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MASTER’S THESIS2009:165 CIV

Universitetstryckeriet, Luleå

Andreas PahkamaaJonas Pavasson

A new welding modeling approach in simulation driven design

MASTER OF SCIENCE PROGRAMME Mechanical Engineering

Luleå University of Technology Department of Applied Physics and Mechanical Engineering

Division of Computer Aided Design

2009:165 CIV • ISSN: 1402 - 1617 • ISRN: LTU - EX - - 09/165 - - SE

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Abstract This thesis is a part of a larger project involving the Faste Laboratory at Luleå University of Technology and the Wingquist Laboratory at Chalmers University of Technology. The interaction between simulation driven design and variation simulations is the main focus of this project. Computational welding mechanics has been developed during the last 30 years and can today be used to predict the outcome of real welding processes e.g. deformations and residual stresses. Hence, these types of simulations are starting to be used as a part of the product development process. The aim is to show that it is possible to perform simulation driven design on welded products in such a way that traditional physical testing can be reduced or even excluded. This thesis was divided into two parts. The aim of the first part was to show that VrWeld, a welding simulation software developed by Goldak Technologies, can perform accurate welding simulations and provide reliable results. This is done by running NeT’s Round Robin Benchmark which consists of a single weld bead on a stainless steel plate. The results from VrWeld were compared to simulation results and residual stress measurements from other Round Robin participants. The second part of the thesis is a case study of a rear axle bridge from a Volvo wheel loader. The deformations caused by welding during manufacturing was measured and compared with simulation results. An alternative welding sequence was simulated to show the possibilities of including these simulations in a simulation driven design process. The results show that it is possible to perform welding simulations in VrWeld for both residual stress analyses and deformation analyses, with the same or better accuracy as other simulation softwares. The results also indicate good opportunities to implement such simulation tools in a simulation driven design process.

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Sammanfattning Detta examensarbete är en del av ett större projekt där Fastelaboratoriet vid Luleå Tekniska Universitet och Wingquistlaboratoriet vid Chalmers Tekniska Högskola samarbetar. Fokus i detta projekt ligger i interaktionen mellan simuleringsdriven produktutveckling och variationssimuleringar. Svetssimuleringar har utvecklats under de senaste 30 åren och kan idag användas för att förutspå effekterna av en svetsprocess, t.ex. deformationer och restspänningar. Därför börjar denna typ av simuleringar att i större utsträckning användas i produktutvecklingsprocessen av svetsade produkter. Målet är att visa att det är möjligt att genomföra simuleringsdriven produktutveckling på svetsade produkter på sådant sätt att fysiska tester kan minskas eller t.o.m. uteslutas helt. Detta examensarbete är uppdelat i två delar. Målet med den första delen var att visa att VrWeld, en mjukvara för svetssimuleringar utvecklad av Goldak Technologies, kan utföra korrekta svetssimuleringar med tillförlitliga resultat. För att visa detta genomfördes NeT’s Round Robin Benchmark som består av enkel svetssträng på en platta av rostfritt stål. Resultaten från VrWeld jämfördes sedan med simuleringsresultat och restspänningsmätningar genomförda av deltagare i Round Robin studien. I den andra delen av examensarbetet genomfördes en fallstudie av en bakre axelbrygga från en Volvo hjullastare. De deformationer som uppstår i samband med tillverkningen mättes och jämfördes med simuleringsresultaten. En alternativ svetsföljd simulerades för att visa på möjligheterna att inkludera den här typen av simuleringar i en simuleringsdriven produktutvecklingsprocess. Resultaten visar att det är möjligt att genomföra korrekta simuleringar i VrWeld för både restspännings- och deformationsanalyser, med samma eller bättre resultat än andra mjukvaror för svetssimuleringar. Resultatet visar även på stora möjligheter att inkludera denna typ av simuleringsverktyg i en simuleringsdriven produktutvecklingsprocess.

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Preface This master’s thesis is the final project of the Master of Science programme in Mechanical Engineering at Luleå University of Technology. The project has been carried out at the Division of Computer Aided Design. We would like to thank our supervisors Dr. Magnus Karlberg, Asc Prof. Mats Näsström and PhD Student Stefan Sandberg at the Division of Computer Aided Design at Luleå University of Technology. We would also like to thank Prof. Lars-Erik Lindgren and PhD student Andreas Lundbäck at the Division of Material Mechanics at Luleå University of Technology. Special thanks to Prof. John Goldak at the Department of Mechanical and Aerospacing Engineering at Carlton University. Also thanks to Prof. Jack Samuelsson and Dr. Zuheir Barsoum at KTH Royal Institute of Technology and Krister Ericsson, Hasse Olsson and Lars-Inge Liljemark at Volvo Construction Equipment AB in Arvika. At last we would like to thank our examiner at the University, Prof. Lennart Karlsson. Andreas Pahkamaa and Jonas Pavasson Luleå, October 2009

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TABLE OF CONTENTS 1 INTRODUCTION ..................................................................................................................................... 13 2 THEORY.................................................................................................................................................... 15

2.1 WELDING............................................................................................................................................ 15 2.1.1 History of welding ......................................................................................................................... 16 2.1.2 MMA.............................................................................................................................................. 16 2.1.3 MIG/MAG ..................................................................................................................................... 16 2.1.4 TIG ................................................................................................................................................ 16 2.1.5 Laser welding ................................................................................................................................ 16 2.1.6 Electron beam welding.................................................................................................................. 17

2.2 EFFECTS OF WELDING ......................................................................................................................... 18 2.2.1 Thermal ......................................................................................................................................... 18 2.2.2 Metallurgical................................................................................................................................. 20 2.2.3 Mechanical.................................................................................................................................... 21

2.3 RESIDUAL STRESS MEASUREMENT METHODS...................................................................................... 22 2.3.1 X-ray diffraction............................................................................................................................ 22 2.3.2 Neutron diffraction........................................................................................................................ 22 2.3.3 Contour ......................................................................................................................................... 22 2.3.4 Strain gauge .................................................................................................................................. 22 2.3.5 Hole drilling.................................................................................................................................. 23

2.4 THE FINITE ELEMENT METHOD .......................................................................................................... 24 2.5 WELDING SIMULATIONS ..................................................................................................................... 25

2.5.1 Material modelling........................................................................................................................ 27 2.5.2 Non-linear deformation and constitutive model............................................................................ 29

2.6 HEAT TRANSFER ................................................................................................................................. 30 2.6.1 Conduction .................................................................................................................................... 30 2.6.2 Convection .................................................................................................................................... 30 2.6.3 Radiation....................................................................................................................................... 30

2.7 MODELLING........................................................................................................................................ 31 2.7.1 Software ........................................................................................................................................ 33

3 NET BENCHMARK................................................................................................................................. 35 3.1 RESULTS ............................................................................................................................................. 38

3.1.1 Thermal calibration ...................................................................................................................... 41 3.1.2 Residual stress analysis................................................................................................................. 44

3.2 CONCLUSIONS – NET BENCHMARK .................................................................................................... 51 4 VCE REAR AXLE BRIDGE CASE STUDY.......................................................................................... 53

4.1 MANUFACTURING METHODOLOGY ..................................................................................................... 54 4.2 WELDING SIMULATIONS ..................................................................................................................... 58

4.2.1 Material model .............................................................................................................................. 59 4.2.2 Welding parameters ...................................................................................................................... 60

4.3 RESULTS – VCE REAR AXLE BRIDGE................................................................................................. 63 4.3.1 Thermal calibration ...................................................................................................................... 64 4.3.2 Deformation analysis .................................................................................................................... 66

4.4 CONCLUSIONS – VCE REAR AXLE BRIDGE CASE STUDY...................................................................... 69 5 DISCUSSION............................................................................................................................................. 71 6 BIBLIOGRAPHY...................................................................................................................................... 73

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APPENDIX A – STAINLESS STEEL AISI 316L............................................................................................ 75 APPENDIX B – REAR AXLE BRIDGE DRAWING ..................................................................................... 76 APPENDIX C – FUSION BOUNDARY REPORTS ....................................................................................... 77 APPENDIX D – ADDED MATERIAL ............................................................................................................. 89 APPENDIX E – STEEL S420N ......................................................................................................................... 90 APPENDIX F – FILLER METAL ESAB OK 12.63........................................................................................ 91 APPENDIX G – CONCENTRICITY MATLAB CODE................................................................................. 92

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Nomenclature E Young’s modulus ν Poisson’s ratio c Heat capacity k Thermal conductivity εT Thermal dilatation

Totijε& Total strain rate eijε& Elastic strain rate p

ijε& Plastic strain rate thijε& Thermal expansion cijε& Creep Trvijε& Strain rate volume change associated with the transformation Trpijε& Strain rate transformation plasticity

wt% Weight percent qr Local heat flux

T∇ Temperature gradient As Surface area of heat transfer Ts Surface temperature Tb Temperature of the fluid h Constant heat transfer coefficient ε Emissivity factor σ Stefan-Boltzmann’s constant T Material temperature ∞T Surrounding temperature

