No abstract

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.

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.

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.