柔性夹钳拉形过程及其数值模拟研究
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摘要
拉伸成形(简称拉形)是蒙皮类零件的重要成形方法，具有模具制造简单和回弹量小等优点。蒙皮件是构成飞机气动外形的主要零件，具有种类多、数量少、结构复杂、外形尺寸大等特点。随着大型三维曲面拉伸件被广泛应用于航空航天、高速铁路、船舶、现代建筑以及其它行业，急需一种新的拉形工艺来改善拉形质量、提高材料利用率和降低生产成本。因此，开展新型拉伸成形设备及工艺研究具有重要意义。
柔性夹钳拉形是一种新型的拉形工艺，其基本原理是用柔性的离散夹钳代替刚性的整体夹钳对板料进行拉形，该工艺具有柔性好、贴模容易、材料利用率高、成形范围大和成形质量好等优点。本文利用有限元软件建立了柔性夹钳拉形有限元模型，对柔性夹钳拉形工艺进行数值模拟，研究了柔性夹钳拉形机的改进参数，柔性夹钳前后拉形回弹和起皱等问题，探讨了多点模具在柔性夹钳前后拉形中的应用，并进行了相关实验验证。
本文的主要研究内容和结论如下：
1.柔性夹钳拉形原理和特点
分析了传统的横向拉形机和纵向拉形机的结构特点，指出了其适用范围。提出了柔性夹钳拉形方法，阐述了柔性夹钳拉形变形协调方法和柔性夹钳拉形原理，介绍了柔性夹钳拉形机的结构特点。在课题组开发的柔性夹钳拉形机上对不规则形状工件进行了柔性夹钳拉形实验，采用三维光学扫描仪对实验件进行了精度测量，介绍了柔性夹钳拉形工艺的应用。
2.柔性夹钳拉形有限元模型的建立
对板材拉形过程进行了力学分析，介绍了板材拉形过程的应力和应变的理论计算公式。阐述了板料塑性成形数值模拟的有限元方程及相关问题。建立了柔性夹钳拉形有限元模型，对环形件和鞍形件在相同条件下进行了柔性夹钳拉形实验和数值模拟，结果表明:实验结果与模拟结果吻合较好，验证了柔性夹钳拉形有限元模型的正确性。
3.柔性夹钳拉形工艺的数值模拟
基于柔性夹钳拉形时夹钳的运动特点，采用了力加载和位移加载两种加载方式对柔性夹钳拉形进行数值模拟，并对力加载和位移加载进行了对比分析。以球形件和鞍形件为例对柔性夹钳拉形和刚性夹钳拉形进行了数值模拟对比，结果表明：与刚性夹钳拉形相比，柔性夹钳拉形可以大幅减小夹持边缘的应力大小，避免应力集中现象，并且能使成形区的应变分布更加均匀，厚度减薄量更小，所需的最小过渡区长度更短。以鞍形件、球形件和M形件为例研究了夹持力大小、夹料块形状、夹钳数量、加载幅值曲线、润滑条件和过渡区长度等工艺参数对柔性夹钳拉形的影响。结果表明：在保证工件完全贴模和夹钳不脱落的情况下，较小的夹持力可以使成形件的应力分布更均匀，降低成形件拉裂的风险；夹料块形状不同时，随着夹持面积的减小，成形件的应力和等效应变也减小，但是减小的幅度很小；在拉伸成形M形等复杂曲面件时，夹钳数量越多，成形件贴模效果越好；加载幅值曲线幂次越高，摩擦系数越小或过渡区长度越长，成形件的应变和厚度分布越均匀，成形质量越好。
4.柔性夹钳拉形机结构改进及其参数的数值模拟
对柔性夹钳拉形机结构进行了改进，并给出了结构示意图。以球形件为例探讨了柔性夹钳前后拉形时垂直缸距夹钳钳口的距离、前拉力大小和夹料块圆角半径对成形结果的影响。结果表明：垂直缸距夹钳钳口距离越小、前拉力越大或夹料块圆角半径越大，球形件的最大应力、拉伸应变和厚度减薄量越小，且成形区的应力、拉伸应变和厚度分布更均匀，成形效果越好。对球形件在后拉和前后拉两种方式下进行了数值模拟，结果说明，球形件前后拉需要的最小贴模力小于后拉需要的最小贴模力，前后拉时有效成形区的拉伸应变和厚度减薄率远小于后拉时有效成形区的拉伸应变和厚度减薄率。
5.柔性夹钳前后拉形回弹和起皱的数值模拟
对拉形后回弹现象进行了力学分析，采用显式和隐式算法相结合的方法计算回弹。研究了材质、润滑条件、预拉率和板材厚度对球形件回弹的影响，结果表明：板材的弹性模量和屈服强度越大、润滑条件越好、预拉率越大或板材越厚，成形件的卸载回弹量越小；四种条件下，柔性夹钳前后拉的回弹量均最小，柔性夹钳后拉的回弹量均居中，刚性夹钳拉形的回弹量均最大。基于板材在不易贴模区域的无约束自由成形的特点，给出了起皱缺陷的判定方法。对柔性夹钳前后拉形时鞍形件的起皱过程进行了数值模拟，分析了不同区域是否起皱的原因。研究了材质、润滑条件、预拉率和板材厚度对鞍形件起皱的影响，结果表明：板材的弹性模量和屈服强度越大、润滑条件越差、预拉率越大或板材越厚，成形件的皱曲量越小；四种条件下，柔性夹钳前后拉的皱曲量均最小，柔性夹钳后拉的回弹量均居中，刚性夹钳拉形的皱曲量均最大。通过数值模拟得出了三种拉形方式下不同板厚时鞍形件无起皱极限图。