σa Stress σb Stress V Voltage A Current W Power kJ Heat input °C Temperature in Celsius Fint Internal forces Fext External loads R Resultant forces B Virtual displacement with virtual strain

UΔ Incremental displacement δa Deformation δb Deformation σ1+n

i Cauchy stress εΔ+1n

i Incremental strain en

iV1+

Current volume of the element

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1 Introduction This thesis is a part of a collaboration project between the Faste Laboratory at Luleå University of Technology and the Wingquist Laboratory at Chalmers University of Technology. In this project researches within the Faste Laboratory will contribute with knowledge of simulation driven design while the Wingquist Laboratory will be focusing on variation simulations. The interaction between these fields is the main focus of this project. Volvo Construction Equipment will provide a rear axle bridge to be evaluated and the software is provided by Goldak Technologies. Computational welding mechanics has been developed during the last 30 years and can today be used to predict the outcome of real welding processes e.g. deformations and residual stresses. Hence, these types of simulations are nowadays used as a part of the product development process [1]. By replacing physical testing with computer simulations a lot of time and money can be saved and more design solutions can be numerically tested leading to more reliable products. The aim of a simulation driven product development process is to enhance the use of computer tools in such a way that the simulations are used to guide the designer towards suitable solutions rather than to check if a specific design suggestion works or not. One simulation driven strategy is to develop tools that are computational effective and that can be used by non-experts while still giving accuracy enough. In this way, calculation work does not have to be sent to another department (traditional “over the wall” strategy) and hence, the designer can test several different solutions in order to find the most appropriate one. The general problem concerning welds is the difficulty to predict, for example residual stresses and deformations in a welded structure. The Volvo rear axle bridge is manufactured by a number of welds where a large amount of physical testing was needed to find a welding procedure that gave acceptable results. In this study, fusion welding simulations will be conducted, where primary the connection between deformations and tolerances in the Volvo rear axle bridge is investigated. Also, an evaluation of the software used for the welding simulations (VrWeld) will be performed on a NeT benchmark. The aim is to show that it is possible to perform simulation driven design on welded products in such a way that traditional “trial and error” work can be reduced or even excluded.

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2 Theory

2.1 Welding Welding is a process that joins materials, usually metals, together. The welding process is often conducted by melting the work pieces and often adding a filler material to form a pool of molten material i.e. the weld pool. When the weld pool is cooling it forms a joint between the work pieces of almost the same strength as the work piece itself, see Figure 1.

Figure 1. Principle of welding.

Many different methods can be used for the welding process such as gas flame, fusion (electric arc, laser and electron beam), friction, ultrasound and explosion. Due to the variety of welding techniques, the process can be performed in many different environments such as open air, under water and in outer space [2]. Fusion welding is a method that involves a heat source, and often a filler material such as a consumable electrode or a wire fed into the weld pool. In some welding processes a protective atmosphere may be generated in the form of an inert (e.g. Argon) or active (e.g. CO2) gas [3]. There are several different types of fusion welding processes that can be used, see Table 1 below for more information of the different welding techniques and their applications. In this project fusion welding will be concerned.

Table 1. Fusion welding techniques [4]. Cost Cleanness of

the weld HAZ width Level of

automation Thickness of plate

MMA

Low Poor – Ok 5 – 6 mm No Any – multipass

MIG

Low – Med Ok 3 – 4 mm Medium Any – multipass

TIG

Low – Med Good 2 -3 mm Medium Any – multipass

Laser Very high Very good < 0.5 mm

Very high Up to 30 mm

Electron Beam

Very high Very good < 0.5 mm Low Up to 250 mm

Work piece Weld pool Heat affected zone

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2.1.1 History of welding The only available welding process until the end of the 19th century was forge welding. The discovery of the electric power resulted in the invention of new welding techniques. The use of these techniques grew rapidly during the early 20th century as World War I and World War II was a driving force for the development of reliable and inexpensive joining methods. In the late 1930s and early 1940s the TIG method was developed to satisfy the demand of a faster welding method especially for aircrafts and landing barges made of light-alloy metals [3]. The MIG/MAG welding method invented in the last years of the 1940s was also a result of this demand [5]. The development continued with the invention of laser beam welding 1960 and electron beam welding followed a decade later [7].

2.1.2 MMA “Manual Metal Arc” welding (MMA) [7] also known as “Shielded Metal Arc Welding” (SMAW), is a manual arc welding process that uses a consumable electrode coated in flux to lay the weld. As the weld is laid the flux coating of the electrode disintegrates and creates a protective layer between the atmosphere and the molten metal. This layer consists of a gas shield or fluxes which melt to give a viscous slag on the welded metal that can be removed after solidification. Both the gas shield and slag protects the weld area from atmospheric contamination. The MMA process is the most widely used method and it is primarily used to weld iron and steels (including stainless steels) but aluminum, nickel and copper alloys can also be welded with this method.

2.1.3 MIG/MAG “Metal Inert Gas” welding (MIG) or “Metal Active Gas” welding (MAG) [5] is also known as “Gas Metal Arc Welding” (GMAW). This process is a semi-automatic or automatic arc welding process in which a continuous and consumable wire electrode and a shielding gas are fed through a welding nozzle. Depending on the chosen metal, thickness of the work piece and the selected shielded gas different methods of metal transfer in the MIG/MAG welding process are used. The four primary metal transfer methods are globular-, short-circuiting-, spray-, and pulsed-spray method. Each method has apparent properties and corresponding advantages and disadvantages. The process is used to weld steel and light metal alloys.

2.1.4 TIG “Tungsten Inert Gas” welding (TIG) [3] also known as “Gas Tungsten Arc Welding” (GTAW) is an arc welding process that uses a non consumable tungsten electrode to produce the weld. The gas shield protects the weld from atmospheric contamination, argon and CO2 are the commonly used gases. Filler metal is used in most cases, but autogenous welds are also possible. TIG is most commonly used to weld thin sections of stainless steel and light metals such as aluminum, magnesium, and copper alloys.

2.1.5 Laser welding Originally laser welding [6] was used for difficult applications where no other welding process would be suitable. Nowadays laser welding is a more commonly used welding process in the metalwork industry. Lasers generate coherent light energy that can be absorbed by the material and converted to heat energy. There exist two main types of lasers that are being used for welding process, CO2 and Nd:YAG. Both CO2 and Nd:YAG lasers operate in the infrared region of the electromagnetic radiation spectrum, invisible to the human eye. The process is used to weld carbon steels, HSLA steels, stainless steels, aluminum and titanium.

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2.1.6 Electron beam welding Electron beam welding (EBW) [8] is a welding process in which a beam of high velocity electrons is applied to the materials being joined. This method is very similar to laser welding in which photons are used instead of electrons. The kinetic energy of the electrons is transformed into heat upon impact with the metal and therefore melts the work pieces and the filler metal (when filler metal is used). During the impact the temperature in the work piece is high while the distortion is low and the work piece cools rapidly. The heat penetrates deep into the work piece enabling the possibility to weld much thicker work pieces than is possible with other welding processes. The welding is often performed in conditions of a vacuum to prevent dispersion of the electron beam, this makes electron beam welding an expensive method. Most of the metals can be welded by the process, but the most commonly welded are stainless steels, super alloys, and reactive and refractory metals. The process is also used to weld dissimilar metals combinations.

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2.2 Effects of welding The welding process influences the structural properties (both in micro and in macro level) and material properties. These welding effects will here be described from a thermal, mechanical and metallurgical point of view, which are coupled as shown in Figure 2 and Table 2.

Figure 2. Thermomechanical coupling in welds [1].

Table 2. Description of thermo mechanical coupling in welds [1].

1 Transformation Rates (microstructure evolution depends on temperature). 2 Latent heats (each phase transformation can have an associated latent heat). They act as a

heat sink on heating and as a heat source on cooling. 3 Phase Transformations (volume changes due to phase changes, plastic and elastic material

behaviour depend on the microstructure of material.) 4 Transformation Rates (microstructure evolution can, particularly martensitic and bainitic

transformations, depend on mechanical deformation). 5 Thermal Expansion (mechanical deformations depend on temperature). 6 Plastic Work (mechanical deformation generates heat in the material and changes the

thermal boundary conditions). In most welding processes this effect is very small.

2.2.1 Thermal The thermal process of welding [9] can shortly be described as addition of heat (and often filler metal) to create a weld pool where the materials can fuse. This is followed by rapid cooling (mostly by the surrounding material) which causes the weld pool to solidify thus completing the creation of the joint. This process of rapid heating and cooling gives rise to residual stresses, deformations and metallurgical transformations. The heat distribution [7] in a welded structure is largely dependent of the welded geometry, the thermal properties of the welded material, the weld method and the welding speed. Figure 3 shows how the heat distribution differs for thin and thick structures. Easterling describes the flow of heat in thin and thick plates to be two- respectively three-dimensional. He also showed that a thicker plate offer a much higher efficiency of cooling which reduces the extent of the heat distribution in the material.

