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Research Papers

Incremental Bending of Three-Dimensional Free Form Metal Plates Using Minimum Energy Principle and Model-Less Control

[+] Author and Article Information
Xiaobing Dang

Department of Mechanical and
Automation Engineering,
Institute of Precision Engineering,
The Chinese University of Hong Kong,
Hong Kong
e-mail: xbdang@mae.cuhk.edu.hk

Kai He

Shenzhen Key Laboratory of
Precision Engineering,
Shenzhen Institutes of Advanced Technology,
Chinese Academy of Sciences,
Shenzhen 518055, China
e-mail: kai.he@siat.ac.cn

Wei Li

Shenzhen Key Laboratory of
Precision Engineering,
Shenzhen Institutes of Advanced Technology,
Chinese Academy of Sciences,
Shenzhen 518055, China
e-mail: wei.li0327@hotmail.com

Qiyang Zuo

Shenzhen Key Laboratory of Precision
Engineering,
Shenzhen Institutes of Advanced Technology,
Chinese Academy of Sciences,
Shenzhen 518055, China;
Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208
e-mail: qy.zuo@siat.ac.cn

Ruxu Du

Professor
Fellow ASME
Department of Mechanical and
Automation Engineering,
Institute of Precision Engineering,
The Chinese University of Hong Kong,
Hong Kong
e-mail: rdu@mae.cuhk.edu.hk

1Corresponding author.

Manuscript received October 16, 2016; final manuscript received January 13, 2017; published online March 9, 2017. Assoc. Editor: Gracious Ngaile.

J. Manuf. Sci. Eng 139(7), 071009 (Mar 09, 2017) (9 pages) Paper No: MANU-16-1548; doi: 10.1115/1.4035796 History: Received October 16, 2016; Revised January 13, 2017

Bending 3D free form metal plates is a common process used in many heavy industries such as shipbuilding. The traditional method is the so-called line heating method, which is not only labor intensive but also inefficient and error-prone. This paper presents a new incremental bending method based on minimum energy principle and model-less control. First, the sheet metal is discretized into a number of strips connected through virtual springs. Next, by applying the minimum energy principle, the punching and supporting points are calculated for the strip. Then, the bended shape of the strip is computed based on the beam bending theory. This process is continued until the final shape is reached. To compensate the bending error, the computer vision-based model-less control is applied. The computer vision detects the bending error based on which additional bending steps are calculated. The new method is tested in a custom build incremental bending machine. Different metal plates are formed. For a metal plate of 1000 × 800 × 5 mm3, the average bending error is less than 3 mm. In comparison with the existing methods, the new method has a number of advantages, including simple, fast, and highly energy efficient.

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Figures

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Fig. 1

Schematic illustration of the incremental bending process

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Fig. 2

The CAD model of the incremental bending machine

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Fig. 3

Discretization of a metal plate

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Fig. 4

Schematic illustration of discretized strips

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Fig. 5

Schematic illustration of the punching and supporting points

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Fig. 6

The punching and supporting points in (a) first-order case: it can be modeled as a cantilever beam; (b) second-order case: it can be modeled as a simply supported beam; and (c) higher-order case: it is a combination of the first- and the second-order cases

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Fig. 7

A typical strain distribution of the strip after one punch: (a) first-order case and (b) second-order case

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Fig. 8

Schematic illustration of the forming process

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Fig. 9

Flow chart of the incremental bending

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Fig. 10

Prototype machine used for experiments

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Fig. 11

Single curvature metal plate bending: (a) the designed surface and (b) the curve of a strip

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Fig. 12

The punching trajectory for single curvature metal plate

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Fig. 13

The experiment result in single curvature metal plate bending: (a) the bended plate; (b) the measured curve of the midline of the plate with a comparison of the designed curve; and (c) the error between the measured curve and the designed curve

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Fig. 14

Three-dimensional free form metal plate bending: (a) the designed surface and (b) the curves of the three strips

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Fig. 15

The punching trajectory for 3D free form metal plate

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Fig. 16

The experiment result in 3D free form metal plate bending: (a) the bended plate; (b) the measured curves of the three strips with a comparison of the designed curves; and (c) the error between the measured curves and the designed curves

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Fig. 17

The matching of the two bended metal plates, one with single curvature surface and the other with 3D free form surface

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Fig. 18

The measured curves at the matching edges of the two bended metal plates: (a) the measured curves and (b) the error

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