Laser Bending Forming and Laser Assisted Prestress Forming Both methods use laser to locally heat the sheet metal structure so as to generate a certain non-uniform temperature field in the local area to further make the sheet metal locally plastic Deformation, in order to achieve the purpose of forming. In order to protect the performance of forming parts, the process needs to strictly limit the laser process parameters. Therefore, to understand the laser process parameters and processing temperature changes, the relationship between the distribution is extremely important. Recently, the Key Laboratory of Advanced Manufacturing Mechanics of Mechanics, Chinese Academy of Sciences, based on the physical model of laser acting on a finite plate, gives an analytical solution of the temperature distribution in the process, which can be used to quickly calculate certain process parameters (power density, spot Radius, moving speed) under the laser temperature distribution. Related Achievements Online Posted by Applied Mathematical Modeling ()
For the laser field model of the temperature field of sheet metal (Figure 1), the main research methods include analytical methods, numerical methods and artificial intelligence methods. The numerical method and artificial intelligence method can simulate complex working conditions more accurately, but in general it takes a lot of time. There is also a need to create a large number of training samples for the AI ​​method. In contrast, the analytical method can predict the temperature field to a certain extent. In this work, the convective heat transfer boundary conditions are considered, and the three-dimensional heat conduction equation of the finite large boundary is solved directly to obtain the temperature field as a function of time. Firstly, the eigenvalue problem corresponding to the model is solved by the method of separation of variables, and a complete set of basis functions (eigenfunctions) is obtained. Then the nonhomogeneous term and temperature function of the equation are expanded on the basis function to the series form, the coefficient is to be determined. Finally, the series is substituted into the original equation, and the coefficients are obtained by integral transformation to obtain the analytical solution of the temperature field (Figure 2). In the actual solution process, due to the exponential term, the series converge faster and the calculation cost is small. In addition, the temperature distribution at any laser scanning path can be handled by a quasi-Monte Carlo method that uses a low-variance sequence. Therefore, for any given laser scanning path, the temperature of any point at any moment can be quickly obtained by this equation. Further, this study verifies the correctness of the solution through experiments and finite element analysis. Verification experiments using aluminum alloy AA6061T6 plate as the object, YAG continuous wave laser system as a light source, and record the laser scanning process P1, P2, P3 point (Figure 1) the temperature history. The results show that the measurement results, the finite element model and the analytical solution are consistent within a certain range.
The above research has won the support of NSFC Youth Fund Project.
Fig.1 The physical model of the laser acting on a finite sheet
Figure 2 Temperature field analytical solution
Figure 3 analytical solution of the experiment, finite element verification
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