Thermal

Metallurgical

Mechanical

1

2

3

4

5

6

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Figure 3. Difference in heat distribution in thin (a) and thick (b) plates [°C].

The heat distribution depends on the welding speed and the difference between a low (v1) and high (v2) welding speeds can be seen in Figure 4. The higher welding speed gives a much narrower weld [7].

Figure 4. Example of difference in heat distribution between low and high welding speed [°C].

Similar relations can be seen when comparing different welding methods. For example, high density energy beam processes such as laser welding gives a narrow weld compared to more traditional methods [8]. For all forms of fusion welding [8] the temperatures exceeds the welded materials melting point. Apart from melting the material in the joint, this high energy input also affects the surrounding material. This zone is often called the heat affected zone (HAZ). A typical cross-section of a butt weld joint can be seen in Figure 5. Three distinguishing zones can bee identified in the picture. The first zone is the weld zone (nr 1 in Figure 5), the second is the heat affected zone (nr. 2 in Figure 5) and the third is the unaffected base material zone (nr. 3 in Figure 5).

Figure 5. Cross-section of a butt weld joint.

v1 v2 v1 < v2

300

600

800

1200

300

600

800

1200

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2.2.2 Metallurgical The HAZ can be divided into a number of sub-zones. Figure 6 shows a schematic diagram of the various sub-zones of the heat-affected zone approximately corresponding to the alloy C0 (0.15 wt % C) indicated on the FE-FE3C equilibrium diagram [7]. The thermal history of each zone has given rise to different metallurgical transformations, thus giving different mechanical properties to the material in the weld and HAZ. The thermal and mechanical history prior to the welding process does also affect the final metallurgical structure of the weld [7].

Figure 6. HAZ and equilibrium diagram [7].

The metallurgical change does not always give satisfying mechanical properties and hence heat treatment of the weld is often necessary [8]. The welds surrounding atmosphere will also affect the quality of the weld. One common problem is hydrogen induced cracking (HIC) or hydrogen assisted cracking (HAC) [1]. Another problem is carburization where the carbon levels can exceed the eutectic composition which is about 4.3 wt% carbon in iron, this will give material properties close to that of cast iron.

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2.2.3 Mechanical The thermal history and metallurgical changes gives rise to deformations and residual stresses, which is one of the major disadvantages when using welding to join materials. By welding simulations it is possible to predict these defects which are an important part in a simulation driven product development process [1]. In the case of welding, deformations and stresses are largely opposed. A high degree of geometrical restraint in welding results in high stresses and small deformations while an unrestrained weld produces results in lower stresses but larger deformations [9]. The principal difference between free and restrained shrinkage is shown in Figure 7. The left beam is allowed to shrink freely while the right beam is restrained.

Figure 7. Difference between free (a) and restrained (b) shrinkage.

In the case of welding, surrounding base material and fixtures restraints the structure. Figure 8 shows the basic deformations modes for a rectangular plate with a centric joint.

Figure 8. Deformation modes of a rectangular plate with a centric jointing weld seam [9].

a) b) σa < σb δa > δb

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2.3 Residual stress measurement methods The methods available for the measurement of residual stresses [19] in components can be categorised in destructive and non-destructive methods. With non-destructive methods, residual stresses are measured without removing a part of the component by, for example cutting or drilling.

2.3.1 X-ray diffraction X-ray diffraction [19] is a non-destructive measurement method. In this technique strain is determined directly from measurements of atomic lattice spacings. Stresses are then calculated from these strains. The X-ray technique is limited to surface measurements as most of the x-ray is absorbed by the engineering material.

2.3.2 Neutron diffraction Neutron diffraction [20] shown in Figure 9 is a non-destructive measurement method similar to the X-ray method. The difference between these two methods is that the neutrons penetrate several centimetres into most engineering materials. This technique is limited to be performed in laboratories with high flux nuclear reactor or accelerator induced neutron sources.

Figure 9. Two directions measured simultaneously [20].

2.3.3 Contour The contour method [21] is a destructive measurement method. Material is removed and the deformations caused by the residual stresses can be measured. The residual stresses can then be calculated “backwards” based on the measured deformations. This method has the potential to measure a full cross-sectional profile of residual stresses in a relatively cheap and time-efficient way. It is simple to use and the equipment required is widely available in many workshops and laboratories. The method itself involves four steps: specimen cut, contour measurement, data reduction and finite element analysis.

2.3.4 Strain gauge Strain gauge measuring [22] is a non-destructive measurement method. This device is used to measure strain on surfaces. The most common type of strain gauge consists of an insulating flexible backing which supports a metallic foil pattern. The gauge shown in Figure 10 is attached to the component to be measured. The foil is deformed when the object is deformed, causing its electrical resistance to change. The signal from the gauge is transmitted by cable to the measurement computer where the calculation, analysis and presentation of the signal is performed.

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Figure 10. Strain gauge. a) No load b) Tensile load c) Compressive load [22].

2.3.5 Hole drilling Hole drilling [19] is another destructive measurement method which is similar to the strain gauge method except that the measurements are conducted after welding. A special three-element strain gauge rosette shown in Figure 11 is installed on the component at the point where residual stresses are to be determined. A hole with width 1.5-3 mm and approximately the same depth is drilled through the centre of the rosette. When material is removed from the stressed component it becomes relaxed and the residual stresses can be calculated from the changes in strain.

Figure 11. Strain gauge rosette.

1

1 2

3

1

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2.4 The Finite Element Method The finite element method (FEM) [10] is a computational technique used to obtain approximate solutions of boundary value problems in various types of engineering. A boundary problem is simply a mathematical problem which consists of one or more dependent variables that must satisfy a system of ordinary differential equation. The finite element method use elements with a volume and known material properties, the volume is the domain of the boundary value problem to be solved and analyzed. Depending on the specific type of engineering being analyzed, the boundary condition can include for example stress, displacement and temperature. The history of the finite element method [9] [10] goes back a decade but has become more useful during the last fifty years. The finite element method used today with piecewise continuous functions was introduced by Courant 1943. In the late 1940s aerospace industry started to use this method more frequently, more complex analysis of airframe structures was a driving force to improve the technology in this specific area. In the late 1950s, the key concepts of stiffness matrices and element assembly existed essentially in the form used today. But the breakthrough for finite element method was during the 1960s with the usage of digital computers. The first software code NASTRAN (1965) was followed by ANSYS, ALGOR, MARC and COSMOS/M. Today most of these solvers are included in softwares that can be used on desktop computers. Welding simulations [11] is one of the engineering techniques that can be analyzed by the finite element method. Like other simulations, welding simulation is useful due to the saving of time and money compared to experimental tests. By using the finite element method it is possible to solve the mechanical, metallurgical and thermal coupling associated with welding.

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2.5 Welding simulations Even today, welding effects is still frequently derived by physical tests which are often expensive and time consuming. Hence, there exist a potential of predicting such effects by simulations. Physical weld simulators that simulate the weld by heating and cooling the material have been used in the past [7]. These expensive and time consuming tests and simulators where and are still the driving force behind the development of computational welding mechanics and welding simulation software. Modern softwares are now able to predict the residual stresses, deformations, microstructural changes and other important phenomena. These and other similar types of softwares are today mostly used to verify that a construction or manufacturing method works and fulfils the requirements of the product. However, there exists a need to increase the usefulness of these softwares and make them play a more central role in the product development process e.g.. simulation driven design. Welding simulations are nowadays mostly performed by experts because of the complexity coupled to the user interaction. In order to enable the usage of such tools for non-experts, more user friendly software that can evaluate the construction and its manufacturing method more frequently and earlier in the product development process is needed, see Figure 12.

Figure 12. Principle of use of simulation software in simulation driven design [1].

Tools for functional evaluation

Tools for evaluation of manufacturing effects

Tools for planning of manufacturing

Concept Design

Preliminary Design

Detailed Design

Inventory of known methods

Preliminary Preparation

Detailed Preparation

DESIGN

MANUFACTURING

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In computational welding mechanics (CWM) or welding simulations, the coupling between the materials mechanical, thermal and metallurgical properties is critical [1]. The way the heat input is modelled is also an important part of the simulations. Lindgren [11] describes the sub domains of CWM according to Figure 13. A staggered approach is normally used where either the mechanical or the thermal problem is solved first giving conditions to solve the remaining problem for that time step [11]. The above-mentioned fields and the modelling are described further in the following subchapters.

Figure 13. Fields in classical computational welding mechanics for fusion welding [11].

Heat transfer

Heat input model

Material properties

Deformation in solid

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2.5.1 Material modelling The material models used in welding simulations must take the multi-physics of welding into account. There are two major issues concerning material models. The first is to determine what the simulation is supposed to investigate, i.e. the aim for the material model [11]. It is important to use a material model that is able to describe the phenomena of interest and nothing more, since there is a direct connection between the complexity of the material model and the calculation time. The most commonly used parameters in welding simulations can be found in Table 3.

