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Metallurgical and Materials Transactions B

, Volume 24, Issue 3, pp 545–545 | Cite as

Erratum to Beam focusing characteristics and alloying element effects on high-intensity electron beam welding

  • P. S. Wei
  • Y. T. Chow
Erratum
  • 132 Downloads

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.

Nomenclature

A

Ur /2α

d

cavity opening diameter

drn

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

ks

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

RA, RB

constituent specific gas constant

rb

Gaussian distribution parameter

rf

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

Tm

temperature

Tx

ambient temperature

U

welding speed

w

weight percentage

X

mole fraction

z

depthwise coordinate

-ga

liquid thermal diffusivity

αf

regularity constant

αs

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

Copyright information

© The Minerals, Metals & Material Society 1993

Authors and Affiliations

  • P. S. Wei
    • 1
  • Y. T. Chow
    • 2
  1. 1.Institute of Mechanical EngineeringNational Sun Yat-Sen UniversityKaohsiungChina
  2. 2.National Chung-Shan Institute of Science and TechnologyChung-LiChina

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