In the field of cold bending, it is necessary to use ball mandrels, especially to bend thin-walled tubes with a small radius. However, the bending process with a ball mandrel is complex and expensive, and it is easy to jam the core ball inside the tube. To solve these issues, we designed two kinds of hollow non-ball mandrel schemes with low stiffness that were suitable for the small radius bending of thin-walled tubes. We evaluated the forming quality of cold bending numerically and the influence of the hollow section length and thickness on the forming indices. Our results showed that the thickness of the hollow section has a greater influence on forming quality than the length. As the hollow section’s thickness increased, the wrinkling rate first declined by approximately 40% and then increased by above 50%. When the thickness was 11 mm in scheme 1 and 13 mm in scheme 2, the wrinkling rate reached minimum values of 1.32% and 1.50%, respectively. As the hollow section’s thickness increased, the flattening rate decreased by more than 60% and the thinning rate increased by about 40%. A multi-objective optimization of forming indices was carried out by ideal point method and grey wolf optimizer. By comparing the forming results before and after optimization, the feasibility of using the proposed hollow mandrel was proved, and the hollow mandrel scheme of standard cylinder is therefore recommended.

中文翻译：

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薄壁管小半径冷弯无球芯棒形状优化设计

在冷弯领域，需要用到球芯棒，特别是弯曲小半径的薄壁管。但用球芯棒折弯工艺复杂，成本高，且容易将芯球卡在管内。针对这些问题，我们设计了两种适合薄壁管小半径弯曲的低刚度空心无球心轴方案。我们对冷弯成形质量进行了数值评估，并分析了空心截面长度和厚度对成形指标的影响。我们的结果表明，空心截面的厚度比长度对成形质量的影响更大。随着空心截面厚度的增加，起皱率先下降约40%，然后增加50%以上。当方案1的厚度为11 mm和方案2的厚度为13 mm时，起皱率分别达到最小值1.32%和1.50%。随着空心截面厚度的增加，压扁率下降60%以上，减薄率提高40%左右。采用理想点法和灰狼优化器对成形指标进行多目标优化。通过比较优化前后的成型结果，证明了使用所提出的空心芯棒的可行性，因此推荐标准圆柱体的空心芯棒方案。采用理想点法和灰狼优化器对成形指标进行多目标优化。通过比较优化前后的成型结果，证明了使用所提出的空心芯棒的可行性，因此推荐标准圆柱体的空心芯棒方案。采用理想点法和灰狼优化器对成形指标进行多目标优化。通过比较优化前后的成型结果，证明了使用所提出的空心芯棒的可行性，因此推荐标准圆柱体的空心芯棒方案。