Table 3. Common material parameters used in welding simulations [1] [11]. Mechanical Thermal Metallurgical Young’s modulus Thermal expansion coefficient Thermal dilatation Yield stress Heat capacity Latent heat Poisson’s ratio Thermal conductivity Transformation induced plasticity Density Emissivity Melting point Many of these parameters are both time and temperature dependent which has to be included in the material model. Some examples of how these parameters vary with temperature are shown below. Figure 14 shows how the strength of boron steel decreases as the temperature rises.

Figure 14. Yield stress versus effective plastic strain of SS 142550-02 at elevated temperatures [12].

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Figure 15 shows the temperature dependency of Young’s modulus and thermal dilatation. The solid line shows how the Young’s modulus decrease as the temperature rises and the dashed line shows the thermal dilatation as a function of temperature. The dilatation irregularity occurs when the austenitic (FCC) phase changes to the less dense phases ferrite (BCC), pearlite (BCC) and martensite (BCT) [13].

Figure 15. Young's modulus (E) and thermal dilatation (εT) of SS 142550-02 [12].

This phase change also gives rise to temperature dependency in the heat capacity and thermal conductivity as shown in Figure 13. Here, the solid line shows the heat capacity while the dashed line shows the thermal conductivity.

Figure 16. Heat capacity (c) and thermal conductivity (k) of SS 142550-02 [12].

These examples show the importance of using material models that are able to describe the physical phenomena that occurs during the welding process. One problem with these more complex material models is the expensive physical tests needed to get sufficient and accurate data.

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2.5.2 Non-linear deformation and constitutive model The large deformations and rotation effects associated with welding calls for the need of nonlinear formulations. The basic equations of nonlinear deformations are the equilibrium equations, constitutive stress-strain relations and geometric compatibility. The relation of these equations can be seen in Figure 17 [11].

Figure 17. Tönti diagram for basic relations in nonlinear deformation [11].

Thermal-elastic-plastic constitutive models [1] decompose the total strain rate Tot

ijε& according to Equation 1

Trpij

Trvij

cij

thij

pij

eij

Totij εεεεεεε &&&&&&& +++++= (1)

where e

ijε& corresponds to the elastic strain rate, pijε& to the plastic strain rate, th

ijε& consists of the

thermal expansion and cijε& of creep. During phase transformations there is an addition of Trv

ijε& ,

which is the strain rate volume change associated with the transformation and Trpijε& which is the

strain rate transformation plasticity.

Stress-strain relations

Equilibrium

Geometric compatibility

extn

in

in

i FFR 1int

11 +++ −=

σ1+ni int

1 fni+ int

1Fni+

Uni Δ+1 un

i Δ+1 εΔ+1n

i

Assembling

Identification of element displacements

uB nim

ni

ni Δ=Δ +++ 111 ε

∫+

⋅= +++

eniV

ni

Tm

ni

ni dVBf

1

11int

1 σ

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2.6 Heat transfer Heat transfer, also known as transfer of thermal energy, is the transition of thermal energy from a hotter to a cooler material. When the temperature of the affected material is different than the surrounding material, heat transfer occurs in such a way that the affected material and the surrounding material strives to reach thermal equilibrium. The heat transfer is described by the second law of thermodynamics, also called Clausius statement. Heat can be transferred in three ways, by conduction, convection and by radiation [1] and [11].

2.6.1 Conduction Conduction [11] is the transfer of heat by direct contact of affected particles. Heat transfer by conduction is caused by adjacent atoms vibrating against each other or by free electron diffusion. Metals are in most cases the best conductors of thermal energy, which is a result of the metals chemical bonding. Metallic bonds have free electrons moving from atom to atom and transfer thermal energy efficient. Thermal conductivity is a material property depending on the metals phase, temperature, density, and molecular bonding. According to Lindgren [11], Fourier’s Law is the only model used in CWM today, see Equation 2.

Tkq ∇−=r (2) qr = local heat flux k = materials conductivity

T∇ = temperature gradient

2.6.2 Convection Convection [24] is the transfer of heat between a solid surface and an adjacent liquid. The convective heat transfer increases when the fluid motion increases or if the bulk motion of fluid enhances. There exist two types of convective heat transfer i.e. natural convection and forced convection. The rate of convective heat transfer is described in Equation 3:

( )bss TTAhq −⋅= (3) As = surface area of heat transfer Ts = surface temperature Tb = temperature of the fluid h = constant heat transfer coefficient

2.6.3 Radiation Radiation [11] is the transfer of heat when no material is present. Radiation also works within vacuum. Heat loss due to radiation can be described according to Equation 4.

( )44∞−⋅= TTq σε (4)

ε = emissivity factor σ = Stefan-Boltzmann’s constant T = material temperature ∞T = surrounding temperature

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2.7 Modelling Before the modelling of the welding process begin, it is suitable to answer a few questions [11]. What is the aim of this simulation? Which accuracy is desired? What kind of phenomena should be captured? etc. Questions that may be the motivation for performing a simulation of welding are given in Table 4. The questions are listed in order of increasing complexity.

Table 4. Scope of a welding simulation [11]. 1. What are the residual stresses? These will be used for determination of risk for buckling,

fatigue, cold cracking or stress corrosion cracking, etc. 2. What are the final deformations? These are wanted in order to check if the tolerance

requirements of a component are fulfilled after the welding procedure. 3. What are the transient stresses and deformations? These may be wanted in order to find

procedures that maintain the gap required for a successful weld. 4. What is the microstructure of the weld and the heat-affected zone? This kind of analysis

also requires a microstructure model. 5. What causes hot cracking? Note that hot cracking phenomena are on the limit of

continuum mechanics as they may be caused by liquid material along grain boundaries exposed to tensile strains. The parameters obtained from simulations must be evaluated with care in order to ascertain if the model can be used to study how the welding process can be changed to reduce hot cracking.

6. Is it possible to join these materials? The finite element method has no knowledge about metallurgy. It may be combined with other types of models that have this knowledge and use the computed results from finite element models.

7. What is the weld penetration? This is very much influenced by the chemical composition, addition of surface-active elements, arc physics, etc. It requires complex fluid mechanics models.

To reduce the calculation time and still get accurate results, meshes used in welding simulations are usually finer near the weld path than in the rest of the structure. The mesh seen in Figure 18 was used by Lundbäck and Runnemalm [9] to simulate EB welding of two Inconel 718 plates.

Figure 18. Finer mesh near weld path [9].

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Another step to further increase the efficiency of the simulation is to use dynamic and adaptive meshes. This is done by increasing the mesh density near areas with large stress and/or temperature gradients and as the gradients decreases the mesh size increases, see Figure 19. Lindgren [11] recommends that the degree of finite element shape functions for the displacements should be one order higher than for the thermal analysis because the temperature field directly becomes the thermal strain in the mechanical analysis. He also recommends that linear elements with reduced integration should be used instead of higher-order elements. It is also mentioned that quad and brick elements, for 2D respective 3D analyses, performs better than linear triangles and tetrahedrons [11]. Another way to reduce the calculation time is to reduce the mesh-dimension of the problem e.g. reducing a three dimensional problem to a two dimensional [11]. Parallel computing is also a way to make the simulations more effective.

Figure 19. Adaptive mesh based on gradients in thermal and mechanical fields [1]. The most common heat input model used in welding simulation is the Gaussian double ellipsoid, see Figure 20 [1]. This heat input model is mostly used for simulation of welding processes with fairly large weld pools. For processes with more concentrated energy distribution, such as laser and electron beam, Lindgren suggests that a conical heat sources can be used [11].

Figure 20. Double ellipsoid heat source with Gaussian distributed heat [1].

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Many welding operations include addition of filler material which hence has to be included in the model. Two ways of including the filler material is described by Lindgren [11] i.e. the quiet and the inactive element approaches. The quiet method includes the filler elements but they are given such material properties that they don’t affect the surrounding structure. When the corresponding filler material is added they are given proper material properties. The inactive method does not assemble these elements until the filler material is added, this calls for a resolving of the equation system. The inactive method gives smaller models, but it takes time to resolve the matrices, especially for three-dimensional models. The quiet method does not have this problem, but if a too low stiffness is chosen it might lead to a poorly conditioned global stiffness matrix.

2.7.1 Software There exist several softwares that are capable of conducting welding simulations. However, in this project Goldak Technologies VrWeld will be used. VrWeld VrWeld [14] is one of the software packages in VrSuite developed by Goldak Technologies. Given CAD files for the parts to be welded, the set of weld procedures to be used, and material properties for the materials being welded, VrWeld enables a designer to simulate the transient 3D temperature field, the evolution of microstructure in low alloy steel welds, transient 3D displacement, stress and strain in the structure as it is being welded.

