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.

Research results performed by researchers have illustrated that applying electric current to a deforming metal can lead to a reduction in the required deformation force and an improvement in the formability. This technique is known as electrically assisted forming and is used in various forming processes. In this paper, the forming of square cups through electrically assisted deep drawing process was investigated experimentally and the effects of process parameters, including current magnitude, pulse frequency, and waveform (sinusoidal and square) on the forming force, thickness distribution, and drawing depth are examined. In this regard, after designing and preparing the test setup and forming square cups, the experimental results obtained were compared to those of the conventional deep drawing tests. The results showed that increasing the current magnitude leads to reducing the maximum thinning and the forming force in the deep drawing process of the formed parts. Furthermore, it was found that at a higher frequency, the deformation force decreases significantly and thickness distribution becomes more uniform. The comparison of the two waveforms of pulses demonstrated that the sinusoidal waveform has a relatively more significant effect on the reduction of the force and thickness distribution and a considerable effect on the drawing depth.