Development a new methodology for measuring deep drawing forces based on dimensionless evaluation

In this research work, dimensionless models based on geometric parameters have been developed for the deep drawing process of rectangular cups to reduce the manufacturing costs on a large scale of application in a noticeable way. In the following, geometric parameters were given in dimensionless form by the Π-Buckingham dimensional analysis method and a series of dimensionless groups were found for both circular and rectangular initial blank. To find the best group of dimensionless geometric parameters, different cup scales 1:1, 2:1, 4:1 and 5:1 are evaluated numerically by ABAQUS Finite Element (FE) software, validated by experimental work. After all effective geometric parameters have been analyzed, the best fitting relational model of dimensionless parameters is found for rectangular and circular blank separately. Various thicknesses of St12 sheet metals were used for experimental validation, which were formed at room temperature. Also, results and response parameters were compared in the simulation process, experimental tests and dimensionless models. By looking at the outcomes, it is demonstrated that the geometric qualities of a large scale can be predicted by a small scale, utilizing the proposed dimensionless model. A comparison of the outcomes for dimensionless models and experimental tests shows that proposed dimensionless models have a high degree of precision in determining geometrical parameters and the prediction of drawing force. Furthermore, the dimensionless analysis was generalized to ensure high precision estimation of geometric values for large geometric scales.