# Verification of reverse calculation program for squeeze casting

Through the inverse algorithm, the mathematical model for calculating the interface heat flux and die surface temperature is established, and the corresponding program is compiled. In order to verify the accuracy of the back calculation program, it is necessary to compare the estimated heat flux with the accurate value. Therefore, a one-dimensional heat conduction model with a length of 10 mm is established in this paper. A given heat flux boundary is applied at one end of the model, and the adiabatic boundary is applied at the other end. The material of the model is H13 steel. The temperature distribution in the model can be obtained by calculation, and the given heat flux and the calculated temperature are marked as “accurate value”. Then, with the calculated temperature as the input data, the corresponding heat flux can be calculated by using the inverse calculation program. By comparing the estimated heat flux with the accurate value, the accuracy of the back calculation program can be verified.

The total action time of given heat flux is 5S, the maximum value of heat flux is 2MW / m2, the action time of triangle region of heat flux is 1s, and the value of heat flux in other time is 0.0005 MW / m2.

Firstly, the equilateral triangle heat flux is used for the given heat flux, as shown in Figure 1. In this example, the temperature distribution at 3mm and 6mm away from the boundary is used as the input condition of the back calculation program. The time interval of the program is Δ t = 1 / F, where f is the sampling frequency of 50 Hz. The future time step R is 4. As shown in Figure 1, the heat flux and surface temperature obtained by inverse calculation are in good agreement with the accurate values. This shows that the back calculation program can accurately calculate the heat flux and surface temperature.

Second, given the heat flux, the right triangle heat flux is used to verify the ability of the inverse program to deal with the rapidly changing heat flux, as shown in Figure 2. All the parameters are the same as those of the equilateral triangle heat flow example. As shown in Figure 2, the maximum heat flux is 2.4 MW / m2, and the maximum calculation error is 51%. This shows that these parameters are not suitable for back calculation program.

Finally, the right triangle heat flux is still used for the given heat flux. In this example, the temperature distribution at 1 mm and 6 mm away from the boundary is used as the input condition of the back calculation program, and the sampling frequency is 200 Hz. As shown in Figure 3, the maximum error between the estimated heat flux and the accurate value is 5%, and the calculated surface temperature is in good agreement with the accurate value. This proves that the program has the ability to deal with rapidly changing heat flux under suitable parameters.

In the process of squeeze casting, the heat flux changes sharply at the time of pouring and pressure application. Therefore, in order to accurately calculate the interface heat transfer coefficient, the thermocouple needs to be installed at 1 mm, 3 mm and 6 mm away from the mold surface, and the sampling frequency of the data acquisition system should be set to 200 Hz.

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