#### Abstract

In order to solve one Gordian knot of how to optimize the control curve of variable blank holder force (VBHF) in the process of sheet deep drawing, some plasticity analyses in theory about carry capacities of one point on the surface of flange and one point on the sidewall during the whole process of deep drawing cylinder parts were carried out firstly, and then instantaneous radial pull-stress and circumferential compress-stress formulas about one random point on the flange could be concluded out by the way of building corresponding stress-strain balance relations, the same as the corresponding max pull-stress formula about one point on the sidewall. By the aid of consulting with correlative energy conversation theorem, Hill anisotropism theory and materials strain-hardening criterion, one minimum wrinkleless VBHF expression which including friction coefficient and normal anisotropism coefficient and one critical fracture limit VBHF expression could be ratiocinated out in sequence, and some corresponding influencing disciplines of all kinds of forming parameters on these two expressions were discussed in detail. In the end, numerical simulations were adopted to validate the feasibility of two simple optimized load curves of VBHF. Final computation results showed that these two simple optimized VBHF curves could not only conduce to more uniform in thickness distribution relative to other’s study results, after calculating mean square deviation of thickness variation with final parts, but also attain to lower peak with thickness variation, which dropping from 7.47% to 6.17% and from 17.65% to 15.39% respectively.