6.多点模具在柔性夹钳前后拉形中的应用及数值模拟
采用课题组开发柔性夹钳前后拉形装置配合多点模具进行柔性夹钳拉形实验，结果表明：工件在过渡区很短的情况下实现了完全贴模，夹钳在拉形过程中随模具形状发生了自协调转动，相邻夹钳间隙区域的板材实现了自由流动。介绍了多点模具成形时特有的成形缺陷——压痕，阐述了两种主要的压痕分布形式。以球形件和鞍形件为例对柔性夹钳前后拉形时的压痕分布进行了数值模拟，结果表明厚向应变可以用来描述压痕。分析了过渡区长度、板材厚度、曲率半径和材质对压痕的影响，结果表明：过渡区越长、板材越厚、曲率半径越大或板材的屈服应力越大，压痕越轻微；通过板料与多点模之间放置弹性垫来抑制压痕。探讨了多点模具与目标工件的关系、冲头坐标的计算方法、多点模具调形软件和回弹补偿方法等问题，对柔性夹钳前后拉形进行回弹补偿数值模拟，并对回弹补偿方法进行实验验证。结果表明：通过两次补偿后，球形件和鞍形件的成形误差都显著减小，实验结果验证了多点模具回弹补偿方法的可行性。
Stretch forming is an important forming method of aircraft skin, which has simple dieand small springback value. The skin parts are the main parts for structuring aerodynamicconfiguration, it has many kinds, small number, complex structure and large dimension.With the wide use of large-scale three-dimensional sheet metal in the fields of aeronauticsand astronautics, high-speed train, ships, modern architectures as well as other industries, iturgent needs a new kind of stretching process to ameliorate stretching quality, improvematerial utilization and reduce production costs. Therefore, it is important to carry outstudy of new type of stretch forming equipment and technology.
Flexible clamp stretch forming is a new kind of stretch forming technology, the basicprinciple is the rigid overall clamp is replaced by flexible discrete clamp, the technique hasgood flexibility, high material utilization, large forming range and good forming quality, inaddition, it also makes the sheet metal attach the die easily. In this paper, the finite elementmodel of flexible clamp stretch forming was set up, and the numerical simulation offlexible clamp stretch forming process were performed. The modified parameters offlexible clamp stretch forming machine were studied, the springback and wrinkle offlexible clamp front and back stretch forming were investigated. Then, the application ofmulti-point die used in flexible clamp front and back stretch forming were discussed, andthe related experiment were verified.