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3 NeT Benchmark The Round-Robin Benchmark was formed by the NeT (European Network on Neutron Techniques Standardization for Structural Integrity) as a part of their mission to develop experimental and numerical techniques and standards for the reliable characterisation of residual stresses in structural welds [17]. The benchmark consists of a 60 mm long single weld bead on the top surface on an austenitic steel plate, see Figure 21. Four nominally identical plates (A11, A12, A21 and A22) were welded under controlled and documented conditions, e.g. the temperature history of the nine thermocouples (T1-T9) seen in Figure 21. Several participants from different organisations/institutes then performed residual stress measurements on the four specimens using various methods. The residual stresses were measured along lines A to D in Figure 21. Welding simulations has then been performed by a number of participants where the temperature history of the thermocouples and the residual stresses has been analyzed in different ways. A compilation of these measurements and simulation results have further been made by Smith [15] [16]. The aim of this part of the thesis is to perform welding simulations on this benchmark using VrWeld with accuracy in the same range as simulation results presented by Smith [15] [16].

Figure 21. Schematic of NeT Benchmark showing positions of thermocouples and lines for evaluation of

residual stresses [15].

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As mentioned above, different simulation approaches have been used by the participants of the NeT Benchmark. The welding simulations that will be performed in VrWeld follow recommendations suggested by Smith [15]. Table 5 shows the simulation parameters used in VrWeld. Remaining settings are VrWeld defaults.

Table 5. Initial simulation parameters. Parameter VrWeld input Heat input model Moving Gaussian ellipsoid heat source.

To be calibrated against thermocouple measurements and real fusion boundary.

Heat input 0.633 kJ/mm => 1436.91 W. VrWeld input 7.18455 V, 200 A. Weld speed 2.27 mm/s Efficiency Approximately 75 %. To be calibrated against thermocouple

measurements. Weld joint length Approximately 60 mm. To be calibrated against thermocouple

measurements and available pictures. Weld joint cross section See Figure 27 Mesh See Figure 28 Restraints See Figure 24 Hardening model Isotropic Wire diameter 0.8 mm Ambient temperature 20 °C Dwell time Approximately 1 s. To be calibrated against thermocouple

measurements. Base material properties Austenitic stainless steel AISI 316L. See Appendix A Weld material properties Austenitic stainless steel AISI 316L. See Appendix A

The heat input model, dwell time and efficiency is calibrated with the thermal history of the thermocouples and the shape of the real fusion boundary. Thermocouples T5, T7 and T9 showed the smallest scatter in measurements and are therefore recommended to be used for calibration [15]. The measurements from the A22 plate are used since those temperature loggings were performed at a higher frequency, see Figure 22.

Figure 22. Plate A22 thermocouple measurements [15].

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Because of a roughly approximated weld joint length and start/end positions there is a need to calibrate the longitudinal positioning of the thermocouples. The initial thermocouple positions are given in Figure 23. These positions were then calibrated by trial and error.

Figure 23. Thermocouples initial positions [15].

The plate is restrained according to Figure 24, this method locks the plates six degrees of freedom without restraining the growth/shrinkage of the plate. In reality the plate was transversally restrained by a vice. However, Smith [15] suggests that an unrestrained plate can be used for the residual stress analysis since simulations with a full contact transversal restraint predicted similar results as for an unrestrained plate.

Figure 24. Nodal constraints.

Six thermocouples were push-fitted into ~1.2 mm deep drilled holes on the top surface of the plate in groups of two: a) Thermocouples T1 and T4 were at the bead start end, 30 mm from the centre of the plate, 8.5 mm and 11.5 mm from the bead centre-line respectively. Note that the total bead width was approximately 8 mm. b) Thermocouples T2 and T5 were at bead mid-length, 8.0 mm and 11.5 mm from the bead centre-line respectively. c) Thermocouples T3 and T6 were at the bead stop end, 30 mm from the centre of the plate, 7.5 mm and 12 mm from the bead centre-line respectively. Two thermocouples were push-fitted into holes drilled from the bottom of the plate on the weld centre-line: d) Thermocouple T7 was approximately 15 mmfrom the stop end of the bead, 10.5 mm below the plate top surface. e) Thermocouple T8was approximately 15 mmfrom the start end of the bead, and w5 mm below the plate top surface. A single thermocouple, T9, was attached to the bottom of the plate at bead mid-length.

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3.1 Results To determine the required mesh density a mesh convergence analysis was performed. Four meshes with varying density was created and the results was compared, see Table 6.

Table 6. Number of elements and calculation time for the four meshes. Mesh Number of elements Coarse 13370 Medium 1 39462 Medium 2 74978 Fine 105838

From Figure 25 and Figure 26 it can be concluded that for stress calculations a finer mesh then the ‘Medium 2’ mesh will not give a more accurate result. Therefore the ´Medium 2’ mesh was used for this benchmark. The total calculation time for the ‘Medium 2’ mesh on a computer with a 2.4 GHz processor was 9.5 hours.

Figure 25. Mesh convergence. Longitudinal stress along line D3. [MPa]

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Figure 26. Mesh convergence. Transversal stress along line D3. [MPa]

The mesh cross section was created based on the sample cross-section seen in Figure 27. The width and height of the weld is approximated to 8 and 0.75 mm. The hole in the sample piece is from a thermocouple.

Figure 27. Mesh cross-section vs. sample cross-section from plate A11.

The total mesh can be seen in Figure 28. The mesh is denser closer to the weld, and as Smith [15] suggested this denser area goes through the whole plate. In this case the whole plate is meshed, while symmetry was used by the participants of the NeT study. The weld bead mesh runs along the whole plate, but only the mid third is actually used in the simulations.

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Figure 28. Total mesh created in VrWeld.

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3.1.1 Thermal calibration Figure 29 shows simulation results and measurements for thermocouples T1-T9 after calibration of heat input parameters.

Figure 29. Simulated temperature (dashed line) vs. thermocouple measurements.

As mentioned earlier Smith [15] suggests that thermocouples T5, T7 and T9 should be used to calibrate the heat input. Figure 30 shows the results for these thermocouples after calibration.

Figure 30. Simulated temperature (dashed line) vs. thermocouple measurements T5-T7-T9.

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The calibrated thermocouple positions are given in Table 7. The coordinates are given with respect to the coordinate system defined in Figure 21.

Table 7. Thermocouple nodal coordinates. [mm] Thermocouple X Y Z

T1 68.5 -1.2 63.0 T2 68.0 -1.2 90.0 T3 67.5 -1.2 120.0 T4 71.5 -1.2 63.0 T5 71.5 -1.2 90.0 T6 72.0 -1.2 120.0 T7 60.0 -10.5 107 T8 60.0 -5.0 77.0 T9 60.0 -17.0 105

Figure 31 shows a comparison between sample and calibrated simulation fusion boundaries. The red contour in the simulation picture shows the material which reaches the metals melting point, which is approximately 1400 °C.

Figure 31 . Comparison between simulated heat input and sample fusion boundary. Transversal cut at

mid weld. The calibrated heat input parameters used are presented in Table 8. These parameters were obtained by traditional “trial and error” work. See Figure 32 for a description of the Gaussian ellipsoid heat source parameters.

Table 8. Heat input parameters. Parameter Value Gaussian ellipsoid heat source parameters a1 = 4 mm

a2 = 1 mm b = 0.5 mm c = 12 mm

Power 1436.91 W (7.18455 V, 200 A) Efficiency 80 % Dwell time 1 s

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Figure 32. Gaussian ellipsoid heat input model.

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3.1.2 Residual stress analysis The residual stresses are plotted along lines B-D, B2, D2 and D3 in Figure 33. Line B-D is positioned at the centre of the plate and the residual stress is plotted from the bottom to the top surface. Line B2 is positioned transversally 2 mm underneath the surface at weld mid length, the residual stress is plotted from the side with thermocouples. Lines D2 and D3 are placed longitudinally 2 respectively 3 mm underneath the surface at weld centre. The stress is plotted from the left side where the weld starts. Figure 34 to Figure 37 shows a comparison of the NeT Round Robin results and the results obtained in VrWeld (green line). Figure 38 to Figure 41 shows contour plots of the longitudinal and transversal residual stresses at longitudinal and transversal cuts.

Figure 33. Lines used for residual stress analysis.

Weld start

Thermocouples

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Figure 34. Longitudinal (a) and transversal (b) residual stress along line B2. VrWeld results vs. NeT

measurements and simulations.

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Figure 35. Longitudinal (a) and transversal (b) residual stress along line B-D. VrWeld results vs. NeT


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Figure 36. Longitudinal (a) and transversal (b) residual stress along line D2. VrWeld results vs. NeT


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Figure 37. Longitudinal (a) and transversal (b) residual stress along line D3. VrWeld results vs. NeT


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Figure 38. Longitudinal residual stress. Transversal cut at mid weld.

Figure 39. Longitudinal residual stress. Longitudinal cut at weld centre.

Weld start

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Figure 40. Transversal residual stress. Transversal cut at mid weld.

Figure 41. Transversal residual stress. Longitudinal cut at weld centre.

