板带不均匀压下面内弯曲过程失稳起皱与参数优化的研究
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摘要
板带不均匀压下面内弯曲成形方法，利用材料不均匀塑性变形，可充分挖掘材料变形潜力，是一种能够发展成为集省能、柔性、高效、精密、绿色于一体的先进塑性加工技术。本文围绕失稳起皱和工艺参数优化这两个需要迫切解决的问题，采用实验研究、理论解析和数值模拟相结合的方法，对这一成形过程展开了深入的研究，得出了如下主要结果：
(1)研究发现了轧制正应力和切向正应力的分布规律：在接触面上，轧制正应力和切向正应力沿宽度方向从外缘向内缘近似呈线性减小趋势，并分别在最外缘和最内缘达到最大和最小值；沿轧制方向，随着变形量的增大呈先轻微增大后逐渐减小的趋势，轧制出口处达到最小值，甚至出现拉应力：在纵向截面，轧制正应力与切向正应力沿轧制方向随着变形量增大呈先轻微增大后减小的趋势，沿厚度方向变化不大。研究揭示了实际加载楔角、接触变形区宽度、材料性能参数和摩擦因子对总功率、总轧制力、平均轧制力以及轧制力距的影响规律：实际加载楔角、接触变形区宽度和强化系数对力能参数的影响都是近似线性增大的趋势；硬化指数增大则力能参数轻微减小；摩擦因子对力能参数的影响不明显。
(2)揭示了板带不均匀压下面内弯曲成形过程基于能量原理的失稳起皱机理，提出了统一的描述内外缘起皱波形的函数，采用变分法推导了服从该波形函数的内外缘起皱能，建立了统一的起皱预测准则；将新建立的统一的起皱预测准则引入到数值模拟系统IBS中，数值预测结果与实验结果的吻合较好；分析了成形过程各参数对起皱的影响规律：随着接触变形区宽度的逐渐增大，先是发生外缘起皱，然后发生内缘起皱，进而才出现稳定成形；随着实际加载楔角的增大，先是发生内缘起皱，然后发生稳定成形，进而出现外缘起皱；硬化指数和强化系数增大，易于稳定成形；摩擦因子对起皱的影响不明显；而且接触变形区宽度对起皱的影响最大。
(3)确定了工艺参数优化的优化目标、设计变量、约束条件，建立了工艺参数优化的数学模型；提出了采用复合形法与黄金分割法相结合的优化方案，开发了工艺参数优化系统，采用实验方法对工艺参数优化系统的可靠性进行了验
西北工业大学工学硕士学位论文
证。该研究为板带面内弯曲成形过程优化工艺参数确定和成形过程精确控制打
下了基础。
本文的研究成果不仅可以进一步完善板带不均匀压下面内弯曲理论与丰富
薄壁件的失稳起皱理论，而且可以为这一先进塑性加工技术的推广应用提供理
论基础，也可以为其它先进塑性加工技术研究和开发提供新思路。
In-plane bending process of strip metal under unequal compressing, making use of the unequal deformation, can be developed into an advanced precision forming process with good flexibility, precision, high efficiency, low consumption, high forming limit and environmental friendly. The instability wrinkling and the parameter optimization are the key problems urgently to be solved in the research and development of the process. In this dissertation, a systematical and thorough investigation on the wrinkling and the parameter optimization of the process has been carried out by using rigid-plastic FEM simulation in conjunction with theoretical analysis and experiment. The new achievements made are as follows:
(1) The normal and shear stress distribution is researched with the finite element code. The results are as the following: the normal and shear stress linearly diminish from external to internal on the interface between the part and the roller, and respectively reach minimum and maximum at the external and internal; the normal and shear stress slightly rise with the increase of deformation along the rolling direction, and reach the minimum at the exit; the normal and shear stress slightly rise with the increase of deformation along the rolling direction, whereas keep constant along the thickness direction of the lengthwise section, then the effect of the forming parameter such as the compress width, the loading wedge angle, the strain-hardening exponent, the strength coefficient and the friction factor on the total power, total rolling force, moment and average rolling force is analyzed. The results are as the following: energetic parameters rises linearly with the compress width, the loading wedge angle and
the strength coefficient increases; energetic parameter decrease as the strain-hardening exponent increasing and the effect of the friction factor on energetic parameter may be ignored.
(2) The mechanism of instability wrinkling in the process based on minimum energy principle is revealed, uniform mathematic description of the wrinkling wave on the strip of in-plane bending is established, the internal and external energy is deduced by energy method, and a uniform criteria of internal and external wrinkling is established; then how to combine the criteria with the FEM simulation system to make the numerical prediction of wrinkling into reality is also resolved in the paper. The effects of the forming parameters on the deforming result are analyzed by the uniform predict criteria. The results show as follows: as the compress width increase, external wrinkling first come into being, then internal winkling do, and finally in-plane bend occur; the loading wedge angle increase, internal winkling first come into being, then
in-plane bend do, and finally external wrinkling occur; in-plane bend is possible to occur with a increase of the strain-hardening exponent and the strength coefficient; and the effect of the friction factor may be ignored.
(3) The thinking of the parameter optimization in the process is bought forward; and then the optimization objective, design variable, constraint condition and the mathematical model of the parameter optimization are proposed, the scheme of complex method combined with the fibonacci method for the process is proposed, the parameter optimization code is developed. The experiments carried out show that the developed code is reliable. The result can lay a basis for the forming parameters rapidly and exactly being decided and regulated.
