Numerical simulation of fluid flow and temperature field in keyhole double‐sided arc welding process on stainless steel

Double‐sided arc welding process powered by a single supply is a type of novel high‐production process. In comparison with the conventional single‐sided arc welding, this process has remarkable advantages in enhancing penetration, minimizing distortion and improving welding production. In this paper, a three‐dimensional steady numerical model is developed for the heat transfer and fluid flow in plasma arc (PA)–gas tungsten arc (GTA) double‐sided keyhole welding process. The model considers the surface tension gradient, electromagnetic force and buoyancy force. A CCD camera is used to observe the size and shape of the keyhole and weld pool. The acquired images are analysed through image processing to obtain the surface diameters of the keyhole on the two sides. A double‐V‐shaped keyhole geometry is then proposed and its characteristic parameters are derived from the images and cross‐section of weld bead. In the numerical model, the keyhole cavum within the weld pool is treated as a whole quality, whose temperature is fixed at the boiling point of the workpiece material. The heat exchange between the keyhole and weld pool is treated as an interior boundary of the workpiece. Based on the numerical model, the distributions of the fluid flow and temperature field are calculated. A comparison of cross‐section of the weld bead with the experimental result shows that the numerical model's accuracy is reasonable. Copyright © 2005 John Wiley & Sons, Ltd.     

Temperature and Moisture Distributions Inside a Layer of Moist Material Placed on a Hot Isothermal Surface

The problem of contact drying of a layer of moist material placed on a hot isothermal surface is considered. A system of heat and mass transfer equations and equations for the initial and boundary conditions are proposed. Luikov's theoretical approach is utilized, but all relevant thermophysical coefficients are considered to be fully dependent on the temperature and moisture content inside the material during the process. The model is solved numerically. Results for temperature and moisture distributions inside the layer of the material obtained using this model are compared to results obtained by solving a model with constant thermophysical coefficients in the governing equations, formed by using the same type of heat and mass transfer equations and equations for the initial and boundary conditions. The process is also examined experimentally, which provided results that enable verification of the proposed models.     

Voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials

In this paper, a new ‘Voronoi cell finite element model’ is developed for solving steady-state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials. The method is based on the natural discretization of a multiple phase domain into basic structural elements by Dirichlet Tessellation. Tessellation process results in a network of polygons called Voronoi polygons. In this paper, formulations are developed for treating these polygons as elements in a finite element mesh. Furthermore, a composite Voronoi cell finite element model is developed to account for the presence of a second phase inclusion within a polygonal element. Various numerical examples are executed for validating the effectiveness of this model in the analysis of the temperature and stress fields for micropolar elastic materials. Effective material properties are derived for microstructures containing different distributions of second phase.     

T型接头旋转激光+GMAW复合焊熔池动态行为数值分析模型

目的 研究T型接头旋转光纤激光+GMAW复合焊熔池的温度场和流态特征,揭示气孔缺陷的产生及抑制机理。方法 依据光学、电磁学、传热学及流体动力学机理,建立T型接头旋转光纤激光+GMAW复合焊熔池数值分析模型。使用Fluent软件对旋转频率分别为50 Hz和100 Hz的T型接头旋转激光+GMAW复合焊进行温度场以及流态特征的模拟,对比不同频率下T型接头横、纵截面,从工艺和焊缝成形角度出发,针对不同频率对熔池、小孔成形以及气孔抑制的影响进行讨论。结果 当旋转频率为50 Hz时,纵截面内小孔最大深度为5.4 mm,横截面熔池内小孔开口直径相对较大,旋转一周后,小孔远离气泡,气泡无法逸出,形成气孔;当旋转频率为100 Hz时,纵截面内小孔深度显著降低,熔池体积明显减小,横截面内小孔最大开口直径和深度均降低,熔池尺寸也有所减小,在时间为0.097 s时,小孔上方区域出现的顺时针涡流不仅能抑制气孔,还能改善熔池的下垂以及立板焊趾处的咬边。结论 随着旋转频率的增大,小孔的最大开口直径和深度均降低,还对熔池具有搅拌作用,使熔池体积变小。     

Laser power coupling efficiency in conduction and keyhole welding of austenitic stainless steel

Laser welding of thin sheets of AISI 304 stainless steel was carried out with high power CW CO₂ laser. The laser power utilized in the welding process was estimated using the experimental results and the dimensionless parameter model for laser welding; and also the energy balance equation model. Variation of laser welding efficiency with welding speed and mode of welding was studied. Welding efficiency was high for high-speed conduction welding of thin sheets and also in keyhole welding process at high laser powers. Effect of pre-oxidization of the surface and powder as filler material on laser power coupling is also reported. The paper also discusses effect of microstructure on the cracking susceptibility of laser welds.     