Weld start

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3.2 Conclusions – NeT Benchmark The thermal calibration involved a large number of parameters. Several thermal simulations were performed where “trial and error” work finally gave a result within measured accuracy. The initial shape of the Gaussian ellipsoid was based on the fusion boundary pictures that were available and was then changed to fit the thermocouple measurements. The efficiency was increased to fit the measurements better, leading to a final efficiency of 80 % which is 5 % higher than Smiths [15] recommendations. Based on the available photographs of the weld bead, it was clear that the length of 60 mm only was an approximation. The weld bead was meshed as a constant cross-section that was extruded along the weld path, this gave the start and stop end sharp edges compared to the softer ends of the real weld. Therefore, the length of the bead had to be elongated to about 62 mm to fit the thermocouple measurements. Due to this elongation of the bead combined with the roughly documented positioning of the thermocouples, adjustment of the longitudinal position were needed. According to Smith [15] there were problems with thermocouple T8 in all four plates. An air pocket behind the thermocouple caused the measurements to be generally lower than the simulated values and the same results were obtained with VrWeld. The measured peak temperature range for the thermocouples was 5-105 °C degrees in the measurements from the four plates [15], therefore there is no need to perform a more thorough calibration. The residual stress analysis conducted in VrWeld shows an accuracy in the same order as the results obtained by the NeT participants. However, the large scatter in the residual stress measurements makes it difficult to conclude which of the simulation results that are the most accurate. However, the results from VrWeld are among the once with the best agreement. The residual stress along line A and C, which is the start and stop end of the bead, has not been evaluated here since no such data were available. The mesh convergence analysis showed that the fine mesh used in this case could have been replaced by a coarser one. The use of symmetry would also decrease the calculation time. Based on the knowledge obtained during the work with the NeT Benchmark it is clear that the accuracy of welding simulations is largely dependent of the thermal input. The parameters needed to describe this input will to some extent still have to rely on physical testing. The scatter in the results from different simulations (conducted by different researches with different tools) shows that the outcome of the simulations will be associated with a certain degree of insecurity, thus physical testing will still be needed, but hopefully to a smaller extent than before. The amount of physical testing should further become less important as the accuracy of the welding simulations increases in the future.

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4 VCE Rear Axle Bridge case study In this case study a rear axle bridge from a Volvo wheel loader is studied, see Figure 42. The axle bridge is positioned in the rear frame according to Figure 43. An axle is mounted in the two holes in the axle bridge, this axle works as a pivot for the rear axle assembly, see Figure 44. The axle is supported by journal bearings which are lubricated with oil from the rear axle differential. Examples of important measurements for this axle bridge are the concentricity between the two holes and the parallelism and perpendicular alignment between the plates, more information can be found in Appendix B. Because of these demands, it is important that the welding process used to manufacture the axle bridge does not introduce too large deformations. Some of the deformations that occur because of the welding must be corrected by machining after the welding, but not all errors can be corrected in this way. The aim of this case study is to show that simulations can be used to predict global deformations due to welding operations in a rear axle bridge.

Figure 42. Volvo wheel loader.

Figure 43. Rear axle bridge position.

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Figure 44. Rear axle bridge and rear axle.

4.1 Manufacturing methodology The rear axle bridge is composed of three steel plates which are cut into correct shape with a gas cutting machine. These plates are then mounted in a fixture and then tack welded as a preparation for the automated MAG welding process that follows. At this stage, one plate is slightly tilted to compensate for the deformations that occur during the solidification and cooling of the weld joints. The upper plate is also moved upwards so that a small gap between the plates is created. After the tack welding is finished the axle bridge is moved to another fixture before the welding process begins, see Figure 45. A close-up picture of a tack weld can be seen in Figure 46. The length of the tack weld is approximately 40 mm.

Figure 45. Rear axle bridge in welding fixture.

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Figure 46. Close-up of tack weld.

The plates are welded with six welds i.e. two full-length welds at one side and four half-length welds at the other side, see Figure 47. This weld path as well as an alternative welding sequence will be evaluated in VrWeld, see Figure 48. The welds are fillet welds with a throat size of at least 6 mm. Before the finished axle bridge is welded into the rear frame machining of the connecting faces and the two holes is performed to correct some of the deformation and other errors from the cutting and welding processes. These faces are highlighted in green in Figure 49.

Figure 47. Rear axle bridge welding sequence.

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Figure 48. Rear axle bridge alternative welding sequence.

Figure 49. Tack welds (red) and surfaces to be machined (green).

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The results from the welding simulations will be compared to measurements from the production at VCE in Arvika. Five axle bridges where measured after being tack welded and the same measurements where taken after the entire welding process was finished, after the fixture was released. The measured distances A, B and C are shown in Figure 50. The results and mean values from these measurements can be found in Table 9. An additional mean value have further been calculated where measures with suspected errors (1 and 5) were excluded.

Figure 50. Measurements used for validation of simulation results.

Table 9. Rear axle bridge measurements. [mm]

A B C Before 430 424 424 Bridge 1 After 424 422 422

Before 429 424 423 Bridge 2 After 427 422 422




Before 429 424,2 423,8 Mean (1-5) After 425,8 423,2 423,4

Mean (2-4) After 427,0 423,0 422,7

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4.2 Welding simulations The axle bridge geometry is created based on a STEP file of the finished axle bridge (welds excluded) provided by VCE. The CAD-model has been modified to have the same appearance as prior to welding and machining i.e.

• Material has been added where machining will be performed i.e. connecting surfaces and holes.

• The plates have been tilted and positioned according to mean values (1-5) of A, B and C in Table 9

• The filler metal geometry has been created based on information obtained in Appendix C. The average throat size was calculated to 7.505 mm. The average penetration of the gap on one side was calculated to 5.87 mm. The other side of the axel bridge was modelled without a gap, thus also without any penetrating filler metal.

• Material has been added to enable a constant mesh cross section for weld 1 and 2. See Appendix D for more information.

The modified CAD-geometry was then exported to VrWeld as an STL-file. The mesh was generated in VrWeld and consists of three parts i.e. two fine meshes close to the weld joints and a coarser mesh for the remaining geometry, see Figure 51. Three different mesh-sizes (coarse, medium and fine) were created and tested to find the required mesh density for deformation analysis of this part.

Figure 51. Simulation mesh (Medium).

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4.2.1 Material model Material data for both the base material (S420N) and the filler metal (ESAB OK 12.63) was found for room temperature. However, for elevated temperatures material data from a similar HSLA material (HT36-Steel) has been used to estimate the missing data [18] [23]. The yield stress temperature dependency was estimated based on the ratio between yield stress at elevated temperature and room temperature, see Table 10 and Figure 52. At 1000°C and 1500 °C, the same yield stresses was set for both materials. The complete material models can be found in Appendix E and Appendix F.

Table 10. Approximated yield stress temperature dependency. °C Yield stress ratio

σT/ σT0 S420N [MPa]

ESAB OK 12.63 [MPa]

0 1.0 420.0 525.0 400 0.8 336.0 420.0 700 0.065 27.30 34.10 1000 - 3.000 3.000 1500 - 0.007 0.007

Figure 52. Approximated yield limit temperature dependency [18].

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4.2.2 Welding parameters The welding simulations are performed in VrWeld with the simulation parameters listed in Table 11. The Gaussian ellipsoid i.e. the approximated shape of the heat input, is calibrated with the fusion boundary samples shown in Figure 53. Complete reports of these fusion boundary measurements can be found in Appendix C. An initial guess of the depth and width of the ellipsoid is based on measurements ‘b’ and ‘c’ shown in Figure 53. The fixture used during welding is modelled according to Figure 54. An alternative and less rigid fixture shown in Figure 55 is also investigated. After the axle bridge has cooled, a springback analysis will be run with constraints according to Figure 56. The efficiency interval is set to 70-85% [8]. The remaining settings are set to VrWeld defaults.

Table 11. Simulation parameters Parameter VrWeld input Heat input model Moving Gaussian ellipsoid heat source.

To be calibrated against real fusion boundary, see Figure 53. Heat input 10880 W (34 V, 320 A) Weld speed 37 cm/min Efficiency 70-85 % [8] Weld joint cross section Throat size 7.505 mm. Tack welds 3 x 40 mm. Start, mid and end on each weld Mesh See Figure 51 Restraints 0-1400 s according to Figure 54/Figure 55

1400-1500 s according to Figure 56 Hardening model Isotropic Wire diameter 1.2 mm Ambient temperature 300 °K Dwell time Approximately 0.5 s for each weld. Base material and properties Steel S420N see Appendix E Weld material and properties ESAB OK1263 see Appendix F

Figure 53. Sample fusion boundaries.

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Figure 54. Fixture constraints.

Figure 55. Alternative fixture constraints.

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Figure 56. Springback constraints.

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4.3 Results – VCE Rear Axle Bridge To determine the required mesh density a convergence analysis was performed. Three meshes with varying density was created where the results of the distances A, B and C was compared, see Table 12. The simulations were performed on a 2.4 GHz processor.

