The design of a drawing die based on the logistic function for the energy analysis of drawing force

• A new drawing die which can satisfy the requirement of stream function well is designed. • The drawing force calculated by this new die is smaller than those calculated by the conical die and elliptic die. • The die in this paper can alleviate the problem of stress concentration and reduce die wear. The existing drawing processes through a conical die or a traditional curved die will consume high forming energy, workpiece fracture and big die wear. To solve this problem, a die with smooth streamline is designed and the corresponding drawing process is analyzed in the paper. As such, the deformed metal from the die entrance to its exit is described based on the logistic function. Then, the kinematically admissible velocity field is constructed according to the die. Based on the velocity field, the internal plastic deformation energy rate, shear energy rate, friction energy rate and total energy rate are obtained by the energy analysis. By the upper bound method, the analytical solutions of drawing force and stress state coefficients are obtained, and the optimal die angle is derived. Meanwhile, the finite element simulation is carried out to verify the correctness of the analytical drawing force, and the advantage of the present die is discovered by comparing with other dies. The results reflect that the drawing forces of the present die are in good agreement with its simulated ones, and the maximum error between them is less than 2.30%. Moreover, the drawing force of the present die is the minimal, and the stress concentration is reduced, which can reduce the possibility of workpiece fracture and die wear.