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

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.