Table 12. Number of elements and calculation time for axle bridge meshes. Mesh Number of elements Calculation time Coarse 18 369 17,5 h Medium 33 880 52,0 h Fine 68 197 172,5 h

From Table 12 and Figure 57 and it can be concluded that for deformation analyses the ‘Medium’ mesh density gives a suitable compromise between accuracy and calculation time, and was therefore used for the alternative analyses. No mesh convergence could be determined. Figure 58 shows the resolution and shape of the ‘Medium’ mesh by comparing a mesh cross section and a sample cross-section.

Figure 57. Simulation result mesh dependency.

Figure 58. Mesh cross-section vs. sample cross-section.

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4.3.1 Thermal calibration Figure 59 shows a comparison between initial and final heat input. Figure 60 and Figure 61 shows a comparison between the final heat input and the fusion boundary samples. The red contours in the simulation pictures show the material which exceeds the metals melting point, which is approximately 1475 °C. The calibrated heat input parameters are presented in Table 13. These parameters were obtained by traditional “trial and error” methodology. The initial guess was based upon measurements from fusion boundary samples. A description of the Gaussian ellipsoid heat source parameters can be found in Figure 20. The efficiency was set to 85 % for all cases.

Figure 59. Comparison between initial (left) an final (right) heat input.

Table 13. Calibrated Gaussian ellipsoid heat source parameters. Heat input Gaussian ellipsoid heat source parameters Initial guess a1 = 14 mm

a2 = 7 mm b = 8.4075 mm c = 10.85 mm

Final a1 = 10 mm a2 = 6 mm b = 6 mm c = 8 mm

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Figure 60. Comparison between simulated heat input and sample fusion boundary, bottom plate.

Figure 61. Comparison between simulated heat input and sample fusion boundary, upper plate.

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4.3.2 Deformation analysis Table 14 shows a comparison between measured and simulated results for the distances A, B and C. Table 15 shows a comparison between the measured range and simulated results. Table 16 further show results for the distances A, B and C from the simulation with an alternative fixture and the simulation with an alternative welding sequence.

Table 14. Measurements vs. simulation results. A B C

Before 429 424,2 423,8 After (1-5) 425,8 423,2 423,4

Measured Mean

After (2-4) 427,0 423,0 422,7 After

(Fixed 1400 s) 427,29 424,07 424,43 Simulated

Coarse After

(Springback 1500 s) 427,48 424,56 425,00

After (Fixed 1400 s)

427,62 423,42 423,78 Simulated Medium

After (Springback 1500 s)

427,84 423,85 424,30


426,53 424,49 424,92 Simulated Fine


426,82 425,07 425,66

Table 15. Comparison between measured range and simulated results. Measured Range Simulated (Fine)

A 424-427 426,82 B 422-425 425,07 C 422-427 425,66

Table 16. Results from alternative simulations. A B C


427,74 423,55 423,98 Simulated Alternative fixture


427,84 423,86 424,27


428,40 422,74 422,30 Simulated Welding sequence 2


428,60 423,21 422,79

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Figure 62 shows the final deformation of the fine mesh after springback. Note that the displacements are amplified 20 times. The other simulations showed very similar deformation behaviours.

Figure 62. Deformation after springback, displacement x20.

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Figure 63 and Figure 64 illustrates the resulting concentricity of the two axle holes for the original and alternative welding sequences when the original fixture was used. The magnified box in the upper right corner shows the midpoints of the circles. The concentricities are calculated to 0.4434 mm for the original weld sequence and 0.8003 mm for the alternative weld sequence. The concentricity is derived by approximating the shape and position of the two circles from three nodes from each hole. The entire Matlab-code for this procedure can be found in Appendix G.

Figure 63. Concentricity original weld sequence.

Figure 64. Concentricity alternative weld sequence.

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4.4 Conclusions – VCE rear axle bridge case study The thermal calibration for the rear axle bridge simulations was conducted with fusion boundary samples. This method is not as accurate as calibration with thermocouple data (as in the NeT Benchmark). However, fusion boundary calibration is cheaper and more applicable in early stages of the product development process when no real product is yet available. In this case, where the axle bridge is already under production, thermocouple measurements would be of interest to get a more accurate calibration. The calibrated thermal input resulted in a smaller area with molten metal compared to the fusion boundary samples, even though the efficiency was set to the maximum value of 85 % for MIG/MAG welding listed by Blondeau [8]. The Gaussian ellipsoid was given a short length in comparison to its cross section area in an attempt to increase the overall temperature in the weld joint. Though, an even shorter heat source will increase the calculation time as the length of the heat source is one of the parameters that determine the size of the time steps. A shorter heat source may further lead to instability problems in the heat input. The results of the fine simulation are within the range of the measured deformations, apart from the range of length B which is 0.07 mm outside the measured range. Since the measurements are conducted by hand with a measuring tape it is difficult to tell if the variations come from measurement errors or if the manufacturing process actually gives this scatter. It is therefore difficult to conclude how accurate the simulations actually are. A larger amount of axle bridges has to be measured with a more precise measuring method to get statistically secured data. The complexity of the deformation seen in Figure 62 indicates that additional measurements might be necessary to capture the behaviour of the deformations. No mesh convergence could be observed for the three meshes that where investigated. More meshes should be investigated to solve this question. One source of error could be that the fixtures that are introduced by constraining the node closest to the real position of the fixture. This leads to different fixture modelling for each mesh since the constrained nodes position will not be the same. This is especially problematic for coarser meshes. Therefore, it would be of interest to perform a mesh convergence analysis where the fixture is equivalently introduced regardless of the mesh density. The calculation time for this specific project with the ‘Medium’ mesh was around 52 h on a 2.4 GHz processor. This calculation time may be reduced by use of so called “Fast Simulations” where the entire weld, or a big portion of it, is applied instantly which was outside the scope of this thesis. ”Fast simulations” are especially useful for cases as this with very long welds in comparison to the relatively small size of the weld cross section (almost 4 m total weld length of a weld with a throat size of approximately 7.5 mm). Material data for elevated temperatures are generally difficult to find since they are expensive to derive. Once a complete material model has been derived, it is therefore seldom shared. In this case, a material model was constructed based on available material data for room temperature. The material data for elevated temperatures was obtained from a similar HSLA steel (HT36-steel) [18] [23]. This approximation could be a source of error and hence, finding a more accurate material model is a recommendation for future work. The results from the simulation with the less rigid fixture differed slightly from the results from the original fixture. However, this difference decreased after springback when the

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fixtures where released. Since the fixture modelling influences the results, it is recommended to further investigate the influence of different fixture modelling approaches. In reality a fixture is never completely rigid, therefore the elasticity of the real fixture should be modelled to get a more accurate result. Another disadvantage of using nodal constraints is the lack of heat transfer from the part to the fixture, which is the case in reality. The alternative welding sequence resulted in larger deformations in the entire structure. This way of testing different welding sequences shows that it is possible to investigate the outcome of different welding approaches with computer simulations, thus reducing the amount of physical testing needed to find a proper welding approach.

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5 Discussion The NeT Round Robin Benchmark showed that VrWeld is able to perform welding simulations with accuracy in the same range or better than other welding simulation software. However, to obtain accurate results it is important that the simulation input parameters are described correctly, e.g. material data, thermal input, welding parameters and boundary conditions. It has been shown that it is possible to predict the deformations (lengths A, B and C) of a rear axle bridge within the range of 1-5 mm. However, in order to determine the accuracy of the simulations more accurate measurements is needed. It has also been shown that the outcome of different welding parameters, such as the different welding sequences, can be investigated. The different kinds of analyses that where performed in this thesis had different requirements of mesh densities. For deformation analyses, a relatively coarse mesh could be used while residual stress analyses required a slightly more dense mesh. Since the thermal analyses are run in a relatively short time it was possible to use a fine mesh to increase the resolution in the heat affected zone. This approach was especially helpful for calibration of the thermal input. Specially designed tools for thermal calibration would improve today’s software since such calibration is necessary for all projects. This thesis has shown that with the method used for the NeT Benchmark and the rear axle bridge it should be possible to carry through simulation driven design on welded products. Once a robust process for welding simulations has been developed it should be possible to optimize the welding process of existing and future products, e.g. minimization of deformations or residual stresses. This could be done by investigating different welding sequences, joint geometries, fixtures, welding methods, welding powers etc.

