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A new technique for three-dimensional transient heat transfer computations of autogenous arc welding

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An Erratum to this article was published on 01 June 1991

Abstract

Three-dimensional (3-D) transient temperature variations during autogenous gas tungsten arc welding are determined. The heat diffusion equation is solved using an efficient semidiscrete technique. The model employs a combination of unequally spaced grids concentrated near the moving torch in order to minimize the total number of nodes. Finite differencing is used for the spatial terms. The resulting ordinary differential equations for the transient evolution of thermal transport are solved using the fourth-order Runge-Kutta technique. The temperaturedependent thermal properties and latent heats of phase transformations are accounted for. Computations are carried out for a rectangular parallelepiped with convective and radiative surface thermal conditions. Sample results are presented first for the evolution of thermal profiles during ideal welding conditions. These are next compared with variations obtained due to defects, such as weld track misalignment and inclusions. The potential use of this model in the development of an expert welding system using infrared imagery is indicated.

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Abbreviations

Bi:

grid Biot number in the coarse zone

C p :

specific heat of the solid based on uniform and constant properties

Fo:

grid Fourier number based on uniform and constant properties

h :

surface heat transfer coefficient

H :

local enthalpy per unit volume in the fine zone

i :

nodal index in thex direction

j :

nodal index in they direction

k :

nodal index in the z direction

K :

material thermal conductivity (subscripted values refer to the fine zone)

q :

volumetric energy generation rate in the fine zone

q0 :

volumetric energy generation rate under the arc center

Q:

energy input rate by the torch into the workpiece

t :

time

T :

local temperature within the workpiece in a coordinate system moving with the arc

Tinf :

ambient temperature

v x :

velocity component of torch motion in thex direction during misalignment referenced to a fixed coordinate system

v y :

velocity component of torch motion in they direction referenced to a fixed coordinate system

x :

coordinate axis along the lateral direction

Δx :

grid size

X f :

distance of the closestyz face of a flaw from the origin

Δxf :

dimension of the nonfusion zone in thex direction

y :

coordinate axis along the direction of torch motion

Δyf :

dimension of the nonfusion zone in they direction

z:

coordinate axis extending downward into the workpiece from the surface

Δzf :

dimension of the nonfusion zone in the z direction

z f :

depth at which a flaw begins

α :

thermal diffusivity in the medium and coarse zones

ε :

surface emissivity value in the fine zone

ρ :

density

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Author information

Authors and Affiliations

  1. United States Navy, 93943, Monterey, CA

    Robert L. Ule (Lieutenant Commander)

  2. Department of Mechanical Engineering, 93943, Monterey, CA

    Yogendra Joshi (Associate Professor)

  3. United States Navy, Naval Postgraduate School, 93943, Monterey, CA

    Eugene B. Sedy (Lieutenant)

Authors
  1. Robert L. Ule
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  2. Yogendra Joshi
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  3. Eugene B. Sedy
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Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/BF02651237.

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Ule, R.L., Joshi, Y. & Sedy, E.B. A new technique for three-dimensional transient heat transfer computations of autogenous arc welding. Metall Trans B 21, 1033–1047 (1990). https://doi.org/10.1007/BF02670274

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  • DOI: https://doi.org/10.1007/BF02670274

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