A new robust theoretical prediction model for flange wrinkling in conventional spinning

Flange wrinkling is one of the most common defects affecting the forming quality of workpieces in conventional spinning. To this end, the flange wrinkling mechanism is analyzed and a new robust theoretical prediction model for the flange wrinkling is developed in this work. It is found that the initiation of flange wrinkling is closely related to the excessive circumferential compressive stress in the zone affected by the roller action rather than the whole flange. Then, a theoretical model for the critical circumferential stress producing flange wrinkling is developed based on the generalized variational principle of limit analysis. By comparing the instant maximum circumferential stress in the zone affected by the roller action with the calculated critical stress, the flange wrinkling can be predicted. Compared with the prediction model based on energy method, the main improvements of the new model can be summarized as follows. First of all, the incremental displacement amplitude of deflection mode in the effective compressive region, which dramatically affects the critical stress but overlooked in the model based on energy method, is considered in the new model. Secondly, the sheet blank is regarded as a rigid plastic material in the new model, so the calculation of elastoplastic matrix which is very sensitive to the mechanical states does not need to be considered, thereby avoiding the adverse effect of the extraction deviation of mechanical states on prediction accuracy. Thus, compared with the prediction model based on energy method, the new model has higher prediction accuracy and better robustness under the extraction deviation of mechanical states. In addition to realizing the prediction of flange wrinkling, the new model can also be used to analyze the influence of sheet blank geometric parameters and material parameters on the initiation of flange wrinkling under various forming conditions. In view of this, the new model is applied to reveal the influence of material parameters (material strengthening coefficient K, hardening index n and elastic modulus E) on the initiation of flange wrinkling by combining response surface methodology and central composite design (CCD). The results show that K has the greatest influence on the initiation of flange wrinkling, followed by E and n. Considering the interaction between the parameters, the interaction between K and E also has a greater effect on the initiation of flange wrinkling. The smaller E and larger K are helpful to reduce the risk of flange wrinkling. Changing the value of n has no significant effect on delaying the occurrence of flange wrinkling. The results can deepen the understanding on the prediction and rules of flange wrinkling in conventional spinning.