Although the extrapolation method is relatively simple to calculate the interface heat transfer coefficient, the calculation error is easy to enlarge and the temperature measurement accuracy is too high. The inverse algorithm is the most commonly used method to solve the heat transfer coefficient of the casting die interface. Its central idea is to minimize the difference between the measured and calculated temperature at a specific position.
Beck The inverse algorithm is to measure the temperature change of liquid metal and mold directly through experiments, and assume that the heat flux or the heat transfer coefficient of casting mold interface is constant or that these parameters change linearly in a certain period of time. On this basis, the temperature field is solved, and the least square method is used to make the temperature difference between the measured temperature and the calculated temperature In order to obtain the heat transfer coefficient of the interface, the difference between the heat transfer coefficient and the heat transfer coefficient is minimized. In the early research of interface heat transfer in, Ho and pehlke used Beck inverse algorithm to study the interface heat transfer between casting and die. Liu Baicheng, Xiong Shoumei and others are the early domestic scholars who used Beck algorithm to calculate the heat transfer coefficient of the casting mold interface. They studied the heat transfer behavior of the interface between the casting and the mold in the metal mold casting process, and elaborated the influence of the solidification process of the interface on the heat transfer behavior of the interface. After that, a large number of scholars used Beck inverse algorithm to study the interface heat transfer behavior of EPC, directional solidification, squeeze casting, die casting and continuous casting.
In addition to Beck inverse algorithm, regularization method and optimization method are also the methods that researchers focus on.
Tikhonov et al. Obtained the objective function for solving the heat transfer coefficient of casting die interface in solidification process according to the regularized universal function, which is the regularization method for calculating the heat transfer coefficient of casting die interface. Sui Dashan et al. Studied the heat transfer behavior of casting mold interface based on regularization method, and discussed the stability of parameter identification in various algorithms. Dong et al. Used regularization method to study the interface heat transfer behavior between Ni based superalloy and shell during investment casting.