An analytical solution for the estimation of the drawing force in three dimensional plate drawing processes

• We analytically compute the drawing force in 3D rectangular plate drawing processes.
• The new analytical solution is obtained using the limit analysis technique.
• It is based on a new 3D consistent velocity field.
• The material strain-hardening and the Coulomb friction can be accounted.
• The average friction stress is estimated using a new 3D stress-based solution.

An analytical solution for the estimation of the drawing force requested to perform a three dimensional drawing of a rectangular plate is presented.It has been developed using the limit analysis technique, on the basis of a three-dimensional velocity field, under the main assumptions of constant friction and perfect plasticity.To overcome the limitations given by these hypothesis, some extensions of the proposed upper bound model are presented, accounting for the material strain hardening and for the Coulomb friction between the plate and the die, thus avoiding the need to calibrate physically meaningless coefficients.The effectiveness of the proposed results is demonstrated by comparison with both experimental results and new numerical solutions.