The achievements of this study are important to further developing the unequal deformation theory, and the plastic wrinkling theory of thin-wall component. Furthermore, it lays a theoretical foundation for generalization and industrialization of this process, also offers a new idea to the R&D of the advanced plastic processing technologies.
(1)研究发现了轧制正应力和切向正应力的分布规律：在接触面上，轧制正应力和切向正应力沿宽度方向从外缘向内缘近似呈线性减小趋势，并分别在最外缘和最内缘达到最大和最小值；沿轧制方向，随着变形量的增大呈先轻微增大后逐渐减小的趋势，轧制出口处达到最小值，甚至出现拉应力：在纵向截面，轧制正应力与切向正应力沿轧制方向随着变形量增大呈先轻微增大后减小的趋势，沿厚度方向变化不大。研究揭示了实际加载楔角、接触变形区宽度、材料性能参数和摩擦因子对总功率、总轧制力、平均轧制力以及轧制力距的影响规律：实际加载楔角、接触变形区宽度和强化系数对力能参数的影响都是近似线性增大的趋势；硬化指数增大则力能参数轻微减小；摩擦因子对力能参数的影响不明显。
(2)揭示了板带不均匀压下面内弯曲成形过程基于能量原理的失稳起皱机理，提出了统一的描述内外缘起皱波形的函数，采用变分法推导了服从该波形函数的内外缘起皱能，建立了统一的起皱预测准则；将新建立的统一的起皱预测准则引入到数值模拟系统IBS中，数值预测结果与实验结果的吻合较好；分析了成形过程各参数对起皱的影响规律：随着接触变形区宽度的逐渐增大，先是发生外缘起皱，然后发生内缘起皱，进而才出现稳定成形；随着实际加载楔角的增大，先是发生内缘起皱，然后发生稳定成形，进而出现外缘起皱；硬化指数和强化系数增大，易于稳定成形；摩擦因子对起皱的影响不明显；而且接触变形区宽度对起皱的影响最大。
(3)确定了工艺参数优化的优化目标、设计变量、约束条件，建立了工艺参数优化的数学模型；提出了采用复合形法与黄金分割法相结合的优化方案，开发了工艺参数优化系统，采用实验方法对工艺参数优化系统的可靠性进行了验
西北工业大学工学硕士学位论文
证。该研究为板带面内弯曲成形过程优化工艺参数确定和成形过程精确控制打
下了基础。
本文的研究成果不仅可以进一步完善板带不均匀压下面内弯曲理论与丰富
薄壁件的失稳起皱理论，而且可以为这一先进塑性加工技术的推广应用提供理
论基础，也可以为其它先进塑性加工技术研究和开发提供新思路。
In-plane bending process of strip metal under unequal compressing, making use of the unequal deformation, can be developed into an advanced precision forming process with good flexibility, precision, high efficiency, low consumption, high forming limit and environmental friendly. The instability wrinkling and the parameter optimization are the key problems urgently to be solved in the research and development of the process. In this dissertation, a systematical and thorough investigation on the wrinkling and the parameter optimization of the process has been carried out by using rigid-plastic FEM simulation in conjunction with theoretical analysis and experiment. The new achievements made are as follows:
(1) The normal and shear stress distribution is researched with the finite element code. The results are as the following: the normal and shear stress linearly diminish from external to internal on the interface between the part and the roller, and respectively reach minimum and maximum at the external and internal; the normal and shear stress slightly rise with the increase of deformation along the rolling direction, and reach the minimum at the exit; the normal and shear stress slightly rise with the increase of deformation along the rolling direction, whereas keep constant along the thickness direction of the lengthwise section, then the effect of the forming parameter such as the compress width, the loading wedge angle, the strain-hardening exponent, the strength coefficient and the friction factor on the total power, total rolling force, moment and average rolling force is analyzed. The results are as the following: energetic parameters rises linearly with the compress width, the loading wedge angle and
the strength coefficient increases; energetic parameter decrease as the strain-hardening exponent increasing and the effect of the friction factor on energetic parameter may be ignored.
(2) The mechanism of instability wrinkling in the process based on minimum energy principle is revealed, uniform mathematic description of the wrinkling wave on the strip of in-plane bending is established, the internal and external energy is deduced by energy method, and a uniform criteria of internal and external wrinkling is established; then how to combine the criteria with the FEM simulation system to make the numerical prediction of wrinkling into reality is also resolved in the paper. The effects of the forming parameters on the deforming result are analyzed by the uniform predict criteria. The results show as follows: as the compress width increase, external wrinkling first come into being, then internal winkling do, and finally in-plane bend occur; the loading wedge angle increase, internal winkling first come into being, then
in-plane bend do, and finally external wrinkling occur; in-plane bend is possible to occur with a increase of the strain-hardening exponent and the strength coefficient; and the effect of the friction factor may be ignored.
(3) The thinking of the parameter optimization in the process is bought forward; and then the optimization objective, design variable, constraint condition and the mathematical model of the parameter optimization are proposed, the scheme of complex method combined with the fibonacci method for the process is proposed, the parameter optimization code is developed. The experiments carried out show that the developed code is reliable. The result can lay a basis for the forming parameters rapidly and exactly being decided and regulated.
The achievements of this study are important to further developing the unequal deformation theory, and the plastic wrinkling theory of thin-wall component. Furthermore, it lays a theoretical foundation for generalization and industrialization of this process, also offers a new idea to the R&D of the advanced plastic processing technologies.
引文
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