Abstract 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.

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一种新的传统纺纱法兰起皱的稳健理论预测模型

摘要 法兰起皱是常规旋压加工中最常见的影响工件成形质量的缺陷之一。为此，对法兰起皱机理进行了分析，并在这项工作中开发了一种新的法兰起皱理论预测模型。研究发现，法兰起皱的发生与受滚子作用影响的区域而不是整个法兰处的周向压应力过大密切相关。然后，基于极限分析的广义变分原理，建立了产生法兰起皱的临界周向应力的理论模型。通过比较受滚子作用影响区域的瞬时最大周向应力与计算出的临界应力，可以预测法兰起皱。与基于能量法的预测模型相比，新模型的主要改进可归纳如下。首先，新模型考虑了有效受压区挠度模态的增量位移幅值，它对临界应力的影响显着，但在基于能量法的模型中被忽略。其次，新模型中将板坯视为刚性塑性材料，因此不需要考虑对力学状态非常敏感的弹塑性基体的计算，从而避免了力学状态提取偏差的不利影响。关于预测精度。因此，与基于能量法的预测模型相比，新模型在机械状态提取偏差下具有更高的预测精度和更好的鲁棒性。除了实现法兰起皱的预测外，新模型还可用于分析板坯几何参数和材料参数在各种成形条件下对法兰起皱的影响。鉴于此，应用新模型，结合响应面法和中心复合设计（CCD），揭示材料参数（材料强化系数K、硬化指数n和弹性模量E）对翼缘起皱的影响。结果表明，K对法兰起皱的影响最大，其次是E和n。考虑参数之间的相互作用，K 和 E 之间的相互作用对法兰起皱的开始也有更大的影响。较小的 E 和较大的 K 有助于降低法兰起皱的风险。改变n值对延缓法兰起皱的发生没有显着影响。研究结果可以加深对常规纺纱法兰起皱的预测和规律的理解。