Objective Precision achievable by laser bending is a critical factor affecting its practical application. It is difficult to control the accuracy of the bending angle at a high level due to the influence of factors, such as the geometric size and initial state of a sheet and the process parameters, even for linear scanning of a single scanning path. To achieve high-precision single-curved laser bending, not only the error of the bending angle at the single scanning path should be considered but also other factors that will affect the accuracy of bending, so as to devise a strategy to improve bending accuracy. In this research, we improve the scanning path planning method and propose a method to compensate for the error of the laser-bending angle. Each time the bend at a scanning path is completed, the bending angle at the next scanning path is redetermined to compensate for the bending angle error in the previous scanning path. This method allows a large tolerance for the bending angle at each scanning path, which reduces the process requirements. The proposed method will help realize the high-precision of 3D laser bending and the further practical application of laser bending.
Methods First, using the improved Denavit-Hatenberg (D-H) modeling method in robotics, the coordinate system of each bending section of a sheet is established, and the mathematical description of the curved sheet and target single surface in the same coordinate system is obtained by coordinate transformation. Therefore, the problem of sheet bending error is transformed into a problem of deviation of the segment to be bent from the target surface. Then, based on the D-H modeling method, the geometric influence factors of the bending angle tolerance at different scanning paths of cylindrical surface forming as well as the degree to which these factors affect the forming accuracy are analyzed. Afterward, based on the fact that a bending section completed first will not affect the forming error of a bending section completed later, a compensation method for the bending angle error at each scanning path is proposed. The deviation of the bending section from the scanning path is compared for two cases (using and not using the compensation method during forming) by forming simulation. Finally, an experiment is designed to verify the error compensation method; the improved D-H modeling method is also used to measure the bending angle in the experiment. During the experiment, the influence of factors, such as the initial state of a sheet and the perpendicularity between the sheet and laser displacement sensor, on the measurement results are considered. The heating conditions are obtained through laser-bending experiments on small-sized sheets.
Results and Discussions The tolerance design for cylindrical surface forming shows that the number of scanning paths have the greatest influence on the bending angle tolerance at a single scanning path (Fig. 4). Compared with a method with one-sided initial profile deviation, the proposed path planning method with two-sided initial profile deviation can reduce the number of scanning paths under the same maximum profile deviation or scanning paths (Fig. 6). The proposed method can effectively reduce the deviation of the curved section from the planned path. Without error compensation, the deviation is much greater under the same bending angle error, compared with using error compensation (Fig. 9). A half-sine surface forming experiment is designed to verify the error compensation method. The formed half-sine surface has high accuracy, and the overall profile deviation is about -0.15--0.25 mm (Figure 14).
Conclusions The improved D-H modeling method can be conveniently used for tolerance analysis, error compensation, and bending angle measurement of single-curved surface laser bending. Through the tolerance design of the bending angle of the laser bending forming of a cylindrical surface, it is found that the number of scanning paths has the most significant influence on the bending angle tolerance at each scanning path. Particularly, the number of scanning paths affects the overall size of the bending angle tolerance; the more the number of scanning paths, the narrower the bending angle tolerance band at each scanning path. The proposed path planning method with two-sided initial profile deviation can reduce the initial profile deviation of path planning. The proposed error compensation method improves the accuracy of the single-curved laser bending. It has a low tolerance requirements for the bending angle of a single scanning path and allows the two-sided error of the curved section to the target surface. The forming experiment of a half-sine surface is designed to verify the error compensation method. The formed parts have high accuracy, which show that the proposed error compensation method is effective.
