Abstract
Effects of focusing characteristics of the beam as well as concentrations of a volatile alloying element in the workpiece on the shape of the cavity produced by a high-energy beam are systematically and quantitatively investigated. The energy flux of the focused energy beam is independently specified by the convergence angle, the energy distribution parameter at the focal spot, and the focal spot location relative to the workpiece surface. Energy flux at any cross section of the beam is a Gaussian distribution. The geometry of the cavity is determined by satisfying interfacial energy and momentum balances. By accounting for beam focusing characteristics, the cavity surface temperatures, depths of penetration, and cavity shapes are found to agree with experimental data. The opening diameter and depth of the cavity depend primarily upon the energy distribution parameter at the workpiece surface for a surface-focused weld t increase in the content of the volatile alloying element zinc in aluminum exhibits a pronounced influence on the shape of the cavity.
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Abbreviations
- A :
-
Ur /2α
- d :
-
cavity opening diameter
- dr n :
-
differential length normal to the energy beam, as shown in Figure 1
- f, F :
-
dimensional and dimensionless focal spot position measured from workpiece surface,F =f/rf
- g :
-
gravitational acceleration
- h :
-
cavity penetration depth
- k :
-
liquid thermal conductivity
- k s :
-
solid thermal conductivity
- l :
-
depthwise coordinate along cavity wall shown in Figure 1
- n :
-
normal to cavity surface toward workpiece
- p, P :
-
vapor pressure and total vapor pressure
- q, Q :
-
energy flux and beam power
- r :
-
polar coordinate
- R A, RB :
-
constituent specific gas constant
- r b :
-
Gaussian distribution parameter
- r f :
-
energy distribution parameter at focal spot
- r :
-
local cavity radius
- s :
-
distance between energy-beam axis and cavity center
- T,Tc :
-
temperature, constant, and melting
- T m :
-
temperature
- T x :
-
ambient temperature
- U :
-
welding speed
- w :
-
weight percentage
- X :
-
mole fraction
- z:
-
depthwise coordinate
- -ga :
-
liquid thermal diffusivity
- α f :
-
regularity constant
- α s :
-
solid thermal diffusivity
- gb :
-
half convergence angle shown in Figure 1
- β′ :
-
angle shown in Figure 1
- γ :
-
activity coefficient
- τ:
-
angle shown in Figure 1
- σ-, σm :
-
surface tension and surface tension at melting temperature; σ= σm + (dσ/dT) (T- Tm), wheredσ/dT is a constant
- ϕ :
-
polar angle shown in Figure 1
- A :
-
solvent
- b :
-
boiling
- B :
-
alloying element
- m :
-
iteration number mean value vapor phase
- *:
-
dimensionless quantity
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Formerly Graduate Student, Institute of Mechanical Engineering.
The online version of the original article can be found athttp://dx.doi.org/10.1007/BF02654040
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Wei, P.S., Chow, Y.T. Erratum to Beam focusing characteristics and alloying element effects on high-intensity electron beam welding. Metall Trans B 24, 545 (1993). https://doi.org/10.1007/BF02666439
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DOI: https://doi.org/10.1007/BF02666439