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Research Papers

An Integrated Computational Welding Mechanics With Direct-Search Optimization for Mitigation of Distortion in an Aluminum Bar Using Side Heating

[+] Author and Article Information
Mahyar Asadi

Mechanical Engineering,
The University of Ottawa, Ottawa,
ON K1N 6N5, Canada
e-mail: masadi@uottawa.ca

John A. Goldak

Mechanical and Aerospace Engineering,
Carleton University, Ottawa,
ON K1S 5B6, Canada
e-mail: jgoldak@mrco2.carleton.ca

1Corresponding author.

Manuscript received October 16, 2012; final manuscript received August 29, 2013; published online November 5, 2013. Editor: Y. Lawrence Yao.

J. Manuf. Sci. Eng 136(1), 011007 (Nov 05, 2013) (10 pages) Paper No: MANU-12-1308; doi: 10.1115/1.4025406 History: Received October 16, 2012; Revised August 29, 2013

Using a computational weld mechanics (CWM) frame-work for exploring a design space, a recent direct-search algorithm from Kolda, Lewis and Torczon is modified to use a least-square approximation to improve the method of following a path to the minimum in the algorithm. To compare the original and modified algorithms, a CWM optimization problem on a 152 × 1220 × 12.5 mm bar of Aluminum 5052-H32 to minimize the weld distortion mitigated by a side heating technique is solved. The CWM optimization problem is to find the best point in the space of side heater design parameters: power, heated area, longitudinal and transverse distance from the weld such that the final distortion is as low as possible (minimized). This CWM optimization problem is constrained to keep the stress level generated by the side heaters, in the elastic region to avoid adding an additional permanent plastic strain to the bar. The number of iterations, size of design of experiments (DOE) matrix required and CPU time to find the minimum for the two algorithms are compared.

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References

Figures

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Fig. 1

Specimen dimensions, fixities, welding direction, and locations of thermocouples, strain gauges, a dial gauge, and extensometers used in validation activity [18]

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Fig. 2

A 2D view of the 3D mesh employed in the analysis

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Fig. 3

Deflection in y direction at the end of the process (×50). Horizontal and vertical axis are x and y.

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Fig. 4

Double ellipsoid parameters; front a2, rear a1, width b, and depth c

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Fig. 5

Relative position of side heater torch to the welding torch in aluminium bar to mitigate the distortion

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Fig. 6

Constraint showing the feasible region for two side heater parameters; power and area. Nodes on the gray zone have the maximum temperature in the side heater below 480 K and therefore generate no-plastic strain.

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Fig. 7

Taguchi main effects plots for r, η, y, and x

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Fig. 8

The objective function response from Table 3

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Fig. 9

The original direct-search algorithm results (Table 4) is illustrated graphically to show the path followed by the algorithm to the minimum

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Fig. 10

The least-square direct-search algorithm results (Table 5) is illustrated in the short path. It is compared to the original direct search, i.e. longer path (Table 4), to show the path followed by either algorithms to the minimum.

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Fig. 11

Final deflection for the weld with no mitigation, when the side heater only applied and the weld mitigated by the side heater. Distance is from the left bottom corner to the right bottom corner of the bar and unit is meter.

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Fig. 12

Longitudinal residual stress in the bar after welding is complete for the weld with no mitigation, when the side heater is only applied and the weld mitigated by the side heater. Residual stress is plotted for a line normal to the weld from the top edge to the bottom edge of the bar at the midlength of the bar. Units are Pa and m for stress and distance, respectively.

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