The main contents and conclusions of this paper are as follows:
1. Principle and characters of flexible clamp stretch forming
The structural features of the traditional horizontal stretch forming machine andvertical stretch forming machine were analyzed, and their applied scope were pointed out.The deform conformity method and principle of flexible clamp stretch forming wereelaborated, and the characteristics of flexible clamp stretch forming machine was described.Then, flexible clamp stretch forming experiment of irregular shaped part was carried out, the forming precision of experimental part was measured by using three-dimensionaloptical scanner, and the application of flexible clamp stretch forming technology wasintroduced.
2. Establishment of finite element model of flexible clamp stretch forming
Mechanics analysis of stretch forming was done, and the theoretical calculation of thestress and strain are introduced. The finite element equation of numerical simulation forsheet plastic forming and related issues were elaborated. Then finite element model offlexible clamp stretch forming was set up. Flexible clamp stretch forming experiments andnumerical simulations for toroidal and saddle-shaped parts were done under the sameconditions, the results show that the experimental results are consistent with the simulatedresults, which verified the correctness of the finite element model.
3. Numerical simulation of flexible clamp stretch forming process
The loading methods of force loading and displacement loading were adopted forflexible clamp stretch forming based on the moving characteristics of clamp, and thecomparative analysis for two kinds of loading methods was done by numerical simulation.The contrast between rigid clamp stretch forming and flexible clamp stretch forming forspherical and saddle-shaped parts were carried out, the results show that the flexible clampstretch forming mode can decrease the stress in the edge of clamp jaws greatly and avoidthe stress concentration phenomenon, enable the strain distribution of the forming zonemore uniform, reduce the thinning ratio and shorten the minimum transitional length. Theeffects of the magnitude of clamping force, the shape of clamping block, the number ofclamp, the loading curve, the lubrication conditions and the transitional length on theforming quality of parts were investigated through the flexible clamp stretch forming forspherical part, saddle-shaped part and M-shaped part. The results show that a smallerclamping force can make the formed part has a more uniform stress in the case of theformed part completely attach to the stretching die and not to clamp shedding, which alsoreduce the risk of crack. With the decreasing of clamping area, the stress and equivalentstrain of formed part decrease slightly when the shape of clamping block is different. Abetter fitting quality of complex surfaces such as the M-shaped part can be got when thenumber of clamp is larger. The higher the power of loading curve, the smaller the frictioncoefficient, or the longer the transitional length is, the more uniform stretching strain andthickness, or the better the forming quality will be.
4. Structural modification and parameter simulation of flexible clamp stretchforming machine
The structural modification of flexible clamp stretch forming machine was conducted, and the structural diagram was given. Taking the spherical part as the objective part, theeffects of the location of vertical cylinder, the magnitude of vertical force due to thevertical cylinder and the fillet radii of clamping block on the forming quality wereinvestigated. The results show that the smaller the distance between the vertical cylinderand the edge of clamp jaws or the larger the vertical force due to the vertical cylinder or thelarger the fillet radius of the clamping block is, the smaller the maximum stress, strain andthickness thinning ratio will be, and more uniform stress, strain and thickness of formingzone will be. The numerical simulations of flexible clamp back stretch forming andflexible clamp front and back stretch forming were compared, and the results show that theminimum forming force, the stretching strain and thickness thinning ratio of spherical partformed by flexible clamp front and back stretch forming is less than that formed byflexible clamp back stretch forming.
