg/m3

L11 96,76 L21 299,31 L31 520,37

L12 965,54 L22 3384 L32 7232,8

L13 311,46 L23 1090,8 L33 2115,7

L14 374,4 L24 1183,1 L34 1923,9

Sliced basket parts (steel): B1 [kg] Steel density: φ=7850 kg/m3

B111 87,67 B121 84,42 B131 176,17

B112 443,15 B122 210,22 B132 365,62

B113 147,85 B123 69,6 B133 197,29

B114 243,39 B124 119,35 B134 241,83

Adding load L to corresponding B1 resulting in B2 [kg]

B211 184,44 B221 383,73 B231 696,54

B212 1408,69 B222 3594,22 B232 7598,42

B213 459,31 B223 1160,4 B233 2312,99

B214 617,79 B224 1302,45 B234 2165,73

Sliced basket parts volume: B3 [m3]

B311 1,12E-02 B321 1,08E-02 B331 2,24E-02

B312 5,65E-02 B322 2,68E-02 B332 4,66E-02

B313 1,88E-02 B323 8,87E-03 B333 2,51E-02

B314 3,10E-02 B324 1,52E-02 B334 3,08E-02


New densities computed for each sliced part of the basket representing different materials.

Computed densities are to be used during analysis in ANSYS.

43

23 B

BB

mkg

volumemass

==

=ϕ

B411 1,12E-02 B421 1,08E-02 B431 2,24E-02

B412 5,65E-02 B422 2,68E-02 B432 4,66E-02

B413 1,88E-02 B423 8,87E-03 B433 2,51E-02

B414 3,10E-02 B424 1,52E-02 B434 3,08E-02

Load case 2: Y-direction


L11 214,16 L21 296,63 L31 354,94 L41 50,71

L12 1979,4 L22 3071,9 L32 4776,4 L42 1754,7

L13 611,44 L23 979,36 L33 1534 L43 393,18

L14 697,93 L24 1165,9 L34 1489,2 L44 128,44

Sliced basket parts (steel): C1 [kg] Steel density: φ=7850 kg/m3

C111 111,43 C121 72,22 C131 97,39 C141 67,22

C112 399,12 C122 119,73 C132 180,05 C142 319,2

C113 132,55 C123 38,62 C133 77,7 C143 165,86

C114 189,72 C124 110 C134 209,89 C144 94,94

Adding load L to corresponding C1 resulting in C2 [kg]

C211 325,59 C221 368,85 C231 452,33 C241 117,93

C212 2378,52 C222 3191,63 C232 4956,45 C242 2073,9

C213 743,99 C223 1017,98 C233 1611,7 C243 559,04

C214 887,65 C224 1275,9 C234 1699,09 C244 223,38

Sliced basket parts volume: C3 [m3]

C311 0,014195 C321 0,0092 C331 0,012406 C341 0,008563

C312 0,050844 C322 0,015252 C332 0,022936 C342 0,040663

C313 0,016885 C323 0,00492 C333 0,009898 C343 0,021129

C314 0,024168 C324 0,014013 C334 0,026738 C344 0,012094



Comuted densities are to be used during analysis in ANSYS.

43

23 C

CC

mkg

volumemass

==

=ϕ

C411 22936,95 C421 40091,63 C431 36460,5 C441 13772,44

C412 46780,74 C422 209259,8 C432 216099,2 C442 51002,14

C413 44062,19 C423 206902,9 C433 162826,1 C443 26458,42

C414 36728,32 C424 91051,17 C434 63545,89 C444 18470,32

Load case 3: X-direction


L11 15,93 L21 46,88 L31 65,66

L12 135,99 L22 459,85 L32 645,67

L13 198,68 L23 946,6 L33 1598,9

L14 975,61 L24 4925,9 L34 9482,5

Sliced basket parts (steel): A1 [kg] Steel density: φ=7850 kg/m3

A111 27,829 A121 30,72 A131 38,35

A112 87,19 A122 37,3 A132 45,17

A113 113,42 A123 61,95 A133 99,95

A114 646,1 A124 403,83 A134 805,93

Adding load L to corresponding A1 resulting in A2 [kg]

A211 43,76 A221 77,6 A231 104,01

A212 223,18 A222 497,15 A232 690,84

A213 312,1 A223 1008,55 A233 1698,85

A214 1621,71 A224 5329,73 A234 10288,43

Sliced basket parts volume: A3 [m3]

A311 0,003545 A321 0,003913 A331 0,004886

A312 0,011106 A322 0,004751 A332 0,005754

A313 0,014448 A323 0,007891 A333 0,012733

A314 0,082306 A324 0,051444 A334 0,10267



Computed densities are to be used during analysis in ANSYS.

43

23 A

AA

mkg

volumemass

==

=ϕ

A411 12343,23 A421 19829,05 A431 21289,04

A412 20095,08 A422 104636,1 A432 120056,5

A413 21601,61 A423 127806,4 A433 133421,4

A414 19703,42 A424 103602,6 A434 100208,7

Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar F1

Appendix F

Figure F.1: The sub-model for x direction

Figure F.2: The sub-model for y direction

Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar G1

Appendix G

Figure G.1: The generated mesh with different element sizes

Figure G.2: The denser mesh

The element size

of mesh is 30 mm

for the rest of the

model.

Denser mesh

with the element

size of 0,25 mm

Authors: Nermin Dzanic, Martin Lindholm and Metin Uçar H1

Appendix H Existing welds - z acceleration

Figure H.1: The same point for acceleration in x

Figure H.2: The same point for acceleration in y


Existing welds - y acceleration


Figure H.4:The same point for acceleration in z


Existing welds – x acceleration


Figure H.6: The same point for acceleration in z


Adjusted welds – z acceleration




Adjusted welds – y acceleration




Adjusted welds – x acceleration



School of Technology and Design SE- 351 95 Växjö

Sweden tel +46 470-70 80 00, fax +46 470-76 85 40

www.vxu.se

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