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Research Papers

# Heating Position Planning in Laser Forming of Single Curved Shapes Based on Probability Convergence

[+] Author and Article Information
Hong Shen

School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China;
State Key Laboratory of Mechanical System
and Vibration,
Shanghai 200240, China
e-mail: sh_0320@sjtu.edu.cn

Yutao Zheng, Han Wang

School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China

Zhenqiang Yao

School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China;
State Key Laboratory of Mechanical System
and Vibration,
Shanghai 200240, China

Manuscript received November 2, 2015; final manuscript received December 16, 2015; published online June 20, 2016. Assoc. Editor: Matteo Strano.

J. Manuf. Sci. Eng 138(9), 091003 (Jun 20, 2016) (7 pages) Paper No: MANU-15-1547; doi: 10.1115/1.4032394 History: Received November 02, 2015; Revised December 16, 2015

## Abstract

Inverse problem in laser forming involves the heating position planning and the determination of heating parameters. In this study, the heating positions are optimized in laser forming of single curved shapes based on the processing efficiency. The algorithm uses a probability function to initialize the heating position that is considered to be the bending points. The optimization process is to minimize the total processing time through adjusting the heating positions by considering the boundary conditions of the offset distances, the minimum bending angle, and the minimum distance between two adjacent heating positions. The optimized results are compared with those obtained by the distance-based model as well as the experimental data.

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## Figures

Fig. 1

Schematic of laser forming process of a single curve shape

Fig. 2

Overall strategy for planning heating positions based on the processing time

Fig. 3

The partition of the target curve

Fig. 4

Boundary condition: error band

Fig. 5

Boundary condition: minimum bending angle

Fig. 6

Boundary condition: minimum distance between two heating positions. (a) Move left, (b) move right, and (c) move both sides.

Fig. 7

Flowchart of generating the new heating position

Fig. 8

Heating point moving between the error band

Fig. 9

Experimental setup of laser forming: (a) laser heating, (b) displacement sensor, and (c) measurement scheme

Fig. 10

Experiment-determined relationship between laser power, scanning velocity, and bending angle: (a) fitted surface by RSM (R2: 0.9873) and (b) error distribution (RMSE: 0.03259 deg)

Fig. 11

Case 1: Heating position planning based on the distance-based model

Fig. 12

Case 1: Heating position planning based on the present model

Fig. 13

Case 2: Heating position planning based on the distance-based model

Fig. 14

Case 2: Heating position planning based on the present model

Fig. 15

Experimental samples for cases 1 and 2

Fig. 16

Experimental results based on the present model: (a) case 1 and (b) case 2

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