5. Numerical simulation of springback and wrinkle for flexible clamp front andback stretch forming
The mechanics analysis of springback was done, and the combination of implicit andexplicit method was determined to compute springback. The influences of material,lubrication conditions, pre-stretched ratio and thickness on the springback value ofspherical part were studied. The results show that the larger the elastic modulus and yieldstrength, the better the lubrication conditions, the larger the pre-stretched ratio or thethicker the thickness is, the smaller the springback value will be. In the above fourinfluence conditions, the springback value of flexible clamp front and back stretch formingis minimum, that of flexible clamp back stretch forming is middle, and that of rigid clampstretch forming is maximum. The judge method of wrinkling defect based on the formingcharacteristics of sheet metal in the unconstrained region was determined. Numericalsimulation of wrinkling process for saddle-shaped part formed by flexible clamp front andback stretch forming was carried out, and the reason of wrinkle in different areas ofsaddle-shaped part was analyzed. The effects of material, lubrication conditions,pre-stretched ratio and thickness on the wrinkle of saddle-shaped part were studied. Theresults show that the larger the elastic modulus and yield strength, the worse the lubricationconditions, the larger the pre-stretched ratio or the thicker the thickness is, the smaller thewrinkling value will be. In the above four influence conditions, the wrinkling value offlexible clamp front and back stretch forming is minimum, that of flexible clamp backstretch forming is middle, and that of rigid clamp stretch forming is maximum. Thenon-wrinkle critical graph of saddle-shaped parts with different thickness was obtainedunder the three kinds of stretching methods.
6. Application and numerical simulation of multi-point die in flexible clamp frontand back stretch forming
The flexible clamp front and back stretch forming machine was developed andexperiments were conducted by using multi-point die. The results show that the workpiecesfit the die completely in the case of transitional length is very short, the clamps changewith the shape of stretching die, and the sheet metal in the gap regions of adjacent clampsachieves free flowing. Indentation is the unique forming defect of multi-point forming, andtwo kind distributed forms of indentation are elaborated. The numerical simulations ofindentation for spherical and saddle-shaped parts formed by flexible clamp back and downstretch forming show that indentation can be described by thickness strain. The effects oftransitional length, thickness, curvature radius and material on the indentation of sphericaland saddle-shaped parts were studied. The results show that the longer the transitionallength, the thicker the thickness, the larger the curvature radius or the larger the yieldstrength is, the more gentle the indentation will be. Then, the elastic cushion was used forsuppressing indentation. The relationship between the multi-point die and target workpiece,the calculating scheme of punch coordinate, the multi-point CAD/CAM software andspringback compensation method were investigated. Numerical simulation of springbackcompensation and related forming experiment were done. The results show that theforming error reduced significantly through two-times compensation, and the formingexperiment verified the feasibility of the springback compensation method.