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6 Bibliography [1] Goldak, John A & Mehdi, Akhlaghi (2005). Computational welding mechanics. [2] Knutson-Ek, Bo (1983). Svetsning lödning samt grundmaterialets beredning. [3] Jönsson, Stig (1989). TIG-svetsning. [4] UK Material science department (2000). University of Liverpool. Fusion welding. (Electronic). 3 monitor pages. Available: http://www.matter.org.uk/steelmatter/manufacturing/welding/fusion.html. (2009-06-08). [5] MIG/MAG svetsning (1986). Grundbok. [6] Miller, Carl B. U.S Laser Corporation. Laser welding article. (Electronic). 7 monitor pages. Available: http://www.uslasercorp.com/envoy/welding.html. (2009-06-08). [7] Easterling, Kenneth (1992). Introduction to the physical metallurgy of welding. [8] Blondeau, Régis (2001). Metallurgy and mechanics of welding. [9] Lundbäck, Andreas (2003). Finite element modelling and simulation of welding of aerospace components. Lic.thesis. Luleå University of Technology, Sweden. [10] Hutton, David V (2004). Fundamentals of finite element analysis. [11] Lindgren, Lars-Erik (2007). Computational welding mechanics. [12] Bergman, Greger (1999). Modelling and simulation of simultaneous forming and quenching. Doctoral thesis. Luleå University of Technology, Sweden. [13] Åkerström, Paul (2006). Modelling and Simulation of Hot Stamping. Doctoral Thesis. Luleå University of Technology. [14] Goldak, John A. GOLDAK technologies Incorporation. VrWeld. (Electronic). 2 monitor pages. Available: http://www.goldaktec.com/vrweld.html (2009-06-16). [15] M.C. Smith & A.C. Smith. NeT bead-on-plate round robin: Comparison of transient thermal predictions and measurements, International Journal of Pressure Vessels and Piping, 86, 2009, pp 96-109. [16] M.C. Smith & A.C. Smith. NeT bead-on-plate round robin: Comparison of residual stress predictions and measurements, International Journal of Pressure Vessels and Piping, 86, 2009, pp 79-95. [17] C.E. Truman. The NeT residual stress measurement and modelling round robin on a single weld bead-on-plate specimen, International Journal of Pressure Vessels and Piping, 86, 2009, pp 1-2. [18] Lars-Erik. Lindgren. Finite element modeling and simulation of welding. Part 3: Efficiency and integration, Journal of Thermal Stresses, 24, 2001, pp 305-334. [19] Näsström, Mats O (1992). Thermo-mechanical modelling of welding with experimental verification. Doctoral thesis. Luleå University of Technology, Sweden. [20] Pratihar S, Turski M, Edwards L, Bouchard P.J. Neutron diffraction residual stress measurements in a 316L stainless steel bead-on-plate weld specimen, International Journal of Pressure Vessels and Piping, 86, 2009, pp 13-19. [21] Turski M, Edwards L. Residual stress measurement of a 316L stainless steel bead-on-plate specimen utilising the contour method, International Journal of Pressure Vessels and Piping, 86, 2009, pp 126-131. [22] Tano, Kent (2005). Continuous monitoring of mineral processes with special focus on tumbling mills. Doctoral thesis. Luleå University of Technology, Sweden. [23] Andersson, B.A.B. Thermal stresses in a submerged-arc welded joint considering phase transformation. Journal of Engineering Materials and Technology, 100, 1978, pp 356-362. [24] Baehr, Hans D & Stephan, Karl (1998). Heat and Mass Transfer.

http://www.matter.org.uk/steelmatter/manufacturing/welding/fusion.html

http://www.uslasercorp.com/envoy/welding.html

http://www.goldaktec.com/vrweld.html

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Appendix A – Stainless Steel AISI 316L Material: AISI316L_Steel Complete material model can be found on attached CD/DVD.

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Appendix B – Rear Axle Bridge drawing

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Appendix C – Fusion boundary reports

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Appendix D – Added material Material has been added according to Figure 65 and Figure 66 to ease the meshing process. This added material allows for a constant cross-section when creating the denser mesh for weld 1 and 2. The denser meshes have been extruded in the direction of the weld joints.

Figure 65. Added material to upper plate.

Figure 66. Result of added material.

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Appendix E – Steel S420N Material: S420N Based on HslaAndersson_Steel, only modified properties listed in appendix. Complete material model can be found on attached CD/DVD Property: poissonRatio fileType: table functionOf: temperature #~last modified: Mon Nov 1 11:07:30 EST 2004 by bahe #from Lars-Erik Lindgren #Journal of Thermal Stresses 24:305-334, 2001 #Mod by AP #273 0.28 273 0.28 673 0.3 1773 0.48 -------------------------------------------------- Property: yieldStress fileType: table functionOf: temperature #~last modified: Wed Sept 15 10:14:32 EST 2004 by bahe #created by Ba He #from Lars-Erik Lindgren #Journal of Thermal Stresses 24: 305-334,2001 #for weld: 4.6e8 # 3.7e8 # 3e7 #Mod by AP #273 4.2e8 #673 3.36e8 #973 2.73e7 273 4.2e8 673 3.36e8 973 2.73e7 1273 3e6 1773 7000 -------------------------------------------------- Property: youngsModulus fileType: table functionOf: temperature #~last modified: Wed Sep 15 10:06:24 EDT 2004 by bahe #Created by Ba He #date created 20040811 #from Lars-Erik Lindgren #Journal of Thermal Stresses; 24: 305-334, 2001 #Mod by AP #273 2.05e11 273 2.05e11 673 1.8e11 1273 1e10 1773 1e5 --------------------------------------------------

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Appendix F – Filler Metal ESAB OK 12.63 Material: ESAB 12.63 Based on HslaAndersson_Steel, only modified properties listed in appendix. Complete material model can be found on attached CD/DVD Property: poissonRatio fileType: table functionOf: temperature #~last modified: Mon Nov 1 11:07:30 EST 2004 by bahe #from Lars-Erik Lindgren #Journal of Thermal Stresses 24:305-334, 2001 #Mod by AP #273 0.28 273 0.28 673 0.3 1773 0.48 -------------------------------------------------- Property: yieldStress fileType: table functionOf: temperature #~last modified: Wed Sept 15 10:14:32 EST 2004 by bahe #created by Ba He #from Lars-Erik Lindgren #Journal of Thermal Stresses 24: 305-334,2001 #for weld: 4.6e8 # 3.7e8 # 3e7 #Mod by AP #273 5.25e8 #673 4.20e8 #973 3.41e7 273 5.25e8 673 4.20e8 973 3.41e7 1273 3e6 1773 7000 -------------------------------------------------- Property: youngsModulus fileType: table functionOf: temperature #~last modified: Wed Sep 15 10:06:24 EDT 2004 by bahe #Created by Ba He #date created 20040811 #from Lars-Erik Lindgren #Journal of Thermal Stresses; 24: 305-334, 2001 #Mod by AP #273 2.05e11 273 2.05e11 673 1.8e11 1273 1e10 1773 1e5 --------------------------------------------------

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Appendix G – Concentricity MATLAB code clear all % Program for approximation of circles and calculation of concentricity % Enter coordinates for three arbitrary points on circle 1 & 2 % Window size figure('Position',[200 200 700 600]) wx0 = -0.1; wx1 = 0.1; wy0 = 0.85; wy1 = 1.05; % Resolution u = 1000; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % CIRCLE 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% p1 = [y,z]; % Coordinates point 1 p2 = [y,z]; % Coordinates point 2 p3 = [y,z]; % Coordinates point 3 % Equation system, circle A = [1 p1(1) p1(2) 1 p2(1) p2(2) 1 p3(1) p3(2)]; b = [(p1(1)^2+p1(2)^2) (p2(1)^2+p2(2)^2) (p3(1)^2+p3(2)^2)]; % Solve equation system x = A\b; % Results r = x(1); a = x(2); b = x(3); % Visualization of circle 1 x = linspace(wx0,wx1,u); y = linspace(wy0,wy1,u); [X, Y] = meshgrid(x,y); Z = r + a*X +b*Y - X.^2 -Y.^2; contour(X,Y,Z,[0,0],'b'), hold on axis([wx0 wx1 wy0 wy1]) plot(p1(1),p1(2),'*'), hold on plot(p2(1),p2(2),'*'), hold on plot(p3(1),p3(2),'*'), hold on % Visualization of circle 1 centre a1 = a/2; b1 = b/2; plot(a1,b1,'*'), hold on

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % CIRCLE 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% p4 = [y,z]; % Coordinates point 1 p5 = [y,z]; % Coordinates point 2 p6 = [y,z]; % Coordinates point 3 % Equation system, circle C = [1 p4(1) p4(2) 1 p5(1) p5(2) 1 p6(1) p6(2)]; d = [(p4(1)^2+p4(2)^2) (p5(1)^2+p5(2)^2) (p6(1)^2+p6(2)^2)]; % Solve equation system z = C\d; % Results r = z(1); a = z(2); b = z(3); % Visualization of circle 2 x = linspace(wx0,wx1,u); y = linspace(wy0,wy1,u); [X, Y] = meshgrid(x,y); Z = r + a*X +b*Y - X.^2 -Y.^2; contour(X,Y,Z,[0,0],'r'), hold on axis([wx0 wx1 wy0 wy1]) plot(p4(1),p4(2),'r*'), hold on plot(p5(1),p5(2),'r*'), hold on plot(p6(1),p6(2),'r*'), hold on % Visualization of circle 2 centre a2 = a/2; b2 = b/2; plot(a2,b2,'r*'), hold on scrsz = get(0,'ScreenSize'); xlabel('y-axis') ylabel('z-axis') %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Calculation of concentricity %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Koncentricitet_mm = sqrt((a2-a1)^2+(b2-b1)^2)*1000

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