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Research Papers

Partial Differential Equation-Based Multivariable Control Input Optimization for Laser-Aided Powder Deposition Processes

[+] Author and Article Information
Xiaoqing Cao

International Center for Automotive Research,
Clemson University,
4 Research Drive,
Greenville, SC 29607
e-mail: xiaoqin@g.clemson.edu

Beshah Ayalew

Mem. ASME
International Center for Automotive Research,
Clemson University,
4 Research Drive,
Greenville, SC 29607
e-mail: beshah@clemson.edu

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received June 26, 2014; final manuscript received July 14, 2015; published online October 1, 2015. Assoc. Editor: Jack Zhou.

J. Manuf. Sci. Eng 138(3), 031001 (Oct 01, 2015) (8 pages) Paper No: MANU-14-1348; doi: 10.1115/1.4031265 History: Received June 26, 2014; Revised July 14, 2015

This paper deals with the systematic optimization method for multiple input variables (laser irradiation power and scanning speed) in a class of laser-aided powder deposition (LAPD) processes. These processes are normally described by a coupled system of nonlinear partial differential equations (PDEs). To begin with, a desired solid–liquid (S/L) interface geometry is first approximated from a few practical process target parameters that define the desired process properties. Then, the control problem is formulated as one of seeking the optimal combination of process inputs that achieves close tracking of the desired S/L interface in quasi-steady state. The paper details the derivation of the adjoint-based solution for this PDE-constrained multivariable control input optimization problem. The effectiveness of the proposed method is illustrated via a case study on a laser cladding process.

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Figures

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Fig. 1

Schematic of the LAPD processes

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Fig. 2

Mathematical modeling of the process

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Fig. 3

Evolution of multiple control inputs (laser power and scanning speed) in the optimization. Optimal control inputs u= 495.5 W and v= 7.27 mm/s

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Fig. 4

Iterations of S/L interface in the optimization. Optimized S/L interface approaches the well-designed (desired) S/L interface under the proposed computational algorithm.

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Fig. 5

Iterations of temperature error percentage on S/L interface. Temperature T on the predefined S/L interface approaches the melting temperature Tm (where S/L interface is defined) with optimization iterations, resulting in a close tracking of the predefined S/L interface under the proposed computational algorithm.

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Fig. 6

Iterations of objective function in the optimization

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Fig. 7

Parabolic S/L interface approximation. The well-designed S/L interface (dashed line) serves as an ideal case where the process target parameters are included with physical feasibility. The practically designed S/L interface (solid line) is approximated from the proposed parabolic function in Eq. (8).

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Fig. 8

Comparison of optimized S/L interfaces with and without the weighting function. With the proposed weighting method (solid line), a better tracking in terms of the process target parameters is achieved compared with that without this weighting method (dashed line).

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