柔性夹钳拉形是一种新型的拉形工艺，其基本原理是用柔性的离散夹钳代替刚性的整体夹钳对板料进行拉形，该工艺具有柔性好、贴模容易、材料利用率高、成形范围大和成形质量好等优点。本文利用有限元软件建立了柔性夹钳拉形有限元模型，对柔性夹钳拉形工艺进行数值模拟，研究了柔性夹钳拉形机的改进参数，柔性夹钳前后拉形回弹和起皱等问题，探讨了多点模具在柔性夹钳前后拉形中的应用，并进行了相关实验验证。
本文的主要研究内容和结论如下：
1.柔性夹钳拉形原理和特点
分析了传统的横向拉形机和纵向拉形机的结构特点，指出了其适用范围。提出了柔性夹钳拉形方法，阐述了柔性夹钳拉形变形协调方法和柔性夹钳拉形原理，介绍了柔性夹钳拉形机的结构特点。在课题组开发的柔性夹钳拉形机上对不规则形状工件进行了柔性夹钳拉形实验，采用三维光学扫描仪对实验件进行了精度测量，介绍了柔性夹钳拉形工艺的应用。
2.柔性夹钳拉形有限元模型的建立
对板材拉形过程进行了力学分析，介绍了板材拉形过程的应力和应变的理论计算公式。阐述了板料塑性成形数值模拟的有限元方程及相关问题。建立了柔性夹钳拉形有限元模型，对环形件和鞍形件在相同条件下进行了柔性夹钳拉形实验和数值模拟，结果表明:实验结果与模拟结果吻合较好，验证了柔性夹钳拉形有限元模型的正确性。
3.柔性夹钳拉形工艺的数值模拟
基于柔性夹钳拉形时夹钳的运动特点，采用了力加载和位移加载两种加载方式对柔性夹钳拉形进行数值模拟，并对力加载和位移加载进行了对比分析。以球形件和鞍形件为例对柔性夹钳拉形和刚性夹钳拉形进行了数值模拟对比，结果表明：与刚性夹钳拉形相比，柔性夹钳拉形可以大幅减小夹持边缘的应力大小，避免应力集中现象，并且能使成形区的应变分布更加均匀，厚度减薄量更小，所需的最小过渡区长度更短。以鞍形件、球形件和M形件为例研究了夹持力大小、夹料块形状、夹钳数量、加载幅值曲线、润滑条件和过渡区长度等工艺参数对柔性夹钳拉形的影响。结果表明：在保证工件完全贴模和夹钳不脱落的情况下，较小的夹持力可以使成形件的应力分布更均匀，降低成形件拉裂的风险；夹料块形状不同时，随着夹持面积的减小，成形件的应力和等效应变也减小，但是减小的幅度很小；在拉伸成形M形等复杂曲面件时，夹钳数量越多，成形件贴模效果越好；加载幅值曲线幂次越高，摩擦系数越小或过渡区长度越长，成形件的应变和厚度分布越均匀，成形质量越好。
4.柔性夹钳拉形机结构改进及其参数的数值模拟
对柔性夹钳拉形机结构进行了改进，并给出了结构示意图。以球形件为例探讨了柔性夹钳前后拉形时垂直缸距夹钳钳口的距离、前拉力大小和夹料块圆角半径对成形结果的影响。结果表明：垂直缸距夹钳钳口距离越小、前拉力越大或夹料块圆角半径越大，球形件的最大应力、拉伸应变和厚度减薄量越小，且成形区的应力、拉伸应变和厚度分布更均匀，成形效果越好。对球形件在后拉和前后拉两种方式下进行了数值模拟，结果说明，球形件前后拉需要的最小贴模力小于后拉需要的最小贴模力，前后拉时有效成形区的拉伸应变和厚度减薄率远小于后拉时有效成形区的拉伸应变和厚度减薄率。
5.柔性夹钳前后拉形回弹和起皱的数值模拟
对拉形后回弹现象进行了力学分析，采用显式和隐式算法相结合的方法计算回弹。研究了材质、润滑条件、预拉率和板材厚度对球形件回弹的影响，结果表明：板材的弹性模量和屈服强度越大、润滑条件越好、预拉率越大或板材越厚，成形件的卸载回弹量越小；四种条件下，柔性夹钳前后拉的回弹量均最小，柔性夹钳后拉的回弹量均居中，刚性夹钳拉形的回弹量均最大。基于板材在不易贴模区域的无约束自由成形的特点，给出了起皱缺陷的判定方法。对柔性夹钳前后拉形时鞍形件的起皱过程进行了数值模拟，分析了不同区域是否起皱的原因。研究了材质、润滑条件、预拉率和板材厚度对鞍形件起皱的影响，结果表明：板材的弹性模量和屈服强度越大、润滑条件越差、预拉率越大或板材越厚，成形件的皱曲量越小；四种条件下，柔性夹钳前后拉的皱曲量均最小，柔性夹钳后拉的回弹量均居中，刚性夹钳拉形的皱曲量均最大。通过数值模拟得出了三种拉形方式下不同板厚时鞍形件无起皱极限图。
6.多点模具在柔性夹钳前后拉形中的应用及数值模拟
采用课题组开发柔性夹钳前后拉形装置配合多点模具进行柔性夹钳拉形实验，结果表明：工件在过渡区很短的情况下实现了完全贴模，夹钳在拉形过程中随模具形状发生了自协调转动，相邻夹钳间隙区域的板材实现了自由流动。介绍了多点模具成形时特有的成形缺陷——压痕，阐述了两种主要的压痕分布形式。以球形件和鞍形件为例对柔性夹钳前后拉形时的压痕分布进行了数值模拟，结果表明厚向应变可以用来描述压痕。分析了过渡区长度、板材厚度、曲率半径和材质对压痕的影响，结果表明：过渡区越长、板材越厚、曲率半径越大或板材的屈服应力越大，压痕越轻微；通过板料与多点模之间放置弹性垫来抑制压痕。探讨了多点模具与目标工件的关系、冲头坐标的计算方法、多点模具调形软件和回弹补偿方法等问题，对柔性夹钳前后拉形进行回弹补偿数值模拟，并对回弹补偿方法进行实验验证。结果表明：通过两次补偿后，球形件和鞍形件的成形误差都显著减小，实验结果验证了多点模具回弹补偿方法的可行性。
Stretch forming is an important forming method of aircraft skin, which has simple dieand small springback value. The skin parts are the main parts for structuring aerodynamicconfiguration, it has many kinds, small number, complex structure and large dimension.With the wide use of large-scale three-dimensional sheet metal in the fields of aeronauticsand astronautics, high-speed train, ships, modern architectures as well as other industries, iturgent needs a new kind of stretching process to ameliorate stretching quality, improvematerial utilization and reduce production costs. Therefore, it is important to carry outstudy of new type of stretch forming equipment and technology.