基于复合热源的铝合金激光-MIG复合焊接的有限元模拟

针对15mm厚Al-Mg-Zn铝合金试板多层多道激光-MIG复合焊接过程,综合考虑了脉冲MIG焊接过程大量焊丝的填充带入熔池的熔滴热量和激光焊接过程中的小孔能量沉积效应,建立了复合热源模型。使用ABAQUS有限元软件对上述焊接过程进行了温度场模拟,同时采用非线性弹性边界条件来模拟真实的工装约束作用;通过与实验结果进行对比,模拟的焊缝形貌与试验吻合得较好。     

Imposing Dirichlet boundary conditions in the extended finite element method

This paper is devoted to the imposition of Dirichlet‐type conditions within the extended finite element method (X‐FEM). This method allows one to easily model surfaces of discontinuity or domain boundaries on a mesh not necessarily conforming to these surfaces. Imposing Neumann boundary conditions on boundaries running through the elements is straightforward and does preserve the optimal rate of convergence of the background mesh (observed numerically in earlier papers). On the contrary, much less work has been devoted to Dirichlet boundary conditions for the X‐FEM (or the limiting case of stiff boundary conditions). In this paper, we introduce a strategy to impose Dirichlet boundary conditions while preserving the optimal rate of convergence. The key aspect is the construction of the correct Lagrange multiplier space on the boundary. As an application, we suggest to use this new approach to impose precisely zero pressure on the moving resin front in resin transfer moulding (RTM) process while avoiding remeshing. The case of inner conditions is also discussed as well as two important practical cases: material interfaces and phase‐transformation front capturing. Copyright © 2006 John Wiley & Sons, Ltd.     

DRM-MD approach for modeling laser–material interaction with axial symmetry

A dual reciprocity method multi-domain (DRM-MD) approach for modeling laser–material interaction with axial symmetry was developed. The proposed approach is based on the fundamental solution for the Laplace equation in 2D and is much simpler for implementation than the dual reciprocity boundary element method (DRBEM) based on the fundamental solution for axisymmetric problems incorporating elliptic integrals. The thermal model of laser–material interaction was applied for the cases of mono as well as multi-layer structures. Different aspects of interaction up to the melting point of considered materials are presented. The effect of temperature dependence of the absorption coefficients on the process of laser heating was considered. Numerical results for spatial as well as temporal temperature distribution inside the material bulk are presented and compared to analytical solutions.     

A study on the metal flow in full penetration laser beam welding for titanium alloy

A mathematical model for flow simulation of full penetration laser beam welding of titanium alloy is presented. In this model, the heat source comprises a plane heat source on the top surface and a cylindrical heat source along the z-direction, which takes into account the plasma effect and the keyhole absorption. By solving the conservation equations of energy, momentum and mass, the temperature and flow fields are obtained. The momentum interpolation scheme with under-relaxation parameter is used to simplify the calculation algorithm and save the storage space of computer. The mushy region is introduced to provide a simple method to dispose of the pressure and velocity boundary conditions. Results calculated from the models are found to agree with the experimental results for the geometry profile of weld. The calculated results indicate the metal flow is the main reason for forming the typical “hourglass” cross-section profile.     

Process control of laser conduction welding by thermal imaging measurement with a color camera

Conduction welding offers an alternative to keyhole welding. Compared with keyhole welding, it is an intrinsically stable process because vaporization phenomena are minimal. However, as with keyhole welding, an on-line process-monitoring system is advantageous for quality assurance to maintain the required penetration depth, which in conduction welding is more sensitive to changes in heat sinking. The maximum penetration is obtained when the surface temperature is just below the boiling point, and so we normally wish to maintain the temperature at this level. We describe a two-color optical system that we have developed for real-time temperature profile measurement of the conduction weld pool. The key feature of the system is the use of a complementary metal-oxide semiconductor standard color camera leading to a simplified low-cost optical setup. We present and discuss the real-time temperature measurement and control performance of the system when a defocused beam from a high power Nd:YAG laser is used on 5 mm thick stainless steel workpieces.     

