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Research Papers: Heat Transfer in Manufacturing

# Simplified Two-Dimensional Analytical Model for Friction Stir Welding Heat Transfer

[+] Author and Article Information
Satish Perivilli1

Department of Mechanical Engineering, Tennessee Technological University, Cookeville, TN 38505svperivill21@tntech.edu

John Peddieson, Jie Cui

Department of Mechanical Engineering, Tennessee Technological University, Cookeville, TN 38505

1

Corresponding author; present address: TRAX LLC., Forest, VA 24551.

J. Heat Transfer 130(9), 092101 (Jul 03, 2008) (9 pages) doi:10.1115/1.2927401 History: Received January 17, 2007; Revised March 27, 2007; Published July 03, 2008

## Abstract

A two-dimensional heat transfer problem pertaining to friction stir welding is developed by converting various pin tool configurations of interest to a simplified pin only configuration by assigning an equivalent heat flux to the pin surface. Mechanical dissipation heating, responsible for the welding, is modeled by means of a thermal boundary condition at the pin surface. A series solution is developed for the temperature distributions in the workpiece (assumed to be infinite) and these distributions are analyzed at various radial and circumferential locations. It is found that the closed form solutions developed are not influenced greatly by the truncation numbers of this series. Maximum reduced temperatures pertinent to configurations available in literature are estimated from the series and one term solutions developed and compared with those observed. Furthermore, the applicability of one term solution of this series is tested for various parametric combinations based on models available in literature. It is found that the one term solution can be applied to within a reasonable range of the process governing parameters.

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## Figures

Figure 6

Circumferential reduced radial heat flux distributions for mechanical dissipation heating (P=0.1, B=0, and ε=1)

Figure 7

Circumferential reduced temperature distributions for mechanical dissipation heating ((—) Eq. 64 and (▲) Eq. 60 with N=0, P=0.1, B=0, and ε=1)

Figure 1

Coordinate systems used for analysis

Figure 2

Schematic of various FSW pin tool configurations (() pin tool; (⧅) workpiece)

Figure 3

Variation of actual and idealized yield stress with temperature for aluminum alloys

Figure 4

Circumferential reduced temperature distribution for mechanical dissipation heating and selected summation maxima, ((—) Eq. 60 with N=1–5; (▲) Eq. 60 with N=0, P=0.1, B=0, and ε=1)

Figure 5

Circumferential reduced temperature distributions for mechanical dissipation heating (P=0.1, B=0, and ε=1)

Figure 8

Circumferential reduced temperature distributions for constant surface temperature (P=0.1 and B=0)

Figure 9

Circumferential reduced temperature distributions for constant surface heat flux (P=0.1 and B=0)

Figure 10

Circumferential reduced temperature distributions for mechanical dissipation heating ((—) series solution and (▲) one term solution with P=0.1, B=0.001, and ε=1.0)

Figure 11

Circumferential reduced temperature distributions for mechanical dissipation heating ((—) series solution and (▲) one term solution with P=0.1, B=0.003, and ε=1.0)

Figure 12

Circumferential reduced temperature distributions for mechanical dissipation heating ((—) series solution and (▲) one term solution with P=0.1, B=0.002, and ε=0.05)

Figure 13

Circumferential reduced temperature distributions for mechanical dissipation heating ((—) series solution and (▲) one term solution with P=0.1, B=0.002, and ε=1.0)

Figure 14

Circumferential reduced temperature distributions for mechanical dissipation heating ((—) series solution and (▲) one term solution with P=0.1, B=0, and ε=0.15)

Figure 15

Circumferential reduced temperature distributions for mechanical dissipation heating ((—) series solution and (▲) one term solution with P=0.3, B=0, and ε=0.15)

Figure 16

Circumferential reduced temperature distributions for mechanical dissipation heating ((—) series solution and (▲) one term solution with P=0.5, B=0, and ε=0.15)

## Errata

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