Abstract Free bending technology is a new bending process for manufacturing freeform tube products. When manufacturing a complex spatial product, the variation of bending curvatures and torsions will accompany with a frequent changing of forming parameters, which will increase the manufacturing difficulties greatly. Until now, there is no effective way for determining the forming parameters of a complex spatial product precisely. In this paper, the characters of stable elements and unstable elements are analyzed. A mathematical collection is established for describing the geometrical characters of unstable elements. By using the new describing method, it is possible for establishing the relationship between the characteristics of unstable elements and forming parameters. And then a knowledge base can be built for storing the relationships. Based on these researches, a procedure for acquiring the forming parameters of a complex spatial tube product in free bending technology is proposed. The procedure can be described as follows: (1) use the known unstable elements in knowledge base to converge a complex spatial tube; (2) acquire its preforming parameters through the knowledge base; (3) compensate the motion of clamp to acquire the optimized forming parameters. The strategy is successfully applied on a typical spatial tube product and the final optimized forming parameters are exhibited.

中文翻译：

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自由弯曲技术中复杂空间管制品成形参数获取的新策略

摘要 自由弯曲技术是制造自由曲面管制品的一种新的弯曲工艺。在制造复杂的空间产品时，弯曲曲率和扭转的变化会伴随着成形参数的频繁变化，这将大大增加制造难度。到目前为止，还没有有效的方法来精确确定复杂空间产品的成形参数。本文分析了稳定元素和不稳定元素的特性。建立了描述不稳定元素几何特征的数学集合。通过使用新的描述方法，可以建立不稳定元素特性与成形参数之间的关系。然后可以建立一个知识库来存储这些关系。在这些研究的基础上，提出了一种自由弯曲技术中复杂空间管产品成形参数的获取方法。该过程可以描述如下：（1）利用知识库中已知的不稳定元素收敛一个复杂的空间管；(2)通过知识库获取其预成型参数；(3) 补偿夹具的运动以获得优化的成形参数。该策略成功应用于典型的空间管产品，并展示了最终优化的成型参数。(2)通过知识库获取其预成型参数；(3) 补偿夹具的运动以获得优化的成形参数。该策略成功应用于典型的空间管产品，并展示了最终优化的成型参数。(2)通过知识库获取其预成型参数；(3) 补偿夹具的运动以获得优化的成形参数。该策略成功应用于典型的空间管产品，并展示了最终优化的成型参数。