Laser welding of AZ31B magnesium alloy to Zn-coated steel

The characteristics of laser lap welding of AZ31B magnesium alloy to Zn-coated steel were investigated. Welding was difficult when the laser beam was irradiated onto the AZ31B alloy and the processing parameters were set to obtain a keyhole welding mode. The difference in the physical properties between the two materials resulted in unstable welding process particularly when the laser beam penetrated into the steel specimen and a keyhole was formed therein. By switching to a conduction mode, the process stability was improved and successful welding could be achieved because the liquid metal film remained unbroken and the laser beam did not penetrate into the material. A 25 mm wide joint failed in tensile shear testing at loads exceeding 6000 N. This high joint strength was attributed to the formation of a 450 nm thick layer of Fe₃Al intermetallic compound on the steel surface as a result of the interaction between Al from the AZ31B alloy and Fe. The presence of Zn-coating layer was essential to eliminate the negative effects of oxides on the joining process.     

Melt pool vorticity in deep penetration laser material welding

In the present study, the vorticity of melt motion in the keyhole and weld pool has been evaluated in case of high power CO₂ laser beam welding. The circulation of vorticity is obtained as a function of Reynolds number for a given keyhole volume which is linked to Mach number variation. The shear stress and thermal fluxes present in the turbulent pool are linked to diffusivity and Prandtl number variation. It was shown that below a critical value of Rayleigh number, the conduction mode of melt transfer signifying beam absorption becomes dominant. Above this value, convective heat transfer indicates melting and evaporation occurring in the weld pool during laser welding. The evaporative recoil pressure expels the liquid while surface tension and hydrostatic pressure help to retain the melt in the keyhole cavity in this high power laser beam welding. The understanding of several hydrodynamic phenomena occuring in the weld pool is valuable not only for understanding basic mechanistic aspects but also for process optimization involved in laser beam welding.     

Gaussian Process Modeling of a Functional Output with Information from Boundary and Initial Conditions and Analytical Approximations

A partial differential equation (PDE) models a physical quantity as a function of space and time. These models are often solved numerically with the finite element (FE) method and the computer output consists of values of the solution on a fine grid over the spatial and temporal domain. When the simulations are time-consuming, Gaussian process (GP) models can be used to approximate the relationship between the functional output and the computer inputs, which consists of boundary and initial conditions. The Dirichlet boundary and initial conditions give the functional output values on parts of the space-time domain boundary. Although this information can help improve prediction of the output, it has not been used to construct GP models. In addition, analytical solutions of the PDE derived by simplifying the PDE can often be obtained, which can help further improve performance of the GP model. This article proposes a Karhunen–Loève (KL) expansion-based GP model that satisfies the Dirichlet boundary and initial conditions almost surely, and effectively uses information from analytical approximations to the PDE solution. Real examples demonstrate the improved prediction performance achieved by using these sources of prior information. Supplementary materials for this article are available online.     

Model for CO2 laser welding of stainless steel,titanium, and nickel: parametric study

Abstract

The present work has been carried out experimentally and theoretically with the aim of studying the effect of the operative pressure on the weld beads of different materials (AISI 304, Ti–6Al–4V, and Ni), welded using a CO₂ laser beam. At the same time, the reliability of a properly developed analytical model of the laser beam welding process has been confirmed. Such a model, taking into account the dynamics of the process itself, describes the laser induced thermal fields in terms of two heat sources, the first one representing the keyhole effect and the second one, the role played by the plume. A comparison between the experimental data and the beads predicted using the model gives satisfactory results, with average errors less than 5% for Ti–6Al–4V and ~10% for AISI 304 and Ni. The model allows the quantitative evaluation of the power distribution between the keyhole and the plume and a deeper understanding of the entire process.

