Inverse determination of laser power on laser welding with a given width penetration by a modified Newton–Raphson method

In this paper, the inverse determination of the laser power in welding process with a given width penetration using the modified Newton–Raphson method (MRN) is presented. The advantage of this inverse method does not adopt the nonlinear least-squares error to formulate the inverse problem, but it is implemented a direct comparison between the known melting temperature and the computed melting temperature. The isothermal elliptic shape at the bottom surface is considered, and two “auxiliary” variables including a semi-major axis and an elliptic center are added into the formulation. Two examples are used to demonstrate the proposed method. The results shows that the proposed method is an accurate and robust method to inversely estimate the laser power for a given width penetration.