Flexible clamp stretch forming is a new kind of stretch forming technology, the basicprinciple is the rigid overall clamp is replaced by flexible discrete clamp, the technique hasgood flexibility, high material utilization, large forming range and good forming quality, inaddition, it also makes the sheet metal attach the die easily. In this paper, the finite elementmodel of flexible clamp stretch forming was set up, and the numerical simulation offlexible clamp stretch forming process were performed. The modified parameters offlexible clamp stretch forming machine were studied, the springback and wrinkle offlexible clamp front and back stretch forming were investigated. Then, the application ofmulti-point die used in flexible clamp front and back stretch forming were discussed, andthe related experiment were verified.
The main contents and conclusions of this paper are as follows:
1. Principle and characters of flexible clamp stretch forming
The structural features of the traditional horizontal stretch forming machine andvertical stretch forming machine were analyzed, and their applied scope were pointed out.The deform conformity method and principle of flexible clamp stretch forming wereelaborated, and the characteristics of flexible clamp stretch forming machine was described.Then, flexible clamp stretch forming experiment of irregular shaped part was carried out, the forming precision of experimental part was measured by using three-dimensionaloptical scanner, and the application of flexible clamp stretch forming technology wasintroduced.
2. Establishment of finite element model of flexible clamp stretch forming
Mechanics analysis of stretch forming was done, and the theoretical calculation of thestress and strain are introduced. The finite element equation of numerical simulation forsheet plastic forming and related issues were elaborated. Then finite element model offlexible clamp stretch forming was set up. Flexible clamp stretch forming experiments andnumerical simulations for toroidal and saddle-shaped parts were done under the sameconditions, the results show that the experimental results are consistent with the simulatedresults, which verified the correctness of the finite element model.
3. Numerical simulation of flexible clamp stretch forming process
The loading methods of force loading and displacement loading were adopted forflexible clamp stretch forming based on the moving characteristics of clamp, and thecomparative analysis for two kinds of loading methods was done by numerical simulation.The contrast between rigid clamp stretch forming and flexible clamp stretch forming forspherical and saddle-shaped parts were carried out, the results show that the flexible clampstretch forming mode can decrease the stress in the edge of clamp jaws greatly and avoidthe stress concentration phenomenon, enable the strain distribution of the forming zonemore uniform, reduce the thinning ratio and shorten the minimum transitional length. Theeffects of the magnitude of clamping force, the shape of clamping block, the number ofclamp, the loading curve, the lubrication conditions and the transitional length on theforming quality of parts were investigated through the flexible clamp stretch forming forspherical part, saddle-shaped part and M-shaped part. The results show that a smallerclamping force can make the formed part has a more uniform stress in the case of theformed part completely attach to the stretching die and not to clamp shedding, which alsoreduce the risk of crack. With the decreasing of clamping area, the stress and equivalentstrain of formed part decrease slightly when the shape of clamping block is different. Abetter fitting quality of complex surfaces such as the M-shaped part can be got when thenumber of clamp is larger. The higher the power of loading curve, the smaller the frictioncoefficient, or the longer the transitional length is, the more uniform stretching strain andthickness, or the better the forming quality will be.
