These process factors, such as pouring temperature, pouring speed, vacuum degree and mold temperature, have an impact on the molding of lost foam casting. According to the structure of the lost foam casting, select the appropriate pouring process parameters, and finally determine the pouring temperature, pouring speed and vacuum degree as the three main process conditions as the influencing factors. The main purpose of the author’s test is to explore the tendency of hot crack defects in lost foam castings when the pouring temperature is 1560~1600 ℃, the vacuum degree is 0.04~0.06 MPa, and the pouring speed is 74~104 mm/s. The side injection gating system is selected to analyze the parts with high hot cracking tendency of the lost foam casting. According to the maximum value of the hot cracking index, the Box-Behnken effect surface method is adopted. Through the analysis of the test results, the optimal process parameter combination is sought to maximize the quality of the lost foam casting.

The Box-Behnken experimental design can evaluate the nonlinear relationship between indicators and factors, find out the optimal region, establish the model of the optimal region, and find out the optimal value of the response. The hot crack index Y is used as the response value. In ProCAST software, the hot crack index is defined based on the hot crack criterion of stress and strain, which qualitatively explains the tendency of hot crack in lost foam castings. The levels of pouring temperature T, vacuum M and pouring speed V are shown in Table 1. The evaluation index is the size of the hot crack index in the lost foam casting. The size of the hot crack index in the hot crack indicator can directly reflect the hot crack defect tendency of the lost foam casting. The higher the hot crack index, the greater the probability of hot crack occurrence.

Horizontal	T /℃	M/MPa	V /( mm·s^－1 )
-1	1 560	0.04	74
0	1 580	0.05	89
1	1 600	0.06	104

The Box-Behnken test design was carried out by using Design-expert software. The test plan consists of 17 groups of tests. ProCAST software was used to simulate each group of tests.

The regression equation is obtained by fitting with Design-expert software:

According to the test results, a second-order response model is constructed, and the significance test and variance analysis are carried out for the established mathematical model. The significance of the model is expressed by P, and the smaller P is, the more significant the model is. The fitting degree of the regression equation is expressed by R2. The larger R2 is, the greater the fitting degree is. The overall model P is 0.0008, the mismatched term P is 0.135 3, greater than 0.05, not significant, and the regression equation R2 is 0.951 6, indicating that the regression quadratic equation is extremely significant, which can be used for prediction and analysis. The true value and predicted value of the model are shown in the figure. The abscissa is the true value, and the ordinate is the predicted response value obtained by fitting the second-order regression equation. The slash indicates that the predicted value is equal to the true value. It can be seen from the figure that the fitting points are around the oblique line, which indicates that the second-order model has a high reliability.