Predicting Tearing Force for Square Cup Deep Drawing Process by Dimensionless Analysis of the Effective Geometric Parameters

In this research, a dimensionless model was developed based on the geometric parameters for the deep drawing process to reduce the manufacturing cost of square cup deep drawing in the large scales. In the following, a series of groups were found for dimensionless ratios based on the geometric parameters of the square cup by Π-Buckingham dimensional analysis method in the two states of circular and square sheets. In order to find the best group of dimensionless geometric parameters, three scales of cups were numerically evaluated by commercial finite elements software. The results were validated by an experimental test. After analyzing all the effective geometric parameters, a fittest dimensionless equation was obtained. The st12 metal sheet was used for experimental validation in the room temperature. Moreover, the results and tearing force as target parameter were compared in simulation states, experimental tests and the proposed dimensionless model based on Π-Buckingham theory. By comparing the results in the two states of the circular and square sheets, it can be concluded that the geometric characteristics of the main scale sample can be predicted by a sample in a small size through the proposed dimensionless model. Comparison of the results of the dimensionless model and experiments show that the proposed model has high accuracy in predicting the tearing force and geometric parameters in the square cup deep drawing process.