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In this research, geometric parameters were given in dimensionless form by the Buckingham pi dimensional analysis method, and a series of dimensionless groups were found for deep drawing of the round cup. To find the best group of dimensionless geometric parameters, three scales are evaluated by commercial FE software. After analyzing all effective geometric parameters, a fittest relational model of dimensionless parameters is found. St12 sheet metals were used for experimental validation, which were formed at room temperature. In addition, results and response parameters were compared in the simulation process, experimental tests, and proposed dimensionless models. By looking at the results, it very well may be inferred that geometric qualities of a large scale can be predicted with a small scale by utilizing the proposed dimensionless model. Comparison of the outcomes for dimensionless models and experimental tests shows that the proposed dimensionless models have fine precision in determining geometrical parameters and drawing force estimation. Moreover, generalizing proposed dimensionless model was applied to ensure the estimating precision of geometric values in larger scales by smaller scales.

Investigation of a new methodology for the prediction of drawing force in deep drawing process with respect to dimensionless analysis