4. Structural modification and parameter simulation of flexible clamp stretchforming machine
The structural modification of flexible clamp stretch forming machine was conducted, and the structural diagram was given. Taking the spherical part as the objective part, theeffects of the location of vertical cylinder, the magnitude of vertical force due to thevertical cylinder and the fillet radii of clamping block on the forming quality wereinvestigated. The results show that the smaller the distance between the vertical cylinderand the edge of clamp jaws or the larger the vertical force due to the vertical cylinder or thelarger the fillet radius of the clamping block is, the smaller the maximum stress, strain andthickness thinning ratio will be, and more uniform stress, strain and thickness of formingzone will be. The numerical simulations of flexible clamp back stretch forming andflexible clamp front and back stretch forming were compared, and the results show that theminimum forming force, the stretching strain and thickness thinning ratio of spherical partformed by flexible clamp front and back stretch forming is less than that formed byflexible clamp back stretch forming.
5. Numerical simulation of springback and wrinkle for flexible clamp front andback stretch forming
The mechanics analysis of springback was done, and the combination of implicit andexplicit method was determined to compute springback. The influences of material,lubrication conditions, pre-stretched ratio and thickness on the springback value ofspherical part were studied. The results show that the larger the elastic modulus and yieldstrength, the better the lubrication conditions, the larger the pre-stretched ratio or thethicker the thickness is, the smaller the springback value will be. In the above fourinfluence conditions, the springback value of flexible clamp front and back stretch formingis minimum, that of flexible clamp back stretch forming is middle, and that of rigid clampstretch forming is maximum. The judge method of wrinkling defect based on the formingcharacteristics of sheet metal in the unconstrained region was determined. Numericalsimulation of wrinkling process for saddle-shaped part formed by flexible clamp front andback stretch forming was carried out, and the reason of wrinkle in different areas ofsaddle-shaped part was analyzed. The effects of material, lubrication conditions,pre-stretched ratio and thickness on the wrinkle of saddle-shaped part were studied. Theresults show that the larger the elastic modulus and yield strength, the worse the lubricationconditions, the larger the pre-stretched ratio or the thicker the thickness is, the smaller thewrinkling value will be. In the above four influence conditions, the wrinkling value offlexible clamp front and back stretch forming is minimum, that of flexible clamp backstretch forming is middle, and that of rigid clamp stretch forming is maximum. Thenon-wrinkle critical graph of saddle-shaped parts with different thickness was obtainedunder the three kinds of stretching methods.
6. Application and numerical simulation of multi-point die in flexible clamp frontand back stretch forming
The flexible clamp front and back stretch forming machine was developed andexperiments were conducted by using multi-point die. The results show that the workpiecesfit the die completely in the case of transitional length is very short, the clamps changewith the shape of stretching die, and the sheet metal in the gap regions of adjacent clampsachieves free flowing. Indentation is the unique forming defect of multi-point forming, andtwo kind distributed forms of indentation are elaborated. The numerical simulations ofindentation for spherical and saddle-shaped parts formed by flexible clamp back and downstretch forming show that indentation can be described by thickness strain. The effects oftransitional length, thickness, curvature radius and material on the indentation of sphericaland saddle-shaped parts were studied. The results show that the longer the transitionallength, the thicker the thickness, the larger the curvature radius or the larger the yieldstrength is, the more gentle the indentation will be. Then, the elastic cushion was used forsuppressing indentation. The relationship between the multi-point die and target workpiece,the calculating scheme of punch coordinate, the multi-point CAD/CAM software andspringback compensation method were investigated. Numerical simulation of springbackcompensation and related forming experiment were done. The results show that theforming error reduced significantly through two-times compensation, and the formingexperiment verified the feasibility of the springback compensation method.
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