MST/1591     

Solidification behaviour in plasma are welding

Melting and solidification behaviour in the deep penetrution welding process is different from that in conventional welding process in deep penetration processes there is keyhole formation and the full thickness of the plate receives the are heat input unlike conventional processes in which the heat input is received only by the surface nodes. In the present study, the thermal analysis of molten pool formation and solidification keyhole welding using plasma are welding has been done using the finite element method. The model accounts for the several phenomena associated with welding, like the distributed are heat input over the top surface and along the thickness, the temperature-dependent material properties. convection and radiation heat losses etc. The analysis is performed for different combinations of parameters. viz welding current and welding speed, which have the maximum influence on molten pool shape and solidification behaviour. The model has also been validated by conducting experimental measurement of thermal cycles experienced by the plate for different welding parameters. The weld pool dimensions. viz. the length and widlh are found to increase with inincreasing current and decereasing welding speed. Thermal cycles at locations close to the weld reach a higher value of temperature and the time for peak temperature is also less but at farther locations the peak temperature reached is lower and the time for peak temperature is higher. Details of the model, the experimental results obtained and the solidifications charateristics of the pool are discussed in this paper.     

Der Einfluss von Struktur des Laserimpulses auf die Temperaturverteilung und Wärmespannungen des elastischen Halbraumes

The approximate method for the determination of temperature and stress distributions in an elastic half-space heated by laser impulse on its boundary is derived. The method is based on the solutions for two cases of laser time structure: uniform and linear as well as approximate finite functions. The numerical results are presented for the laser impulses applied in engineering practice.     

Design problem of the profile or the cascade of profiles and construction of orthogonal networks using the Riemann surfaces for the multiform singularities

The complex potential induced by the source-vortex distribution is a multi-values function. In order to treat the field problem defined by the Dirichlet type boundary condition, it is necessary to get its correct value which has to be taken from an appropriate sheet of the Riemann surface. For the analytical formulations of a homogeneous density distribution over a segment or a cascade of segments, it can be done that the multi-value part is located at one of the end points of each segment. An algorithm is proposed to get the appropriate definition according to the relative positions of the induction element with the reception point. The construction of an orthogonal network inside a domain by solving the Dirichlet problem is shown. The simple layer distributions on the boundaries of the domain are used to generate the field in this example. The turbomachine blading design in connection with the flow field problem is described. The proposed method admits the thickness distribution and the bound vortex distribution as the initial data. In the case of the 2D cascade, we show how to define the boundary conditions in order to obtain a properly posed field problem.     

Boundary shape distortion involving dirichlet conditions with application to temperature distribution

Summary This paper presents a variant of the method of separation of variables which enables the determination of the solution of an elliptic differential equation having Dirichlet conditions along an arbitrary curve D forming part of the boundary. The coefficients in the eigenfunction expansions representing the general solution are determined by comparison with a special series representation of the Dirichlet condition along D. This representation is obtained by means of the Gram-Schmidt orthogonalization process which uses as its basic non-orthogonal set of functions a special set derived directly from the eigenfunction expansion. A simple numerical example concerning the temperature distribution in a semi-infinite parallel slab with a skew end face on which there is a sinusoidal temperature varation illustrates the application of the method. It is shown that the rate of convergence is good and that the asymptotic solution is estimated rapidly and accurately by this method.     

A higher‐order potential flow method for thick bodies,thin surfaces and wakes

A higher‐order panel method for analysing the three‐dimensional potential flow fields around bodies and wakes is presented. The geometric surfaces are represented by continuous curved patches, with no discretization into panels. These geometric patches hold singularity distributions that have C2 continuity, and which are solved by applying Dirichlet or Neumann boundary conditions at discrete collocation points. While higher‐order methods have previously been developed for thick bodies and Dirichlet boundary conditions, this potential flow method is capable of modelling continuous geometry and singularity surfaces over thin bodies and wakes. The continuous surface method has a number of advantages over conventional constant panel methods. Firstly, as curved geometries are represented exactly, changing the order of the solution does not modify the physical shape of the configuration under investigation. Furthermore, the continuous singularity distributions allow velocities to be evaluated accurately across the entire surface rather than just at collocation points. This means that pressure distributions can be calculated exactly without interpolation, and streamlines can be constructed very close to surfaces without problems of divergence. Finally, body and wake surfaces do not exhibit the strong modelling singularities that can present difficulties with wake relaxation. Copyright © 2007 John Wiley & Sons, Ltd.