Evaluation of drawing force by a new dimensionless method in deep drawing process

In this research, geometric parameters were given in dimensionless form by the Π- Buckingham dimensional analysis method in the dimensionless group for deep drawing of a round cup. To find the best group of dimensionless parameters and the fittest dimensionless relational model, three scales of the cup are evaluated numerically by a commercial finite element software and stepwise regression modeling. After analyzing all effective geometric parameters, a fittest relational model among dimensionless parameters is found. In addition, the results of the new dimensionless model were compared with the simulation process and experimental tests. From the results, it is inferred that the geometric qualities of a large scale can be predicted with a small scale by the proposed dimensionless model. Comparing the results of the dimensionless model with experimental tests shows that the proposed dimensionless model has fine precision in the determination of geometrical parameters and drawing force estimation. Moreover, to evaluate the accuracy of the proposed dimensionless model, the predicted value of the model has been compared by the experimental results. It is shown that the dimensionless ratios of geometrical parameters can significantly affect the estimation of the drawing force by the proposed dimensionless model, but based on similarity law, because of the constant value of these dimensionless parameters in different scales, they could not be used for dimensionless analysis separately. It is also inferred that because of the effect of contact area on the coefficient of friction, which is changed by scale changing, the only dimensionless parameter that can significantly change the drawing force is the coefficient of friction. Finally, it is shown that the dimensionless geometrical parameter and the coefficient friction should be combined for dimensionless analysis.